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+# A FRAMEWORK FOR THE QUANTITATIVE EVALUATION OF DISENTANGLED REPRESENTATIONS
+
+Christopher K. I. Williams
+
+Cian Eastwood School of Informatics University of Edinburgh, UK c.eastwood@ed.ac.uk
+
+School of Informatics University of Edinburgh, UK and Alan Turing Institute, London, UK ckiw@inf.ed.ac.uk
+
+# ABSTRACT
+
+Recent AI research has emphasised the importance of learning disentangled representations of the explanatory factors behind data. Despite the growing interest in models which can learn such representations, visual inspection remains the standard evaluation metric. While various desiderata have been implied in recent definitions, it is currently unclear what exactly makes one disentangled representation better than another. In this work we propose a framework for the quantitative evaluation of disentangled representations when the ground-truth latent structure is available. Three criteria are explicitly defined and quantified to elucidate the quality of learnt representations and thus compare models on an equal basis. To illustrate the appropriateness of the framework, we employ it to compare quantitatively the representations learned by recent state-of-the-art models.
+
+# 1 INTRODUCTION
+
+To gain a conceptual understanding of our world, models must first learn to understand the factorial structure of low-level sensory input without supervision (Bengio et al., 2013; Lake et al., 2016; Higgins et al., 2017). As argued in several notable works (Desjardins et al., 2012; Bengio et al., 2013; Chen et al., 2016; Higgins et al., 2017), this understanding can only be gained if the model learns to disentangle the underlying explanatory factors hidden in unlabelled input.
+
+A disentangled representation is generally described as one which separates the factors of variation, explicitly representing the important attributes of the data (Desjardins et al., 2012; Bengio et al., 2013; Cohen & Welling, 2014b; Kulkarni et al., 2015; Chen et al., 2016; Higgins et al., 2017). For example, given an image dataset of human faces, a disentangled representation may consist of separate dimensions (or features) for the face size, hairstyle, eye colour, facial expression, etc. Ultimately, we would like to learn representations that are invariant to irrelevant changes in the data. However, the relevant downstream tasks are generally unknown at training time and hence it is difficult to deduce a priori which features will be useful. Thus, the most robust method is to disentangle as many factors of variation as possible, discarding as little information as possible (Desjardins et al., 2012; Bengio et al., 2013).
+
+Despite the expanding literature on models which seek to learn disentangled representations (Desjardins et al., 2012; Reed et al., 2014; Zhu et al., 2014; Cheung et al., 2014; Larsen et al., 2015; Makhzani et al., 2015; Yang et al., 2015; Kulkarni et al., 2015; Whitney et al., 2016; Chen et al., 2016; Higgins et al., 2017; Denton & Birodkar, 2017), visual inspection remains the standard evaluation metric. While the work of Higgins et al. (2017) partially addresses this issue (as discussed in section 3) and various definitions have implied additional desiderata like interpretability (Bengio et al., 2013; Kulkarni et al., 2015; Chen et al., 2016), invariance (Goodfellow et al., 2009; Cohen & Welling, 2014a;b; Lenc & Vedaldi, 2015) and equivariance (Kivinen & Williams, 2011; Lenc & Vedaldi, 2015; Jayaraman & Grauman, 2015), current research generally lacks a clear metric for quantitatively evaluating and comparing disentangled representations.
+
+In this work we propose a framework for the quantitative evaluation of disentangled representations when the ground-truth latent structure is available. To elucidate the quality of learnt representations and thus compare models on an equal basis, desiderata of disentangled representations are explicitly defined and quantified. These unified desiderata help define the disentangled representations which we seek and remove the need for a subjective visual evaluation by a human arbiter. To illustrate the appropriateness of this framework, we employ it to compare quantitatively the representations learned by principal components analysis (PCA), the variational autoencoder (VAE, Kingma & Welling 2013), $\beta$ -VAE (Higgins et al., 2017) and information maximising generative adversarial networks (InfoGAN, Chen et al. 2016).
+
+In the remainder of this paper, we begin by detailing the theoretical framework and how it facilitates the quantitative evaluation of disentangled representations. Next we review related desiderata and metrics for evaluating disentangled representations. Finally, we describe the dataset and model specifics before presenting the experimental results.
+
+# 2 THEORETICAL FRAMEWORK
+
+Models for disentangled factor learning seek a compact data representation or code $^ c$ of dimension $D$ , which consists of disentangled and interpretable latent variables. For synthetic data, the $K$ - dimensional generative factors $_ { z }$ are designed to be an ideal such representation. Thus if $D = K$ the ideal disentangled code $c ^ { * }$ should be some (scaled) permutation of $_ { z }$ , i.e. they should be related by a generalised permutation matrix (or monomial matrix1). If $D > K$ , one would expect to obtain this monomial structure along with a number of ‘dead’ or irrelevant units in $^ c$ which are not predictive of $/$ informative about $_ { z }$ . Thus, we can quantitatively evaluate the codes learned by a given model $M$ using the following steps:
+
+1. Train $M$ on a synthetic dataset with generative factors $_ { z }$   
+2. Retrieve $^ c$ for each sample $_ { \textbf { \em x } }$ in the dataset $( { \pmb c } = M ( { \pmb x } ) )$ )   
+3. Train regressor $f$ to predict $_ z$ given $\pmb { c } \left( \hat { \pmb { z } } = f ( \pmb { c } ) \right)$   
+4. Quantify $f$ ’s deviation from the ideal mapping and the prediction error
+
+We now detail the proposed evaluation metrics, i.e., steps 3 and 4. We train $K$ regressors to predict the value of $K$ generative factors. The regressor $f _ { j }$ predicts $z _ { j }$ given $^ c$ , that is, it learns a mapping $f _ { j } ( \pmb { c } ) : \mathbb { R } ^ { D }  \mathbb { R } ^ { 1 }$ . We use regressors that can provide a matrix of relative importances $R$ , where $R _ { i j }$ denotes the relative importance of $c _ { i }$ in predicting $z _ { j }$ (see section 4.3). This allows us to explicitly define and quantify three criteria of disentangled representations or codes which are implicit in recent definitions (Desjardins et al., 2012; Bengio et al., 2013; Kulkarni et al., 2015; Chen et al., 2016; Higgins et al., 2017), namely disentanglement, completeness and informativeness.
+
+Disentanglement. The degree to which a representation factorises or disentangles the underly  
+ing factors of variation, with each variable (or dimension) capturing at most one generative factor. $D _ { i }$ ode variable denotes the $c _ { i }$ is qtrop ntifiand $D _ { i } = ( 1 - \bar { H } _ { K } ( P _ { i . } ) )$ , whereotes the   
+$\begin{array} { r } { H _ { K } ( P _ { i . } ) = - \sum _ { k = 0 } ^ { K - 1 } P _ { i k } \log _ { K } P _ { i k } } \end{array}$ $P _ { i j } = \left. R _ { i j } \right/ \sum _ { k = 0 } ^ { K - 1 } { R _ { i k } }$ $c _ { i }$ $z _ { j }$ $c _ { i }$   
+erative factor, the score will be 1. If $c _ { i }$ is equally important for predicting all generative factors, the   
+score will be 0. $D _ { i }$ can be visualised by examining row $i$ of the Hinton diagrams as in Figure 3.
+
+In order to account for dead or irrelevant units in $^ c$ , relative code variable importance $\begin{array} { r l } { \rho _ { i } } & { { } = } \end{array}$ $\textstyle \sum _ { j } R _ { i j } / \sum _ { i j } R _ { i j }$ is used to construct a weighted average $\sum _ { i } \rho _ { i } D _ { i }$ expressing overall disentanglement. If a code variable $c _ { i }$ is irrelevant for predicting $_ z$ , then its $\rho _ { i }$ (and thus contribution to the overall disentanglement) will be near zero.
+
+Completeness. The degree to which each underlying factor is captured by a single code variable. where The completeness score $\begin{array} { r } { H _ { D } ( \tilde { P } _ { . j } ) = - \sum _ { d = 0 } ^ { D - 1 } \tilde { P } _ { d j } \log _ { D } \tilde { P } _ { i j } } \end{array}$ $C _ { j }$ in capturing generative factor denotes the entropy of the $z _ { j }$ is quantified by $\tilde { P } _ { \cdot j }$ distribution. If a single code $C _ { j } \stackrel { - } { = } ( 1 - H _ { D } ( \tilde { P } _ { . j } ) )$ , variable contributes to $z _ { j }$ ’s prediction, the score will be 1 (complete). If all code variables equally contribute to $z _ { j }$ ’s prediction, the score will be 0 (maximally overcomplete). $C _ { j }$ can be visualised by examining column $j$ of the Hinton diagrams as in Figure 3.
+
+![](images/d7192b67fedf5af6fa91adc1d0479689d288b3e40dcbac013e322a5a868c2253.jpg)  
+Figure 1: Visualising disentanglement and completeness.
+
+Informativeness. The amount of information that a representation captures about the underlying factors of variation. To be useful for natural tasks which require knowledge of the important attributes of the data (e.g. object recognition), representations must ultimately capture information about the underlying factors of variation (Bengio et al., 2013; Chen et al., 2016). The informativeness of code $^ c$ about generative factor $z _ { j }$ is quantified by the prediction error $E ( z _ { j } , \hat { z } _ { j } )$ (averaged over the dataset), where $E$ is an appropriate error function and $\hat { z } _ { j } = f _ { j } ( \pmb { c } )$ . It is important to note that the prediction error $E ( z _ { j } , \hat { z } _ { j } )$ , and thus this informativeness metric, is dependent on the capacity of $f$ , with linear regressors only capable of extracting information about $_ z$ in $^ c$ that is explicitly represented. Hence this informativeness metric is also dependent on a model’s ability to explicitly represent information about $_ z$ in $^ c$ , which in turn is dependent on the model’s ability to disentangle the underlying factors of variation $( z )$ . Thus the informativeness metric has some overlap with the disentanglement metric, with the size of the overlap determined by the capacity of $f$ (no overlap with infinite capacity).
+
+While the disentanglement score quantifies the number of generative factors captured by a given code variable, the completeness score quantifies the number of code variables which capture a given generative factor. Together, these scores quantify the deviation from the ideal one-to-one mapping between $_ z$ and $K$ of the dimensions in $^ c$ . Figure 1 illustrates this idea.
+
+Despite the overlap between the disentanglement and informativeness metrics with low-capacity linear regressors, these are ultimately distinct criteria. While disentanglement requires each code variable in $^ c$ to be only perturbed by changes in a single $z$ , informativeness requires these perturbations to be systematic and thus informative. This motivates the use of non-linear regressors in section 4.3.
+
+While the ideal code would be able to explicitly represent each generative factor with a single variable, models with generic priors cannot be expected to learn such complete and explicit codes. For example, generative factors which are drawn from a distribution on a circle cannot be accurately captured by single code variables on which unwrapped prior distributions are imposed. Thus, with generic priors like the standard normal, information about such topologically distinct generative factors may be non-linearly encoded across multiple code variables. Empirical results in Appendix C and (Higgins et al., 2017, fig. 7) support this idea, with several code variables resembling non-linear functions (like the sine and cosine) of the object azimuth. This further motivates the use of non-linear regressors in section 4.3.
+
+Our criteria assume that it is possible to recover the latent factors $_ { z }$ from the data. If the data $_ { \textbf { \em x } }$ depends on a linear combination of (some of) the underlying $z$ ’s with a spherically symmetric distribution, then it will only be possible to recover these components up to a rotation matrix. This is the well-known issue of the rotation of factors in the linear factor analysis model (see e.g., Mardia, Kent, and Bibby 1979, sec. 9.6), and also leads to the condition in independent components analysis (ICA) that at most one of the $z$ ’s can be Gaussian (Hyvarinen et al., 2001). In this case, the infor- ¨ mativeness metric remains valid but the disentanglement and completeness metrics do not as they are dependent on the arbitrary rotation which determines $^ c$ ’s alignment with $_ z$ . Although $_ { z }$ may be used to compute the rotation matrix which best aligns $^ c$ and $_ z$ , we ultimately wish to evaluate models which will not have access to $_ z$ at test time.
+
+# 3 RELATED WORK
+
+The question of how well a learned representation $^ c$ matches the true generative factors $_ { z }$ has been considered in the ‘square’ case of independent components analysis (ICA), where $D = K$ . In the ICA case, the data is generated as $\textstyle { \boldsymbol { x } } = A { \boldsymbol { z } }$ and the learned representation is obtained as $\mathbf { \boldsymbol { c } } = W \mathbf { \boldsymbol { x } }$ , where $A$ is the mixing matrix and $W$ is the learned ‘un-mixing’ matrix. Ideally $P = W A$ will be equal to a permutation matrix. Yang $\&$ Amari (1997, sec. 6.1) propose an error metric to assess how close $P$ is to a permutation matrix2. This metric takes the form
+
+$$
+E = \sum _ { i } \left( \sum _ { j } \frac { \left| p _ { i j } \right| } { \operatorname* { m a x } _ { k } \left| p _ { i k } \right| } - 1 \right) + \sum _ { j } \left( \sum _ { i } \frac { \left| p _ { i j } \right| } { \operatorname* { m a x } _ { k } \left| p _ { k j } \right| } - 1 \right) ,
+$$
+
+summing two terms which have similar goals to our disentanglement and completeness scores respectively, although expressed by comparing with the maximum value in the row or column, rather than via an entropic measure. Note that, due to the linear structure of ICA, there is no explicit mapping between $^ c$ and $_ z$ . We report separate scores as they capture distinct criteria and go beyond this metric by handling the non-square case when $D > K$ .
+
+Predicting $_ { z }$ from $^ c$ has also been considered previously. Higgins et al. (2017, sec. A.5) use a linear classifier to predict discrete settings of $_ { z }$ and thus quantify the amount of explicit information about $_ z$ in $^ c$ , albeit with a discretisation step which we find unnecessary. Higgins et al. (2017, sec. 3) also propose a disentanglement metric. With this method, one of the generative factors say $z _ { k }$ is held fixed, and pairs of $_ { \textbf { \em x } }$ ’s are drawn, generated with different random $_ { z }$ ’s except for the fixed $z _ { k }$ . Pairwise absolute differences of the resulting codes $\lvert c _ { 1 } - c _ { 2 } \rvert$ are then computed and averaged over repetitions before being used to train a linear classifier to predict which generative factor was held fixed. In our view this is unnecessarily cumbersome—by setting up a regression problem to predict $_ { z }$ from $^ c$ as we have done, the structure of the $R _ { i j }$ matrix can be interrogated to quantify the degree of disentanglement. In addition, this facilitates the quantification of additional criteria, namely completeness and informativeness, without needing to generate any additional datasets.
+
+Glorot et al. (2011, fig. 3) predict $_ z$ from $^ c$ using a lasso regressor but only to qualitatively assess disentanglement, visually assessing the overlap of important features for the separate tasks of domain recognition and sentiment classification. Karaletsos et al. (2015) do so with an unspecified regressor, thus quantifying informativeness. In addition, they devise a quantitative metric to determine a model’s ability to disentangle the underlying factors of variation in images. In particular, they predict the order of query-specific oracle triplets of images, where the order indicates image similarity with respect to a query (e.g., ‘Where is the light condition most similar in terms of azimuth?’). However, the proposed metric is specifically designed to evaluate their ‘oracle-prioritized belief network’ and thus overly cumbersome to be used as a generic disentanglement metric.
+
+Properties such as invariance and equivariance have been proposed as desiderata for representations or codes (Goodfellow et al., 2009; Kivinen & Williams, 2011; Cohen & Welling, 2014b; Lenc & Vedaldi, 2015; Jayaraman & Grauman, 2015). In our view these qualities arise naturally from a properly disentangled and informative code. Consider, for example, the code of an object which consists of separate variables for its class (e.g., cup, bottle, banana etc.), position, pose, texture etc. If the object is translated, its position code variable(s) will transform accordingly (equivariance), but other code variables will remain invariant.
+
+# 4 EXPERIMENTS
+
+We employ the framework to compare quantitatively the codes learned by PCA, the VAE, $\beta$ -VAE and InfoGAN. The results can be reproduced with our open source implementation3.
+
+# 4.1 DATA
+
+We use the graphics renderer described in (Moreno et al., 2016) to generate $2 0 0 , 0 0 0 6 4 \times 6 4$ colour images of an object (teapot) with varying pose and colour (see Figure 2). For simplicity, the camera is centred on the object, the scene background is removed and additional generative factors (shape and lighting) are held constant. Each generative factor is independently sampled from its respective uniform distribution: azimuth $( z _ { 0 } ) \setminus U [ 0 , 2 \pi ]$ , elevation $( \bar { z _ { 1 } } ) \sim U [ \bar { 0 } , \pi / 2 ]$ , $\operatorname { r e d } ( z _ { 2 } ) \sim U [ 0 , 1 ]$ , green $( z _ { 3 } ) \sim U [ 0 , 1 ]$ , $\mathrm { \ u e } ( z _ { 4 } ) \sim U [ 0 , 1 ]$ . We divide the images into training (160,000), validation (20,000) and test (20,000) sets before removing images which contain particular generative factor combinations to faciliate the evaluation of zeroshot performance (see Appendix B.2). This left 142,927, 17,854 and 17,854 images in the training, validation and test sets respectively.
+
+![](images/f76c659e3dd0a8e21b4860bbabc80e443dcc50da388afa658fe64386dade9c96.jpg)  
+Figure 2: Data samples.
+
+# 4.2 MODELS
+
+Generative modelling has become one of the leading approaches to unsupervised representation learning, with several recent works imposing additional learning constraints to encourage the model to learn disentangled representations (Desjardins et al., 2012; Reed et al., 2014; Zhu et al., 2014; Cohen & Welling, 2014a; Cheung et al., 2014; Larsen et al., 2015; Makhzani et al., 2015; Chen et al., 2016; Higgins et al., 2017). Of these models, it can be argued that $\beta$ -VAE (Higgins et al., 2017) and InfoGAN (Chen et al., 2016) are the most promising due to their scalability and lack of assumptions about the underling factors of variation. Thus, we evaluate the codes learned by these models and compare them to the VAE $\beta = 1 \AA$ ) and PCA.
+
+For fair comparison, we train all models with 10 code variables and use the same network architectures for the VAE, $\beta$ -VAE and InfoGAN. More specifically, we use the same residual networks (ResNets, He et al. 2016) for the encoders/discriminator and the decoders/generator (see Table 2), and train InfoGAN with 10 continous ‘latent codes’(Chen et al., 2016) and 0 noise variables. We found that these ResNets produced the sharpest images and best visual disentanglement for all generative models, outperforming popular architectures for ( $\beta .$ -)VAE (Larsen et al., 2015; Higgins et al., 2017) and InfoGAN (Kulkarni et al., 2015). We fit $\beta = 6$ and $\lambda = 6$ for $\beta$ -VAE and InfoGAN respectively by balancing reconstruction/generation quality and visual disentanglement (see Appendix D), where $\lambda$ is the mutual information coefficient. See Appendix A for further details.
+
+# 4.3 REGRESSORS
+
+Lasso. We begin with linear regressors and encourage a sparse mapping between $^ c$ and $_ { z }$ with an $\ell _ { 1 }$ regularisation penalty (lasso regressors). With the inputs and targets normalised to have zero mean and unit variance, the magnitude of the resulting regression weights rank the learnt code variables $c _ { 0 } , \ldots , c _ { D - 1 }$ in order of relative importance to the prediction. That is, they reveal which code variables capture information about a given generative factor. Thus, we define the matrix of relative importances $R$ as $R _ { i j } = | W _ { i j } |$ for linear regression, where $R _ { i j }$ denotes the relative importance of $c _ { i }$ in predicting $z _ { j }$ and $| W _ { i j } |$ denotes the magnitude of the weight used to scale $c _ { i }$ in predicting $z _ { j }$ . We fit the $\ell _ { 1 }$ penalty coefficient $\alpha$ on the validation set to achieve the lowest prediction error.
+
+Random forest. We use random forest regressors due to their inbuilt ability to determine the relative importance of each feature to a given prediction, thus allowing us to directly specify the matrix of relative importances $R$ . Random forests average the predictions and feature importances from each decision tree in the ensemble. The number of times a tree chooses to split on a particular input variable determines its importance to the prediction. Thus, the relative importance of each input variable $c _ { i }$ is given by the number of cases split on $c _ { i }$ over the total number of splits (Breiman et al., 1984). As performance generally improves with the number of trees $n$ in the ensemble, we fix $n = 1 0$ . The remaining parameter, tree depth, is determined on the validation set (lowest prediction error).
+
+<table><tr><td colspan="4">(a) Lasso</td><td colspan="4">(b)Random forest</td></tr><tr><td>Code</td><td>Disent.</td><td>Compl.</td><td>Inform.</td><td>Code</td><td>Disent.</td><td>Compl.</td><td>Inform.</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PCA</td><td>0.29</td><td>0.32</td><td>0.44</td><td>PCA</td><td>0.50</td><td>0.52</td><td>0.27</td></tr><tr><td>VAE (β = 1)</td><td>0.67</td><td>0.62</td><td>0.37</td><td>VAE (β = 1)</td><td>0.86</td><td>0.75</td><td>0.09</td></tr><tr><td>β-VAE (β = 6)</td><td>0.66</td><td>0.59</td><td>0.35</td><td>β-VAE (β = 6)</td><td>0.90</td><td>0.76</td><td>0.10</td></tr><tr><td>InfoGAN</td><td>0.75</td><td>0.72</td><td>0.23</td><td>InfoGAN</td><td>0.91</td><td>0.87</td><td>0.13</td></tr></table>
+
+Table 1: Average model scores. ‘Inform.’ indicates (average) normalised root-mean-square error (NRMSE) in predicting $_ z$ .
+
+# 4.4 RESULTS
+
+Overview. Table 1 presents the average disentanglement, completeness and informativeness scores for PCA, the VAE, $\beta$ -VAE and InfoGAN for the (a) lasso and (b) random forest regressors. With both regressors, PCA achieves the worst disentanglement, completeness and informativeness scores (highest error in predicting $_ z$ ) while the VAE $\mathbf { \nabla } \beta = 1 \mathbf { \dot { \varepsilon } } ,$ ) and $\beta$ -VAE $\beta = 6 )$ ) achieve very similar disentanglement, completeness and informativeness scores to each other. While InfoGAN achieves the best disentanglement, completeness and informativeness scores with the lasso regressor, the VAE and $\beta$ -VAE achieve similar disentanglement and informativeness scores to it with (the increased capacity of) the random forest regressor.
+
+Disentanglement. InfoGAN achieves the highest average disentanglement with both regressors (although $\beta$ -VAE closely follows with the random forest regressor). That is, each variable in InfoGAN’s code (c−InfoGAN) is closest (on average) to capturing a single generative factor, making $c -$ InfoGAN the most disentangled code (see Appendix B.1 for the full / per-variable results). Figure 3 helps to identify the generative factors captured by a given code variable and thus visualise the disentanglement. For example, comparing $c _ { 0 }$ across all models in Figure 3 (the first rows), it is clear that $c _ { 0 } { - } \mathrm { V A E }$ , $c _ { 0 } { - } \beta \mathrm { V A E }$ and $c _ { 0 } { \mathrm { - I n f o G A N } }$ (almost) solely capture information about $z _ { \mathrm { 0 } }$ while $c _ { 0 } { - } \mathrm { P C A }$ captures information about almost all generative factors.
+
+Completeness. InfoGAN also achieves the highest average completeness with both regressors. That is, $c - .$ InfoGAN is closest (on average) to capturing each generative factor with a single code variable, making $c - .$ InfoGAN the most complete code. In contrast, the low completeness score (overcompleteness) of $c { \mathrm { - P C A } }$ reveals that it uses several code variables to capture each generative factor (again, see Appendix B.1 for the full $/$ per-variable results). Figure 3 helps to identify the code variables which capture a given generative factor and thus visualise the completeness. For example, Figure 3 shows that several ��dead’ or redundant code variables $( c _ { 5 } , c _ { 6 } , c _ { 7 } )$ enable a high degree of completeness in $c -$ InfoGAN. In addition, comparing $z _ { 0 }$ (azimuth) across all models in Figure 3b (the first columns), it is clear that InfoGAN uses three code variables $( c _ { 0 } , c _ { 1 } , c _ { 8 } )$ to capture $z _ { \mathrm { 0 } }$ while PCA, VAE, and $\beta$ -VAE use significantly more. In particular, Figure 3 shows that $c { \mathrm { - P C A } }$ is severely overcomplete in capturing $z _ { \mathrm { 0 } }$ , with each of its constituent variables capturing distinct information about $z _ { \mathrm { 0 } }$ . With an ideal code, Figure 3 would show a single large square in $K$ rows and each column, indicating a one-to-one mapping between $_ z$ and $K$ of the dimensions in $^ c$ .
+
+Informativeness. With the lasso regressor, c−InfoGAN is most predictive of / informative about $_ z$ . That is, $c - .$ InfoGAN contains the most easily-extractable $/$ explicit information about $_ { z }$ . This is supported by Figure 5, which plots each $z$ against the corresponding ‘most important’ code variable(s) (as indicated by the $R$ matrix) and reveals (primarily) linear relationships between $_ { z }$ and c−InfoGAN. Despite being significantly deeper with many more parameters, $c { \mathrm { - V A E } }$ and $\displaystyle c { - \beta \mathrm { V A E } }$ are only slightly more predictive of $_ z$ than $c { \mathrm { - P C A } }$ with this linear regressor, indicating that the information about $_ z$ in $c { \mathrm { - V A E } }$ and $\displaystyle c { - \beta \mathrm { V A E } }$ is not easily-extractable / explicit (again, this is supported by the relationships depicted in Figure 5).
+
+All model codes better predict $_ z$ with the random forest regressor, particularly $c { \mathrm { - V A E } }$ and $\displaystyle c { - \beta \mathrm { V A E } }$ . In fact, $c { \mathrm { - V A E } }$ and $\textstyle { c - } \beta \mathrm { V A E }$ are the most predictive of $/$ informative about $_ { z }$ with this non-linear regressor, with the increased capacity allowing significantly more information about $_ z$ to be extracted from these codes. As discussed in section 2, the prediction error with this (nonlinear) regressor is likely a better quantification of informativeness as it is less dependent on the ability of the model to explicitly represent information about $_ z$ in $^ c$ .
+
+![](images/fb851eeda23ab9d9cbe5970eb98c698d678e3655d4394140d5e5d3b65c5e527e.jpg)  
+Figure 3: Visualising $\pmb { R }$ . Square size indicates magnitude, i.e. relative importance. Row $i$ illustrates the importance of $c _ { i }$ to each prediction and thus the disentanglement. Column $j$ illustrates the importance of each code variable for predicting $z _ { j }$ and thus the completeness.
+
+# 5 CONCLUSION
+
+In this work we have presented a framework for the quantitative evaluation of disentangled representations when the ground-truth latent structure is available. The quality of learnt representations is elucidated through the explicit definition and quantification of three criteria: disentanglement, completeness and informativeness. To illustrate the appropriateness of our framework, we employed it to compare quantitatively the codes learned by PCA, the VAE, $\beta$ -VAE and InfoGAN.
+
+While our framework is limited to synthetic datasets where it is possible to recover $_ z$ , reliable disentanglement is far from solved even in this restricted setting. Hence, we believe our framework and its constituent metrics take a substantial and important step forward in understanding learned representations. We have made the code and dataset publicly available in the hope that this facilitates further model comparisons and eventually the establishment of quantitative benchmarks for disentangled factor learning. While we have focused on image data in this work, future work may explore the applicability of our framework to other types of synthetic data.
+
+# 6 ACKNOWLEDGEMENTS
+
+We would like to thank Pol Moreno and Akash Srivastava for helpful discussions. We would also like to thank Pol for generating the dataset. Finally, we would like to thank the anonymous reviewers for their constructive criticisms which were helpful in refining this paper. The work of CW is supported in part by EPSRC grant EP/N510129/1 to the Alan Turing Institute.
+
+# REFERENCES
+
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+
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+
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+
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+
+# A EXPERIMENTAL SETUP
+
+For all generative models, we use the ResNet architectures shown in Table 2 for the encoder / discriminatior $( D )$ / auxilary network $( Q )$ and the decoder / generator $( G )$ . We optimize using Adam (Kingma & Ba, 2014) with a learning rate of 1e-4 and a batch size of 64. For the stable training of InfoGAN, we fix the latent codes’ standard deviations to 1 and use the objective of the improved Wasserstein GAN (IWGAN) (Gulrajani et al., 2017), simply appending InfoGAN’s approximate mutual information penalty. As in Gulrajani et al. (2017), we use layer normalization (Ba et al., 2016) instead of batch normalization (Ioffe & Szegedy, 2015) in $D$ . As in Chen et al. (2016), $Q$ shares all convolutional layers with the discriminator (or ‘critic’ with WGAN objective) $D$ , each adding their own final output layer. As $Q$ parametrises the approximate posterior over continous latent codes $Q ( c | \pmb { x } )$ , we simply take the mean returned by $Q ( { \pmb x } )$ as the code or representation for a given image. Further details on the experimental setup are provided in our open-source implementation.
+
+Table 2: (β-)VAE / InfoGAN architecture. Each network has 4 residual blocks (all but the first and last rows). The input to each residual block is added to its output (with appropriate downsampling/upsampling to ensure that the dimensions match). Downsampling (↓) is performed with mean pooling. $\uparrow$ indicates nearest-neighbour upsampling. When batch normalization (BN) is applied to convolutional layers, per-channel normalization is used.   
+
+<table><tr><td rowspan=1 colspan=2>Encoder /D/ Q                Decoder /G</td></tr><tr><td rowspan=1 colspan=1>3x3 64 conv.</td><td rowspan=1 colspan=1>FC 4:4.8.64</td></tr><tr><td rowspan=1 colspan=1>BN,ReLU,3x3 64 convBN, ReLU,3×3 128 conv,↓</td><td rowspan=1 colspan=1>BN,ReLU, 3x3 512 conv ↑BN,ReLU, 3×3 512 conv</td></tr><tr><td rowspan=1 colspan=1>BN, ReLU, 3x3 128 convBN,ReLU,3x3 256 conv,↓</td><td rowspan=1 colspan=1>BN, ReLU, 3x3 256 conv ↑BN, ReLU, 3x3 256 conv</td></tr><tr><td rowspan=1 colspan=1>BN, ReLU, 3x3 256 convBN,ReLU,3×3 512 conv,↓</td><td rowspan=1 colspan=1>BN, ReLU, 3x3 128 conv ↑BN,ReLU, 3×3 128 conv</td></tr><tr><td rowspan=1 colspan=1>BN, ReLU,3x3 512 convBN, ReLU,3×3 512 conv,↓</td><td rowspan=1 colspan=1>BN,ReLU,3x3 64 conv ↑BN,ReLU,3x3 64 conv</td></tr><tr><td rowspan=1 colspan=1>FC Output</td><td rowspan=1 colspan=1>BN,ReLU,3x33 conv, tanh</td></tr></table>
+
+# B EXTENDED RESULTS
+
+# B.1 FULL TABLE / PER-FACTOR RESULTS
+
+Tables 3 and 4 give the full regression results, i.e. the per-factor disentanglement, completeness and informativeness. As each target is normalised to have a standard deviation of 1, the root-mean-square error (RMSE) in predicting each target is naturally normalised relative to the constant regressor which guesses the expected value of the targets. Hence, we report the NRMSE.
+
+# B.2 ZEROSHOT
+
+Disentangled representations should enable a model to perform zero-shot inference, that is, generalise its knowledge beyond the training distribution by recombining previously-learnt factors (Bengio et al., 2013; Higgins et al., 2017). Thus, we can further evaluate the disentangled representations learned by a given model by quantifying its ability to perform zero-shot inference. We use the ground-truth values of the generative factors to create two different data distributions. More specifically, we isolate all images whose generative factor values lie in a particular range to create a ‘gap’ in the original dataset. This gap then serves as our zero-shot data containing unseen factor combinations. Informally, the images in this gap can be described as ‘red’ teapots from ‘above’. Formally, the generative factors of these images satisfy the following condition: $z _ { 2 } > ( z _ { 3 } + 0 . 1 5 )$ and $z _ { 2 } > ( z _ { 4 } + 0 . 1 5 )$ and $z _ { 1 } > \frac { \pi } { 4 }$ . This dataset contained 21,238 images, with (extreme) samples given in Figure 4. Note that zero-shot inference is facilitated by disentangled and informative representations, thus is not a core component of our evaluation, but rather a ‘bonus’.
+
+(a) Disentanglement   
+
+<table><tr><td>Code</td><td>Co</td><td>C1</td><td>C2</td><td>C3</td><td>C4</td><td>C5</td><td>C6</td><td>C7</td><td>C8</td><td>Cg</td><td>W. Avg.</td></tr><tr><td>PCA</td><td>0.16</td><td>0.50</td><td>0.31</td><td>0.09</td><td>0.45</td><td>0.60</td><td>0.11</td><td>1.00</td><td>0.17</td><td>0.51</td><td>0.29</td></tr><tr><td>VAE</td><td>1.00</td><td>0.85</td><td>0.95</td><td>0.68</td><td>0.63</td><td>1.00</td><td>0.30</td><td>0.37</td><td>0.66</td><td>0.95</td><td>0.67</td></tr><tr><td>β-VAE</td><td>1.00</td><td>0.64</td><td>1.00</td><td>0.76</td><td>0.39</td><td>0.89</td><td>0.49</td><td>0.81</td><td>0.45</td><td>0.80</td><td>0.66</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>InfoGAN</td><td>0.83</td><td>0.85</td><td>0.76</td><td>0.66</td><td>0.78</td><td>0.43</td><td>1.00</td><td>1.00</td><td>0.64</td><td>0.74</td><td>0.75</td></tr></table>
+
+(b) Completeness   
+(c) Informativeness   
+
+<table><tr><td>Code</td><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td><td>Avg.</td><td>Code</td><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td><td>Avg.</td></tr><tr><td>PCA</td><td>0.38</td><td>0.39</td><td>0.34</td><td>0.24</td><td></td><td>0.32</td><td>PCA</td><td></td><td></td><td></td><td>0.32</td><td>0.33</td><td>0.44</td></tr><tr><td>VAE</td><td></td><td></td><td></td><td></td><td>0.25</td><td></td><td></td><td>0.83</td><td>0.42</td><td>0.32</td><td></td><td></td><td></td></tr><tr><td></td><td>0.54</td><td>0.37</td><td>0.75</td><td>0.73</td><td>0.73</td><td>0.62</td><td>VAE</td><td>0.61</td><td>0.60</td><td>0.23</td><td>0.21</td><td>0.21</td><td>0.37</td></tr><tr><td>β-VAE</td><td>0.14</td><td>0.39</td><td>0.70</td><td>0.85</td><td>0.88</td><td>0.59</td><td>β-VAE</td><td>0.80</td><td>0.41</td><td>0.19</td><td>0.19</td><td>0.18</td><td>0.35</td></tr><tr><td>InfoGAN</td><td>0.42</td><td>0.72</td><td>0.75</td><td>0.86</td><td>0.84</td><td>0.72</td><td>InfoGAN</td><td>0.48</td><td>0.13</td><td>0.23</td><td>0.16</td><td>0.15</td><td>0.23</td></tr></table>
+
+Table 3: Lasso regression results. (a) Disentanglement scores for each code variable. ‘W. Avg.’ abbreviates weighted average. (b) Completeness scores for each generative factor. $z _ { 0 } , \ldots , z _ { 4 }$ represent azimuth, elevation, red, green and blue generative factors respectively. c) Test set NRMSE.   
+(a) Disentanglement   
+Table 4: Random forest regression results. Caption of Table 3 applies.   
+
+<table><tr><td>Code</td><td></td><td>Co</td><td>C1</td><td>C2</td><td>C3</td><td>C4</td><td>C5</td><td>C6</td><td>C7</td><td>C8</td><td>Cg</td><td>W. Avg.</td><td></td></tr><tr><td>PCA</td><td></td><td>0.25</td><td>0.54</td><td>0.63</td><td>0.10</td><td>0.88</td><td>0.97</td><td>0.16</td><td>0.90</td><td>0.41</td><td>0.72</td><td>0.50</td><td></td></tr><tr><td>VAE</td><td></td><td>0.98</td><td>0.99</td><td>0.91</td><td>0.94</td><td>0.75</td><td>0.99</td><td>0.56</td><td>0.56</td><td>0.92</td><td>0.86</td><td>0.86</td><td></td></tr><tr><td>β-VAE</td><td></td><td>0.96</td><td>0.96</td><td>0.95</td><td>0.99</td><td>0.63</td><td>0.96</td><td>0.69</td><td>0.94</td><td>0.64</td><td>0.98</td><td>0.90</td><td></td></tr><tr><td>InfoGAN</td><td></td><td>0.85</td><td>0.97</td><td>0.91</td><td>0.84</td><td>0.94</td><td>0.68</td><td>0.86</td><td>0.70</td><td>0.71</td><td>0.92</td><td>0.91</td><td></td></tr><tr><td>(b) Completeness</td><td colspan="3"></td><td></td><td></td><td></td><td>(c) Informativeness</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Code 20</td><td colspan="3">21</td><td>23</td><td>24</td><td>Avg</td><td>Code</td><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td><td>Avg.</td></tr><tr><td>PCA</td><td></td><td></td><td>22</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.27</td></tr><tr><td>VAE</td><td>0.31 0.44</td><td>0.51 0.61</td><td>0.67 0.90</td><td>0.56 0.91</td><td>0.56 0.91</td><td>0.52 0.75</td><td>PCA VAE</td><td>0.36 0.14</td><td>0.23 0.09</td><td>0.20 0.09</td><td>0.28 0.06</td><td>0.28 0.06</td><td>0.09</td></tr><tr><td>β-VAE</td><td>0.28</td><td>0.67</td><td>0.90</td><td>0.96</td><td>0.97</td><td>0.76</td><td>β-VAE</td><td>0.18</td><td>0.07</td><td>0.08</td><td>0.09</td><td>0.08</td><td>0.10</td></tr><tr><td>InfoGAN</td><td>0.59</td><td>0.94</td><td>0.91</td><td>0.96</td><td>0.95</td><td>0.87</td><td>InfoGAN</td><td>0.25</td><td>0.07</td><td>0.14</td><td>0.09</td><td>0.10</td><td>0.13</td></tr></table>
+
+Table 5 presents the zeroshot results. With the random forest regressor, $c { \mathrm { - V A E } }$ and $\displaystyle c { - \beta \mathrm { V A E } }$ perform the best with very little increase in prediction error compared to Table 4c, while $c - .$ InfoGAN predicts the value of unseen factor combinations reasonably well.
+
+![](images/12bf251bb375ffe741383d2cc4b3a3941a01d39e89ec679348dd7f9f346d07a8.jpg)  
+Figure 4: Zeroshot samples
+
+<table><tr><td colspan="6">(a) Lasso</td><td colspan="8">(b)Random Forest</td></tr><tr><td>Code</td><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td><td>Avg.</td><td>Code</td><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td><td>Avg.</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PCA</td><td>0.88</td><td>0.80</td><td>0.75</td><td>0.52</td><td>0.54</td><td>0.70</td><td>PCA</td><td>0.44</td><td>0.49</td><td>0.65</td><td>0.56</td><td>0.63</td><td>0.55</td></tr><tr><td>VAE</td><td>0.56</td><td>1.11</td><td>0.52</td><td>0.30</td><td>0.32</td><td>0.56</td><td>VAE</td><td>0.13</td><td>0.13</td><td>0.34</td><td>0.08</td><td>0.07</td><td>0.15</td></tr><tr><td>β-VAE</td><td>0.81</td><td>0.79</td><td>0.32</td><td>0.27</td><td>0.25</td><td>0.49</td><td>β-VAE</td><td>0.18</td><td>0.18</td><td>0.21</td><td>0.12</td><td>0.14</td><td>0.16</td></tr><tr><td>InfoGAN</td><td>0.49</td><td>0.34</td><td>0.93</td><td>0.36</td><td>0.33</td><td>0.49</td><td>InfoGAN</td><td>0.27</td><td>0.18</td><td>0.63</td><td>0.21</td><td>0.25</td><td>0.31</td></tr></table>
+
+Table 5: Zeroshot performance. NRMSE in predicting unseen factor combinations.
+
+# C Z VS. C
+
+Figure 5 plots each generative factor against the corresponding ‘most important’ code variable(s) (as indicated by $R$ ) of each model for 5000 randomly-selected samples. As discussed in section 2, models with generic priors cannot be expected to learn the most complete and explicit representation of topologically distinct factors of variation. Thus, for the wrapped azimuth $\left( z _ { 0 } \right)$ , we plot its value against the 3 most important code variables for each model. Inspecting the relationships depicted in Figure 5, it is clear that the simplest / lowest-order relationship exists between InfoGAN’s code variables and the corresponding generative factors. For example, each unwrapped generative factor $( z _ { 1 } , z _ { 2 } , z _ { 3 } , z _ { 4 } )$ is linearly-related to InfoGAN’s corresponding code variables, while $c _ { 0 }$ and $c _ { 8 }$ resemble scaled sine and cosine functions of the azimuth $\left( z _ { 0 } \right)$ and $c _ { 1 }$ resembles a step function.
+
+![](images/7b9aed0a0a476b94fd74ba0004c73b762f8ca8ead3129555b91f45f0cd0afe8e.jpg)  
+Figure 5: Generative factors vs. important code variables.
+
+# D VISUALLY ASSESSING DISENTANGLEMENT
+
+For each model, we traverse the space of each code variable indepedently to show the effect on generated images and thus visually assess disentanglement. The code variable traversals depicted in Figure 6 for (a) VAE $[ - 3 , 3 ]$ , (b) $\beta$ -VAE $[ - 3 , 3 ]$ and (c) InfoGAN $[ - 1 , 1 ]$ are ordered according to the generative factor $( z )$ which that code best captures in an attempt to align the generated images of all models. There appears to be a high degree of disentanglement in all generative models as each $c _ { i }$ traversal results in a single type of semantic variation.
+
+![](images/ab89eeece7c2b275264781702c6c482abc19c2144b52f50328be646710c675d6.jpg)
+
+![](images/1794813fe6342802141b8748d26b1b716658eaeae75dd12ab1a3290afacc35c7.jpg)  
+Figure 6: Code variable traversals.

parse/train/By-7dz-AZ/By-7dz-AZ_content_list.json

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+[
+    {
+        "type": "text",
+        "text": "A FRAMEWORK FOR THE QUANTITATIVE EVALUATION OF DISENTANGLED REPRESENTATIONS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            99,
+            805,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Christopher K. I. Williams ",
+        "bbox": [
+            475,
+            170,
+            663,
+            184
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Cian Eastwood School of Informatics University of Edinburgh, UK c.eastwood@ed.ac.uk ",
+        "bbox": [
+            184,
+            170,
+            375,
+            226
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "School of Informatics University of Edinburgh, UK and Alan Turing Institute, London, UK ckiw@inf.ed.ac.uk ",
+        "bbox": [
+            475,
+            185,
+            732,
+            239
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            276,
+            544,
+            291
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recent AI research has emphasised the importance of learning disentangled representations of the explanatory factors behind data. Despite the growing interest in models which can learn such representations, visual inspection remains the standard evaluation metric. While various desiderata have been implied in recent definitions, it is currently unclear what exactly makes one disentangled representation better than another. In this work we propose a framework for the quantitative evaluation of disentangled representations when the ground-truth latent structure is available. Three criteria are explicitly defined and quantified to elucidate the quality of learnt representations and thus compare models on an equal basis. To illustrate the appropriateness of the framework, we employ it to compare quantitatively the representations learned by recent state-of-the-art models. ",
+        "bbox": [
+            233,
+            310,
+            764,
+            462
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            493,
+            336,
+            510
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To gain a conceptual understanding of our world, models must first learn to understand the factorial structure of low-level sensory input without supervision (Bengio et al., 2013; Lake et al., 2016; Higgins et al., 2017). As argued in several notable works (Desjardins et al., 2012; Bengio et al., 2013; Chen et al., 2016; Higgins et al., 2017), this understanding can only be gained if the model learns to disentangle the underlying explanatory factors hidden in unlabelled input. ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A disentangled representation is generally described as one which separates the factors of variation, explicitly representing the important attributes of the data (Desjardins et al., 2012; Bengio et al., 2013; Cohen & Welling, 2014b; Kulkarni et al., 2015; Chen et al., 2016; Higgins et al., 2017). For example, given an image dataset of human faces, a disentangled representation may consist of separate dimensions (or features) for the face size, hairstyle, eye colour, facial expression, etc. Ultimately, we would like to learn representations that are invariant to irrelevant changes in the data. However, the relevant downstream tasks are generally unknown at training time and hence it is difficult to deduce a priori which features will be useful. Thus, the most robust method is to disentangle as many factors of variation as possible, discarding as little information as possible (Desjardins et al., 2012; Bengio et al., 2013). ",
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+    {
+        "type": "text",
+        "text": "Despite the expanding literature on models which seek to learn disentangled representations (Desjardins et al., 2012; Reed et al., 2014; Zhu et al., 2014; Cheung et al., 2014; Larsen et al., 2015; Makhzani et al., 2015; Yang et al., 2015; Kulkarni et al., 2015; Whitney et al., 2016; Chen et al., 2016; Higgins et al., 2017; Denton & Birodkar, 2017), visual inspection remains the standard evaluation metric. While the work of Higgins et al. (2017) partially addresses this issue (as discussed in section 3) and various definitions have implied additional desiderata like interpretability (Bengio et al., 2013; Kulkarni et al., 2015; Chen et al., 2016), invariance (Goodfellow et al., 2009; Cohen & Welling, 2014a;b; Lenc & Vedaldi, 2015) and equivariance (Kivinen & Williams, 2011; Lenc & Vedaldi, 2015; Jayaraman & Grauman, 2015), current research generally lacks a clear metric for quantitatively evaluating and comparing disentangled representations. ",
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+        "text": "In this work we propose a framework for the quantitative evaluation of disentangled representations when the ground-truth latent structure is available. To elucidate the quality of learnt representations and thus compare models on an equal basis, desiderata of disentangled representations are explicitly defined and quantified. These unified desiderata help define the disentangled representations which we seek and remove the need for a subjective visual evaluation by a human arbiter. To illustrate the appropriateness of this framework, we employ it to compare quantitatively the representations learned by principal components analysis (PCA), the variational autoencoder (VAE, Kingma & Welling 2013), $\\beta$ -VAE (Higgins et al., 2017) and information maximising generative adversarial networks (InfoGAN, Chen et al. 2016). ",
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+        "text": "In the remainder of this paper, we begin by detailing the theoretical framework and how it facilitates the quantitative evaluation of disentangled representations. Next we review related desiderata and metrics for evaluating disentangled representations. Finally, we describe the dataset and model specifics before presenting the experimental results. ",
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+        "type": "text",
+        "text": "2 THEORETICAL FRAMEWORK ",
+        "text_level": 1,
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+        "text": "Models for disentangled factor learning seek a compact data representation or code $^ c$ of dimension $D$ , which consists of disentangled and interpretable latent variables. For synthetic data, the $K$ - dimensional generative factors $_ { z }$ are designed to be an ideal such representation. Thus if $D = K$ the ideal disentangled code $c ^ { * }$ should be some (scaled) permutation of $_ { z }$ , i.e. they should be related by a generalised permutation matrix (or monomial matrix1). If $D > K$ , one would expect to obtain this monomial structure along with a number of ‘dead’ or irrelevant units in $^ c$ which are not predictive of $/$ informative about $_ { z }$ . Thus, we can quantitatively evaluate the codes learned by a given model $M$ using the following steps: ",
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+        "text": "1. Train $M$ on a synthetic dataset with generative factors $_ { z }$   \n2. Retrieve $^ c$ for each sample $_ { \\textbf { \\em x } }$ in the dataset $( { \\pmb c } = M ( { \\pmb x } ) )$ )   \n3. Train regressor $f$ to predict $_ z$ given $\\pmb { c } \\left( \\hat { \\pmb { z } } = f ( \\pmb { c } ) \\right)$   \n4. Quantify $f$ ’s deviation from the ideal mapping and the prediction error ",
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+        "text": "We now detail the proposed evaluation metrics, i.e., steps 3 and 4. We train $K$ regressors to predict the value of $K$ generative factors. The regressor $f _ { j }$ predicts $z _ { j }$ given $^ c$ , that is, it learns a mapping $f _ { j } ( \\pmb { c } ) : \\mathbb { R } ^ { D }  \\mathbb { R } ^ { 1 }$ . We use regressors that can provide a matrix of relative importances $R$ , where $R _ { i j }$ denotes the relative importance of $c _ { i }$ in predicting $z _ { j }$ (see section 4.3). This allows us to explicitly define and quantify three criteria of disentangled representations or codes which are implicit in recent definitions (Desjardins et al., 2012; Bengio et al., 2013; Kulkarni et al., 2015; Chen et al., 2016; Higgins et al., 2017), namely disentanglement, completeness and informativeness. ",
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+        "text": "Disentanglement. The degree to which a representation factorises or disentangles the underly  \ning factors of variation, with each variable (or dimension) capturing at most one generative factor. $D _ { i }$ ode variable denotes the $c _ { i }$ is qtrop ntifiand $D _ { i } = ( 1 - \\bar { H } _ { K } ( P _ { i . } ) )$ , whereotes the   \n$\\begin{array} { r } { H _ { K } ( P _ { i . } ) = - \\sum _ { k = 0 } ^ { K - 1 } P _ { i k } \\log _ { K } P _ { i k } } \\end{array}$ $P _ { i j } = \\left. R _ { i j } \\right/ \\sum _ { k = 0 } ^ { K - 1 } { R _ { i k } }$ $c _ { i }$ $z _ { j }$ $c _ { i }$   \nerative factor, the score will be 1. If $c _ { i }$ is equally important for predicting all generative factors, the   \nscore will be 0. $D _ { i }$ can be visualised by examining row $i$ of the Hinton diagrams as in Figure 3. ",
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+        "type": "text",
+        "text": "In order to account for dead or irrelevant units in $^ c$ , relative code variable importance $\\begin{array} { r l } { \\rho _ { i } } & { { } = } \\end{array}$ $\\textstyle \\sum _ { j } R _ { i j } / \\sum _ { i j } R _ { i j }$ is used to construct a weighted average $\\sum _ { i } \\rho _ { i } D _ { i }$ expressing overall disentanglement. If a code variable $c _ { i }$ is irrelevant for predicting $_ z$ , then its $\\rho _ { i }$ (and thus contribution to the overall disentanglement) will be near zero. ",
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+        "type": "text",
+        "text": "Completeness. The degree to which each underlying factor is captured by a single code variable. where The completeness score $\\begin{array} { r } { H _ { D } ( \\tilde { P } _ { . j } ) = - \\sum _ { d = 0 } ^ { D - 1 } \\tilde { P } _ { d j } \\log _ { D } \\tilde { P } _ { i j } } \\end{array}$ $C _ { j }$ in capturing generative factor denotes the entropy of the $z _ { j }$ is quantified by $\\tilde { P } _ { \\cdot j }$ distribution. If a single code $C _ { j } \\stackrel { - } { = } ( 1 - H _ { D } ( \\tilde { P } _ { . j } ) )$ , variable contributes to $z _ { j }$ ’s prediction, the score will be 1 (complete). If all code variables equally contribute to $z _ { j }$ ’s prediction, the score will be 0 (maximally overcomplete). $C _ { j }$ can be visualised by examining column $j$ of the Hinton diagrams as in Figure 3. ",
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+        "image_caption": [
+            "Figure 1: Visualising disentanglement and completeness. "
+        ],
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+        "type": "text",
+        "text": "Informativeness. The amount of information that a representation captures about the underlying factors of variation. To be useful for natural tasks which require knowledge of the important attributes of the data (e.g. object recognition), representations must ultimately capture information about the underlying factors of variation (Bengio et al., 2013; Chen et al., 2016). The informativeness of code $^ c$ about generative factor $z _ { j }$ is quantified by the prediction error $E ( z _ { j } , \\hat { z } _ { j } )$ (averaged over the dataset), where $E$ is an appropriate error function and $\\hat { z } _ { j } = f _ { j } ( \\pmb { c } )$ . It is important to note that the prediction error $E ( z _ { j } , \\hat { z } _ { j } )$ , and thus this informativeness metric, is dependent on the capacity of $f$ , with linear regressors only capable of extracting information about $_ z$ in $^ c$ that is explicitly represented. Hence this informativeness metric is also dependent on a model’s ability to explicitly represent information about $_ z$ in $^ c$ , which in turn is dependent on the model’s ability to disentangle the underlying factors of variation $( z )$ . Thus the informativeness metric has some overlap with the disentanglement metric, with the size of the overlap determined by the capacity of $f$ (no overlap with infinite capacity). ",
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+    {
+        "type": "text",
+        "text": "While the disentanglement score quantifies the number of generative factors captured by a given code variable, the completeness score quantifies the number of code variables which capture a given generative factor. Together, these scores quantify the deviation from the ideal one-to-one mapping between $_ z$ and $K$ of the dimensions in $^ c$ . Figure 1 illustrates this idea. ",
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+        "type": "text",
+        "text": "Despite the overlap between the disentanglement and informativeness metrics with low-capacity linear regressors, these are ultimately distinct criteria. While disentanglement requires each code variable in $^ c$ to be only perturbed by changes in a single $z$ , informativeness requires these perturbations to be systematic and thus informative. This motivates the use of non-linear regressors in section 4.3. ",
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+    {
+        "type": "text",
+        "text": "While the ideal code would be able to explicitly represent each generative factor with a single variable, models with generic priors cannot be expected to learn such complete and explicit codes. For example, generative factors which are drawn from a distribution on a circle cannot be accurately captured by single code variables on which unwrapped prior distributions are imposed. Thus, with generic priors like the standard normal, information about such topologically distinct generative factors may be non-linearly encoded across multiple code variables. Empirical results in Appendix C and (Higgins et al., 2017, fig. 7) support this idea, with several code variables resembling non-linear functions (like the sine and cosine) of the object azimuth. This further motivates the use of non-linear regressors in section 4.3. ",
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+    {
+        "type": "text",
+        "text": "Our criteria assume that it is possible to recover the latent factors $_ { z }$ from the data. If the data $_ { \\textbf { \\em x } }$ depends on a linear combination of (some of) the underlying $z$ ’s with a spherically symmetric distribution, then it will only be possible to recover these components up to a rotation matrix. This is the well-known issue of the rotation of factors in the linear factor analysis model (see e.g., Mardia, Kent, and Bibby 1979, sec. 9.6), and also leads to the condition in independent components analysis (ICA) that at most one of the $z$ ’s can be Gaussian (Hyvarinen et al., 2001). In this case, the infor- ¨ mativeness metric remains valid but the disentanglement and completeness metrics do not as they are dependent on the arbitrary rotation which determines $^ c$ ’s alignment with $_ z$ . Although $_ { z }$ may be used to compute the rotation matrix which best aligns $^ c$ and $_ z$ , we ultimately wish to evaluate models which will not have access to $_ z$ at test time. ",
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+    {
+        "type": "text",
+        "text": "3 RELATED WORK ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The question of how well a learned representation $^ c$ matches the true generative factors $_ { z }$ has been considered in the ‘square’ case of independent components analysis (ICA), where $D = K$ . In the ICA case, the data is generated as $\\textstyle { \\boldsymbol { x } } = A { \\boldsymbol { z } }$ and the learned representation is obtained as $\\mathbf { \\boldsymbol { c } } = W \\mathbf { \\boldsymbol { x } }$ , where $A$ is the mixing matrix and $W$ is the learned ‘un-mixing’ matrix. Ideally $P = W A$ will be equal to a permutation matrix. Yang $\\&$ Amari (1997, sec. 6.1) propose an error metric to assess how close $P$ is to a permutation matrix2. This metric takes the form ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/3e8a8cef34ec672453165d3dad47773a0c91614d72446fec88b82cb94eb04f27.jpg",
+        "text": "$$\nE = \\sum _ { i } \\left( \\sum _ { j } \\frac { \\left| p _ { i j } \\right| } { \\operatorname* { m a x } _ { k } \\left| p _ { i k } \\right| } - 1 \\right) + \\sum _ { j } \\left( \\sum _ { i } \\frac { \\left| p _ { i j } \\right| } { \\operatorname* { m a x } _ { k } \\left| p _ { k j } \\right| } - 1 \\right) ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "summing two terms which have similar goals to our disentanglement and completeness scores respectively, although expressed by comparing with the maximum value in the row or column, rather than via an entropic measure. Note that, due to the linear structure of ICA, there is no explicit mapping between $^ c$ and $_ z$ . We report separate scores as they capture distinct criteria and go beyond this metric by handling the non-square case when $D > K$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Predicting $_ { z }$ from $^ c$ has also been considered previously. Higgins et al. (2017, sec. A.5) use a linear classifier to predict discrete settings of $_ { z }$ and thus quantify the amount of explicit information about $_ z$ in $^ c$ , albeit with a discretisation step which we find unnecessary. Higgins et al. (2017, sec. 3) also propose a disentanglement metric. With this method, one of the generative factors say $z _ { k }$ is held fixed, and pairs of $_ { \\textbf { \\em x } }$ ’s are drawn, generated with different random $_ { z }$ ’s except for the fixed $z _ { k }$ . Pairwise absolute differences of the resulting codes $\\lvert c _ { 1 } - c _ { 2 } \\rvert$ are then computed and averaged over repetitions before being used to train a linear classifier to predict which generative factor was held fixed. In our view this is unnecessarily cumbersome—by setting up a regression problem to predict $_ { z }$ from $^ c$ as we have done, the structure of the $R _ { i j }$ matrix can be interrogated to quantify the degree of disentanglement. In addition, this facilitates the quantification of additional criteria, namely completeness and informativeness, without needing to generate any additional datasets. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Glorot et al. (2011, fig. 3) predict $_ z$ from $^ c$ using a lasso regressor but only to qualitatively assess disentanglement, visually assessing the overlap of important features for the separate tasks of domain recognition and sentiment classification. Karaletsos et al. (2015) do so with an unspecified regressor, thus quantifying informativeness. In addition, they devise a quantitative metric to determine a model’s ability to disentangle the underlying factors of variation in images. In particular, they predict the order of query-specific oracle triplets of images, where the order indicates image similarity with respect to a query (e.g., ‘Where is the light condition most similar in terms of azimuth?’). However, the proposed metric is specifically designed to evaluate their ‘oracle-prioritized belief network’ and thus overly cumbersome to be used as a generic disentanglement metric. ",
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+    {
+        "type": "text",
+        "text": "Properties such as invariance and equivariance have been proposed as desiderata for representations or codes (Goodfellow et al., 2009; Kivinen & Williams, 2011; Cohen & Welling, 2014b; Lenc & Vedaldi, 2015; Jayaraman & Grauman, 2015). In our view these qualities arise naturally from a properly disentangled and informative code. Consider, for example, the code of an object which consists of separate variables for its class (e.g., cup, bottle, banana etc.), position, pose, texture etc. If the object is translated, its position code variable(s) will transform accordingly (equivariance), but other code variables will remain invariant. ",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We employ the framework to compare quantitatively the codes learned by PCA, the VAE, $\\beta$ -VAE and InfoGAN. The results can be reproduced with our open source implementation3. ",
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+    {
+        "type": "text",
+        "text": "4.1 DATA ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We use the graphics renderer described in (Moreno et al., 2016) to generate $2 0 0 , 0 0 0 6 4 \\times 6 4$ colour images of an object (teapot) with varying pose and colour (see Figure 2). For simplicity, the camera is centred on the object, the scene background is removed and additional generative factors (shape and lighting) are held constant. Each generative factor is independently sampled from its respective uniform distribution: azimuth $( z _ { 0 } ) \\setminus U [ 0 , 2 \\pi ]$ , elevation $( \\bar { z _ { 1 } } ) \\sim U [ \\bar { 0 } , \\pi / 2 ]$ , $\\operatorname { r e d } ( z _ { 2 } ) \\sim U [ 0 , 1 ]$ , green $( z _ { 3 } ) \\sim U [ 0 , 1 ]$ , $\\mathrm { \\ u e } ( z _ { 4 } ) \\sim U [ 0 , 1 ]$ . We divide the images into training (160,000), validation (20,000) and test (20,000) sets before removing images which contain particular generative factor combinations to faciliate the evaluation of zeroshot performance (see Appendix B.2). This left 142,927, 17,854 and 17,854 images in the training, validation and test sets respectively. ",
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+        "img_path": "images/f76c659e3dd0a8e21b4860bbabc80e443dcc50da388afa658fe64386dade9c96.jpg",
+        "image_caption": [
+            "Figure 2: Data samples. "
+        ],
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+    {
+        "type": "text",
+        "text": "4.2 MODELS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Generative modelling has become one of the leading approaches to unsupervised representation learning, with several recent works imposing additional learning constraints to encourage the model to learn disentangled representations (Desjardins et al., 2012; Reed et al., 2014; Zhu et al., 2014; Cohen & Welling, 2014a; Cheung et al., 2014; Larsen et al., 2015; Makhzani et al., 2015; Chen et al., 2016; Higgins et al., 2017). Of these models, it can be argued that $\\beta$ -VAE (Higgins et al., 2017) and InfoGAN (Chen et al., 2016) are the most promising due to their scalability and lack of assumptions about the underling factors of variation. Thus, we evaluate the codes learned by these models and compare them to the VAE $\\beta = 1 \\AA$ ) and PCA. ",
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+    {
+        "type": "text",
+        "text": "For fair comparison, we train all models with 10 code variables and use the same network architectures for the VAE, $\\beta$ -VAE and InfoGAN. More specifically, we use the same residual networks (ResNets, He et al. 2016) for the encoders/discriminator and the decoders/generator (see Table 2), and train InfoGAN with 10 continous ‘latent codes’(Chen et al., 2016) and 0 noise variables. We found that these ResNets produced the sharpest images and best visual disentanglement for all generative models, outperforming popular architectures for ( $\\beta .$ -)VAE (Larsen et al., 2015; Higgins et al., 2017) and InfoGAN (Kulkarni et al., 2015). We fit $\\beta = 6$ and $\\lambda = 6$ for $\\beta$ -VAE and InfoGAN respectively by balancing reconstruction/generation quality and visual disentanglement (see Appendix D), where $\\lambda$ is the mutual information coefficient. See Appendix A for further details. ",
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+    {
+        "type": "text",
+        "text": "4.3 REGRESSORS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Lasso. We begin with linear regressors and encourage a sparse mapping between $^ c$ and $_ { z }$ with an $\\ell _ { 1 }$ regularisation penalty (lasso regressors). With the inputs and targets normalised to have zero mean and unit variance, the magnitude of the resulting regression weights rank the learnt code variables $c _ { 0 } , \\ldots , c _ { D - 1 }$ in order of relative importance to the prediction. That is, they reveal which code variables capture information about a given generative factor. Thus, we define the matrix of relative importances $R$ as $R _ { i j } = | W _ { i j } |$ for linear regression, where $R _ { i j }$ denotes the relative importance of $c _ { i }$ in predicting $z _ { j }$ and $| W _ { i j } |$ denotes the magnitude of the weight used to scale $c _ { i }$ in predicting $z _ { j }$ . We fit the $\\ell _ { 1 }$ penalty coefficient $\\alpha$ on the validation set to achieve the lowest prediction error. ",
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+    {
+        "type": "text",
+        "text": "Random forest. We use random forest regressors due to their inbuilt ability to determine the relative importance of each feature to a given prediction, thus allowing us to directly specify the matrix of relative importances $R$ . Random forests average the predictions and feature importances from each decision tree in the ensemble. The number of times a tree chooses to split on a particular input variable determines its importance to the prediction. Thus, the relative importance of each input variable $c _ { i }$ is given by the number of cases split on $c _ { i }$ over the total number of splits (Breiman et al., 1984). As performance generally improves with the number of trees $n$ in the ensemble, we fix $n = 1 0$ . The remaining parameter, tree depth, is determined on the validation set (lowest prediction error). ",
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+    {
+        "type": "table",
+        "img_path": "images/3f4bb8ad30b6e0667440c3e4fba2e1de5ef8cae59ff8b7777e8c4fb5f0126682.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1: Average model scores. ‘Inform.’ indicates (average) normalised root-mean-square error (NRMSE) in predicting $_ z$ . "
+        ],
+        "table_body": "<table><tr><td colspan=\"4\">(a) Lasso</td><td colspan=\"4\">(b)Random forest</td></tr><tr><td>Code</td><td>Disent.</td><td>Compl.</td><td>Inform.</td><td>Code</td><td>Disent.</td><td>Compl.</td><td>Inform.</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PCA</td><td>0.29</td><td>0.32</td><td>0.44</td><td>PCA</td><td>0.50</td><td>0.52</td><td>0.27</td></tr><tr><td>VAE (β = 1)</td><td>0.67</td><td>0.62</td><td>0.37</td><td>VAE (β = 1)</td><td>0.86</td><td>0.75</td><td>0.09</td></tr><tr><td>β-VAE (β = 6)</td><td>0.66</td><td>0.59</td><td>0.35</td><td>β-VAE (β = 6)</td><td>0.90</td><td>0.76</td><td>0.10</td></tr><tr><td>InfoGAN</td><td>0.75</td><td>0.72</td><td>0.23</td><td>InfoGAN</td><td>0.91</td><td>0.87</td><td>0.13</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4.4 RESULTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Overview. Table 1 presents the average disentanglement, completeness and informativeness scores for PCA, the VAE, $\\beta$ -VAE and InfoGAN for the (a) lasso and (b) random forest regressors. With both regressors, PCA achieves the worst disentanglement, completeness and informativeness scores (highest error in predicting $_ z$ ) while the VAE $\\mathbf { \\nabla } \\beta = 1 \\mathbf { \\dot { \\varepsilon } } ,$ ) and $\\beta$ -VAE $\\beta = 6 )$ ) achieve very similar disentanglement, completeness and informativeness scores to each other. While InfoGAN achieves the best disentanglement, completeness and informativeness scores with the lasso regressor, the VAE and $\\beta$ -VAE achieve similar disentanglement and informativeness scores to it with (the increased capacity of) the random forest regressor. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Disentanglement. InfoGAN achieves the highest average disentanglement with both regressors (although $\\beta$ -VAE closely follows with the random forest regressor). That is, each variable in InfoGAN’s code (c−InfoGAN) is closest (on average) to capturing a single generative factor, making $c -$ InfoGAN the most disentangled code (see Appendix B.1 for the full / per-variable results). Figure 3 helps to identify the generative factors captured by a given code variable and thus visualise the disentanglement. For example, comparing $c _ { 0 }$ across all models in Figure 3 (the first rows), it is clear that $c _ { 0 } { - } \\mathrm { V A E }$ , $c _ { 0 } { - } \\beta \\mathrm { V A E }$ and $c _ { 0 } { \\mathrm { - I n f o G A N } }$ (almost) solely capture information about $z _ { \\mathrm { 0 } }$ while $c _ { 0 } { - } \\mathrm { P C A }$ captures information about almost all generative factors. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Completeness. InfoGAN also achieves the highest average completeness with both regressors. That is, $c - .$ InfoGAN is closest (on average) to capturing each generative factor with a single code variable, making $c - .$ InfoGAN the most complete code. In contrast, the low completeness score (overcompleteness) of $c { \\mathrm { - P C A } }$ reveals that it uses several code variables to capture each generative factor (again, see Appendix B.1 for the full $/$ per-variable results). Figure 3 helps to identify the code variables which capture a given generative factor and thus visualise the completeness. For example, Figure 3 shows that several ‘dead’ or redundant code variables $( c _ { 5 } , c _ { 6 } , c _ { 7 } )$ enable a high degree of completeness in $c -$ InfoGAN. In addition, comparing $z _ { 0 }$ (azimuth) across all models in Figure 3b (the first columns), it is clear that InfoGAN uses three code variables $( c _ { 0 } , c _ { 1 } , c _ { 8 } )$ to capture $z _ { \\mathrm { 0 } }$ while PCA, VAE, and $\\beta$ -VAE use significantly more. In particular, Figure 3 shows that $c { \\mathrm { - P C A } }$ is severely overcomplete in capturing $z _ { \\mathrm { 0 } }$ , with each of its constituent variables capturing distinct information about $z _ { \\mathrm { 0 } }$ . With an ideal code, Figure 3 would show a single large square in $K$ rows and each column, indicating a one-to-one mapping between $_ z$ and $K$ of the dimensions in $^ c$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Informativeness. With the lasso regressor, c−InfoGAN is most predictive of / informative about $_ z$ . That is, $c - .$ InfoGAN contains the most easily-extractable $/$ explicit information about $_ { z }$ . This is supported by Figure 5, which plots each $z$ against the corresponding ‘most important’ code variable(s) (as indicated by the $R$ matrix) and reveals (primarily) linear relationships between $_ { z }$ and c−InfoGAN. Despite being significantly deeper with many more parameters, $c { \\mathrm { - V A E } }$ and $\\displaystyle c { - \\beta \\mathrm { V A E } }$ are only slightly more predictive of $_ z$ than $c { \\mathrm { - P C A } }$ with this linear regressor, indicating that the information about $_ z$ in $c { \\mathrm { - V A E } }$ and $\\displaystyle c { - \\beta \\mathrm { V A E } }$ is not easily-extractable / explicit (again, this is supported by the relationships depicted in Figure 5). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "All model codes better predict $_ z$ with the random forest regressor, particularly $c { \\mathrm { - V A E } }$ and $\\displaystyle c { - \\beta \\mathrm { V A E } }$ . In fact, $c { \\mathrm { - V A E } }$ and $\\textstyle { c - } \\beta \\mathrm { V A E }$ are the most predictive of $/$ informative about $_ { z }$ with this non-linear regressor, with the increased capacity allowing significantly more information about $_ z$ to be extracted from these codes. As discussed in section 2, the prediction error with this (nonlinear) regressor is likely a better quantification of informativeness as it is less dependent on the ability of the model to explicitly represent information about $_ z$ in $^ c$ . ",
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+    {
+        "type": "image",
+        "img_path": "images/fb851eeda23ab9d9cbe5970eb98c698d678e3655d4394140d5e5d3b65c5e527e.jpg",
+        "image_caption": [
+            "Figure 3: Visualising $\\pmb { R }$ . Square size indicates magnitude, i.e. relative importance. Row $i$ illustrates the importance of $c _ { i }$ to each prediction and thus the disentanglement. Column $j$ illustrates the importance of each code variable for predicting $z _ { j }$ and thus the completeness. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "",
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+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this work we have presented a framework for the quantitative evaluation of disentangled representations when the ground-truth latent structure is available. The quality of learnt representations is elucidated through the explicit definition and quantification of three criteria: disentanglement, completeness and informativeness. To illustrate the appropriateness of our framework, we employed it to compare quantitatively the codes learned by PCA, the VAE, $\\beta$ -VAE and InfoGAN. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "While our framework is limited to synthetic datasets where it is possible to recover $_ z$ , reliable disentanglement is far from solved even in this restricted setting. Hence, we believe our framework and its constituent metrics take a substantial and important step forward in understanding learned representations. We have made the code and dataset publicly available in the hope that this facilitates further model comparisons and eventually the establishment of quantitative benchmarks for disentangled factor learning. While we have focused on image data in this work, future work may explore the applicability of our framework to other types of synthetic data. ",
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+    {
+        "type": "text",
+        "text": "",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6 ACKNOWLEDGEMENTS ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We would like to thank Pol Moreno and Akash Srivastava for helpful discussions. We would also like to thank Pol for generating the dataset. Finally, we would like to thank the anonymous reviewers for their constructive criticisms which were helpful in refining this paper. The work of CW is supported in part by EPSRC grant EP/N510129/1 to the Alan Turing Institute. ",
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+        "type": "text",
+        "text": "A EXPERIMENTAL SETUP ",
+        "text_level": 1,
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+        "text": "For all generative models, we use the ResNet architectures shown in Table 2 for the encoder / discriminatior $( D )$ / auxilary network $( Q )$ and the decoder / generator $( G )$ . We optimize using Adam (Kingma & Ba, 2014) with a learning rate of 1e-4 and a batch size of 64. For the stable training of InfoGAN, we fix the latent codes’ standard deviations to 1 and use the objective of the improved Wasserstein GAN (IWGAN) (Gulrajani et al., 2017), simply appending InfoGAN’s approximate mutual information penalty. As in Gulrajani et al. (2017), we use layer normalization (Ba et al., 2016) instead of batch normalization (Ioffe & Szegedy, 2015) in $D$ . As in Chen et al. (2016), $Q$ shares all convolutional layers with the discriminator (or ‘critic’ with WGAN objective) $D$ , each adding their own final output layer. As $Q$ parametrises the approximate posterior over continous latent codes $Q ( c | \\pmb { x } )$ , we simply take the mean returned by $Q ( { \\pmb x } )$ as the code or representation for a given image. Further details on the experimental setup are provided in our open-source implementation. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/72d909827111ece8d767cc5d11d309d71ae1b4a9d3347996b7e0309285b17bf1.jpg",
+        "table_caption": [
+            "Table 2: (β-)VAE / InfoGAN architecture. Each network has 4 residual blocks (all but the first and last rows). The input to each residual block is added to its output (with appropriate downsampling/upsampling to ensure that the dimensions match). Downsampling (↓) is performed with mean pooling. $\\uparrow$ indicates nearest-neighbour upsampling. When batch normalization (BN) is applied to convolutional layers, per-channel normalization is used. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=2>Encoder /D/ Q                Decoder /G</td></tr><tr><td rowspan=1 colspan=1>3x3 64 conv.</td><td rowspan=1 colspan=1>FC 4:4.8.64</td></tr><tr><td rowspan=1 colspan=1>BN,ReLU,3x3 64 convBN, ReLU,3×3 128 conv,↓</td><td rowspan=1 colspan=1>BN,ReLU, 3x3 512 conv ↑BN,ReLU, 3×3 512 conv</td></tr><tr><td rowspan=1 colspan=1>BN, ReLU, 3x3 128 convBN,ReLU,3x3 256 conv,↓</td><td rowspan=1 colspan=1>BN, ReLU, 3x3 256 conv ↑BN, ReLU, 3x3 256 conv</td></tr><tr><td rowspan=1 colspan=1>BN, ReLU, 3x3 256 convBN,ReLU,3×3 512 conv,↓</td><td rowspan=1 colspan=1>BN, ReLU, 3x3 128 conv ↑BN,ReLU, 3×3 128 conv</td></tr><tr><td rowspan=1 colspan=1>BN, ReLU,3x3 512 convBN, ReLU,3×3 512 conv,↓</td><td rowspan=1 colspan=1>BN,ReLU,3x3 64 conv ↑BN,ReLU,3x3 64 conv</td></tr><tr><td rowspan=1 colspan=1>FC Output</td><td rowspan=1 colspan=1>BN,ReLU,3x33 conv, tanh</td></tr></table>",
+        "bbox": [
+            302,
+            311,
+            696,
+            469
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "B EXTENDED RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            585,
+            382,
+            602
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "B.1 FULL TABLE / PER-FACTOR RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            621,
+            468,
+            635
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Tables 3 and 4 give the full regression results, i.e. the per-factor disentanglement, completeness and informativeness. As each target is normalised to have a standard deviation of 1, the root-mean-square error (RMSE) in predicting each target is naturally normalised relative to the constant regressor which guesses the expected value of the targets. Hence, we report the NRMSE. ",
+        "bbox": [
+            174,
+            650,
+            825,
+            705
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "B.2 ZEROSHOT ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            728,
+            292,
+            742
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Disentangled representations should enable a model to perform zero-shot inference, that is, generalise its knowledge beyond the training distribution by recombining previously-learnt factors (Bengio et al., 2013; Higgins et al., 2017). Thus, we can further evaluate the disentangled representations learned by a given model by quantifying its ability to perform zero-shot inference. We use the ground-truth values of the generative factors to create two different data distributions. More specifically, we isolate all images whose generative factor values lie in a particular range to create a ‘gap’ in the original dataset. This gap then serves as our zero-shot data containing unseen factor combinations. Informally, the images in this gap can be described as ‘red’ teapots from ‘above’. Formally, the generative factors of these images satisfy the following condition: $z _ { 2 } > ( z _ { 3 } + 0 . 1 5 )$ and $z _ { 2 } > ( z _ { 4 } + 0 . 1 5 )$ and $z _ { 1 } > \\frac { \\pi } { 4 }$ . This dataset contained 21,238 images, with (extreme) samples given in Figure 4. Note that zero-shot inference is facilitated by disentangled and informative representations, thus is not a core component of our evaluation, but rather a ‘bonus’. ",
+        "bbox": [
+            173,
+            757,
+            825,
+            924
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/24fcfcbcf7c6e7ee2f3f451dcdfda1296b9c595f769070046a1f6cb0bec82344.jpg",
+        "table_caption": [
+            "(a) Disentanglement "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Code</td><td>Co</td><td>C1</td><td>C2</td><td>C3</td><td>C4</td><td>C5</td><td>C6</td><td>C7</td><td>C8</td><td>Cg</td><td>W. Avg.</td></tr><tr><td>PCA</td><td>0.16</td><td>0.50</td><td>0.31</td><td>0.09</td><td>0.45</td><td>0.60</td><td>0.11</td><td>1.00</td><td>0.17</td><td>0.51</td><td>0.29</td></tr><tr><td>VAE</td><td>1.00</td><td>0.85</td><td>0.95</td><td>0.68</td><td>0.63</td><td>1.00</td><td>0.30</td><td>0.37</td><td>0.66</td><td>0.95</td><td>0.67</td></tr><tr><td>β-VAE</td><td>1.00</td><td>0.64</td><td>1.00</td><td>0.76</td><td>0.39</td><td>0.89</td><td>0.49</td><td>0.81</td><td>0.45</td><td>0.80</td><td>0.66</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>InfoGAN</td><td>0.83</td><td>0.85</td><td>0.76</td><td>0.66</td><td>0.78</td><td>0.43</td><td>1.00</td><td>1.00</td><td>0.64</td><td>0.74</td><td>0.75</td></tr></table>",
+        "bbox": [
+            218,
+            121,
+            774,
+            198
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/666dd52762e84c6f5d290752255f4359e8a64ece0ff96102539762800d317468.jpg",
+        "table_caption": [
+            "(b) Completeness ",
+            "(c) Informativeness "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Code</td><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td><td>Avg.</td><td>Code</td><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td><td>Avg.</td></tr><tr><td>PCA</td><td>0.38</td><td>0.39</td><td>0.34</td><td>0.24</td><td></td><td>0.32</td><td>PCA</td><td></td><td></td><td></td><td>0.32</td><td>0.33</td><td>0.44</td></tr><tr><td>VAE</td><td></td><td></td><td></td><td></td><td>0.25</td><td></td><td></td><td>0.83</td><td>0.42</td><td>0.32</td><td></td><td></td><td></td></tr><tr><td></td><td>0.54</td><td>0.37</td><td>0.75</td><td>0.73</td><td>0.73</td><td>0.62</td><td>VAE</td><td>0.61</td><td>0.60</td><td>0.23</td><td>0.21</td><td>0.21</td><td>0.37</td></tr><tr><td>β-VAE</td><td>0.14</td><td>0.39</td><td>0.70</td><td>0.85</td><td>0.88</td><td>0.59</td><td>β-VAE</td><td>0.80</td><td>0.41</td><td>0.19</td><td>0.19</td><td>0.18</td><td>0.35</td></tr><tr><td>InfoGAN</td><td>0.42</td><td>0.72</td><td>0.75</td><td>0.86</td><td>0.84</td><td>0.72</td><td>InfoGAN</td><td>0.48</td><td>0.13</td><td>0.23</td><td>0.16</td><td>0.15</td><td>0.23</td></tr></table>",
+        "bbox": [
+            176,
+            227,
+            823,
+            303
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/928d2f0eddeef6c6022821c3ff3e01d024c8dbd2e7d1ef838c610d5dd0905932.jpg",
+        "table_caption": [
+            "Table 3: Lasso regression results. (a) Disentanglement scores for each code variable. ‘W. Avg.’ abbreviates weighted average. (b) Completeness scores for each generative factor. $z _ { 0 } , \\ldots , z _ { 4 }$ represent azimuth, elevation, red, green and blue generative factors respectively. c) Test set NRMSE. ",
+            "(a) Disentanglement ",
+            "Table 4: Random forest regression results. Caption of Table 3 applies. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Code</td><td></td><td>Co</td><td>C1</td><td>C2</td><td>C3</td><td>C4</td><td>C5</td><td>C6</td><td>C7</td><td>C8</td><td>Cg</td><td>W. Avg.</td><td></td></tr><tr><td>PCA</td><td></td><td>0.25</td><td>0.54</td><td>0.63</td><td>0.10</td><td>0.88</td><td>0.97</td><td>0.16</td><td>0.90</td><td>0.41</td><td>0.72</td><td>0.50</td><td></td></tr><tr><td>VAE</td><td></td><td>0.98</td><td>0.99</td><td>0.91</td><td>0.94</td><td>0.75</td><td>0.99</td><td>0.56</td><td>0.56</td><td>0.92</td><td>0.86</td><td>0.86</td><td></td></tr><tr><td>β-VAE</td><td></td><td>0.96</td><td>0.96</td><td>0.95</td><td>0.99</td><td>0.63</td><td>0.96</td><td>0.69</td><td>0.94</td><td>0.64</td><td>0.98</td><td>0.90</td><td></td></tr><tr><td>InfoGAN</td><td></td><td>0.85</td><td>0.97</td><td>0.91</td><td>0.84</td><td>0.94</td><td>0.68</td><td>0.86</td><td>0.70</td><td>0.71</td><td>0.92</td><td>0.91</td><td></td></tr><tr><td>(b) Completeness</td><td colspan=\"3\"></td><td></td><td></td><td></td><td>(c) Informativeness</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Code 20</td><td colspan=\"3\">21</td><td>23</td><td>24</td><td>Avg</td><td>Code</td><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td><td>Avg.</td></tr><tr><td>PCA</td><td></td><td></td><td>22</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.27</td></tr><tr><td>VAE</td><td>0.31 0.44</td><td>0.51 0.61</td><td>0.67 0.90</td><td>0.56 0.91</td><td>0.56 0.91</td><td>0.52 0.75</td><td>PCA VAE</td><td>0.36 0.14</td><td>0.23 0.09</td><td>0.20 0.09</td><td>0.28 0.06</td><td>0.28 0.06</td><td>0.09</td></tr><tr><td>β-VAE</td><td>0.28</td><td>0.67</td><td>0.90</td><td>0.96</td><td>0.97</td><td>0.76</td><td>β-VAE</td><td>0.18</td><td>0.07</td><td>0.08</td><td>0.09</td><td>0.08</td><td>0.10</td></tr><tr><td>InfoGAN</td><td>0.59</td><td>0.94</td><td>0.91</td><td>0.96</td><td>0.95</td><td>0.87</td><td>InfoGAN</td><td>0.25</td><td>0.07</td><td>0.14</td><td>0.09</td><td>0.10</td><td>0.13</td></tr></table>",
+        "bbox": [
+            176,
+            385,
+            823,
+            574
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Table 5 presents the zeroshot results. With the random forest regressor, $c { \\mathrm { - V A E } }$ and $\\displaystyle c { - \\beta \\mathrm { V A E } }$ perform the best with very little increase in prediction error compared to Table 4c, while $c - .$ InfoGAN predicts the value of unseen factor combinations reasonably well. ",
+        "bbox": [
+            174,
+            626,
+            825,
+            667
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/12bf251bb375ffe741383d2cc4b3a3941a01d39e89ec679348dd7f9f346d07a8.jpg",
+        "image_caption": [
+            "Figure 4: Zeroshot samples "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            267,
+            104,
+            728,
+            147
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/de4c825138cb89371fe6edbc53f142c5dfb9bde935cf4ec37413b349e88164d7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"6\">(a) Lasso</td><td colspan=\"8\">(b)Random Forest</td></tr><tr><td>Code</td><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td><td>Avg.</td><td>Code</td><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td><td>Avg.</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PCA</td><td>0.88</td><td>0.80</td><td>0.75</td><td>0.52</td><td>0.54</td><td>0.70</td><td>PCA</td><td>0.44</td><td>0.49</td><td>0.65</td><td>0.56</td><td>0.63</td><td>0.55</td></tr><tr><td>VAE</td><td>0.56</td><td>1.11</td><td>0.52</td><td>0.30</td><td>0.32</td><td>0.56</td><td>VAE</td><td>0.13</td><td>0.13</td><td>0.34</td><td>0.08</td><td>0.07</td><td>0.15</td></tr><tr><td>β-VAE</td><td>0.81</td><td>0.79</td><td>0.32</td><td>0.27</td><td>0.25</td><td>0.49</td><td>β-VAE</td><td>0.18</td><td>0.18</td><td>0.21</td><td>0.12</td><td>0.14</td><td>0.16</td></tr><tr><td>InfoGAN</td><td>0.49</td><td>0.34</td><td>0.93</td><td>0.36</td><td>0.33</td><td>0.49</td><td>InfoGAN</td><td>0.27</td><td>0.18</td><td>0.63</td><td>0.21</td><td>0.25</td><td>0.31</td></tr></table>",
+        "bbox": [
+            176,
+            188,
+            823,
+            285
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 5: Zeroshot performance. NRMSE in predicting unseen factor combinations. ",
+        "bbox": [
+            218,
+            296,
+            774,
+            311
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C Z VS. C ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            335,
+            277,
+            352
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Figure 5 plots each generative factor against the corresponding ‘most important’ code variable(s) (as indicated by $R$ ) of each model for 5000 randomly-selected samples. As discussed in section 2, models with generic priors cannot be expected to learn the most complete and explicit representation of topologically distinct factors of variation. Thus, for the wrapped azimuth $\\left( z _ { 0 } \\right)$ , we plot its value against the 3 most important code variables for each model. Inspecting the relationships depicted in Figure 5, it is clear that the simplest / lowest-order relationship exists between InfoGAN’s code variables and the corresponding generative factors. For example, each unwrapped generative factor $( z _ { 1 } , z _ { 2 } , z _ { 3 } , z _ { 4 } )$ is linearly-related to InfoGAN’s corresponding code variables, while $c _ { 0 }$ and $c _ { 8 }$ resemble scaled sine and cosine functions of the azimuth $\\left( z _ { 0 } \\right)$ and $c _ { 1 }$ resembles a step function. ",
+        "bbox": [
+            173,
+            367,
+            825,
+            493
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/7b9aed0a0a476b94fd74ba0004c73b762f8ca8ead3129555b91f45f0cd0afe8e.jpg",
+        "image_caption": [
+            "Figure 5: Generative factors vs. important code variables. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            193,
+            808,
+            814
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "D VISUALLY ASSESSING DISENTANGLEMENT ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            102,
+            565,
+            118
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "For each model, we traverse the space of each code variable indepedently to show the effect on generated images and thus visually assess disentanglement. The code variable traversals depicted in Figure 6 for (a) VAE $[ - 3 , 3 ]$ , (b) $\\beta$ -VAE $[ - 3 , 3 ]$ and (c) InfoGAN $[ - 1 , 1 ]$ are ordered according to the generative factor $( z )$ which that code best captures in an attempt to align the generated images of all models. There appears to be a high degree of disentanglement in all generative models as each $c _ { i }$ traversal results in a single type of semantic variation. ",
+        "bbox": [
+            173,
+            132,
+            826,
+            218
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/ab89eeece7c2b275264781702c6c482abc19c2144b52f50328be646710c675d6.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            169,
+            231,
+            815,
+            598
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/1794813fe6342802141b8748d26b1b716658eaeae75dd12ab1a3290afacc35c7.jpg",
+        "image_caption": [
+            "Figure 6: Code variable traversals. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            165,
+            123,
+            812,
+            885
+        ],
+        "page_idx": 14
+    }
+]

parse/train/BylQSxHFwr/BylQSxHFwr.md

@@ -0,0 +1,292 @@
+# ATOMNAS: FINE-GRAINED END-TO-END NEURAL ARCHITECTURE SEARCH
+
+Jieru Mei1∗, Yingwei $\mathbf { L i } ^ { 1 * }$ , Xiaochen Lian2, Xiaojie $\mathbf { J i n ^ { 2 } }$ , Linjie Yang2, Alan Yuille1 & Jianchao Yang2
+
+1Johns Hopkins University   
+2ByteDance AI Lab
+
+eijieru@gmail.com, yingwei.li@jhu.edu, {xiaochen.lian, jinxiaojie, linjie.yang}@bytedance.com
+
+alan.l.yuille@gmail.com, yangjianchao@bytedance.com
+
+# ABSTRACT
+
+Search space design is very critical to neural architecture search (NAS) algorithms. We propose a fine-grained search space comprised of atomic blocks, a minimal search unit that is much smaller than the ones used in recent NAS algorithms. This search space allows a mix of operations by composing different types of atomic blocks, while the search space in previous methods only allows homogeneous operations. Based on this search space, we propose a resource-aware architecture search framework which automatically assigns the computational resources (e.g., output channel numbers) for each operation by jointly considering the performance and the computational cost. In addition, to accelerate the search process, we propose a dynamic network shrinkage technique which prunes the atomic blocks with negligible influence on outputs on the fly. Instead of a searchand-retrain two-stage paradigm, our method simultaneously searches and trains the target architecture. Our method achieves state-of-the-art performance under several FLOPs configurations on ImageNet with a small searching cost. We open our entire codebase at: https://github.com/meijieru/AtomNAS.
+
+# 1 INTRODUCTION
+
+Human-designed neural networks are already surpassed by machine-designed ones. Neural Architecture Search (NAS) has become the mainstream approach to discover efficient and powerful network structures (Zoph & Le (2017); Pham et al. (2018); Tan et al. (2019); Liu et al. (2019a)). Although the tedious searching process is conducted by machines, humans still involve extensively in the design of the NAS algorithms. Designing of search spaces is critical for NAS algorithms and different choices have been explored. Cai et al. (2019) and Wu et al. (2019) utilize supernets with multiple choices in each layer to accommodate a sampled network on the GPU. Chen et al. (2019b) progressively grow the depth of the supernet and remove unnecessary blocks during the search. Tan & Le (2019a) propose to search the scaling factor of image resolution, channel multiplier and layer numbers in scenarios with different computation budgets. Stamoulis et al. (2019a) propose to use different kernel sizes in each layer of the supernet and reuse the weights of larger kernels for small kernels. Howard et al. (2019); Tan & Le (2019b) adopts Inverted Residuals with Linear Bottlenecks (MobileNetV2 block) (Sandler et al., 2018), a building block with light-weighted depth-wise convolutions for highly efficient networks in mobile scenarios.
+
+However, the proposed search spaces generally have only a small set of choices for each block. DARTS and related methods (Liu et al., 2019a; Chen et al., 2019b; Liang et al., 2019) use around 10 different operations between two network nodes. Howard et al. (2019); Cai et al. (2019); Wu et al. (2019); Stamoulis et al. (2019a) search the expansion ratios in the MobileNetV2 block but still limit them to a few discrete values. We argue that search space of finer granularity is critical to find optimal neural architectures. Specifically, the searched building block in a supernet should be as small as possible to generate the most diversified model structures.
+
+We revisit the architectures of state-of-the-art networks (Howard et al. (2019); Tan & Le (2019b); He et al. (2016)) and discover a commonly used building structure: convolution - channel-wise operation - convolution. We reinterpret this building structure as an ensemble of computationally independent blocks, which we call atomic blocks. As the minimum search unit, the atomic block constitutes a much larger and more fine-grained search space, within which we are able to search for mixed operations (e.g., convolutions with different kernel sizes and their channel numbers).
+
+For the efficient exploration of the new search space, we propose a NAS framework named AtomNAS which applies network pruning techniques to architecture search. Specifically, we start from an initial large supernet and rewrite every convolution - channel-wise operation - convolution structure of it in the form the weighted sum of atomic blocks; the weights reflect the contribution of the atomic blocks to the network capacity and are called importance factors. For each atomic block, a penalty term in proportion to its FLOPs is enforced on its importance factor; effectively, the penalty makes AtomNAS favor atomic blocks with less FLOPs. By minimizing the combination of the original network loss and the total penalty on the weights, AtomNAS is able to learn both the parameters of the network and the weights of the atomic blocks. At the end of the learning, atomic blocks with very small weights (e.g., $< 0 . 0 0 1$ ) are removed from the network and we obtain the final network which has fewer FLOPs. Since the pruned atomic blocks have little contribution to the network output due to their negligible weights, the final network does not need to be retrained or finetuned.
+
+Training on the large supernet is computationally demanding. We observe that for many pruned atomic blocks, their weights diminish at the early stage of learning and never “revive” throughout the rest of learning. We propose a dynamic network shrinkage technique which removes those atomic blocks on the fly and greatly reduces the run time of AtomNAS.
+
+In our experiment, our method achieves $7 5 . 9 \%$ top-1 accuracy on ImageNet dataset around 360M FLOPs, which is $0 . 9 \%$ higher than state-of-the-art model (Stamoulis et al., 2019a). By further incorporating additional modules, our method achieves $7 7 . 6 \%$ top-1 accuracy. It outperforms MixNet by $0 . 6 \%$ using 363M FLOPs, which is a new state-of-the-art under the mobile scenario.
+
+In summary, the major contributions of our work are:
+
+1. We design a fine-grained search space which includes the exact number of channels and mixed operations (e.g., combination of different convolution kernels).   
+2. We propose an NAS framework, AtomNAS. Within the framework, an efficient end-to-end NAS algorithm is proposed which can simultaneously search the network architecture and train the final model. No finetuning is needed after the algorithm finishes.   
+3. With the proposed search space and AtomNAS, we achieve state-of-the-art performance on ImageNet dataset under mobile setting.
+
+# 2 RELATED WORK
+
+# 2.1 NEURAL ARCHITECTURE SEARCH
+
+Recently, there is a growing interest in automated neural architecture design. Reinforce learning based NAS methods (Zoph & Le, 2017; Tan et al., 2019; Tan & Le, 2019b;a) are usually computational intensive, thus hampering its usage with limited computational budget. To accelerate the search procedure, ENAS (Pham et al., 2018) represents the search space using a directed acyclic graph and aims to search the optimal subgraph within the large supergraph. A training strategy of parameter sharing among subgraphs is proposed to significantly increase the searching efficiency. The similar idea of optimizing optimal subgraphs within a supergraph is also adopted by Liu et al. (2019a); Jin et al. (2019); Xu et al. (2020); Wu et al. (2019); Guo et al. (2019); Cai et al. (2019). Stamoulis et al. (2019a); Yu et al. (2020) further share the parameters of different paths within a block using super-kernel representation. A prominent disadvantage of the above methods is that their coarse search spaces only support selecting one out of a set of choices (e.g., selecting one kernel size from $\{ 3 , 5 , { \bar { 7 } } \}$ ). MixNet tries to benefit from mixed operations by using a predefined set of mixed operations $\{ \{ 3 \} , \{ 3 , 5 \} , \{ 3 , 5 , 7 \} , \{ 3 , 5 , 7 , 9 \} \}$ , where the channels are equally distributed among different kernel sizes. Due to this limitation, it is difficult to learn optimal architectures under computational resource constraints. On the contrary, our method takes advantage of the fine-grained search space and is able to search for more flexible network architectures satisfying various resource constraints. The fine-grained search space proposed in this paper is exponentially larger than previous search space. For reference, the total number of possible structures within the experiment is around $1 0 ^ { 1 6 2 }$ , compared with $1 0 ^ { 2 1 }$ for FBNet. Recently, to improve the final performance of the searched architectures, $\mathrm { Y u }$ et al. (2020) utilizes knowledge distillation which is orthogonal to our method. It could be easily integrated into our method by Eq. (5) thanks to the end-to-end learning paradigm of our method.
+
+![](images/c62dc520ca55c4bc08bf4281cc4ae4652738759989a5499f1a0de93542e42793.jpg)  
+Figure 1: Illustration of the ensemble perspective. Arrow means operators. The structure of two convolutions joined by a channel-wise operation is mathematically equivalent to the ensemble of multiple atomic blocks, according to Eq. (2). Colored rectangles represent tensors, with numbers inside indicating their channel numbers; The shaded path on the right is one example of atomic block.
+
+# 2.2 NETWORK PRUNING
+
+Assuming that many parameters in the network are unnecessary, network pruning methods start from a computation-intensive model, identify the unimportant connections and remove them to get a compact and efficient network. Early method (Han et al., 2016) simultaneously learns the important connections and weights. However, non-regularly removing connections in these works makes it hard to achieve theoretical speedup ratio on realistic hardwares due to extra overhead in caching and indexing. To tackle this problem, structured network pruning methods (He et al., 2017b; Liu et al., 2017; Luo et al., 2017; Ye et al., 2018; Gordon et al., 2018) are proposed to prune structured components in networks, e.g. the entire channel and kernel. In this way, empirical acceleration can be achieved on modern computing devices. Liu et al. (2017); Ye et al. (2018); Gordon et al. (2018) encourage channel-level sparsity by imposing the L-1 regularizer on the channel dimension, which is also used by our method. Recently, Liu et al. (2019b) show that in structured network pruning, the learned weights are unimportant. This suggests structured network pruning is actually a neural architecture search focusing on channel numbers. Our method jointly searches the channel numbers and a mix of operations, which is a much larger search space.
+
+# 3 ATOMNAS
+
+We formulate our neural architecture search method in a fine-grained search space with the atomic block used as the basic search unit. An atomic block is comprised of two convolutions connected by a channel-wise operation. By stacking atomic blocks, we obtain larger building blocks (e.g. residual block and MobileNetV2 block proposed in a variety of state-of-the-art models including ResNet, MobileNet V2/V3 (He et al., 2016; Howard et al., 2019; Sandler et al., 2018). In Section 3.1, We first show larger network building blocks (e.g. MobileNetV2 block) can be represented by an ensembles of atomic blocks. Based on this view, we propose a fine-grained search space using atomic blocks. In Section 3.2, we propose a resource-aware atomic block selection method for end-to-end architecture search. Finally, we propose a dynamic network shrinkage technique in Section 3.3, which greatly reduces the search cost.
+
+# 3.1 FINE-GRAINED SEARCH SPACE
+
+Under the typical block-wise NAS paradigm (Tan et al., 2019; Tan & Le, 2019b), the search space of each block in a neural network is represented as the Cartesian product $\begin{array} { r } { \mathcal { C } = \prod _ { i = 1 } \mathcal { P } _ { i } } \end{array}$ , where each $\mathcal { P } _ { i }$ is the set of all choices of the $i$ -th configuration such as kernel size, number of channels and type of operation. For example, ${ \mathcal { C } } = \{ { \mathrm { c o n v } } $ , depth-wise conv, dilated conv $\} \times \{ 3 , 5 \} \times \{ 2 4 , 3 2 , 6 4 , 1 \dot { 2 } \dot { 8 } \}$ represents a search space of three types of convolutions by two kernel sizes and four options of channel number. A block in the resulting model can only pick one convolution type from the three and one output channel number from the four values. This paradigm greatly limits the search space due to the few choices of each configuration. Here we present a more fine-grained search space by decomposing the network into smaller and more basic building blocks.
+
+We denote $f ^ { c ^ { \prime } , c } ( X )$ as a convolution operator, where $X$ is the input tensor and $c , c ^ { \prime }$ are the input and output channel numbers respectively. A wide range of manually-designed and NAS architectures share a structure that joins two convolutions by a channel-wise operation:
+
+$$
+Y = \left( f _ { 1 } ^ { c ^ { \prime \prime } , c ^ { \prime } } \circ g \circ f _ { 0 } ^ { c ^ { \prime } , c } \right) ( X )
+$$
+
+where $g$ is a channel-wise operator. For example, in VGG (Simonyan & Zisserman, 2015) and a Residual Block (He et al., 2016), $f _ { 0 }$ and $f _ { 1 }$ are convolutions and $g$ is one of Maxpool, ReLU and BN-ReLU; in a MobileNetV2 block (Sandler et al., 2018), $f _ { 0 }$ and $f _ { 1 }$ are point-wise convolutions and $g$ is depth-wise convolution with BN-ReLU in the MobileNetV2 block. Eq. (1) can be reformulated as follows:
+
+$$
+Y = \sum _ { i = 1 } ^ { c ^ { \prime } } \left( f _ { 1 } ^ { c ^ { \prime \prime } , 1 } [ i , : ] \circ g [ i , : ] \circ f _ { 0 } ^ { 1 , c } [ : , i ] \right) ( X ) ,
+$$
+
+where $f _ { 0 } ^ { 1 , c } [ : , i ]$ is the $i$ -th convolution kernel of $f _ { 0 } , g [ i , : ]$ is the operator of the $i$ -th channel of $g$ and $\{ f _ { 1 } ^ { c ^ { \prime \prime } , 1 } [ i , : ] \} _ { i = 1 } ^ { c ^ { \prime } }$ are obtained by splitting the kernel tensor of $f _ { 1 }$ along the the input channel dimension. Each term in the summation can be seen as a computationally independent block, which is called atomic block. Fig. (1) demonstrate this reformulation. By determining whether to keep each atomic block in the final model individually, the search of channel number $c ^ { \prime }$ is enabled through channel selection, which greatly enlarges the search space.
+
+This formulation also naturally includes the selection of operators. To gain a better understanding, we first generalize Eq. (2) as:
+
+$$
+Y = \sum _ { i = 1 } ^ { c ^ { \prime } } \left( f _ { 1 i } ^ { c ^ { \prime \prime } , 1 } \circ g _ { i } \circ f _ { 0 i } ^ { 1 , c } \right) ( X ) .
+$$
+
+Note the array indices $i$ are moved to subscripts. In this formulation, we can use different types of operators for $f _ { 0 i } , f _ { 1 i }$ and $g _ { i }$ ; in other words, $f _ { 0 } , f _ { 1 }$ and $g$ can each be a combination of different operators and each atomic block can use different operators such as convolutions with different kernel sizes.
+
+Formally, the search space is formulated as a supernet which is built based on the structure in Eq. (1); such structure satisfies Eq. (3) and thus can be represented by atomic blocks; each of $f _ { 0 }$ , $f _ { 1 }$ and $g$ is a combination of operators. The new search space includes some state-of-the-art network architectures. For example, by allowing $g$ to be a combination of convolutions with different kernel sizes, the MixConv block in MixNet (Tan & Le, 2019b) becomes a special case in our search space. In addition, our search space facilitates discarding any number of channels in $g$ , resulting in a more fine-grained channel configuration. In comparison, the channel numbers are determined heuristically in Tan & Le (2019b).
+
+# 3.2 RESOURCE-AWARE ATOMIC BLOCK SEARCH
+
+In this work, we adopt a differentiable neural architecture search paradigm where the model structure is discovered in a full pass of model training. With the supernet defined above, the final model can be produced by discarding part of the atomic blocks during training. Following DARTS (Liu et al.
+
+(2019a)), we introduce a importance factor $\alpha$ to scale the output of each atomic block in the supernet. Eq. (3) then becomes
+
+$$
+Y = \sum _ { i = 1 } ^ { c ^ { \prime } } \alpha _ { i } \left( f _ { 1 i } ^ { c ^ { \prime \prime } , 1 } \circ g _ { i } \circ f _ { 0 i } ^ { 1 , c } \right) ( X ) .
+$$
+
+Here, each $\alpha _ { i }$ is tied with an atomic block comprised of three operators $f _ { 1 i } ^ { c ^ { \prime \prime } , 1 } , g _ { i }$ and $f _ { 0 i } ^ { 1 , c }$ . The importance factors are learned jointly with the network weights. Once the training finishes, the atomic blocks that have negligible effect (i.e., those with factors smaller than a threshold) on the network output are discarded.
+
+We still need to address two issues related to the importance factors $\alpha _ { i }$ ’s. The first issue is where in the supernet we should put the $\alpha$ ? Let’s first consider the case when $g$ only contains linear operations, e.g., convolution, batch normalization and linear activation like ReLU. If $g$ contains at least one BN layer, The scaling parameters in the BN layers can be directly used as such importance factors (Liu et al. (2017)). If $g$ has no BN layers, which is rare, we can place $\alpha$ anywhere between $f _ { 0 }$ and $f _ { 1 }$ ; however, we need to apply regularization terms to the weights of $f _ { 0 }$ and $f _ { 1 }$ (e.g., weight decays) in order to prevent weights in $f _ { 0 }$ and $f _ { 1 }$ from getting too large and canceling the effect of $\alpha$ . When $g$ contains non-linear operations, e.g., Swish activation and Sigmoid activation, we can only put $\alpha$ behind $f _ { 1 }$ .
+
+The second issue is how to avoid performance deterioration after discarding some of the atomic blocks. For example, DARTS discards operations with small scale factors after iterative training of model parameters and scale factors. Since the scale factors of the discarded operations are not small enough, the performance of the network will be affected which needs re-training to adjust the weights again. In order to maintain the performance of the supernet after dropping some atomics blocks, the importance factors $\alpha$ of those atomic blocks should be sufficiently small. Inspired by the channel pruning work in Liu et al. (2017), we add L1 norm penalty loss on $\alpha$ , which effectively pushes many importance factors to near-zero values. At the end of learning, atomic blocks with $\alpha$ close to zero are removed from the supernet. Note that since the BN scales change more dramatically during training due to the regularization term, the running statistics of BNs might be inaccurate and needs to be calculated again using the training set.
+
+With the added regularization term, the training loss is
+
+$$
+\begin{array} { c } { \displaystyle { \mathcal { L } = \mathcal { E } + \lambda \sum _ { i \in \mathcal { S } } c _ { i } \big | \alpha _ { i } \big | , } } \\ { \displaystyle { \phantom { \frac { \sum _ { i } } { c _ { i } } } } } \\ { \displaystyle { c _ { i } = \hat { c } _ { i } \big / \sum _ { k \in \mathcal { S } } \hat { c } _ { k } } } \end{array}
+$$
+
+where $\lambda$ is the coefficient of L1 penalty term, $s$ is the index set of all atomic blocks, and $\mathcal { E }$ is the conventional training loss (e.g., cross-entropy loss combined with the regularization term like weight decay and distillation loss.). $\left| \alpha _ { i } \right|$ is weighted by coefficient $c _ { i }$ which is proportional to the computation cost of $i$ -th atomic block, i.e. $\hat { c } _ { i }$ . By using computation costs aware regularization, we encourage the model to learn network structures that strike a good balance between accuracy and efficiency. In this paper, we use FLOPs as the criteria of computation cost. Other metrics such as latency and energy consumption can be used similarly. As a result, the whole loss function $\mathcal { L }$ trades off between accuracy and FLOPs.
+
+# 3.3 DYNAMIC NETWORK SHRINKAGE
+
+Usually, the supernet is much larger than the final search result. We observe that many atomic blocks become “dead” starting from the early stage of the search, i.e., their importance factors $\alpha$ are close to zero till the end of the search. To utilize computational resources more efficiently and speed up the search process, we propose a dynamic network shrinkage algorithm which cuts down the network architecture by removing atomic blocks once they are deemed “dead”.
+
+We adopt a conservative strategy to decide whether an atomic block is “dead”: for importance factors $\alpha$ , we maintain its momentum $\hat { \alpha }$ which is updated as
+
+$$
+\hat { \alpha } \gets \beta \hat { \alpha } + ( 1 - \beta ) \alpha ^ { t } ,
+$$
+
+![](images/8452b3f0bed69446364463d4f08930963c12f719fae460817acd40a604bf6420.jpg)  
+Figure 2: FLOPs change of the supernet during the searching and training for AtomNAS-C. The crossed-out region corresponds to the saved computation compared to training the supernet without the dynamic shrinkage. The region in yellow corresponds to the extra cost compared with training the final model from scratch, the cost of which is the region below the red dashed line.
+
+Initialize the supernet and the exponential moving average;   
+while epoch $\leq$ max epoch do Update network weights and importance factors $\alpha$ by minimizing the loss function $\mathcal { L }$ ; Update the $\hat { \alpha }$ by Eq. (7); if Total FLOPs of dead blocks $\geq \Delta$ then Remove dead blocks from the supernet; end Recalculate BN’s statistics by forwarding some training examples; Validate the performance of the current supernet;
+
+end
+
+Algorithm 1: Dynamic network shrinkage
+
+where $\alpha ^ { t }$ is the importance factors at $t$ -th iteration and $\beta$ is the decay term. An atomic block is considered “dead” if both $\hat { \alpha }$ and $\alpha ^ { t }$ are smaller than a threshold, which is set to 0.001 throughout experiments.
+
+Once the total FLOPs of “dead” blocks reach a predefined threshold, we remove those blocks from the supernet. As discussed above, we recalculate BN’s running statistics before deploying the network. The whole training process is presented in Algorithm 1.
+
+We show the FLOPs of a sample network during the search process in Fig. 2. We start from a supernet with 1521M FLOPs and dynamically discard “dead” atomic blocks to reduce search cost. The overall search and train cost only increases by $1 7 . 2 \%$ compared to that of training the searched model from scratch.
+
+# 4 EXPERIMENT
+
+We first describe the implementation details in Section 4.1 and then compare AtomNAS with previous state-of-the-art methods under various FLOPs constraints in Section 4.2. In Section 4.3, we provide more detailed analysis about AtomNAS. Finally, in Section 4.4, we demonstrate the transferability of AtomNAS networks by evaluating them on detection and instance segmentation tasks.
+
+# 4.1 IMPLEMENTATION DETAILS
+
+The architecture of the supernet we use for the experiments is shown in table on the right of Fig. 3. The supernet contains 21 AtomNAS blocks, the searchable block in our supernet; the picture on the right of Fig. 3 illustrates the structure of an AtomNAS block, where $f _ { 0 }$ is a $1 \times 1$ pointwise convolutions that expands the input channel number from $C$ to $3 \times 6 C$ ; $g$ is a mix of three depth-wise convolutions with kernel sizes of $3 \times 3 , 5 \times 5$ and $7 \times 7 .$ and $f _ { 1 }$ is another $1 \times 1$ pointwise convolutions that projects the channel number to the output channel number. Similar to MobileNetV2 (Sandler et al., 2018), if the output dimension stays the same as the input dimension, we use a skip connection to add the input to the output. AtomNAS block is effectively an ensemble of $3 \times 6 C$ atomic blocks, whose underlying search space covers the MobileNetV2 block (Sandler et al., 2018) and its multikernel variant, MixConv (Tan & Le, 2019b). Within AtomNAS block, we are able to optimize the distribution of computation resources (i.e., channel numbers) among the three types of depth-wise convolution.
+
+<table><tr><td> Input Shape</td><td>Block</td><td>f</td><td>n</td><td>stride</td></tr><tr><td>224²×3</td><td>3x3 conv</td><td>32(16)</td><td>1</td><td>2</td></tr><tr><td>112² × 32(16)</td><td>3x3 MB</td><td>16</td><td>1</td><td>1</td></tr><tr><td>112²×16</td><td>searchable</td><td>24</td><td>4</td><td>2</td></tr><tr><td>56²×24</td><td>searchable</td><td>40</td><td>4</td><td>2</td></tr><tr><td>28²×40</td><td>searchable</td><td>80</td><td>4</td><td>2</td></tr><tr><td>14²×80</td><td>searchable</td><td>96</td><td>4</td><td>1</td></tr><tr><td>14²×96</td><td>searchable</td><td>192</td><td>4</td><td>2</td></tr><tr><td>7²×192</td><td>searchable</td><td>320</td><td>1</td><td>1</td></tr><tr><td>7² ×320</td><td>avgpool</td><td>1</td><td>1</td><td>1</td></tr><tr><td>1280</td><td>fc</td><td>1000</td><td>1</td><td>1</td></tr></table>
+
+![](images/78737b107a3bb2660818aad97a17a467bfe2d6a4fecbb0f8a568d8da71c9fab3.jpg)  
+Figure 3: (Left) The searchable block of the supernet. $f _ { 0 }$ and $f _ { 1 }$ are fixed to $1 \times 1$ pointwise convolutions; $g$ here is a mix of three convolutions with kernel sizes of $3 \times 3$ , $5 \times 5$ and $7 \times 7$ . $f _ { 0 }$ expands the input channel number from $C$ to $1 8 C$ and $f _ { 1 }$ projects the channel number to the output channel number. If the output dimension stays the same as the input dimension, we use a skip connection to add the input to the output. (Right) Architecture of the supernet. Column-Block denotes the block type; MB denotes MobileNetV2 block; ”searchable” means a searchable block shown on the left. Column-f denotes the output channel number of a block. Column-n denotes the number of blocks. Column-s denotes the stride of the first block in a stage. The output channel numbers of the first convolution are 16 for AtomNAS-A, 32 for AtomNAS-B and AtomNAS-C.
+
+We use the same training configuration (e.g., RMSProp optimizer, EMA on weights and exponential learning rate decay) as Tan et al. (2019); Stamoulis et al. (2019a) and do not use extra data augmentation such as MixUp (Zhang et al., 2018) and AutoAugment (Cubuk et al., 2018). We find that using this configuration is sufficient for our method to achieve good performance. Our results are shown in Table 1 and Table 3. When training the supernet, we use a total batch size of 2048 on 32 Tesla V100 GPUs and train for 350 epochs. For our dynamic network shrinkage algorithm, we set the momentum factor $\beta$ in Eq. (7) to 0.9999. At the beginning of the training, all of the weights are randomly initialized. To avoid removing atomic blocks with high penalties (i.e., FLOPs) prematurely, the weight of the penalty term in Eq. (5) is increased from 0 to the target $\lambda$ by a linear scheduler during the first 25 epochs. By setting the weight of the L1 penalty term $\lambda$ to be $1 . { \overset { \cdot } { 8 } } \times 1 0 ^ { - 4 }$ , $1 . 2 \times 1 0 ^ { - 4 }$ and ${ \bar { 1 } } . 0 \times 1 0 ^ { - 4 }$ respectively, we obtain networks with three different sizes: AtomNAS-A, AtomNAS-B, and AtomNAS-C. They have the similar FLOPs as previous state-of-the-art networks under 400M: MixNet-S (Tan & Le, 2019b), MixNet-M (Tan & Le, 2019b) and SinglePath (Stamoulis et al., 2019a). In Appendix A, we visualize the architecture of AtomNAS-C.
+
+# 4.2 EXPERIMENTS ON IMAGENET
+
+We apply AtomNAS to search high performance light-weight model on ImageNet 2012 classification task (Deng et al., 2009). Table 1 compares our methods with previous state-of-the-art models, either manually designed or searched.
+
+With models directly produced by AtomNAS, our method achieves the new state-of-the-art under all FLOPs constraints. Especially, AtomNAS-C achieves $7 5 . 9 \%$ top-1 accuracy with only 360M FLOPs, and surpasses all other models, including models like PDARTS and DenseNAS which have much higher FLOPs.
+
+![](images/a3282b42db113d5bd5627597a598ce86c508613a9ae6e5b0b656cf8c4b6d66f8.jpg)  
+Figure 4: FLOPs versus accuracy on ImageNet. † means methods use extra techniques like Swish activation and Squeeze-and-Excitation module.
+
+Techniques like Swish activation function (Ramachandran et al., 2018) and Squeeze-and-Excitation (SE) module (Hu et al., 2018) consistently improve the accuracy with marginal FLOPs cost. For a fair comparison with methods that use these techniques, we directly modify the searched network by replacing all ReLU activation with Swish and add SE module with ratio 0.5 to every block and then retrain the network from scratch. Note that unlike other methods, we do not search the configuration of Swish and SE, and therefore the performance might not be optimal. Extra data augmentations such as MixUp and AutoAugment are still not used. We train the models from scratch with a total batch size of 4096 on 32 Tesla V100 GPUs for 250 epochs.
+
+Simply adding these techniques improves the results further. AtomNAS- $\mathbf { A } +$ achieves $7 6 . 3 \%$ top1 accuracy with 260M FLOPs, which outperforms many heavier models including MnasNet-A2. Without extra data augmentations, it performs as well as Efficient-B0 (Tan & Le, 2019a) by using 130M less FLOPs. It also outperforms the previous state-of-the-art MixNet-S by $0 . 5 \%$ . In addition, AtomNAS- $C +$ improves the top-1 accuracy on ImageNet to $7 7 . 6 \%$ , surpassing previous state-ofthe-art MixNet-M by $0 . 6 \%$ and becomes the overall best performing model under 400M FLOPs.
+
+Fig. 4 visualizes the top-1 accuracy on ImageNet for different models. It’s clear that our fine-grained search space and the end-to-end resource-aware search method boost the performance significantly.
+
+# 4.3 ANALYSIS
+
+# 4.3.1 RESOURCE-AWARE REGULARIZATION
+
+To demonstrate the effectiveness of the resource-aware regularization in Section 3.2, we compare it with a baseline without FLOPs-related coefficients $c _ { i }$ , which is widely used in network pruning (Liu et al., 2017; He et al., 2017b). Table 2 shows the results. First, by using the same L1 penalty coefficient $\lambda = 1 . 0 \times 1 0 ^ { - 4 }$ , the baseline achieves a network with similar performance but using much more FLOPs; then by increasing $\lambda$ to $1 . 5 \times 1 0 ^ { - 4 }$ , the baseline obtain a network which has similar FLOPs but inferior performance (i.e., about $1 . 0 \%$ lower). In Fig. 6b we visualized the ratio of different types of atomic blocks of the baseline network obtained by $\bar { \lambda ( \mathrm { = 1 . 5 \times 1 0 ^ { - 4 } } }$ . The baseline network keeps more atomic blocks in the earlier blocks, which have higher computation cost due to higher input resolution. On the contrary, AtomNAS is aware of the resource constraint, thus keeping more atomic blocks in the later blocks and achieving much better performance.
+
+# 4.3.2 BN RECALIBRATION
+
+As the BN’s running statistics might be inaccurate as explained in Section 3.2 and Section 3.3, we re-calculate the running statistics of BN before inference, by forwarding 131k randomly sampled training images through the network. Table 3 shows the impact of the BN recalibration. The top-1 accuracies of AtomNAS-A, AtomNAS-B, and AtomNAS-C on ImageNet improve by $1 . 4 \%$ , $1 . { \bar { 7 } } \%$ , and $1 . 2 \%$ respectively, which clearly shows the benefit of BN recalibration.
+
+Table 1: Comparision with state-of-the-arts on ImageNet under the mobile setting. † denotes methods using extra network modules such as Swish activation and Squeeze-and-Excitation module. ‡ denotes using extra data augmentation such as MixUp and AutoAugment. ∗ denotes models searched and trained simultaneously.   
+
+<table><tr><td>Model</td><td>Parameters</td><td>FLOPs</td><td>Top-1(%)</td><td>Top-5(%)</td></tr><tr><td>MobileNetV1 (Howard et al., 2017)</td><td>4.2M</td><td>575M</td><td>70.6</td><td>89.5</td></tr><tr><td>MobileNetV2 (Sandler et al., 2018)</td><td>3.4M</td><td>300M</td><td>72.0</td><td>91.0</td></tr><tr><td>MobileNetV2 (our impl.)</td><td>3.4M</td><td>301M</td><td>73.6</td><td>91.5</td></tr><tr><td>MobileNetV2 (1.4)</td><td>6.9M</td><td>585M</td><td>74.7</td><td>92.5</td></tr><tr><td>ShuffleNetV2 (Ma et al.,2018)</td><td>3.5M</td><td>299M</td><td>72.6</td><td>=</td></tr><tr><td>ShuffleNetV2 2×</td><td>7.4M</td><td>591M</td><td>74.9</td><td></td></tr><tr><td>FBNet-A (Wu et al., 2019)</td><td>4.3M</td><td>249M</td><td>73.0</td><td></td></tr><tr><td>FBNet-C</td><td>5.5M</td><td>375M</td><td>74.9</td><td></td></tr><tr><td>Proxyless (mobile) (Cai et al., 2019)</td><td>4.1M</td><td>320M</td><td>74.6</td><td>92.2</td></tr><tr><td>SinglePath (Stamoulis et al., 2019a)</td><td>4.4M</td><td>334M</td><td>75.0</td><td>92.2</td></tr><tr><td>NASNet-A (Zoph &amp; Le,2017)</td><td>5.3M</td><td>564M</td><td>74.0</td><td>91.6</td></tr><tr><td>DARTS (second order) (Liu et al., 2019a)</td><td>4.9M</td><td>595M</td><td>73.1</td><td>-</td></tr><tr><td>PDARTS (cifar 10) (Chen et al., 2019b)</td><td>4.9M</td><td>557M</td><td>75.6</td><td>92.6</td></tr><tr><td>DenseNAS-A (Fang et al., 2019)</td><td>7.9M</td><td>501M</td><td>75.9</td><td>92.6</td></tr><tr><td>FairNAS-A (Chu et al., 2019b)</td><td>4.6M</td><td>388M</td><td>75.3</td><td>92.4</td></tr><tr><td>AtomNAS-A*</td><td>3.9M</td><td>258M</td><td>74.6</td><td>92.1</td></tr><tr><td>AtomNAS-B*</td><td>4.4M</td><td>326M</td><td>75.5</td><td>92.6</td></tr><tr><td>AtomNAS-C*</td><td>4.7M</td><td>360M</td><td>75.9</td><td>92.7</td></tr><tr><td>SCARLET-A† (Chu et al., 2019a)</td><td>6.7M</td><td>365M</td><td>76.9</td><td>93.4</td></tr><tr><td>MnasNet-A1† (Tan et al., 2019)</td><td>3.9M</td><td>312M</td><td>75.2</td><td>92.5</td></tr><tr><td>MnasNet-A2t</td><td>4.8M</td><td>340M</td><td>75.6</td><td>92.7</td></tr><tr><td>MixNet-St (Tan &amp; Le, 2019b)</td><td>4.1M</td><td>256M</td><td>75.8</td><td>92.8</td></tr><tr><td>MixNet-M†</td><td>5.0M</td><td>360M</td><td>77.0</td><td>93.3</td></tr><tr><td>EfficientNet-Bot‡ (Tan &amp; Le, 2019a)</td><td>5.3M</td><td>390M</td><td>76.3</td><td>93.2</td></tr><tr><td>SE-DARTS+†‡ (Liang et al., 2019)</td><td>6.1M</td><td>594M</td><td>77.5</td><td>93.6</td></tr><tr><td>AtomNAS-A+†</td><td>4.7M</td><td>260M</td><td>76.3</td><td>93.0</td></tr><tr><td>AtomNAS-B+†</td><td>5.5M</td><td>329M</td><td>77.2</td><td>93.5</td></tr><tr><td>AtomNAS-C+†</td><td>5.9M</td><td>363M</td><td>77.6</td><td>93.6</td></tr></table>
+
+Table 2: Influence of awareness of resource metric. The upper block uses equal penalties for all atomic blocks. The lower part uses our resource-aware atomic block selection.   
+
+<table><tr><td>入</td><td>FLOPs</td><td>Top-1(%)</td></tr><tr><td>1.0×10-4</td><td>445M</td><td>76.1</td></tr><tr><td>1.5 ×10-4</td><td>370M</td><td>74.9</td></tr><tr><td>1.0×10-4</td><td>360M</td><td>75.9</td></tr></table>
+
+# 4.3.3 COST OF DYNAMIC NETWORK SHRINKAGE
+
+Our dynamic network shrinkage algorithm speedups the search and train process significantly. For AtomNAS-C, the total time for search-and-training is 25.5 hours. For reference, training the final architecture from scratch takes 22 hours. Note that as the supernet shrinks, both the GPU memory consumption and forward-backward time are significantly reduced. Thus it’s possible to dynamically change the batch size once having sufficient GPU memory, which would further speed up the whole procedure.
+
+Table 3: Influence of BN recalibration.   
+
+<table><tr><td>Model</td><td>w/o Recalibration</td><td>w/Recalibration</td></tr><tr><td>AtomNAS-A</td><td>73.2</td><td>74.6 (+1.4)</td></tr><tr><td>AtomNAS-B</td><td>73.8</td><td>75.5 (+1.7)</td></tr><tr><td>AtomNAS-C</td><td>74.7</td><td>75.9 (+1.2)</td></tr></table>
+
+# 4.4 EXPERIMENTS ON COCO DETECTION AND INSTANCE SEGMENTATION
+
+In this section, we assess the performance of AtomNAS models as feature extractors for object detection and instance segmentation on COCO dataset (Lin et al., 2014). We first pretrain AtomNAS models (without Swish activation function (Ramachandran et al., 2018) and Squeeze-and-Excitation (SE) module (Hu et al., 2018)) on ImageNet, use them as drop-in replacements for the backbone in the Mask-RCNN model (He et al., 2017a) by building the detection head on top of the last feature map, and finetune the model on COCO dataset.
+
+We use the open-source code MMDetection (Chen et al., 2019a). All the models are trained on COCO train2017 with batch size 16 and evaluated on COCO val2017. Following the schedule used in the open-source implementation of TPU-trained Mask-RCNN , the learning rate starts at 0.02 and decreases by a scale of 10 at 15-th and 20th epoch respectively. The models are trained for 23 epochs in total.
+
+Table 4 compares the results with other baseline backbone models. The detection results of baseline models are from Stamoulis et al. (2019b). We can see that all three AtomNAS models outperform the baselines on object detection task. The results demonstrate that our models have better transferability than the baselines, which may due to mixed operations, a.k.a multi-scale here, are more important to object detection and instance segmentation.
+
+Table 4: Comparision with baseline backbones on COCO object detection and instance segmentation. Cls denotes the ImageNet top-1 accuracy; detect-mAP and seg-mAP denotes mean average precision for detection and instance segmentation on COCO dataset. The results of baseline models are from Stamoulis et al. (2019b). SinglePath $^ +$ (Stamoulis et al., 2019b) contains SE module.   
+
+<table><tr><td>Model</td><td>FLOPs</td><td>Cls (%)</td><td>detect-mAP (%)</td><td>seg-mAP (%)</td></tr><tr><td>MobileNetV2 (Sandler et al., 2018)</td><td>301M</td><td>73.6</td><td>30.5</td><td>1</td></tr><tr><td>Proxyless (mobile) (Cai et al., 2019)</td><td>320M</td><td>74.6</td><td>32.9</td><td>=</td></tr><tr><td>Proxyless (mobile) (our impl.)</td><td>320M</td><td>74.9</td><td>32.7</td><td>30.0</td></tr><tr><td>SinglePath+ (Stamoulis et al., 2019b)</td><td>353M</td><td>75.6</td><td>33.0</td><td>1</td></tr><tr><td>SinglePath (our impl.)</td><td>334M</td><td>75.0</td><td>32.0</td><td>29.7</td></tr><tr><td>AtomNAS-A</td><td>258M</td><td>74.6</td><td>32.7</td><td>30.1</td></tr><tr><td>AtomNAS-B</td><td>326M</td><td>75.5</td><td>33.6</td><td>30.8</td></tr><tr><td>AtomNAS-C</td><td>360M</td><td>75.9</td><td>34.1</td><td>31.4</td></tr></table>
+
+# 5 CONCLUSION
+
+In this paper, we revisit the common structure, i.e., two convolutions joined by a channel-wise operation, and reformulate it as an ensemble of atomic blocks. This perspective enables a much larger and more fine-grained search space. For efficiently exploring the huge fine-grained search space, we propose an end-to-end framework named AtomNAS, which conducts architecture search and network training jointly. The searched networks achieve significantly better accuracy than previous state-of-the-art methods while using small extra cost.
+
+# REFERENCES
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+![](images/a32d42420361ceba48ac3630b92aad453623f3484101b00fc26aaaf222acef71.jpg)  
+A VISUALIZATION   
+Figure 5: The architecture of AtomNAS-C. Blue, orange, cyan blocks denote atomic blocks with kernel size 3, 5 and 7 respectively; the heights of these blocks are proportional to their expand ratios.
+
+We plot the structure of the searched architecture AtomNAS-C in Fig. 5, from which we see more flexibility of channel number selection, not only among different operators within each block, but also across the network. In Fig. 6a, we visualize the ratio between atomic blocks with different kernel sizes in all 21 search blocks. First, we notice that all search blocks have convolutions of all three kernel sizes, showing that AtomNAS learns the importance of using multiple kernel sizes in network architecture. Another observation is that AtomNAS tends to keep more atomic blocks at the later stage of the network. This is because in earlier stage, convolutions of the same kernel size costs more FLOPs; AtomNAS is aware of this (thanks to its resource-aware regularization) and try to keep as less as possible computationally costly atomic blocks.
+
+![](images/17291dab22b27a4c559585f81d3d24d7e8d873b0d22d623f4573327d8ad24bb7.jpg)  
+Figure 6: Ratio of different types of atomic blocks in all 21 searchable blocks. The text above each pie tells the total number of atomic blocks of the corresponding block in the original supernet. Grey denotes dead atomic blocks; blue, orange, and cyan represent atomic blocks using depth-wise convolutions with kernel size $3 , 5 , 7$ respectively. Blocks without skip connection are highlighted by bold text. (a) Visualization for AtomNAS-C. (b) Visualization for baseline (i.e., without FLOPs related coefficients $c _ { i }$ ).

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+        "text": "Jieru Mei1∗, Yingwei $\\mathbf { L i } ^ { 1 * }$ , Xiaochen Lian2, Xiaojie $\\mathbf { J i n ^ { 2 } }$ , Linjie Yang2, Alan Yuille1 & Jianchao Yang2 ",
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+        "text": "1Johns Hopkins University   \n2ByteDance AI Lab ",
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+    {
+        "type": "text",
+        "text": "eijieru@gmail.com, yingwei.li@jhu.edu, {xiaochen.lian, jinxiaojie, linjie.yang}@bytedance.com ",
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+        "text": "alan.l.yuille@gmail.com, yangjianchao@bytedance.com ",
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+    {
+        "type": "text",
+        "text": "ABSTRACT ",
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+        "text": "Search space design is very critical to neural architecture search (NAS) algorithms. We propose a fine-grained search space comprised of atomic blocks, a minimal search unit that is much smaller than the ones used in recent NAS algorithms. This search space allows a mix of operations by composing different types of atomic blocks, while the search space in previous methods only allows homogeneous operations. Based on this search space, we propose a resource-aware architecture search framework which automatically assigns the computational resources (e.g., output channel numbers) for each operation by jointly considering the performance and the computational cost. In addition, to accelerate the search process, we propose a dynamic network shrinkage technique which prunes the atomic blocks with negligible influence on outputs on the fly. Instead of a searchand-retrain two-stage paradigm, our method simultaneously searches and trains the target architecture. Our method achieves state-of-the-art performance under several FLOPs configurations on ImageNet with a small searching cost. We open our entire codebase at: https://github.com/meijieru/AtomNAS. ",
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+        "text": "1 INTRODUCTION ",
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+        "text": "Human-designed neural networks are already surpassed by machine-designed ones. Neural Architecture Search (NAS) has become the mainstream approach to discover efficient and powerful network structures (Zoph & Le (2017); Pham et al. (2018); Tan et al. (2019); Liu et al. (2019a)). Although the tedious searching process is conducted by machines, humans still involve extensively in the design of the NAS algorithms. Designing of search spaces is critical for NAS algorithms and different choices have been explored. Cai et al. (2019) and Wu et al. (2019) utilize supernets with multiple choices in each layer to accommodate a sampled network on the GPU. Chen et al. (2019b) progressively grow the depth of the supernet and remove unnecessary blocks during the search. Tan & Le (2019a) propose to search the scaling factor of image resolution, channel multiplier and layer numbers in scenarios with different computation budgets. Stamoulis et al. (2019a) propose to use different kernel sizes in each layer of the supernet and reuse the weights of larger kernels for small kernels. Howard et al. (2019); Tan & Le (2019b) adopts Inverted Residuals with Linear Bottlenecks (MobileNetV2 block) (Sandler et al., 2018), a building block with light-weighted depth-wise convolutions for highly efficient networks in mobile scenarios. ",
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+        "text": "However, the proposed search spaces generally have only a small set of choices for each block. DARTS and related methods (Liu et al., 2019a; Chen et al., 2019b; Liang et al., 2019) use around 10 different operations between two network nodes. Howard et al. (2019); Cai et al. (2019); Wu et al. (2019); Stamoulis et al. (2019a) search the expansion ratios in the MobileNetV2 block but still limit them to a few discrete values. We argue that search space of finer granularity is critical to find optimal neural architectures. Specifically, the searched building block in a supernet should be as small as possible to generate the most diversified model structures. ",
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+        "text": "For the efficient exploration of the new search space, we propose a NAS framework named AtomNAS which applies network pruning techniques to architecture search. Specifically, we start from an initial large supernet and rewrite every convolution - channel-wise operation - convolution structure of it in the form the weighted sum of atomic blocks; the weights reflect the contribution of the atomic blocks to the network capacity and are called importance factors. For each atomic block, a penalty term in proportion to its FLOPs is enforced on its importance factor; effectively, the penalty makes AtomNAS favor atomic blocks with less FLOPs. By minimizing the combination of the original network loss and the total penalty on the weights, AtomNAS is able to learn both the parameters of the network and the weights of the atomic blocks. At the end of the learning, atomic blocks with very small weights (e.g., $< 0 . 0 0 1$ ) are removed from the network and we obtain the final network which has fewer FLOPs. Since the pruned atomic blocks have little contribution to the network output due to their negligible weights, the final network does not need to be retrained or finetuned. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Training on the large supernet is computationally demanding. We observe that for many pruned atomic blocks, their weights diminish at the early stage of learning and never “revive” throughout the rest of learning. We propose a dynamic network shrinkage technique which removes those atomic blocks on the fly and greatly reduces the run time of AtomNAS. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In our experiment, our method achieves $7 5 . 9 \\%$ top-1 accuracy on ImageNet dataset around 360M FLOPs, which is $0 . 9 \\%$ higher than state-of-the-art model (Stamoulis et al., 2019a). By further incorporating additional modules, our method achieves $7 7 . 6 \\%$ top-1 accuracy. It outperforms MixNet by $0 . 6 \\%$ using 363M FLOPs, which is a new state-of-the-art under the mobile scenario. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In summary, the major contributions of our work are: ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1. We design a fine-grained search space which includes the exact number of channels and mixed operations (e.g., combination of different convolution kernels).   \n2. We propose an NAS framework, AtomNAS. Within the framework, an efficient end-to-end NAS algorithm is proposed which can simultaneously search the network architecture and train the final model. No finetuning is needed after the algorithm finishes.   \n3. With the proposed search space and AtomNAS, we achieve state-of-the-art performance on ImageNet dataset under mobile setting. ",
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+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.1 NEURAL ARCHITECTURE SEARCH ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently, there is a growing interest in automated neural architecture design. Reinforce learning based NAS methods (Zoph & Le, 2017; Tan et al., 2019; Tan & Le, 2019b;a) are usually computational intensive, thus hampering its usage with limited computational budget. To accelerate the search procedure, ENAS (Pham et al., 2018) represents the search space using a directed acyclic graph and aims to search the optimal subgraph within the large supergraph. A training strategy of parameter sharing among subgraphs is proposed to significantly increase the searching efficiency. The similar idea of optimizing optimal subgraphs within a supergraph is also adopted by Liu et al. (2019a); Jin et al. (2019); Xu et al. (2020); Wu et al. (2019); Guo et al. (2019); Cai et al. (2019). Stamoulis et al. (2019a); Yu et al. (2020) further share the parameters of different paths within a block using super-kernel representation. A prominent disadvantage of the above methods is that their coarse search spaces only support selecting one out of a set of choices (e.g., selecting one kernel size from $\\{ 3 , 5 , { \\bar { 7 } } \\}$ ). MixNet tries to benefit from mixed operations by using a predefined set of mixed operations $\\{ \\{ 3 \\} , \\{ 3 , 5 \\} , \\{ 3 , 5 , 7 \\} , \\{ 3 , 5 , 7 , 9 \\} \\}$ , where the channels are equally distributed among different kernel sizes. Due to this limitation, it is difficult to learn optimal architectures under computational resource constraints. On the contrary, our method takes advantage of the fine-grained search space and is able to search for more flexible network architectures satisfying various resource constraints. The fine-grained search space proposed in this paper is exponentially larger than previous search space. For reference, the total number of possible structures within the experiment is around $1 0 ^ { 1 6 2 }$ , compared with $1 0 ^ { 2 1 }$ for FBNet. Recently, to improve the final performance of the searched architectures, $\\mathrm { Y u }$ et al. (2020) utilizes knowledge distillation which is orthogonal to our method. It could be easily integrated into our method by Eq. (5) thanks to the end-to-end learning paradigm of our method. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/c62dc520ca55c4bc08bf4281cc4ae4652738759989a5499f1a0de93542e42793.jpg",
+        "image_caption": [
+            "Figure 1: Illustration of the ensemble perspective. Arrow means operators. The structure of two convolutions joined by a channel-wise operation is mathematically equivalent to the ensemble of multiple atomic blocks, according to Eq. (2). Colored rectangles represent tensors, with numbers inside indicating their channel numbers; The shaded path on the right is one example of atomic block. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 NETWORK PRUNING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Assuming that many parameters in the network are unnecessary, network pruning methods start from a computation-intensive model, identify the unimportant connections and remove them to get a compact and efficient network. Early method (Han et al., 2016) simultaneously learns the important connections and weights. However, non-regularly removing connections in these works makes it hard to achieve theoretical speedup ratio on realistic hardwares due to extra overhead in caching and indexing. To tackle this problem, structured network pruning methods (He et al., 2017b; Liu et al., 2017; Luo et al., 2017; Ye et al., 2018; Gordon et al., 2018) are proposed to prune structured components in networks, e.g. the entire channel and kernel. In this way, empirical acceleration can be achieved on modern computing devices. Liu et al. (2017); Ye et al. (2018); Gordon et al. (2018) encourage channel-level sparsity by imposing the L-1 regularizer on the channel dimension, which is also used by our method. Recently, Liu et al. (2019b) show that in structured network pruning, the learned weights are unimportant. This suggests structured network pruning is actually a neural architecture search focusing on channel numbers. Our method jointly searches the channel numbers and a mix of operations, which is a much larger search space. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 ATOMNAS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We formulate our neural architecture search method in a fine-grained search space with the atomic block used as the basic search unit. An atomic block is comprised of two convolutions connected by a channel-wise operation. By stacking atomic blocks, we obtain larger building blocks (e.g. residual block and MobileNetV2 block proposed in a variety of state-of-the-art models including ResNet, MobileNet V2/V3 (He et al., 2016; Howard et al., 2019; Sandler et al., 2018). In Section 3.1, We first show larger network building blocks (e.g. MobileNetV2 block) can be represented by an ensembles of atomic blocks. Based on this view, we propose a fine-grained search space using atomic blocks. In Section 3.2, we propose a resource-aware atomic block selection method for end-to-end architecture search. Finally, we propose a dynamic network shrinkage technique in Section 3.3, which greatly reduces the search cost. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 FINE-GRAINED SEARCH SPACE ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Under the typical block-wise NAS paradigm (Tan et al., 2019; Tan & Le, 2019b), the search space of each block in a neural network is represented as the Cartesian product $\\begin{array} { r } { \\mathcal { C } = \\prod _ { i = 1 } \\mathcal { P } _ { i } } \\end{array}$ , where each $\\mathcal { P } _ { i }$ is the set of all choices of the $i$ -th configuration such as kernel size, number of channels and type of operation. For example, ${ \\mathcal { C } } = \\{ { \\mathrm { c o n v } } $ , depth-wise conv, dilated conv $\\} \\times \\{ 3 , 5 \\} \\times \\{ 2 4 , 3 2 , 6 4 , 1 \\dot { 2 } \\dot { 8 } \\}$ represents a search space of three types of convolutions by two kernel sizes and four options of channel number. A block in the resulting model can only pick one convolution type from the three and one output channel number from the four values. This paradigm greatly limits the search space due to the few choices of each configuration. Here we present a more fine-grained search space by decomposing the network into smaller and more basic building blocks. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We denote $f ^ { c ^ { \\prime } , c } ( X )$ as a convolution operator, where $X$ is the input tensor and $c , c ^ { \\prime }$ are the input and output channel numbers respectively. A wide range of manually-designed and NAS architectures share a structure that joins two convolutions by a channel-wise operation: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6460bfc4b60d3051c0b0972101c1db030c16707fd1e1516fc084b13982ca2b63.jpg",
+        "text": "$$\nY = \\left( f _ { 1 } ^ { c ^ { \\prime \\prime } , c ^ { \\prime } } \\circ g \\circ f _ { 0 } ^ { c ^ { \\prime } , c } \\right) ( X )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            400,
+            324,
+            598,
+            352
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $g$ is a channel-wise operator. For example, in VGG (Simonyan & Zisserman, 2015) and a Residual Block (He et al., 2016), $f _ { 0 }$ and $f _ { 1 }$ are convolutions and $g$ is one of Maxpool, ReLU and BN-ReLU; in a MobileNetV2 block (Sandler et al., 2018), $f _ { 0 }$ and $f _ { 1 }$ are point-wise convolutions and $g$ is depth-wise convolution with BN-ReLU in the MobileNetV2 block. Eq. (1) can be reformulated as follows: ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/64a9b4eeccad6ef5b388fd232f49f5d8736e2f9c4e354fd2f5dad55e86acc410.jpg",
+        "text": "$$\nY = \\sum _ { i = 1 } ^ { c ^ { \\prime } } \\left( f _ { 1 } ^ { c ^ { \\prime \\prime } , 1 } [ i , : ] \\circ g [ i , : ] \\circ f _ { 0 } ^ { 1 , c } [ : , i ] \\right) ( X ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            348,
+            429,
+            648,
+            474
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $f _ { 0 } ^ { 1 , c } [ : , i ]$ is the $i$ -th convolution kernel of $f _ { 0 } , g [ i , : ]$ is the operator of the $i$ -th channel of $g$ and $\\{ f _ { 1 } ^ { c ^ { \\prime \\prime } , 1 } [ i , : ] \\} _ { i = 1 } ^ { c ^ { \\prime } }$ are obtained by splitting the kernel tensor of $f _ { 1 }$ along the the input channel dimension. Each term in the summation can be seen as a computationally independent block, which is called atomic block. Fig. (1) demonstrate this reformulation. By determining whether to keep each atomic block in the final model individually, the search of channel number $c ^ { \\prime }$ is enabled through channel selection, which greatly enlarges the search space. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This formulation also naturally includes the selection of operators. To gain a better understanding, we first generalize Eq. (2) as: ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/efd4b3dca4eac52e76c61709f698b3c6e587428587f11d0c0dd20961ee625b76.jpg",
+        "text": "$$\nY = \\sum _ { i = 1 } ^ { c ^ { \\prime } } \\left( f _ { 1 i } ^ { c ^ { \\prime \\prime } , 1 } \\circ g _ { i } \\circ f _ { 0 i } ^ { 1 , c } \\right) ( X ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            385,
+            611,
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+            656
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note the array indices $i$ are moved to subscripts. In this formulation, we can use different types of operators for $f _ { 0 i } , f _ { 1 i }$ and $g _ { i }$ ; in other words, $f _ { 0 } , f _ { 1 }$ and $g$ can each be a combination of different operators and each atomic block can use different operators such as convolutions with different kernel sizes. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Formally, the search space is formulated as a supernet which is built based on the structure in Eq. (1); such structure satisfies Eq. (3) and thus can be represented by atomic blocks; each of $f _ { 0 }$ , $f _ { 1 }$ and $g$ is a combination of operators. The new search space includes some state-of-the-art network architectures. For example, by allowing $g$ to be a combination of convolutions with different kernel sizes, the MixConv block in MixNet (Tan & Le, 2019b) becomes a special case in our search space. In addition, our search space facilitates discarding any number of channels in $g$ , resulting in a more fine-grained channel configuration. In comparison, the channel numbers are determined heuristically in Tan & Le (2019b). ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 RESOURCE-AWARE ATOMIC BLOCK SEARCH ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this work, we adopt a differentiable neural architecture search paradigm where the model structure is discovered in a full pass of model training. With the supernet defined above, the final model can be produced by discarding part of the atomic blocks during training. Following DARTS (Liu et al. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "(2019a)), we introduce a importance factor $\\alpha$ to scale the output of each atomic block in the supernet. Eq. (3) then becomes ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5d510d7d07a99e3977d51487e00c889d7ed35c52974308e80b7e5ceed97e6163.jpg",
+        "text": "$$\nY = \\sum _ { i = 1 } ^ { c ^ { \\prime } } \\alpha _ { i } \\left( f _ { 1 i } ^ { c ^ { \\prime \\prime } , 1 } \\circ g _ { i } \\circ f _ { 0 i } ^ { 1 , c } \\right) ( X ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            130,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Here, each $\\alpha _ { i }$ is tied with an atomic block comprised of three operators $f _ { 1 i } ^ { c ^ { \\prime \\prime } , 1 } , g _ { i }$ and $f _ { 0 i } ^ { 1 , c }$ . The importance factors are learned jointly with the network weights. Once the training finishes, the atomic blocks that have negligible effect (i.e., those with factors smaller than a threshold) on the network output are discarded. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We still need to address two issues related to the importance factors $\\alpha _ { i }$ ’s. The first issue is where in the supernet we should put the $\\alpha$ ? Let’s first consider the case when $g$ only contains linear operations, e.g., convolution, batch normalization and linear activation like ReLU. If $g$ contains at least one BN layer, The scaling parameters in the BN layers can be directly used as such importance factors (Liu et al. (2017)). If $g$ has no BN layers, which is rare, we can place $\\alpha$ anywhere between $f _ { 0 }$ and $f _ { 1 }$ ; however, we need to apply regularization terms to the weights of $f _ { 0 }$ and $f _ { 1 }$ (e.g., weight decays) in order to prevent weights in $f _ { 0 }$ and $f _ { 1 }$ from getting too large and canceling the effect of $\\alpha$ . When $g$ contains non-linear operations, e.g., Swish activation and Sigmoid activation, we can only put $\\alpha$ behind $f _ { 1 }$ . ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The second issue is how to avoid performance deterioration after discarding some of the atomic blocks. For example, DARTS discards operations with small scale factors after iterative training of model parameters and scale factors. Since the scale factors of the discarded operations are not small enough, the performance of the network will be affected which needs re-training to adjust the weights again. In order to maintain the performance of the supernet after dropping some atomics blocks, the importance factors $\\alpha$ of those atomic blocks should be sufficiently small. Inspired by the channel pruning work in Liu et al. (2017), we add L1 norm penalty loss on $\\alpha$ , which effectively pushes many importance factors to near-zero values. At the end of learning, atomic blocks with $\\alpha$ close to zero are removed from the supernet. Note that since the BN scales change more dramatically during training due to the regularization term, the running statistics of BNs might be inaccurate and needs to be calculated again using the training set. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "With the added regularization term, the training loss is ",
+        "bbox": [
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+            542,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/392cf2ad650a0cdebde9946db2f2a675f79b2750b72dc259f47f74f24245dc8a.jpg",
+        "text": "$$\n\\begin{array} { c } { \\displaystyle { \\mathcal { L } = \\mathcal { E } + \\lambda \\sum _ { i \\in \\mathcal { S } } c _ { i } \\big | \\alpha _ { i } \\big | , } } \\\\ { \\displaystyle { \\phantom { \\frac { \\sum _ { i } } { c _ { i } } } } } \\\\ { \\displaystyle { c _ { i } = \\hat { c } _ { i } \\big / \\sum _ { k \\in \\mathcal { S } } \\hat { c } _ { k } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            561,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\lambda$ is the coefficient of L1 penalty term, $s$ is the index set of all atomic blocks, and $\\mathcal { E }$ is the conventional training loss (e.g., cross-entropy loss combined with the regularization term like weight decay and distillation loss.). $\\left| \\alpha _ { i } \\right|$ is weighted by coefficient $c _ { i }$ which is proportional to the computation cost of $i$ -th atomic block, i.e. $\\hat { c } _ { i }$ . By using computation costs aware regularization, we encourage the model to learn network structures that strike a good balance between accuracy and efficiency. In this paper, we use FLOPs as the criteria of computation cost. Other metrics such as latency and energy consumption can be used similarly. As a result, the whole loss function $\\mathcal { L }$ trades off between accuracy and FLOPs. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3 DYNAMIC NETWORK SHRINKAGE ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Usually, the supernet is much larger than the final search result. We observe that many atomic blocks become “dead” starting from the early stage of the search, i.e., their importance factors $\\alpha$ are close to zero till the end of the search. To utilize computational resources more efficiently and speed up the search process, we propose a dynamic network shrinkage algorithm which cuts down the network architecture by removing atomic blocks once they are deemed “dead”. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We adopt a conservative strategy to decide whether an atomic block is “dead”: for importance factors $\\alpha$ , we maintain its momentum $\\hat { \\alpha }$ which is updated as ",
+        "bbox": [
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+            875,
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c83f85d5f7e14e2abc92fddce9868915a44e7df772e11dd0c799785290b463ec.jpg",
+        "text": "$$\n\\hat { \\alpha } \\gets \\beta \\hat { \\alpha } + ( 1 - \\beta ) \\alpha ^ { t } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            423,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/8452b3f0bed69446364463d4f08930963c12f719fae460817acd40a604bf6420.jpg",
+        "image_caption": [
+            "Figure 2: FLOPs change of the supernet during the searching and training for AtomNAS-C. The crossed-out region corresponds to the saved computation compared to training the supernet without the dynamic shrinkage. The region in yellow corresponds to the extra cost compared with training the final model from scratch, the cost of which is the region below the red dashed line. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            333,
+            101,
+            660,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Initialize the supernet and the exponential moving average;   \nwhile epoch $\\leq$ max epoch do Update network weights and importance factors $\\alpha$ by minimizing the loss function $\\mathcal { L }$ ; Update the $\\hat { \\alpha }$ by Eq. (7); if Total FLOPs of dead blocks $\\geq \\Delta$ then Remove dead blocks from the supernet; end Recalculate BN’s statistics by forwarding some training examples; Validate the performance of the current supernet; ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "end ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1: Dynamic network shrinkage ",
+        "bbox": [
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+            525
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\alpha ^ { t }$ is the importance factors at $t$ -th iteration and $\\beta$ is the decay term. An atomic block is considered “dead” if both $\\hat { \\alpha }$ and $\\alpha ^ { t }$ are smaller than a threshold, which is set to 0.001 throughout experiments. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Once the total FLOPs of “dead” blocks reach a predefined threshold, we remove those blocks from the supernet. As discussed above, we recalculate BN’s running statistics before deploying the network. The whole training process is presented in Algorithm 1. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We show the FLOPs of a sample network during the search process in Fig. 2. We start from a supernet with 1521M FLOPs and dynamically discard “dead” atomic blocks to reduce search cost. The overall search and train cost only increases by $1 7 . 2 \\%$ compared to that of training the searched model from scratch. ",
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+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENT ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We first describe the implementation details in Section 4.1 and then compare AtomNAS with previous state-of-the-art methods under various FLOPs constraints in Section 4.2. In Section 4.3, we provide more detailed analysis about AtomNAS. Finally, in Section 4.4, we demonstrate the transferability of AtomNAS networks by evaluating them on detection and instance segmentation tasks. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.1 IMPLEMENTATION DETAILS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The architecture of the supernet we use for the experiments is shown in table on the right of Fig. 3. The supernet contains 21 AtomNAS blocks, the searchable block in our supernet; the picture on the right of Fig. 3 illustrates the structure of an AtomNAS block, where $f _ { 0 }$ is a $1 \\times 1$ pointwise convolutions that expands the input channel number from $C$ to $3 \\times 6 C$ ; $g$ is a mix of three depth-wise convolutions with kernel sizes of $3 \\times 3 , 5 \\times 5$ and $7 \\times 7 .$ and $f _ { 1 }$ is another $1 \\times 1$ pointwise convolutions that projects the channel number to the output channel number. Similar to MobileNetV2 (Sandler et al., 2018), if the output dimension stays the same as the input dimension, we use a skip connection to add the input to the output. AtomNAS block is effectively an ensemble of $3 \\times 6 C$ atomic blocks, whose underlying search space covers the MobileNetV2 block (Sandler et al., 2018) and its multikernel variant, MixConv (Tan & Le, 2019b). Within AtomNAS block, we are able to optimize the distribution of computation resources (i.e., channel numbers) among the three types of depth-wise convolution. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/2b650784a0ee572234b2c38a01bf5dd4c19f8d803ffdd3a1f490a973dba2b9b8.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td> Input Shape</td><td>Block</td><td>f</td><td>n</td><td>stride</td></tr><tr><td>224²×3</td><td>3x3 conv</td><td>32(16)</td><td>1</td><td>2</td></tr><tr><td>112² × 32(16)</td><td>3x3 MB</td><td>16</td><td>1</td><td>1</td></tr><tr><td>112²×16</td><td>searchable</td><td>24</td><td>4</td><td>2</td></tr><tr><td>56²×24</td><td>searchable</td><td>40</td><td>4</td><td>2</td></tr><tr><td>28²×40</td><td>searchable</td><td>80</td><td>4</td><td>2</td></tr><tr><td>14²×80</td><td>searchable</td><td>96</td><td>4</td><td>1</td></tr><tr><td>14²×96</td><td>searchable</td><td>192</td><td>4</td><td>2</td></tr><tr><td>7²×192</td><td>searchable</td><td>320</td><td>1</td><td>1</td></tr><tr><td>7² ×320</td><td>avgpool</td><td>1</td><td>1</td><td>1</td></tr><tr><td>1280</td><td>fc</td><td>1000</td><td>1</td><td>1</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/78737b107a3bb2660818aad97a17a467bfe2d6a4fecbb0f8a568d8da71c9fab3.jpg",
+        "image_caption": [
+            "Figure 3: (Left) The searchable block of the supernet. $f _ { 0 }$ and $f _ { 1 }$ are fixed to $1 \\times 1$ pointwise convolutions; $g$ here is a mix of three convolutions with kernel sizes of $3 \\times 3$ , $5 \\times 5$ and $7 \\times 7$ . $f _ { 0 }$ expands the input channel number from $C$ to $1 8 C$ and $f _ { 1 }$ projects the channel number to the output channel number. If the output dimension stays the same as the input dimension, we use a skip connection to add the input to the output. (Right) Architecture of the supernet. Column-Block denotes the block type; MB denotes MobileNetV2 block; ”searchable” means a searchable block shown on the left. Column-f denotes the output channel number of a block. Column-n denotes the number of blocks. Column-s denotes the stride of the first block in a stage. The output channel numbers of the first convolution are 16 for AtomNAS-A, 32 for AtomNAS-B and AtomNAS-C. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We use the same training configuration (e.g., RMSProp optimizer, EMA on weights and exponential learning rate decay) as Tan et al. (2019); Stamoulis et al. (2019a) and do not use extra data augmentation such as MixUp (Zhang et al., 2018) and AutoAugment (Cubuk et al., 2018). We find that using this configuration is sufficient for our method to achieve good performance. Our results are shown in Table 1 and Table 3. When training the supernet, we use a total batch size of 2048 on 32 Tesla V100 GPUs and train for 350 epochs. For our dynamic network shrinkage algorithm, we set the momentum factor $\\beta$ in Eq. (7) to 0.9999. At the beginning of the training, all of the weights are randomly initialized. To avoid removing atomic blocks with high penalties (i.e., FLOPs) prematurely, the weight of the penalty term in Eq. (5) is increased from 0 to the target $\\lambda$ by a linear scheduler during the first 25 epochs. By setting the weight of the L1 penalty term $\\lambda$ to be $1 . { \\overset { \\cdot } { 8 } } \\times 1 0 ^ { - 4 }$ , $1 . 2 \\times 1 0 ^ { - 4 }$ and ${ \\bar { 1 } } . 0 \\times 1 0 ^ { - 4 }$ respectively, we obtain networks with three different sizes: AtomNAS-A, AtomNAS-B, and AtomNAS-C. They have the similar FLOPs as previous state-of-the-art networks under 400M: MixNet-S (Tan & Le, 2019b), MixNet-M (Tan & Le, 2019b) and SinglePath (Stamoulis et al., 2019a). In Appendix A, we visualize the architecture of AtomNAS-C. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 EXPERIMENTS ON IMAGENET ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We apply AtomNAS to search high performance light-weight model on ImageNet 2012 classification task (Deng et al., 2009). Table 1 compares our methods with previous state-of-the-art models, either manually designed or searched. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "With models directly produced by AtomNAS, our method achieves the new state-of-the-art under all FLOPs constraints. Especially, AtomNAS-C achieves $7 5 . 9 \\%$ top-1 accuracy with only 360M FLOPs, and surpasses all other models, including models like PDARTS and DenseNAS which have much higher FLOPs. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a3282b42db113d5bd5627597a598ce86c508613a9ae6e5b0b656cf8c4b6d66f8.jpg",
+        "image_caption": [
+            "Figure 4: FLOPs versus accuracy on ImageNet. † means methods use extra techniques like Swish activation and Squeeze-and-Excitation module. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            99,
+            725,
+            301
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Techniques like Swish activation function (Ramachandran et al., 2018) and Squeeze-and-Excitation (SE) module (Hu et al., 2018) consistently improve the accuracy with marginal FLOPs cost. For a fair comparison with methods that use these techniques, we directly modify the searched network by replacing all ReLU activation with Swish and add SE module with ratio 0.5 to every block and then retrain the network from scratch. Note that unlike other methods, we do not search the configuration of Swish and SE, and therefore the performance might not be optimal. Extra data augmentations such as MixUp and AutoAugment are still not used. We train the models from scratch with a total batch size of 4096 on 32 Tesla V100 GPUs for 250 epochs. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Simply adding these techniques improves the results further. AtomNAS- $\\mathbf { A } +$ achieves $7 6 . 3 \\%$ top1 accuracy with 260M FLOPs, which outperforms many heavier models including MnasNet-A2. Without extra data augmentations, it performs as well as Efficient-B0 (Tan & Le, 2019a) by using 130M less FLOPs. It also outperforms the previous state-of-the-art MixNet-S by $0 . 5 \\%$ . In addition, AtomNAS- $C +$ improves the top-1 accuracy on ImageNet to $7 7 . 6 \\%$ , surpassing previous state-ofthe-art MixNet-M by $0 . 6 \\%$ and becomes the overall best performing model under 400M FLOPs. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Fig. 4 visualizes the top-1 accuracy on ImageNet for different models. It’s clear that our fine-grained search space and the end-to-end resource-aware search method boost the performance significantly. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3 ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3.1 RESOURCE-AWARE REGULARIZATION ",
+        "text_level": 1,
+        "bbox": [
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+            650,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the effectiveness of the resource-aware regularization in Section 3.2, we compare it with a baseline without FLOPs-related coefficients $c _ { i }$ , which is widely used in network pruning (Liu et al., 2017; He et al., 2017b). Table 2 shows the results. First, by using the same L1 penalty coefficient $\\lambda = 1 . 0 \\times 1 0 ^ { - 4 }$ , the baseline achieves a network with similar performance but using much more FLOPs; then by increasing $\\lambda$ to $1 . 5 \\times 1 0 ^ { - 4 }$ , the baseline obtain a network which has similar FLOPs but inferior performance (i.e., about $1 . 0 \\%$ lower). In Fig. 6b we visualized the ratio of different types of atomic blocks of the baseline network obtained by $\\bar { \\lambda ( \\mathrm { = 1 . 5 \\times 1 0 ^ { - 4 } } }$ . The baseline network keeps more atomic blocks in the earlier blocks, which have higher computation cost due to higher input resolution. On the contrary, AtomNAS is aware of the resource constraint, thus keeping more atomic blocks in the later blocks and achieving much better performance. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3.2 BN RECALIBRATION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As the BN’s running statistics might be inaccurate as explained in Section 3.2 and Section 3.3, we re-calculate the running statistics of BN before inference, by forwarding 131k randomly sampled training images through the network. Table 3 shows the impact of the BN recalibration. The top-1 accuracies of AtomNAS-A, AtomNAS-B, and AtomNAS-C on ImageNet improve by $1 . 4 \\%$ , $1 . { \\bar { 7 } } \\%$ , and $1 . 2 \\%$ respectively, which clearly shows the benefit of BN recalibration. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/b5bb155aa3c4f7096ab746b8b8b94d2e74b5b3a23dde4e1b45b5af2fd3273b61.jpg",
+        "table_caption": [
+            "Table 1: Comparision with state-of-the-arts on ImageNet under the mobile setting. † denotes methods using extra network modules such as Swish activation and Squeeze-and-Excitation module. ‡ denotes using extra data augmentation such as MixUp and AutoAugment. ∗ denotes models searched and trained simultaneously. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Parameters</td><td>FLOPs</td><td>Top-1(%)</td><td>Top-5(%)</td></tr><tr><td>MobileNetV1 (Howard et al., 2017)</td><td>4.2M</td><td>575M</td><td>70.6</td><td>89.5</td></tr><tr><td>MobileNetV2 (Sandler et al., 2018)</td><td>3.4M</td><td>300M</td><td>72.0</td><td>91.0</td></tr><tr><td>MobileNetV2 (our impl.)</td><td>3.4M</td><td>301M</td><td>73.6</td><td>91.5</td></tr><tr><td>MobileNetV2 (1.4)</td><td>6.9M</td><td>585M</td><td>74.7</td><td>92.5</td></tr><tr><td>ShuffleNetV2 (Ma et al.,2018)</td><td>3.5M</td><td>299M</td><td>72.6</td><td>=</td></tr><tr><td>ShuffleNetV2 2×</td><td>7.4M</td><td>591M</td><td>74.9</td><td></td></tr><tr><td>FBNet-A (Wu et al., 2019)</td><td>4.3M</td><td>249M</td><td>73.0</td><td></td></tr><tr><td>FBNet-C</td><td>5.5M</td><td>375M</td><td>74.9</td><td></td></tr><tr><td>Proxyless (mobile) (Cai et al., 2019)</td><td>4.1M</td><td>320M</td><td>74.6</td><td>92.2</td></tr><tr><td>SinglePath (Stamoulis et al., 2019a)</td><td>4.4M</td><td>334M</td><td>75.0</td><td>92.2</td></tr><tr><td>NASNet-A (Zoph &amp; Le,2017)</td><td>5.3M</td><td>564M</td><td>74.0</td><td>91.6</td></tr><tr><td>DARTS (second order) (Liu et al., 2019a)</td><td>4.9M</td><td>595M</td><td>73.1</td><td>-</td></tr><tr><td>PDARTS (cifar 10) (Chen et al., 2019b)</td><td>4.9M</td><td>557M</td><td>75.6</td><td>92.6</td></tr><tr><td>DenseNAS-A (Fang et al., 2019)</td><td>7.9M</td><td>501M</td><td>75.9</td><td>92.6</td></tr><tr><td>FairNAS-A (Chu et al., 2019b)</td><td>4.6M</td><td>388M</td><td>75.3</td><td>92.4</td></tr><tr><td>AtomNAS-A*</td><td>3.9M</td><td>258M</td><td>74.6</td><td>92.1</td></tr><tr><td>AtomNAS-B*</td><td>4.4M</td><td>326M</td><td>75.5</td><td>92.6</td></tr><tr><td>AtomNAS-C*</td><td>4.7M</td><td>360M</td><td>75.9</td><td>92.7</td></tr><tr><td>SCARLET-A† (Chu et al., 2019a)</td><td>6.7M</td><td>365M</td><td>76.9</td><td>93.4</td></tr><tr><td>MnasNet-A1† (Tan et al., 2019)</td><td>3.9M</td><td>312M</td><td>75.2</td><td>92.5</td></tr><tr><td>MnasNet-A2t</td><td>4.8M</td><td>340M</td><td>75.6</td><td>92.7</td></tr><tr><td>MixNet-St (Tan &amp; Le, 2019b)</td><td>4.1M</td><td>256M</td><td>75.8</td><td>92.8</td></tr><tr><td>MixNet-M†</td><td>5.0M</td><td>360M</td><td>77.0</td><td>93.3</td></tr><tr><td>EfficientNet-Bot‡ (Tan &amp; Le, 2019a)</td><td>5.3M</td><td>390M</td><td>76.3</td><td>93.2</td></tr><tr><td>SE-DARTS+†‡ (Liang et al., 2019)</td><td>6.1M</td><td>594M</td><td>77.5</td><td>93.6</td></tr><tr><td>AtomNAS-A+†</td><td>4.7M</td><td>260M</td><td>76.3</td><td>93.0</td></tr><tr><td>AtomNAS-B+†</td><td>5.5M</td><td>329M</td><td>77.2</td><td>93.5</td></tr><tr><td>AtomNAS-C+†</td><td>5.9M</td><td>363M</td><td>77.6</td><td>93.6</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/5802b181ae3c7ec93af55966a9a6b97bffb4593871e63250495008a1e09710d3.jpg",
+        "table_caption": [
+            "Table 2: Influence of awareness of resource metric. The upper block uses equal penalties for all atomic blocks. The lower part uses our resource-aware atomic block selection. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>入</td><td>FLOPs</td><td>Top-1(%)</td></tr><tr><td>1.0×10-4</td><td>445M</td><td>76.1</td></tr><tr><td>1.5 ×10-4</td><td>370M</td><td>74.9</td></tr><tr><td>1.0×10-4</td><td>360M</td><td>75.9</td></tr></table>",
+        "bbox": [
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+            690,
+            620,
+            771
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.3.3 COST OF DYNAMIC NETWORK SHRINKAGE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            811,
+            529,
+            827
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Our dynamic network shrinkage algorithm speedups the search and train process significantly. For AtomNAS-C, the total time for search-and-training is 25.5 hours. For reference, training the final architecture from scratch takes 22 hours. Note that as the supernet shrinks, both the GPU memory consumption and forward-backward time are significantly reduced. Thus it’s possible to dynamically change the batch size once having sufficient GPU memory, which would further speed up the whole procedure. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/9ffcbfddd00a3aeae27f962e454a0acd138b019c2c062404b3fc1ed6d27a7964.jpg",
+        "table_caption": [
+            "Table 3: Influence of BN recalibration. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>w/o Recalibration</td><td>w/Recalibration</td></tr><tr><td>AtomNAS-A</td><td>73.2</td><td>74.6 (+1.4)</td></tr><tr><td>AtomNAS-B</td><td>73.8</td><td>75.5 (+1.7)</td></tr><tr><td>AtomNAS-C</td><td>74.7</td><td>75.9 (+1.2)</td></tr></table>",
+        "bbox": [
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+            132,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "4.4 EXPERIMENTS ON COCO DETECTION AND INSTANCE SEGMENTATION",
+        "text_level": 1,
+        "bbox": [
+            173,
+            236,
+            702,
+            251
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "In this section, we assess the performance of AtomNAS models as feature extractors for object detection and instance segmentation on COCO dataset (Lin et al., 2014). We first pretrain AtomNAS models (without Swish activation function (Ramachandran et al., 2018) and Squeeze-and-Excitation (SE) module (Hu et al., 2018)) on ImageNet, use them as drop-in replacements for the backbone in the Mask-RCNN model (He et al., 2017a) by building the detection head on top of the last feature map, and finetune the model on COCO dataset. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We use the open-source code MMDetection (Chen et al., 2019a). All the models are trained on COCO train2017 with batch size 16 and evaluated on COCO val2017. Following the schedule used in the open-source implementation of TPU-trained Mask-RCNN , the learning rate starts at 0.02 and decreases by a scale of 10 at 15-th and 20th epoch respectively. The models are trained for 23 epochs in total. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Table 4 compares the results with other baseline backbone models. The detection results of baseline models are from Stamoulis et al. (2019b). We can see that all three AtomNAS models outperform the baselines on object detection task. The results demonstrate that our models have better transferability than the baselines, which may due to mixed operations, a.k.a multi-scale here, are more important to object detection and instance segmentation. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/5d0f4328b40f8b38d7f317039d8865ead12f2e29c4754d78eccda80b05f10f3e.jpg",
+        "table_caption": [
+            "Table 4: Comparision with baseline backbones on COCO object detection and instance segmentation. Cls denotes the ImageNet top-1 accuracy; detect-mAP and seg-mAP denotes mean average precision for detection and instance segmentation on COCO dataset. The results of baseline models are from Stamoulis et al. (2019b). SinglePath $^ +$ (Stamoulis et al., 2019b) contains SE module. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>FLOPs</td><td>Cls (%)</td><td>detect-mAP (%)</td><td>seg-mAP (%)</td></tr><tr><td>MobileNetV2 (Sandler et al., 2018)</td><td>301M</td><td>73.6</td><td>30.5</td><td>1</td></tr><tr><td>Proxyless (mobile) (Cai et al., 2019)</td><td>320M</td><td>74.6</td><td>32.9</td><td>=</td></tr><tr><td>Proxyless (mobile) (our impl.)</td><td>320M</td><td>74.9</td><td>32.7</td><td>30.0</td></tr><tr><td>SinglePath+ (Stamoulis et al., 2019b)</td><td>353M</td><td>75.6</td><td>33.0</td><td>1</td></tr><tr><td>SinglePath (our impl.)</td><td>334M</td><td>75.0</td><td>32.0</td><td>29.7</td></tr><tr><td>AtomNAS-A</td><td>258M</td><td>74.6</td><td>32.7</td><td>30.1</td></tr><tr><td>AtomNAS-B</td><td>326M</td><td>75.5</td><td>33.6</td><td>30.8</td></tr><tr><td>AtomNAS-C</td><td>360M</td><td>75.9</td><td>34.1</td><td>31.4</td></tr></table>",
+        "bbox": [
+            179,
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
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+        "text": "In this paper, we revisit the common structure, i.e., two convolutions joined by a channel-wise operation, and reformulate it as an ensemble of atomic blocks. This perspective enables a much larger and more fine-grained search space. For efficiently exploring the huge fine-grained search space, we propose an end-to-end framework named AtomNAS, which conducts architecture search and network training jointly. The searched networks achieve significantly better accuracy than previous state-of-the-art methods while using small extra cost. ",
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+    {
+        "type": "image",
+        "img_path": "images/a32d42420361ceba48ac3630b92aad453623f3484101b00fc26aaaf222acef71.jpg",
+        "image_caption": [
+            "A VISUALIZATION ",
+            "Figure 5: The architecture of AtomNAS-C. Blue, orange, cyan blocks denote atomic blocks with kernel size 3, 5 and 7 respectively; the heights of these blocks are proportional to their expand ratios. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We plot the structure of the searched architecture AtomNAS-C in Fig. 5, from which we see more flexibility of channel number selection, not only among different operators within each block, but also across the network. In Fig. 6a, we visualize the ratio between atomic blocks with different kernel sizes in all 21 search blocks. First, we notice that all search blocks have convolutions of all three kernel sizes, showing that AtomNAS learns the importance of using multiple kernel sizes in network architecture. Another observation is that AtomNAS tends to keep more atomic blocks at the later stage of the network. This is because in earlier stage, convolutions of the same kernel size costs more FLOPs; AtomNAS is aware of this (thanks to its resource-aware regularization) and try to keep as less as possible computationally costly atomic blocks. ",
+        "bbox": [
+            173,
+            463,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/17291dab22b27a4c559585f81d3d24d7e8d873b0d22d623f4573327d8ad24bb7.jpg",
+        "image_caption": [
+            "Figure 6: Ratio of different types of atomic blocks in all 21 searchable blocks. The text above each pie tells the total number of atomic blocks of the corresponding block in the original supernet. Grey denotes dead atomic blocks; blue, orange, and cyan represent atomic blocks using depth-wise convolutions with kernel size $3 , 5 , 7$ respectively. Blocks without skip connection are highlighted by bold text. (a) Visualization for AtomNAS-C. (b) Visualization for baseline (i.e., without FLOPs related coefficients $c _ { i }$ ). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            169,
+            116,
+            828,
+            767
+        ],
+        "page_idx": 13
+    }
+]

parse/train/HysBZSqlx/HysBZSqlx.md

@@ -0,0 +1,189 @@
+# PLAYING SNES IN THE RETRO LEARNING ENVIRONMENT
+
+Nadav Bhonker\*, Shai Rozenberg\* and Itay Hubara
+
+Department of Electrical Engineering   
+Technion, Israel Institute of Technology   
+$( ^ { * } )$ indicates equal contribution   
+{nadavbh,shairoz}@tx.technion.ac.il   
+itayhubara@gmail.com
+
+# ABSTRACT
+
+Mastering a video game requires skill, tactics and strategy. While these attributes may be acquired naturally by human players, teaching them to a computer program is a far more challenging task. In recent years, extensive research was carried out in the field of reinforcement learning and numerous algorithms were introduced, aiming to learn how to perform human tasks such as playing video games. As a result, the Arcade Learning Environment (ALE) (Bellemare et al., 2013) has become a commonly used benchmark environment allowing algorithms to train on various Atari 2600 games. In many games the state-of-the-art algorithms outperform humans. In this paper we introduce a new learning environment, the Retro Learning Environment — RLE, that can run games on the Super Nintendo Entertainment System (SNES), Sega Genesis and several other gaming consoles. The environment is expandable, allowing for more video games and consoles to be easily added to the environment, while maintaining the same interface as ALE. Moreover, RLE is compatible with Python and Torch. SNES games pose a significant challenge to current algorithms due to their higher level of complexity and versatility.
+
+# 1 INTRODUCTION
+
+Controlling artificial agents using only raw high-dimensional input data such as image or sound is a difficult and important task in the field of Reinforcement Learning (RL). Recent breakthroughs in the field allow its utilization in real-world applications such as autonomous driving (Shalev-Shwartz et al., 2016), navigation (Bischoff et al., 2013) and more. Agent interaction with the real world is usually either expensive or not feasible, as the real world is far too complex for the agent to perceive. Therefore in practice the interaction is simulated by a virtual environment which receives feedback on a decision made by the algorithm. Traditionally, games were used as a RL environment, dating back to Chess (Campbell et al., 2002), Checkers (Schaeffer et al., 1992), backgammon (Tesauro, 1995) and the more recent Go (Silver et al., 2016). Modern games often present problems and tasks which are highly correlated with real-world problems. For example, an agent that masters a racing game, by observing a simulated driver’s view screen as input, may be usefull for the development of an autonomous driver. For high-dimensional input, the leading benchmark is the Arcade Learning Environment (ALE) (Bellemare et al., 2013) which provides a common interface to dozens of Atari 2600 games, each presents a different challenge. ALE provides an extensive benchmarking platform, allowing a controlled experiment setup for algorithm evaluation and comparison. The main challenge posed by ALE is to successfully play as many Atari 2600 games as possible (i.e., achieving a score higher than an expert human player) without providing the algorithm any game-specific information (i.e., using the same input available to a human - the game screen and score). A key work to tackle this problem is the Deep Q-Networks algorithm (Mnih et al., 2015), which made a breakthrough in the field of Deep Reinforcement Learning by achieving human level performance on 29 out of 49 games. In this work we present a new environment — the Retro Learning Environment (RLE). RLE sets new challenges by providing a unified interface for Atari 2600 games as well as more advanced gaming consoles. As a start we focused on the Super Nintendo Entertainment
+
+System (SNES). Out of the five SNES games we tested using state-of-the-art algorithms, only one was able to outperform an expert human player. As an additional feature, RLE supports research of multi-agent reinforcement learning (MARL) tasks (Bus¸oniu et al., 2010). We utilize this feature by training and evaluating the agents against each other, rather than against a pre-configured in-game AI. We conducted several experiments with this new feature and discovered that agents tend to learn how to overcome their current opponent rather than generalize the game being played. However, if an agent is trained against an ensemble of different opponents, its robustness increases. The main contributions of the paper are as follows:
+
+• Introducing a novel RL environment with significant challenges and an easy agent evaluation technique (enabling agents to compete against each other) which could lead to new and more advanced RL algorithms.   
+• A new method to train an agent by enabling it to train against several opponents, making the final policy more robust.   
+• Encapsulating several different challenges to a single RL environment.
+
+# 2 RELATED WORK
+
+# 2.1 ARCADE LEARNING ENVIRONMENT
+
+The Arcade Learning Environment is a software framework designed for the development of RL algorithms, by playing Atari 2600 games. The interface provided by ALE allows the algorithms to select an action and receive the Atari screen and a reward in every step. The action is the equivalent to a human’s joystick button combination and the reward is the difference between the scores at time stamp $t$ and $t - 1$ . The diversity of games for Atari provides a solid benchmark since different games have significantly different goals. Atari 2600 has over 500 games, currently over 70 of them are implemented in ALE and are commonly used for algorithm comparison.
+
+# 2.2 INFINITE MARIO
+
+Infinite Mario (Togelius et al., 2009) is a remake of the classic Super Mario game in which levels are randomly generated. On these levels the Mario AI Competition was held. During the competition, several algorithms were trained on Infinite Mario and their performances were measured in terms of the number of stages completed. As opposed to ALE, training is not based on the raw screen data but rather on an indication of Mario’s (the player’s) location and objects in its surrounding. This environment no longer poses a challenge for state of the art algorithms. Its main shortcoming lie in the fact that it provides only a single game to be learnt. Additionally, the environment provides hand-crafted features, extracted directly from the simulator, to the algorithm. This allowed the use of planning algorithms that highly outperform any learning based algorithm.
+
+# 2.3 OPENAI GYM
+
+The OpenAI gym (Brockman et al., 2016) is an open source platform with the purpose of creating an interface between RL environments and algorithms for evaluation and comparison purposes. OpenAI Gym is currently very popular due to the large number of environments supported by it. For example ALE, Go, MouintainCar and VizDoom (Zhu et al., 2016), an environment for the learning of the 3D first-person-shooter game ”Doom”. OpenAI Gym’s recent appearance and wide usage indicates the growing interest and research done in the field of RL.
+
+# 2.4 OPENAI UNIVERSE
+
+Universe (Universe, 2016) is a platform within the OpenAI framework in which RL algorithms can train on over a thousand games. Universe includes very advanced games such as GTA V, Portal as well as other tasks (e.g. browser tasks). Unlike RLE, Universe doesn’t run the games locally and requires a VNC interface to a server that runs the games. This leads to a lower frame rate and thus longer training times.
+
+# 2.5 MALMO
+
+Malmo (Johnson et al., 2016) is an artificial intelligence experimentation platform of the famous game ”Minecraft”. Although Malmo consists of only a single game, it presents numerous challenges since the ”Minecraft” game can be configured differently each time. The input to the RL algorithms include specific features indicating the ”state” of the game and the current reward.
+
+# 2.6 DEEPMIND LAB
+
+DeepMind Lab (Dee) is a first-person 3D platform environment which allows training RL algorithms on several different challenges: static/random map navigation, collect fruit (a form of reward) and a laser-tag challenge where the objective is to tag the opponents controlled by the in-game AI. In LAB the agent observations are the game screen (with an additional depth channel) and the velocity of the character. LAB supports four games (one game - four different modes).
+
+# 2.7 DEEP Q-LEARNING
+
+In our work, we used several variant of the Deep Q-Network algorithm (DQN) (Mnih et al., 2015), an RL algorithm whose goal is to find an optimal policy (i.e., given a current state, choose action that maximize the final score). The state of the game is simply the game screen, and the action is a combination of joystick buttons that the game responds to (i.e., moving ,jumping). DQN learns through trial and error while trying to estimate the ”Q-function”, which predicts the cumulative discounted reward at the end of the episode given the current state and action while following a policy $\pi$ . The Q-function is represented using a convolution neural network that receives the screen as input and predicts the best possible action at it’s output. The Q-function weights $\theta$ are updated according to:
+
+$$
+\theta _ { t + 1 } ( s _ { t } , a _ { t } ) = \theta _ { t } + \alpha ( R _ { t + 1 } + \gamma \operatorname* { m a x } _ { a } ( Q _ { t } ( s _ { t + 1 } , a ; \theta _ { t } ^ { \prime } ) ) - Q _ { t } ( s _ { t } , a _ { t } ; \theta _ { t } ) ) \nabla _ { \theta } Q _ { t } ( s _ { t } , a _ { t } ; \theta _ { t } ) ,
+$$
+
+where $s _ { t }$ , $s _ { t + 1 }$ are the current and next states, $a _ { t }$ is the action chosen, $\alpha$ is the step size, $\gamma$ is the discounting factor $R _ { t + 1 }$ is the reward received by applying $a _ { t }$ at $s _ { t }$ . $\theta ^ { \prime }$ represents the previous weights of the network that are updated periodically. Other than DQN, we examined two leading algorithms on the RLE: Double Deep Q-Learning (D-DQN) (Van Hasselt et al., 2015), a DQN based algorithm with a modified network update rule. Dueling Double DQN (Wang et al., 2015), a modification of D-DQN’s architecture in which the $\mathbf { Q }$ -function is modeled using a state (screen) dependent estimator and an action dependent estimator.
+
+# 3 THE RETRO LEARNING ENVIRONMENT
+
+# 3.1 SUPER NINTENDO ENTERTAINMENT SYSTEM
+
+The Super Nintendo Entertainment System (SNES) is a home video game console developed by Nintendo and released in 1990. A total of 783 games were released, among them, the iconic Super Mario World, Donkey Kong Country and The Legend of Zelda. Table (1) presents a comparison between Atari 2600, Sega Genesis and SNES game consoles, from which it is clear that SNES and Genesis games are far more complex.
+
+# 3.2 IMPLEMENTATION
+
+To allow easier integration with current platforms and algorithms, we based our environment on the ALE, with the aim of maintaining as much of its interface as possible. While the ALE is highly coupled with the Atari emulator, Stella1, RLE takes a different approach and separates the learning environment from the emulator. This was achieved by incorporating an interface named LibRetro (libRetro site), that allows communication between front-end programs to game-console emulators. Currently, LibRetro supports over 15 game consoles, each containing hundreds of games, at an estimated total of over 7,000 games that can potentially be supported using this interface. Examples of supported game consoles include Nintendo Entertainment System, Game Boy, N64, Sega Genesis,
+
+Saturn, Dreamcast and Sony PlayStation. We chose to focus on the SNES game console implemented using the $\operatorname { s n e s } 9 \mathrm { x } ^ { 2 }$ as it’s games present interesting, yet plausible to overcome challenges. Additionally, we utilized the Genesis-Plus- $\mathbf { \Delta } G \mathbf { X } ^ { 3 }$ emulator, which supports several Sega consoles: Genesis/Mega Drive, Master System, Game Gear and SG-1000.
+
+# 3.3 SOURCE CODE
+
+RLE is fully available as open source software for use under GNU’s General Public License4. The environment is implemented in $\mathrm { C } { + } { + }$ with an interface to algorithms in $\mathrm { C } { + } { + }$ , Python and Lua. Adding a new game to the environment is a relatively simple process.
+
+# 3.4 RLE INTERFACE
+
+RLE provides a unified interface to all games in its supported consoles, acting as an RL-wrapper to the LibRetro interface. Initialization of the environment is done by providing a game (ROM file) and a gaming-console (denoted by ’core’). Upon initialization, the first state is the initial frame of the game, skipping all menu selection screens. The cores are provided with the RLE and installed together with the environment. Actions have a bit-wise representation where each controller button is represented by a one-hot vector. Therefore a combination of several buttons is possible using the bit-wise OR operator. The number of valid buttons combinations is larger than 700, therefore only the meaningful combinations are provided. The environments observation is the game screen, provided as a 3D array of 32 bit per pixel with dimensions which vary depending on the game. The reward can be defined differently per game, usually we set it to be the score difference between two consecutive frames. By setting different configuration to the environment, it is possible to alter in-game properties such as difficulty (i.e easy, medium, hard), its characters, levels, etc.
+
+Table 1: Atari 2600, SNES and Genesis comparison   
+
+<table><tr><td></td><td>Atari 2600</td><td>SNES</td><td>Genesis</td></tr><tr><td>Number of Games</td><td>565</td><td>783</td><td>928</td></tr><tr><td>CPU speed</td><td>1.19MHz</td><td>3.58MHz</td><td>7.6 MHz</td></tr><tr><td>ROM size</td><td>2-4KB</td><td>0.5-6MB</td><td>16 MBytes</td></tr><tr><td>RAM size</td><td>128 bytes</td><td>128KB</td><td>72KB</td></tr><tr><td>Color depth</td><td>8 bit</td><td>16 bit</td><td>16 bit</td></tr><tr><td>Screen Size</td><td>160x210</td><td>256x224 or 512x448</td><td>320x224</td></tr><tr><td>Number of controller buttons</td><td>5</td><td>12</td><td>11</td></tr><tr><td>Possible buttons combinations</td><td>18</td><td>over 720</td><td>over100</td></tr></table>
+
+# 3.5 ENVIRONMENT CHALLENGES
+
+Integrating SNES and Genesis with RLE presents new challenges to the field of RL where visual information in the form of an image is the only state available to the agent. Obviously, SNES games are significantly more complex and unpredictable than Atari games. For example in sports games, such as NBA, while the player (agent) controls a single player, all the other nine players’ behavior is determined by pre-programmed agents, each exhibiting random behavior. In addition, many SNES games exhibit delayed rewards in the course of their play (i.e., reward for an actions is given many time steps after it was performed). Similarly, in some of the SNES games, an agent can obtain a reward that is indirectly related to the imposed task. For example, in platform games, such as Super Mario, reward is received for collecting coins and defeating enemies, while the goal of the challenge is to reach the end of the level which requires to move to keep moving to the right. Moreover, upon completing a level, a score bonus is given according to the time required for its completion. Therefore collecting coins or defeating enemies is not necessarily preferable if it consumes too much time. Analysis of such games is presented in section 4.2. Moreover, unlike Atari that consists of eight directions and one action button, SNES has eight-directions pad and six actions buttons. Since combinations of buttons are allowed, and required at times, the actual actions space may be larger than 700, compared to the maximum of 18 actions in Atari. Furthermore, the background in SNES is very rich, filled with details which may move locally or across the screen, effectively acting as non-stationary noise since it provided little to no information regarding the state itself. Finally, we note that SNES utilized the first 3D games. In the game Wolfenstein, the player must navigate a maze from a first-person perspective, while dodging and attacking enemies. The SNES offers plenty of other 3D games such as flight and racing games which exhibit similar challenges. These games are much more realistic, thus inferring from SNES games to ”real world” tasks, as in the case of self driving cars, might be more beneficial. A visual comparison of two games, Atari and SNES, is presented in Figure (1).
+
+![](images/c343c235f708c978ceb3c66883ef1bc74d461f57a56abbdde15e4c7c355130b2.jpg)  
+Figure 1: Atari 2600 and SNES game screen comparison: Left: ”Boxing” an Atari 2600 fighting game , Right: ”Mortal Kombat” a SNES fighting game. Note the exceptional difference in the amount of details between the two games. Therefore, distinguishing a relevant signal from noise is much more difficult.
+
+Table 2: Comparison between RLE and the latest RL environments   
+
+<table><tr><td>Characteristics</td><td>RLE</td><td>OpenAI Universe</td><td>Inifinte Mario</td><td>ALE</td><td>Project Malmo</td><td>DeepMind Lab</td></tr><tr><td>Number of Games</td><td>8 out of 7000+</td><td>1000+</td><td>1</td><td>74</td><td>1</td><td>4</td></tr><tr><td>In game adjustments1</td><td>Yes</td><td>NO</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td>Frame rate</td><td>530fps(SNES)</td><td>60fps</td><td>5675fps2</td><td>120fps</td><td>&lt;7000fps</td><td>&lt;1000fps</td></tr><tr><td>Observation (Input)</td><td>screen, RAM</td><td>Screen</td><td>hand crafted features</td><td>screen, RAM</td><td>hand crafted features</td><td>screen+depth and velocity</td></tr></table>
+
+1 Allowing changes in-the game configurations (e.g., changing difficulty, characters, etc.) 2 Measured on an i7-5930k CPU
+
+# 4 EXPERIMENTS
+
+# 4.1 EVALUATION METHODOLOGY
+
+The evaluation methodology that we used for benchmarking the different algorithms is the popular method proposed by (Mnih et al., 2015). Each examined algorithm is trained until either it reached convergence or 100 epochs (each epoch corresponds to 50,000 actions), thereafter it is evaluated by performing 30 episodes of every game. Each episode ends either by reaching a terminal state or after 5 minutes. The results are averaged per game and compared to the average result of a human player. For each game the human player was given two hours for training, and his performances were evaluated over 20 episodes. As the various algorithms don’t use the game audio in the learning process, the audio was muted for both the agent and the human. From both, humans and agents score, a random agent score (an agent performing actions randomly) was subtracted to assure that learning indeed occurred. It is important to note that DQN’s $\epsilon$ -greedy approach (select a random action with a small probability ) is present during testing thus assuring that the same sequence of actions isn’t repeated. While the screen dimensions in SNES are larger than those of Atari, in our experiments we maintained the same pre-processing of DQN (i.e., downscaling the image to $8 4 \mathrm { x } 8 4$ pixels and converting to gray-scale). We argue that downscaling the image size doesn’t affect a human’s ability to play the game, therefore suitable for RL algorithms as well. To handle the large action space, we limited the algorithm’s actions to the minimal button combinations which provide unique behavior. For example, on many games the R and L action buttons don’t have any use therefore their use and combinations were omitted.
+
+# 4.1.1 RESULTS
+
+A thorough comparison of the four different agents’ performances on SNES games can be seen in Figure (). The full results can be found in Table (3). Only in the game Mortal Kombat a trained agent was able to surpass a expert human player performance as opposed to Atari games where the same algorithms have surpassed a human player on the vast majority of the games.
+
+One example is Wolfenstein game, a 3D first-person shooter game, requires solving 3D vision tasks, navigating in a maze and detecting object. As evident from figure (2), all agents produce poor results indicating a lack of the required properties. By using $\epsilon$ -greedy approach the agents weren’t able to explore enough states (or even other rooms in our case). The algorithm’s final policy appeared as a random walk in a 3D space. Exploration based on visited states such as presented in Bellemare et al. (2016) might help addressing this issue. An interesting case is Gradius III, a side-scrolling, flight-shooter game. While the trained agent was able to master the technical aspects of the game, which includes shooting incoming enemies and dodging their projectiles, it’s final score is still far from a human’s. This is due to a hidden game mechanism in the form of ”power-ups”, which can be accumulated, and significantly increase the players abilities. The more power-ups collected without being use — the larger their final impact will be. While this game-mechanism is evident to a human, the agent acts myopically and uses the power-up straight away5.
+
+# 4.2 REWARD SHAPING
+
+As part of the environment and algorithm evaluation process, we investigated two case studies. First is a game on which DQN had failed to achieve a better-than-random score, and second is a game on which the training duration was significantly longer than that of other games.
+
+In the first case study, we used a 2D back-view racing game ”F-Zero”. In this game, one is required to complete four laps of the track while avoiding other race cars. The reward, as defined by the score of the game, is only received upon completing a lap. This is an extreme case of a reward delay. A lap may last as long as 30 seconds, which span over 450 states (actions) before reward is received. Since DQN’s exploration is a simple $\epsilon$ -greedy approach, it was not able to produce a useful strategy. We approached this issue using reward shaping, essentially a modification of the reward to be a function of the reward and the observation, rather than the reward alone. Here, we define the reward to be the sum of the score and the agent’s speed (a metric displayed on the screen of the game). Indeed when the reward was defined as such, the agents learned to finish the race in first place within a short training period.
+
+The second case study is the famous game of Super Mario. In this game the agent, Mario, is required to reach the right-hand side of the screen, while avoiding enemies and collecting coins. We found this case interesting as it involves several challenges at once: dynamic background that can change drastically within a level, sparse and delayed rewards and multiple tasks (such as avoiding enemies and pits, advancing rightwards and collecting coins). To our surprise, DQN was able to reach the end of the level without any reward shaping, this was possible since the agent receives rewards for events (collecting coins, stomping on enemies etc.) that tend to appear to the right of the player, causing the agent to prefer moving right. However, the training time required for convergence was significantly longer than other games. We defined the reward as the sum of the in-game reward and a bonus granted according the the player’s position, making moving right preferable. This reward proved useful, as training time required for convergence decreased significantly. The two games above can be seen in Figure (3).
+
+![](images/bc091b132abd4d7dd822cfd5331445d53a249c7c126f3c705d27348524a9b0f7.jpg)  
+Figure 2: DQN, DDQN and Duel-DDQN performance. Results were normalized by subtracting the a random agent’s score and dividing by the human player score. Thus 100 represents a human player and zero a random agent.
+
+Figure (4) illustrates the agent’s average value function . Though both were able complete the stage trained upon, the convergence rate with reward shaping is significantly quicker due to the immediate realization of the agent to move rightwards.
+
+![](images/6115ac16545e2eda72ae0985fb74a79f6bad9b9335f734e027bfab1b8e91f33f.jpg)  
+Figure 3: Left: The game Super Mario with added bonus for moving right, enabling the agent to master them game after less training time. Right: The game $F$ -Zero. By granting a reward for speed the agent was able to master this game, as oppose to using solely the in-game reward.
+
+![](images/b3b131ac05f655fc64be6ed77f008ae156cc49163d0a95ba3b5ea54be829a02d.jpg)  
+Figure 4: Averaged action-value (Q) for Super Mario trained with reward bonus for moving right (blue) and without (red).
+
+# 4.3 MULTI-AGENT REINFORCEMENT LEARNING
+
+In this section we describe our experiments with RLE’s multi-agent capabilities. We consider the case where the number of agents, $n = 2$ and the goals of the agents are opposite, as in $r _ { 1 } = - r _ { 2 }$ . This scheme is known as fully competitive (Bus¸oniu et al., 2010). We used the simple singleagent RL approach (as described by Bus¸oniu et al. (2010) section 5.4.1) which is to apply to single agent approach to the multi-agent case. This approach was proved useful in Crites and Barto (1996) and Mataric (1997). More elaborate schemes are possible such as the minimax-Q algo-´ rithm (Littman, 1994), (Littman, 2001). These may be explored in future works. We conducted three experiments on this setup: the first use was to train two different agents against the in-game AI, as done in previous sections, and evaluate their performance by letting them compete against each other. Here, rather than achieving the highest score, the goal was to win a tournament which consist of 50 rounds, as common in human-player competitions. The second experiment was to initially train two agents against the in-game AI, and resume the training while competing against each other. In this case, we evaluated the agent by playing again against the in-game AI, separately. Finally, in our last experiment we try to boost the agent capabilities by alternated it’s opponents, switching between the in-game AI and other trained agents.
+
+# 4.3.1 MULTI-AGENT REINFORCEMENT LEARNING RESULTS
+
+We chose the game Mortal Kombat, a two character side viewed fighting game (a screenshot of the game can be seen in Figure (1), as a testbed for the above, as it exhibits favorable properties: both players share the same screen, the agent’s optimal policy is heavily dependent on the rival’s behavior, unlike racing games for example. In order to evaluate two agents fairly, both were trained using the same characters maintaining the identity of rival and agent. Furthermore, to remove the impact of the starting positions of both agents on their performances, the starting positions were initialized randomly.
+
+In the first experiment we evaluated all combinations of DQN against D-DQN and Dueling D-DQN. Each agent was trained against the in-game AI until convergence. Then 50 matches were performed between the two agents. DQN lost 28 out of 50 games against Dueling D-DQN and 33 against D-DQN. D-DQN lost 26 time to Dueling D-DQN. This win balance isn’t far from the random case, since the algorithms converged into a policy in which movement towards the opponent is not required rather than generalize the game. Therefore, in many episodes, little interaction between the two agents occur, leading to a semi-random outcome.
+
+In our second experiment, we continued the training process of a the D-DQN network by letting it compete against the Dueling D-DQN network. We evaluated the re-trained network by playing 30 episodes against the in-game AI. After training, D-DQN was able to win 28 out of 30 games, yet when faced again against the in-game AI its performance deteriorated drastically (from an average of 17000 to an average of -22000). This demonstrated a form of catastrophic forgetting (Goodfellow et al., 2013) even though the agents played the same game.
+
+In our third experiment, we trained a Dueling D-DQN agent against three different rivals: the ingame AI, a trained DQN agent and a trained Dueling-DQN agent, in an alternating manner, such that in each episode a different rival was playing as the opponent with the intention of preventing the agent from learning a policy suitable for just one opponent. The new agent was able to achieve a score of 162,966 (compared to the ”normal” dueling D-DQN which achieved 169,633). As a new and objective measure of generalization, we’ve configured the in-game AI difficulty to be ”very hard” (as opposed to the default ”medium” difficulty). In this metric the alternating version achieved 83,400 compared to -33,266 of the dueling D-DQN which was trained in default setting. Thus, proving that the agent learned to generalize to other policies which weren’t observed while training.
+
+# 4.4 FUTURE CHALLENGES
+
+As demonstrated, RLE presents numerous challenges that have yet to be answered. In addition to being able to learn all available games, the task of learning games in which reward delay is extreme, such as F-Zero without reward shaping, remains an unsolved challenge. Additionally, some games, such as Super Mario, feature several stages that differ in background and the levels structure. The task of generalizing platform games, as in learning on one stage and being tested on the other, is another unexplored challenge. Likewise surpassing human performance remains a challenge since current state-of-the-art algorithms still struggling with the many SNES games.
+
+# 5 CONCLUSION
+
+We introduced a rich environment for evaluating and developing reinforcement learning algorithms which presents significant challenges to current state-of-the-art algorithms. In comparison to other environments RLE provides a large amount of games with access to both the screen and the ingame state. The modular implementation we chose allows extensions of the environment with new consoles and games, thus ensuring the relevance of the environment to RL algorithms for years to come (see Table (2)). We’ve encountered several games in which the learning process is highly dependent on the reward definition. This issue can be addressed and explored in RLE as reward definition can be done easily. The challenges presented in the RLE consist of: 3D interpretation, delayed reward, noisy background, stochastic AI behavior and more. Although some algorithms were able to play successfully on part of the games, to fully overcome these challenges, an agent must incorporate both technique and strategy. Therefore, we believe, that the RLE is a great platform for future RL research.
+
+# 6 ACKNOWLEDGMENTS
+
+The authors are grateful to the Signal and Image Processing Lab (SIPL) staff for their support, Alfred Agrell and the LibRetro community for their support and Marc G. Bellemare for his valuable inputs.
+
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+
+# Appendices
+
+Experimental Results
+
+Table 3: Average results of DQN, D-DQN, Dueling D-DQN and a Human player   
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>DQN</td><td rowspan=1 colspan=1>D-DQN</td><td rowspan=1 colspan=1> Dueling D-DQN</td><td rowspan=1 colspan=1>Human</td></tr><tr><td rowspan=1 colspan=1>F-Zer0</td><td rowspan=1 colspan=1>3116</td><td rowspan=1 colspan=1>3636</td><td rowspan=1 colspan=1>5161</td><td rowspan=1 colspan=1>6298</td></tr><tr><td rowspan=1 colspan=1>Gradius III</td><td rowspan=1 colspan=1>7583</td><td rowspan=1 colspan=1>12343</td><td rowspan=1 colspan=1>16929</td><td rowspan=1 colspan=1>24440</td></tr><tr><td rowspan=1 colspan=1>Mortal Kombat</td><td rowspan=1 colspan=1>83733</td><td rowspan=1 colspan=1>56200</td><td rowspan=1 colspan=1>169300</td><td rowspan=1 colspan=1>132441</td></tr><tr><td rowspan=1 colspan=1> Super Mario</td><td rowspan=1 colspan=1>11765</td><td rowspan=1 colspan=1>16946</td><td rowspan=1 colspan=1>20030</td><td rowspan=1 colspan=1>36386</td></tr><tr><td rowspan=1 colspan=1>Wolfenstein</td><td rowspan=1 colspan=1>100</td><td rowspan=1 colspan=1>83</td><td rowspan=1 colspan=1>40</td><td rowspan=1 colspan=1>2952</td></tr></table>

parse/train/HysBZSqlx/HysBZSqlx_content_list.json

@@ -0,0 +1,934 @@
+[
+    {
+        "type": "text",
+        "text": "PLAYING SNES IN THE RETRO LEARNING ENVIRONMENT ",
+        "text_level": 1,
+        "bbox": [
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+            98,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Nadav Bhonker\\*, Shai Rozenberg\\* and Itay Hubara ",
+        "bbox": [
+            184,
+            170,
+            550,
+            185
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Department of Electrical Engineering   \nTechnion, Israel Institute of Technology   \n$( ^ { * } )$ indicates equal contribution   \n{nadavbh,shairoz}@tx.technion.ac.il   \nitayhubara@gmail.com ",
+        "bbox": [
+            184,
+            186,
+            522,
+            253
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            290,
+            544,
+            305
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Mastering a video game requires skill, tactics and strategy. While these attributes may be acquired naturally by human players, teaching them to a computer program is a far more challenging task. In recent years, extensive research was carried out in the field of reinforcement learning and numerous algorithms were introduced, aiming to learn how to perform human tasks such as playing video games. As a result, the Arcade Learning Environment (ALE) (Bellemare et al., 2013) has become a commonly used benchmark environment allowing algorithms to train on various Atari 2600 games. In many games the state-of-the-art algorithms outperform humans. In this paper we introduce a new learning environment, the Retro Learning Environment — RLE, that can run games on the Super Nintendo Entertainment System (SNES), Sega Genesis and several other gaming consoles. The environment is expandable, allowing for more video games and consoles to be easily added to the environment, while maintaining the same interface as ALE. Moreover, RLE is compatible with Python and Torch. SNES games pose a significant challenge to current algorithms due to their higher level of complexity and versatility. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            573,
+            336,
+            588
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Controlling artificial agents using only raw high-dimensional input data such as image or sound is a difficult and important task in the field of Reinforcement Learning (RL). Recent breakthroughs in the field allow its utilization in real-world applications such as autonomous driving (Shalev-Shwartz et al., 2016), navigation (Bischoff et al., 2013) and more. Agent interaction with the real world is usually either expensive or not feasible, as the real world is far too complex for the agent to perceive. Therefore in practice the interaction is simulated by a virtual environment which receives feedback on a decision made by the algorithm. Traditionally, games were used as a RL environment, dating back to Chess (Campbell et al., 2002), Checkers (Schaeffer et al., 1992), backgammon (Tesauro, 1995) and the more recent Go (Silver et al., 2016). Modern games often present problems and tasks which are highly correlated with real-world problems. For example, an agent that masters a racing game, by observing a simulated driver’s view screen as input, may be usefull for the development of an autonomous driver. For high-dimensional input, the leading benchmark is the Arcade Learning Environment (ALE) (Bellemare et al., 2013) which provides a common interface to dozens of Atari 2600 games, each presents a different challenge. ALE provides an extensive benchmarking platform, allowing a controlled experiment setup for algorithm evaluation and comparison. The main challenge posed by ALE is to successfully play as many Atari 2600 games as possible (i.e., achieving a score higher than an expert human player) without providing the algorithm any game-specific information (i.e., using the same input available to a human - the game screen and score). A key work to tackle this problem is the Deep Q-Networks algorithm (Mnih et al., 2015), which made a breakthrough in the field of Deep Reinforcement Learning by achieving human level performance on 29 out of 49 games. In this work we present a new environment — the Retro Learning Environment (RLE). RLE sets new challenges by providing a unified interface for Atari 2600 games as well as more advanced gaming consoles. As a start we focused on the Super Nintendo Entertainment ",
+        "bbox": [
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+            604,
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+            922
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "System (SNES). Out of the five SNES games we tested using state-of-the-art algorithms, only one was able to outperform an expert human player. As an additional feature, RLE supports research of multi-agent reinforcement learning (MARL) tasks (Bus¸oniu et al., 2010). We utilize this feature by training and evaluating the agents against each other, rather than against a pre-configured in-game AI. We conducted several experiments with this new feature and discovered that agents tend to learn how to overcome their current opponent rather than generalize the game being played. However, if an agent is trained against an ensemble of different opponents, its robustness increases. The main contributions of the paper are as follows: ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• Introducing a novel RL environment with significant challenges and an easy agent evaluation technique (enabling agents to compete against each other) which could lead to new and more advanced RL algorithms.   \n• A new method to train an agent by enabling it to train against several opponents, making the final policy more robust.   \n• Encapsulating several different challenges to a single RL environment. ",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+            348,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 ARCADE LEARNING ENVIRONMENT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            381,
+            464,
+            396
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The Arcade Learning Environment is a software framework designed for the development of RL algorithms, by playing Atari 2600 games. The interface provided by ALE allows the algorithms to select an action and receive the Atari screen and a reward in every step. The action is the equivalent to a human’s joystick button combination and the reward is the difference between the scores at time stamp $t$ and $t - 1$ . The diversity of games for Atari provides a solid benchmark since different games have significantly different goals. Atari 2600 has over 500 games, currently over 70 of them are implemented in ALE and are commonly used for algorithm comparison. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2 INFINITE MARIO ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            525,
+            331,
+            539
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Infinite Mario (Togelius et al., 2009) is a remake of the classic Super Mario game in which levels are randomly generated. On these levels the Mario AI Competition was held. During the competition, several algorithms were trained on Infinite Mario and their performances were measured in terms of the number of stages completed. As opposed to ALE, training is not based on the raw screen data but rather on an indication of Mario’s (the player’s) location and objects in its surrounding. This environment no longer poses a challenge for state of the art algorithms. Its main shortcoming lie in the fact that it provides only a single game to be learnt. Additionally, the environment provides hand-crafted features, extracted directly from the simulator, to the algorithm. This allowed the use of planning algorithms that highly outperform any learning based algorithm. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.3 OPENAI GYM ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            696,
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+            710
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The OpenAI gym (Brockman et al., 2016) is an open source platform with the purpose of creating an interface between RL environments and algorithms for evaluation and comparison purposes. OpenAI Gym is currently very popular due to the large number of environments supported by it. For example ALE, Go, MouintainCar and VizDoom (Zhu et al., 2016), an environment for the learning of the 3D first-person-shooter game ”Doom”. OpenAI Gym’s recent appearance and wide usage indicates the growing interest and research done in the field of RL. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.4 OPENAI UNIVERSE ",
+        "text_level": 1,
+        "bbox": [
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+            827,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Universe (Universe, 2016) is a platform within the OpenAI framework in which RL algorithms can train on over a thousand games. Universe includes very advanced games such as GTA V, Portal as well as other tasks (e.g. browser tasks). Unlike RLE, Universe doesn’t run the games locally and requires a VNC interface to a server that runs the games. This leads to a lower frame rate and thus longer training times. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.5 MALMO ",
+        "text_level": 1,
+        "bbox": [
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+            117
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Malmo (Johnson et al., 2016) is an artificial intelligence experimentation platform of the famous game ”Minecraft”. Although Malmo consists of only a single game, it presents numerous challenges since the ”Minecraft” game can be configured differently each time. The input to the RL algorithms include specific features indicating the ”state” of the game and the current reward. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.6 DEEPMIND LAB ",
+        "text_level": 1,
+        "bbox": [
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+            202,
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+            217
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "DeepMind Lab (Dee) is a first-person 3D platform environment which allows training RL algorithms on several different challenges: static/random map navigation, collect fruit (a form of reward) and a laser-tag challenge where the objective is to tag the opponents controlled by the in-game AI. In LAB the agent observations are the game screen (with an additional depth channel) and the velocity of the character. LAB supports four games (one game - four different modes). ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.7 DEEP Q-LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            315,
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+            329
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In our work, we used several variant of the Deep Q-Network algorithm (DQN) (Mnih et al., 2015), an RL algorithm whose goal is to find an optimal policy (i.e., given a current state, choose action that maximize the final score). The state of the game is simply the game screen, and the action is a combination of joystick buttons that the game responds to (i.e., moving ,jumping). DQN learns through trial and error while trying to estimate the ”Q-function”, which predicts the cumulative discounted reward at the end of the episode given the current state and action while following a policy $\\pi$ . The Q-function is represented using a convolution neural network that receives the screen as input and predicts the best possible action at it’s output. The Q-function weights $\\theta$ are updated according to: ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c8d5f50d23cda48b75c0cef615e97baf7b3fef2d3ce913077b3383d97c22304b.jpg",
+        "text": "$$\n\\theta _ { t + 1 } ( s _ { t } , a _ { t } ) = \\theta _ { t } + \\alpha ( R _ { t + 1 } + \\gamma \\operatorname* { m a x } _ { a } ( Q _ { t } ( s _ { t + 1 } , a ; \\theta _ { t } ^ { \\prime } ) ) - Q _ { t } ( s _ { t } , a _ { t } ; \\theta _ { t } ) ) \\nabla _ { \\theta } Q _ { t } ( s _ { t } , a _ { t } ; \\theta _ { t } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            194,
+            472,
+            781,
+            494
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $s _ { t }$ , $s _ { t + 1 }$ are the current and next states, $a _ { t }$ is the action chosen, $\\alpha$ is the step size, $\\gamma$ is the discounting factor $R _ { t + 1 }$ is the reward received by applying $a _ { t }$ at $s _ { t }$ . $\\theta ^ { \\prime }$ represents the previous weights of the network that are updated periodically. Other than DQN, we examined two leading algorithms on the RLE: Double Deep Q-Learning (D-DQN) (Van Hasselt et al., 2015), a DQN based algorithm with a modified network update rule. Dueling Double DQN (Wang et al., 2015), a modification of D-DQN’s architecture in which the $\\mathbf { Q }$ -function is modeled using a state (screen) dependent estimator and an action dependent estimator. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 THE RETRO LEARNING ENVIRONMENT ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 SUPER NINTENDO ENTERTAINMENT SYSTEM ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            650,
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+            664
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The Super Nintendo Entertainment System (SNES) is a home video game console developed by Nintendo and released in 1990. A total of 783 games were released, among them, the iconic Super Mario World, Donkey Kong Country and The Legend of Zelda. Table (1) presents a comparison between Atari 2600, Sega Genesis and SNES game consoles, from which it is clear that SNES and Genesis games are far more complex. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2 IMPLEMENTATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            762,
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+            776
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To allow easier integration with current platforms and algorithms, we based our environment on the ALE, with the aim of maintaining as much of its interface as possible. While the ALE is highly coupled with the Atari emulator, Stella1, RLE takes a different approach and separates the learning environment from the emulator. This was achieved by incorporating an interface named LibRetro (libRetro site), that allows communication between front-end programs to game-console emulators. Currently, LibRetro supports over 15 game consoles, each containing hundreds of games, at an estimated total of over 7,000 games that can potentially be supported using this interface. Examples of supported game consoles include Nintendo Entertainment System, Game Boy, N64, Sega Genesis, ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Saturn, Dreamcast and Sony PlayStation. We chose to focus on the SNES game console implemented using the $\\operatorname { s n e s } 9 \\mathrm { x } ^ { 2 }$ as it’s games present interesting, yet plausible to overcome challenges. Additionally, we utilized the Genesis-Plus- $\\mathbf { \\Delta } G \\mathbf { X } ^ { 3 }$ emulator, which supports several Sega consoles: Genesis/Mega Drive, Master System, Game Gear and SG-1000. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 SOURCE CODE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            176,
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+            190
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "RLE is fully available as open source software for use under GNU’s General Public License4. The environment is implemented in $\\mathrm { C } { + } { + }$ with an interface to algorithms in $\\mathrm { C } { + } { + }$ , Python and Lua. Adding a new game to the environment is a relatively simple process. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4 RLE INTERFACE ",
+        "text_level": 1,
+        "bbox": [
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+            262,
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+            276
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "RLE provides a unified interface to all games in its supported consoles, acting as an RL-wrapper to the LibRetro interface. Initialization of the environment is done by providing a game (ROM file) and a gaming-console (denoted by ’core’). Upon initialization, the first state is the initial frame of the game, skipping all menu selection screens. The cores are provided with the RLE and installed together with the environment. Actions have a bit-wise representation where each controller button is represented by a one-hot vector. Therefore a combination of several buttons is possible using the bit-wise OR operator. The number of valid buttons combinations is larger than 700, therefore only the meaningful combinations are provided. The environments observation is the game screen, provided as a 3D array of 32 bit per pixel with dimensions which vary depending on the game. The reward can be defined differently per game, usually we set it to be the score difference between two consecutive frames. By setting different configuration to the environment, it is possible to alter in-game properties such as difficulty (i.e easy, medium, hard), its characters, levels, etc. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/e4b3991dd2289083d8f9c63aefed8d0ecdbf6c189b0cefdc67521223558e9bea.jpg",
+        "table_caption": [
+            "Table 1: Atari 2600, SNES and Genesis comparison "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Atari 2600</td><td>SNES</td><td>Genesis</td></tr><tr><td>Number of Games</td><td>565</td><td>783</td><td>928</td></tr><tr><td>CPU speed</td><td>1.19MHz</td><td>3.58MHz</td><td>7.6 MHz</td></tr><tr><td>ROM size</td><td>2-4KB</td><td>0.5-6MB</td><td>16 MBytes</td></tr><tr><td>RAM size</td><td>128 bytes</td><td>128KB</td><td>72KB</td></tr><tr><td>Color depth</td><td>8 bit</td><td>16 bit</td><td>16 bit</td></tr><tr><td>Screen Size</td><td>160x210</td><td>256x224 or 512x448</td><td>320x224</td></tr><tr><td>Number of controller buttons</td><td>5</td><td>12</td><td>11</td></tr><tr><td>Possible buttons combinations</td><td>18</td><td>over 720</td><td>over100</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.5 ENVIRONMENT CHALLENGES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            666,
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+            680
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Integrating SNES and Genesis with RLE presents new challenges to the field of RL where visual information in the form of an image is the only state available to the agent. Obviously, SNES games are significantly more complex and unpredictable than Atari games. For example in sports games, such as NBA, while the player (agent) controls a single player, all the other nine players’ behavior is determined by pre-programmed agents, each exhibiting random behavior. In addition, many SNES games exhibit delayed rewards in the course of their play (i.e., reward for an actions is given many time steps after it was performed). Similarly, in some of the SNES games, an agent can obtain a reward that is indirectly related to the imposed task. For example, in platform games, such as Super Mario, reward is received for collecting coins and defeating enemies, while the goal of the challenge is to reach the end of the level which requires to move to keep moving to the right. Moreover, upon completing a level, a score bonus is given according to the time required for its completion. Therefore collecting coins or defeating enemies is not necessarily preferable if it consumes too much time. Analysis of such games is presented in section 4.2. Moreover, unlike Atari that consists of eight directions and one action button, SNES has eight-directions pad and six actions buttons. Since combinations of buttons are allowed, and required at times, the actual actions space may be larger than 700, compared to the maximum of 18 actions in Atari. Furthermore, the background in SNES is very rich, filled with details which may move locally or across the screen, effectively acting as non-stationary noise since it provided little to no information regarding the state itself. Finally, we note that SNES utilized the first 3D games. In the game Wolfenstein, the player must navigate a maze from a first-person perspective, while dodging and attacking enemies. The SNES offers plenty of other 3D games such as flight and racing games which exhibit similar challenges. These games are much more realistic, thus inferring from SNES games to ”real world” tasks, as in the case of self driving cars, might be more beneficial. A visual comparison of two games, Atari and SNES, is presented in Figure (1). ",
+        "bbox": [
+            173,
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+            872
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            103,
+            825,
+            256
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/c343c235f708c978ceb3c66883ef1bc74d461f57a56abbdde15e4c7c355130b2.jpg",
+        "image_caption": [
+            "Figure 1: Atari 2600 and SNES game screen comparison: Left: ”Boxing” an Atari 2600 fighting game , Right: ”Mortal Kombat” a SNES fighting game. Note the exceptional difference in the amount of details between the two games. Therefore, distinguishing a relevant signal from noise is much more difficult. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            271,
+            825,
+            448
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/b040839ad2a120426f6375d21eaa3da78cefaeca2dcfc21ef51480cedc576092.jpg",
+        "table_caption": [
+            "Table 2: Comparison between RLE and the latest RL environments "
+        ],
+        "table_footnote": [
+            "1 Allowing changes in-the game configurations (e.g., changing difficulty, characters, etc.) 2 Measured on an i7-5930k CPU "
+        ],
+        "table_body": "<table><tr><td>Characteristics</td><td>RLE</td><td>OpenAI Universe</td><td>Inifinte Mario</td><td>ALE</td><td>Project Malmo</td><td>DeepMind Lab</td></tr><tr><td>Number of Games</td><td>8 out of 7000+</td><td>1000+</td><td>1</td><td>74</td><td>1</td><td>4</td></tr><tr><td>In game adjustments1</td><td>Yes</td><td>NO</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td>Frame rate</td><td>530fps(SNES)</td><td>60fps</td><td>5675fps2</td><td>120fps</td><td>&lt;7000fps</td><td>&lt;1000fps</td></tr><tr><td>Observation (Input)</td><td>screen, RAM</td><td>Screen</td><td>hand crafted features</td><td>screen, RAM</td><td>hand crafted features</td><td>screen+depth and velocity</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
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+    {
+        "type": "text",
+        "text": "4.1 EVALUATION METHODOLOGY ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The evaluation methodology that we used for benchmarking the different algorithms is the popular method proposed by (Mnih et al., 2015). Each examined algorithm is trained until either it reached convergence or 100 epochs (each epoch corresponds to 50,000 actions), thereafter it is evaluated by performing 30 episodes of every game. Each episode ends either by reaching a terminal state or after 5 minutes. The results are averaged per game and compared to the average result of a human player. For each game the human player was given two hours for training, and his performances were evaluated over 20 episodes. As the various algorithms don’t use the game audio in the learning process, the audio was muted for both the agent and the human. From both, humans and agents score, a random agent score (an agent performing actions randomly) was subtracted to assure that learning indeed occurred. It is important to note that DQN’s $\\epsilon$ -greedy approach (select a random action with a small probability \u000f) is present during testing thus assuring that the same sequence of actions isn’t repeated. While the screen dimensions in SNES are larger than those of Atari, in our experiments we maintained the same pre-processing of DQN (i.e., downscaling the image to $8 4 \\mathrm { x } 8 4$ pixels and converting to gray-scale). We argue that downscaling the image size doesn’t affect a human’s ability to play the game, therefore suitable for RL algorithms as well. To handle the large action space, we limited the algorithm’s actions to the minimal button combinations which provide unique behavior. For example, on many games the R and L action buttons don’t have any use therefore their use and combinations were omitted. ",
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+    {
+        "type": "text",
+        "text": "4.1.1 RESULTS ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "A thorough comparison of the four different agents’ performances on SNES games can be seen in Figure (). The full results can be found in Table (3). Only in the game Mortal Kombat a trained agent was able to surpass a expert human player performance as opposed to Atari games where the same algorithms have surpassed a human player on the vast majority of the games. ",
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+    {
+        "type": "text",
+        "text": "One example is Wolfenstein game, a 3D first-person shooter game, requires solving 3D vision tasks, navigating in a maze and detecting object. As evident from figure (2), all agents produce poor results indicating a lack of the required properties. By using $\\epsilon$ -greedy approach the agents weren’t able to explore enough states (or even other rooms in our case). The algorithm’s final policy appeared as a random walk in a 3D space. Exploration based on visited states such as presented in Bellemare et al. (2016) might help addressing this issue. An interesting case is Gradius III, a side-scrolling, flight-shooter game. While the trained agent was able to master the technical aspects of the game, which includes shooting incoming enemies and dodging their projectiles, it’s final score is still far from a human’s. This is due to a hidden game mechanism in the form of ”power-ups”, which can be accumulated, and significantly increase the players abilities. The more power-ups collected without being use — the larger their final impact will be. While this game-mechanism is evident to a human, the agent acts myopically and uses the power-up straight away5. ",
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+    {
+        "type": "text",
+        "text": "4.2 REWARD SHAPING ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "As part of the environment and algorithm evaluation process, we investigated two case studies. First is a game on which DQN had failed to achieve a better-than-random score, and second is a game on which the training duration was significantly longer than that of other games. ",
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+    {
+        "type": "text",
+        "text": "In the first case study, we used a 2D back-view racing game ”F-Zero”. In this game, one is required to complete four laps of the track while avoiding other race cars. The reward, as defined by the score of the game, is only received upon completing a lap. This is an extreme case of a reward delay. A lap may last as long as 30 seconds, which span over 450 states (actions) before reward is received. Since DQN’s exploration is a simple $\\epsilon$ -greedy approach, it was not able to produce a useful strategy. We approached this issue using reward shaping, essentially a modification of the reward to be a function of the reward and the observation, rather than the reward alone. Here, we define the reward to be the sum of the score and the agent’s speed (a metric displayed on the screen of the game). Indeed when the reward was defined as such, the agents learned to finish the race in first place within a short training period. ",
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+    {
+        "type": "text",
+        "text": "The second case study is the famous game of Super Mario. In this game the agent, Mario, is required to reach the right-hand side of the screen, while avoiding enemies and collecting coins. We found this case interesting as it involves several challenges at once: dynamic background that can change drastically within a level, sparse and delayed rewards and multiple tasks (such as avoiding enemies and pits, advancing rightwards and collecting coins). To our surprise, DQN was able to reach the end of the level without any reward shaping, this was possible since the agent receives rewards for events (collecting coins, stomping on enemies etc.) that tend to appear to the right of the player, causing the agent to prefer moving right. However, the training time required for convergence was significantly longer than other games. We defined the reward as the sum of the in-game reward and a bonus granted according the the player’s position, making moving right preferable. This reward proved useful, as training time required for convergence decreased significantly. The two games above can be seen in Figure (3). ",
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+    {
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+        "img_path": "images/bc091b132abd4d7dd822cfd5331445d53a249c7c126f3c705d27348524a9b0f7.jpg",
+        "image_caption": [
+            "Figure 2: DQN, DDQN and Duel-DDQN performance. Results were normalized by subtracting the a random agent’s score and dividing by the human player score. Thus 100 represents a human player and zero a random agent. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Figure (4) illustrates the agent’s average value function . Though both were able complete the stage trained upon, the convergence rate with reward shaping is significantly quicker due to the immediate realization of the agent to move rightwards. ",
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+        "img_path": "images/6115ac16545e2eda72ae0985fb74a79f6bad9b9335f734e027bfab1b8e91f33f.jpg",
+        "image_caption": [
+            "Figure 3: Left: The game Super Mario with added bonus for moving right, enabling the agent to master them game after less training time. Right: The game $F$ -Zero. By granting a reward for speed the agent was able to master this game, as oppose to using solely the in-game reward. "
+        ],
+        "image_footnote": [],
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+        "img_path": "images/b3b131ac05f655fc64be6ed77f008ae156cc49163d0a95ba3b5ea54be829a02d.jpg",
+        "image_caption": [
+            "Figure 4: Averaged action-value (Q) for Super Mario trained with reward bonus for moving right (blue) and without (red). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3 MULTI-AGENT REINFORCEMENT LEARNING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "In this section we describe our experiments with RLE’s multi-agent capabilities. We consider the case where the number of agents, $n = 2$ and the goals of the agents are opposite, as in $r _ { 1 } = - r _ { 2 }$ . This scheme is known as fully competitive (Bus¸oniu et al., 2010). We used the simple singleagent RL approach (as described by Bus¸oniu et al. (2010) section 5.4.1) which is to apply to single agent approach to the multi-agent case. This approach was proved useful in Crites and Barto (1996) and Mataric (1997). More elaborate schemes are possible such as the minimax-Q algo-´ rithm (Littman, 1994), (Littman, 2001). These may be explored in future works. We conducted three experiments on this setup: the first use was to train two different agents against the in-game AI, as done in previous sections, and evaluate their performance by letting them compete against each other. Here, rather than achieving the highest score, the goal was to win a tournament which consist of 50 rounds, as common in human-player competitions. The second experiment was to initially train two agents against the in-game AI, and resume the training while competing against each other. In this case, we evaluated the agent by playing again against the in-game AI, separately. Finally, in our last experiment we try to boost the agent capabilities by alternated it’s opponents, switching between the in-game AI and other trained agents. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3.1 MULTI-AGENT REINFORCEMENT LEARNING RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We chose the game Mortal Kombat, a two character side viewed fighting game (a screenshot of the game can be seen in Figure (1), as a testbed for the above, as it exhibits favorable properties: both players share the same screen, the agent’s optimal policy is heavily dependent on the rival’s behavior, unlike racing games for example. In order to evaluate two agents fairly, both were trained using the same characters maintaining the identity of rival and agent. Furthermore, to remove the impact of the starting positions of both agents on their performances, the starting positions were initialized randomly. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In the first experiment we evaluated all combinations of DQN against D-DQN and Dueling D-DQN. Each agent was trained against the in-game AI until convergence. Then 50 matches were performed between the two agents. DQN lost 28 out of 50 games against Dueling D-DQN and 33 against D-DQN. D-DQN lost 26 time to Dueling D-DQN. This win balance isn’t far from the random case, since the algorithms converged into a policy in which movement towards the opponent is not required rather than generalize the game. Therefore, in many episodes, little interaction between the two agents occur, leading to a semi-random outcome. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In our second experiment, we continued the training process of a the D-DQN network by letting it compete against the Dueling D-DQN network. We evaluated the re-trained network by playing 30 episodes against the in-game AI. After training, D-DQN was able to win 28 out of 30 games, yet when faced again against the in-game AI its performance deteriorated drastically (from an average of 17000 to an average of -22000). This demonstrated a form of catastrophic forgetting (Goodfellow et al., 2013) even though the agents played the same game. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In our third experiment, we trained a Dueling D-DQN agent against three different rivals: the ingame AI, a trained DQN agent and a trained Dueling-DQN agent, in an alternating manner, such that in each episode a different rival was playing as the opponent with the intention of preventing the agent from learning a policy suitable for just one opponent. The new agent was able to achieve a score of 162,966 (compared to the ”normal” dueling D-DQN which achieved 169,633). As a new and objective measure of generalization, we’ve configured the in-game AI difficulty to be ”very hard” (as opposed to the default ”medium” difficulty). In this metric the alternating version achieved 83,400 compared to -33,266 of the dueling D-DQN which was trained in default setting. Thus, proving that the agent learned to generalize to other policies which weren’t observed while training. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.4 FUTURE CHALLENGES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            375,
+            370,
+            388
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "As demonstrated, RLE presents numerous challenges that have yet to be answered. In addition to being able to learn all available games, the task of learning games in which reward delay is extreme, such as F-Zero without reward shaping, remains an unsolved challenge. Additionally, some games, such as Super Mario, feature several stages that differ in background and the levels structure. The task of generalizing platform games, as in learning on one stage and being tested on the other, is another unexplored challenge. Likewise surpassing human performance remains a challenge since current state-of-the-art algorithms still struggling with the many SNES games. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We introduced a rich environment for evaluating and developing reinforcement learning algorithms which presents significant challenges to current state-of-the-art algorithms. In comparison to other environments RLE provides a large amount of games with access to both the screen and the ingame state. The modular implementation we chose allows extensions of the environment with new consoles and games, thus ensuring the relevance of the environment to RL algorithms for years to come (see Table (2)). We’ve encountered several games in which the learning process is highly dependent on the reward definition. This issue can be addressed and explored in RLE as reward definition can be done easily. The challenges presented in the RLE consist of: 3D interpretation, delayed reward, noisy background, stochastic AI behavior and more. Although some algorithms were able to play successfully on part of the games, to fully overcome these challenges, an agent must incorporate both technique and strategy. Therefore, we believe, that the RLE is a great platform for future RL research. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6 ACKNOWLEDGMENTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            744,
+            387,
+            760
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The authors are grateful to the Signal and Image Processing Lab (SIPL) staff for their support, Alfred Agrell and the LibRetro community for their support and Marc G. Bellemare for his valuable inputs. ",
+        "bbox": [
+            173,
+            776,
+            823,
+            805
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+    },
+    {
+        "type": "text",
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+        "bbox": [
+            166,
+            109,
+            826,
+            929
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Appendices ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            99,
+            343,
+            127
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Experimental Results ",
+        "bbox": [
+            174,
+            148,
+            316,
+            162
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/d4b263e24c17a92c14506e3c38d3f893d057400a4258e870acd6467ef5d4b5bd.jpg",
+        "table_caption": [
+            "Table 3: Average results of DQN, D-DQN, Dueling D-DQN and a Human player "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>DQN</td><td rowspan=1 colspan=1>D-DQN</td><td rowspan=1 colspan=1> Dueling D-DQN</td><td rowspan=1 colspan=1>Human</td></tr><tr><td rowspan=1 colspan=1>F-Zer0</td><td rowspan=1 colspan=1>3116</td><td rowspan=1 colspan=1>3636</td><td rowspan=1 colspan=1>5161</td><td rowspan=1 colspan=1>6298</td></tr><tr><td rowspan=1 colspan=1>Gradius III</td><td rowspan=1 colspan=1>7583</td><td rowspan=1 colspan=1>12343</td><td rowspan=1 colspan=1>16929</td><td rowspan=1 colspan=1>24440</td></tr><tr><td rowspan=1 colspan=1>Mortal Kombat</td><td rowspan=1 colspan=1>83733</td><td rowspan=1 colspan=1>56200</td><td rowspan=1 colspan=1>169300</td><td rowspan=1 colspan=1>132441</td></tr><tr><td rowspan=1 colspan=1> Super Mario</td><td rowspan=1 colspan=1>11765</td><td rowspan=1 colspan=1>16946</td><td rowspan=1 colspan=1>20030</td><td rowspan=1 colspan=1>36386</td></tr><tr><td rowspan=1 colspan=1>Wolfenstein</td><td rowspan=1 colspan=1>100</td><td rowspan=1 colspan=1>83</td><td rowspan=1 colspan=1>40</td><td rowspan=1 colspan=1>2952</td></tr></table>",
+        "bbox": [
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+        "page_idx": 10
+    }
+]

parse/train/Skgy464Kvr/Skgy464Kvr.md

@@ -0,0 +1,314 @@
+# DETECTING AND DIAGNOSING ADVERSARIALIMAGES WITH CLASS-CONDITIONAL CAPSULERECONSTRUCTIONS
+
+Yao Qin∗   
+UC San Diego   
+yaq007@eng.ucsd.edu
+
+Nicholas Frosst∗ Google Brain frosst@google.com
+
+Sara Sabour   
+Google Brain   
+sasabour@google.com   
+Colin Raffel   
+Google Brain   
+craffel@google.com
+
+Garrison Cottrell UC San Diego gary@eng.ucsd.edu
+
+Geoffrey Hinton   
+Google Brain   
+geoffhinton@google.com
+
+# ABSTRACT
+
+Adversarial examples raise questions about whether neural network models are sensitive to the same visual features as humans. In this paper, we first detect adversarial examples or otherwise corrupted images based on a class-conditional reconstruction of the input. To specifically attack our detection mechanism, we propose the Reconstructive Attack which seeks both to cause a misclassification and a low reconstruction error. This reconstructive attack produces undetected adversarial examples but with much smaller success rate. Among all these attacks, we find that CapsNets always perform better than convolutional networks. Then, we diagnose the adversarial examples for CapsNets and find that the success of the reconstructive attack is highly related to the visual similarity between the source and target class. Additionally, the resulting perturbations can cause the input image to appear visually more like the target class and hence become non-adversarial. This suggests that CapsNets use features that are more aligned with human perception and have the potential to address the central issue raised by adversarial examples.
+
+# 1 INTRODUCTION
+
+Adversarial examples (Szegedy et al., 2013) are inputs that are designed by an adversary to cause a machine learning system to make a misclassification. A series of studies on adversarial attacks have shown that it is easy to cause misclassifications using visually imperceptible changes to an image under $\ell _ { p }$ -norm based similarity metrics (Goodfellow et al., 2014; Kurakin et al., 2016; Madry et al., 2017; Carlini & Wagner, 2017b; Goodfellow et al., 2018). Since the discovery of adversarial examples, there has been a constant “arms race” between better attacks and better defenses. Many new defenses have been proposed (Song et al., 2017; Gong et al., 2017; Grosse et al., 2017; Metzen et al., 2017), only to be broken shortly thereafter (Carlini & Wagner, 2017a; Athalye et al., 2018). Hinton et al. (2018) showed that capsule models are more robust to simple adversarial attacks than CNNs but Michels et al. (2019) showed that this is not the case for all attacks.
+
+The cycle of attacks and defenses motivates us to rethink both how we can improve the general robustness of neural networks as well as the high-level motivation for this pursuit. One potential path forward is to detect adversarial inputs, instead of attempting to accurately classify them (Schott et al., 2018; Roth et al., 2019). Recent work (Jetley et al., 2018; Gilmer et al., 2018b) argue that adversarial examples can exist within the data distribution, which implies that detecting adversarial examples based on an estimate of the data distribution alone might be insufficient. Instead, in this paper we develop methods for detecting adversarial examples by making use of class-conditional reconstruction networks. These sub-networks, first proposed by Sabour et al. (2017) as part of a Capsule Network (CapsNet), allow a model to produce a reconstruction of its input based on the identity and instantiation parameters of the winning capsule. Interestingly, we find that reconstructing an input from the capsule corresponding to the correct class results in a much lower reconstruction error than reconstructing the input from capsules corresponding to incorrect classes, as shown in Figure 1(a). Motivated by this, we propose using the reconstruction sub-network in a CapsNet as an attack-independent detection mechanism. Specifically, we reconstruct a given input from the pose parameters of the winning capsule and then detect adversarial examples by comparing the difference between the reconstruction distributions for natural and adversarial (or otherwise corrupted) images.
+
+![](images/a2c6adf0cf1f639c8b0fccf3ed956f8e21c832df077bcabef2310e41920598be.jpg)  
+Figure 1: (a) The histogram of $\ell _ { 2 }$ distances between the input and the reconstruction using the correct capsule or other capsules in CapsNet on the real MNIST images. Notice the stark difference between the distributions of reconstructions of the capsule corresponding to the correct class and other capsules. (b) The histograms of $\ell _ { 2 }$ distances between the reconstruction and the input for real and adversarial images for the three models explored in this paper on the MNIST dataset. We use PGD (Madry et al., 2017) with the $\ell _ { \infty }$ bound $\epsilon = 0 . 3$ to create the attacks.
+
+We extend this detection mechanism to standard convolutional neural networks (CNNs) and show its effectiveness against black box and white box attacks on three image datasets; MNIST, FashionMNIST and SVHN. We show that capsule models achieve the strongest attack detection rates and accuracy on these attacks. We then test our method against a stronger attack, the Reconstructive Attack, specifically designed to attack our detection mechanism by generating adversarial examples with a small reconstruction error. With this attack we are able to create undetected adversarial examples, but we show that this attack is less successful in fooling the classifier than a non-reconstructive attack.
+
+Among all these attacks, we find CapsNets perform the best in detecting adversarial examples. To explain the success of CapsNets over CNNs, we further diagnose the adversarial examples for CapsNets and find that 1) the success of the targeted reconstructive attack is highly dependent on the visual similarity between the source image and the target class. 2) many of the resultant attacks resemble members of the target class and so cease to be “adversarial” – i.e., they may also be misclassified by humans. These findings suggest that CapsNets with class conditional reconstructions have the potential to address the real issue with adversarial examples – networks should make predictions based on the same properties of the image that people use rather than using features that can be manipulated by an imperceptible adversarial attack.
+
+In summary, our main contributions are:
+
+• We propose a class-conditional capsule reconstruction based detection method to detect standard white-box/black-box adversarial examples on three datasets. This detection mechanism is attack-agnostic and is successfully extended to standard convolutional neural networks. We test our detection mechanism on the corrupted MNIST dataset and show that it can work as a general out-of-distribution detector.   
+• A stronger reconstructive attack is specifically designed to attack our detection mechanism but becomes less successful in fooling the classifier.   
+• We perform extensive qualitative studies to explain the superior performance of CapsNets in detecting adversarial examples compared to CNNs. The results suggest that the features captured by CapsNets are more aligned with human perception.
+
+# 2 RELATED WORK
+
+Adversarial examples were first introduced in (Biggio et al., 2013; Szegedy et al., 2013), where a given image was modified by following the gradient of a classifier’s output with respect to the image’s pixels. Goodfellow et al. (2014) then developed the more efficient Fast Gradient Sign method (FGSM), which can change the label of the input image $X$ with a similarly imperceptible perturbation that is constructed by taking an $\epsilon$ step in the direction of the gradient. Later, the Basic Iterative Method (BIM) (Kurakin et al., 2016) and Projected Gradient Descent (Madry et al., 2017) can generate stronger attacks improved on FGSM by taking multiple steps in the direction of the gradient. In addition, Carlini & Wagner (2017b) proposed another iterative optimization-based method to construct strong adversarial examples with small perturbations.
+
+An early approach to reducing vulnerability to adversarial examples was proposed by (Goodfellow et al., 2014), where a network was trained on both clean images and adversarially perturbed ones. Since then, there has been a constant “arms race” between better attacks and better defenses; Kurakin et al. (2018) provide an overview of this field. However, many defenses against adversarial examples have been demonstrated to be an effect of “obfuscated gradients” and can be further circumvented under the white-box setting (Athalye et al., 2018).
+
+Another line of work attempts to circumvent adversarial examples by detecting them with a separatelytrained classifier (Gong et al., 2017; Grosse et al., 2017; Metzen et al., 2017) or using statistical properties (Hendrycks & Gimpel, 2016; Li & Li, 2017; Feinman et al., 2017; Grosse et al., 2017). However, many of these approaches were subsequently shown to be flawed (Carlini & Wagner, 2017a; Athalye et al., 2018). The most recent work in detecting adversarial examples (Roth et al., 2019) that has a $9 9 \%$ true positive rate on CIFAR-10 dataset (Krizhevsky, 2009) has also been fully bypassed by later work (Hosseini et al., 2019) which decreased the true positive rate to less than $2 \%$ .
+
+Similar to our work, Schott et al. (2018) also investigated the effectiveness of a class-conditional generative model as a defense mechanism for MNIST digits. However, we differ in some important ways. Their model is in some ways the opposite of ours - they first attempt to generate the input, and then make a classification on the resulting generated images, whereas our method attempts to first classify the input, making use of an otherwise unchanged capsule classification model, and then generates the input from a high level representation. As such, our method does not increase the computational overhead of classifying the input, compared to the approach of Schott et al. (2018). In addition, the work of Schott et al. (2018) is only applied to MNIST, so our results on the more complex datasets represent an improvement.
+
+# 3 PRELIMINARIES
+
+Adversarial Examples Given a clean test image $x$ , its corresponding label $y$ , and a classifier $f ( \cdot )$ which predicts a class label given an input, we refer to $x ^ { \prime } = x + \delta$ as an adversarial example if it is able to fool the classifier into making a wrong prediction $f ( x ^ { \prime } ) \neq f ( x ) = y .$ . The small adversarial perturbation $\delta$ (where “small” is measured under some norm) causes the adversarial example $x ^ { \prime }$ to appear visually similar to the clean image $x$ but to be classified differently. In the unrestricted case where we only require that $f ( x ^ { \prime } ) \neq y$ , we refer to $x ^ { \prime }$ as an “untargeted adversarial example”. A more powerful attack is to generate a “targeted adversarial example”: instead of simply fooling the classifier to make a wrong prediction, we force the classifier to predict some targeted label $f ( x ^ { \prime } ) = t \neq y$ . In this paper, the target label $t$ is selected uniformly at random as any label which is not the ground-truth correct label. As is standard practice in the literature, in this paper we test our detection mechanism on three $\ell _ { \infty }$ norm based attacks (fast gradient sign method (FGSM) (Goodfellow et al., 2014), the basic iterative method (BIM) (Kurakin et al., 2016), projected gradient descent (PGD) (Madry et al., 2017)) and one $\ell _ { 2 }$ norm based attack (Carlini-Wagner (CW) (Carlini & Wagner, 2017b)).
+
+Capsule Networks Capsule Networks (CapsNets) are an alternative architecture for neural networks (Sabour et al., 2017; Hinton et al., 2018). In this work we make use of the CapsNet architecture detailed by (Sabour et al., 2017). Unlike a standard neural network which is made up of layers of scalar-valued units, CapsNets are made up of layers of capsules, that output a vector or matrix. Intuitively, just as one can think of the activation of a unit in a normal neural network as the presence of a feature in the input, the activation of a capsule can be thought of as both the presence of a feature and the pose parameters that represent attributes of that feature. A top-level capsule in a classification network therefore outputs both a classification and pose parameters that represent the instance of that class in the input. This high level representation allows us to train a reconstruction network.
+
+Threat Model In this paper, we test our detection mechanism against both white-box and black-box attacks. For white-box attacks, the adversary has full access to the model as well as its parameters. In particular, the adversary is allowed to compute the gradient through the model to generate adversarial examples. To perform black-box attacks, the adversary is allowed to know the network architecture but not its parameters. Therefore, we retrain a substitute model that has the same architecture as the target model and generate adversarial examples by attacking the substitute model. Then we transfer these attacks to the target model. For $\ell _ { \infty }$ based attacks, we always control the $\ell _ { \infty }$ norm of the adversarial perturbation to be within a relatively small bound $\epsilon _ { \infty }$ , specific to each dataset.
+
+# 4 DETECTING ADVERSARIAL IMAGES BY RECONSTRUCTION
+
+To detect adversarial images, we make use of the reconstruction network proposed in (Sabour et al., 2017), which takes pose parameters $v$ as input and outputs the reconstructed image $r ( v )$ . The reconstruction network is simply a fully connected neural network with two ReLU hidden layers with 512 and 1024 units respectively, with a sigmoid output with the same dimensionality as the dataset. The reconstruction network is trained to minimize the $\ell _ { 2 }$ distance between the input image and the reconstructed image. This same network architecture is used for all the models and datasets we explore. The only difference is what is given to the reconstruction network as input.
+
+# 4.1 MODELS
+
+CapsNet The reconstruction network of the CapsNet is class-conditional: It takes in the pose parameters of all the class capsules and masks all values to 0 except for the pose parameters of the predicted class. We use this reconstruction network for detecting adversarial attacks by measuring the Euclidean distance between the input and a class conditional reconstruction. Specifically, for any given input $x$ , the CapsNet outputs a prediction $f ( x )$ as well as the pose parameters $v$ for all classes. The reconstruction network takes in the pose parameters and then selects the pose parameter corresponding to the predicted class, denoted as $v _ { f ( x ) }$ , to generate a reconstruction $r ( v _ { f ( x ) } )$ . Then we compute the $\ell _ { 2 }$ reconstruction distance $d ( \boldsymbol { x } ) = \| r ( \boldsymbol { v } _ { f ( \boldsymbol { x } ) } ) , \boldsymbol { x } \| _ { 2 }$ between the reconstructed image and the input image, and compare it with a pre-defined detection threshold $\theta$ (described below in Section 4.2). If the reconstruction distance ${ \bar { d } } ( x )$ is higher than the detection threshold $\theta$ , we flag the input as an adversarial example. Figure 1 (b) shows an example of histograms of reconstruction distances for natural images and typical adversarial examples.
+
+$\mathbf { C N N + C R }$ Although our strategy is inspired by the reconstruction networks used in CapsNets, the strategy can be extended to standard convolutional neural networks (CNNs). We create a similar architecture, CNN with conditional reconstruction $( \mathrm { C N N + C R } )$ ), by dividing the penultimate hidden layer of a CNN into groups corresponding to each class. The sum of each neuron group serves as the logit for that particular class and the group itself serves the same purpose as the pose parameters in the CapsNet. We use the same masking mechanism as Sabour et al. (2017) to select the pose parameter corresponding to the predicted label $v _ { f ( x ) }$ and generate the reconstruction based on the selected pose parameters. In this way we extend the class-conditional reconstruction network to standard CNNs.
+
+$\mathbf { C N N + R }$ We can also create a more na¨ıve implementation of our strategy by simply computing the reconstruction from the activations in the entire penultimate layer without any masking mechanism. We call this model the $\mathrm { " C N N { + } R } \mathrm { " }$ model. In this way we are able to study the effect of conditioning on the predicted class.
+
+# 4.2 DETECTION THRESHOLD
+
+We find the threshold $\theta$ for detecting adversarial inputs by measuring the reconstruction error between a validation input image and its reconstruction. If the distance between the input and the reconstruction is above the chosen threshold $\theta$ , we classify the data as adversarial. Choosing the detection threshold $\theta$ involves a trade-off between false positive and false negative detection rates. The optimal threshold depends on the probability of the system being attacked. Such a trade-off is discussed by Gilmer et al. (2018a). In our experiments we don’t tune this parameter and simply set it as the 95th percentile of validation distances. This means our false positive rate on real validation data is $5 \%$ .
+
+Table 1: Success Rate / Undetected Rate of white-box targeted and untargeted attacks on the MNIST dataset. In the table, $S _ { t } / R _ { t }$ is shown for targeted attacks and $S _ { u } / R _ { u }$ is presented for untargeted attacks. A smaller success rate and undetected rate means a stronger defense model. Full results for FashionMNIST and SVHN can be seen in Table 5 in the Appendix.   
+
+<table><tr><td rowspan="2">Networks</td><td colspan="4">Targeted (%)</td><td colspan="4">Untargeted (%)</td></tr><tr><td>FGSM</td><td>BIM</td><td>PGD</td><td>CW</td><td>FGSM</td><td>BIM</td><td>PGD</td><td>CW</td></tr><tr><td>CapsNet</td><td>3/0</td><td>82/0</td><td>86/0</td><td>99/2</td><td>11/0</td><td>99/0</td><td>99/0</td><td>100/19</td></tr><tr><td>CNN+CR</td><td>16/0</td><td>93/0</td><td>95/0</td><td>89/8</td><td>85/0</td><td>100/0</td><td>100/0</td><td>100/28</td></tr><tr><td>CNN+R</td><td>37/0</td><td>100/0</td><td>100/0</td><td>100/47</td><td>64/0</td><td>100/0</td><td>100/0</td><td>100/63</td></tr></table>
+
+# 4.3 EVALUATION METRICS
+
+We use Success Rate to measure the success of attacks. For targeted attacks, the success rate $S _ { t }$ is defined as the proportion of inputs which are classified as the target class, $\begin{array} { r } { S _ { t } = \frac { 1 } { N } \sum _ { i } ^ { N } ( f ( x _ { i } ^ { \prime } ) = } \end{array}$ $t _ { i }$ ), while the success rate for untargeted attacks is defined as the proportion of inputs which are misclassified, $\begin{array} { r } { S _ { u } ~ = ~ \frac { 1 } { N } \sum _ { i } ^ { N } ( f ( x _ { i } ^ { \prime } ) ~ \neq ~ y _ { i } ) } \end{array}$ . Previous work (Carlini & Wagner, $2 0 1 7 \mathrm { a }$ ; Hosseini et al., 2019) used the True Positive Rate to measure the proportion of adversarial examples that are detected, which alone is insufficient to measure the ability of different detection mechanism because the unsuccessful adversarial examples do not have to be detected. Therefore, in this paper, we propose to use the Undetected Rate: the proportion of attacks that are successful and undetected to evaluate the detection mechanism. For targeted attacks, the undetected rate is defined as $\begin{array} { r } { R _ { t } = \frac { 1 } { N } \sum _ { i } ^ { N } ( f ( x _ { i } ^ { \prime } ) = t _ { i } ) \cap ( d ( x _ { i } ^ { \prime } ) \leq \theta ) } \end{array}$ , where $d ( \cdot )$ computes the reconstruction distance of the input and $\theta$ denotes the detection threshold introduced in Section 4.2. Similarly, the undetected rate for untargeted attacks Ru can be defined as Ru = 1N PNi (f (x0i) 6= yi) ∩ (d(x0i) ≤ θ). The smaller undetected rate can also be used to evaluate the attacks (higher is better). We also plot the Undetected Rate vs. False Positive Rate curve to compare the detection performance between different models, where False Positive Rate is defined as the proportion of clean examples that are misclassified as the adversarial example by the detection method.
+
+# 4.4 TEST MODELS AND DATASETS
+
+In all experiments, all three models (CapsNet, $\mathrm { C N N + R }$ , and $\mathbf { C N N + C R }$ ) have the same number of parameters and were trained with Adam (Kingma & Ba, 2014) for the same number of epochs. In general, all models achieved similar test accuracy. We did not do an exhaustive hyperparameter search on these models, instead we chose hyperparameters that allowed each model to perform roughly equivalently on the test sets. We run experiments on three datasets: MNIST (LeCun et al., 1998), FashionMNIST (Xiao et al., 2017), and SVHN (Netzer et al., 2011). The test error rate for each model on these three datasets, as well as details of the model architectures, can be seen in Section A and Section B in the Appendix.
+
+# 5 EXPERIMENTS
+
+We first demonstrate how reconstruction networks can detect standard white and black-box attacks in addition to naturally corrupted images. Then, we introduce the “reconstructive attack”, which is specifically designed to circumvent our defense and show that it is a more powerful attack in this setting. Based on this finding, we qualitatively study the kind of misclassifications caused by the reconstructive attack and argue that they suggest that CapsNets learn features that are better aligned with human perception.
+
+# 5.1 STANDARD ATTACKS
+
+White Box We present the success and undetected rates for several targeted and untargeted attacks on MNIST (Table 1), FashionMNIST, and SVHN (Table 5 presented in the Appendix). Our method is able to accurately detect many attacks with very low undetected rates. Capsule models almost always have the lowest undetected rates out of our three models. It is worth noting that this method performs best with the simplest dataset, MNIST, and that the highest undetected rates are found with the Carlini-Wagner attack on the SVHN dataset. This illustrates both the strength of this attack and a shortcoming of our defense, namely that our detection mechanism relies on $\ell _ { 2 }$ image distance as a proxy for visual similarity, and in the case of higher dimensional color datasets such as SVHN, this proxy is less meaningful.
+
+Table 2: Error Rate/Undetected Rate on the Corrupted MNIST dataset. A smaller error rate and undetected rate means a better defense model.   
+
+<table><tr><td>Corruption</td><td>Clean</td><td>Gaussian Noise</td><td>Gaussian Blur</td><td>Line</td><td>Dotted Line</td><td>Elastic Transform</td></tr><tr><td>CapsNet</td><td>0.6/0.2</td><td>12.1/0.0</td><td>10.3/4.1</td><td>19.6/0.1</td><td>4.3/0.0</td><td>11.3/0.8</td></tr><tr><td>CNN+CR</td><td>0.7/0.3</td><td>9.8/0.0</td><td>6.7/4.2</td><td>17.6/0.1</td><td>4.2/0.0</td><td>11.1/1.1</td></tr><tr><td>CNN+R</td><td>0.6/0.4</td><td>6.7/0.0</td><td>8.9/6.4</td><td>18.9/0.1</td><td>3.1/0.0</td><td>12.2/2.1</td></tr><tr><td>Corruption</td><td>Saturate</td><td>JPEG</td><td>Quantize</td><td>Sheer</td><td>Spatter</td><td>Rotate</td></tr><tr><td>CapsNet</td><td>3.5/0.0</td><td>0.8/0.4</td><td>0.7/0.1</td><td>1.6/0.4</td><td>1.9/0.2</td><td>6.5/2.2</td></tr><tr><td>CNN+CR</td><td>1.5/0.0</td><td>0.8/0.5</td><td>0.9/0.1</td><td>2.1/0.4</td><td>1.8/0.4</td><td>6.1/1.6</td></tr><tr><td>CNN+R</td><td>1.2/0.0</td><td>0.7/0.5</td><td>0.7/0.2</td><td>2.2/0.7</td><td>1.8/0.4</td><td>6.5/3.4</td></tr><tr><td>Corruption</td><td>Contrast</td><td>Inverse</td><td>Canny Edge</td><td>Fog</td><td>Frost</td><td>Zigzag</td></tr><tr><td>CapsNet</td><td>92.0/0.0</td><td>91.0/0.0</td><td>21.5/0.0</td><td>83.7/0.0</td><td>70.6/0.0</td><td>16.9/0.0</td></tr><tr><td>CNN+CR</td><td>72.0/32.6</td><td>78.1/0.0</td><td>34.6/0.0</td><td>66.0/0.5</td><td>37.6/0.0</td><td>18.4/0.0</td></tr><tr><td>CNN+R</td><td>73.4/49.4</td><td>88.1/0.0</td><td>23.4/0.0</td><td>65.6/0.1</td><td>36.2/0.0</td><td>17.5/0.0</td></tr></table>
+
+Black Box We also tested our detection mechanism results on black box attacks. Given the low undetected rates in the white-box settings, it is not surprising that our detection method is able to detect black box attacks as well. In fact, on the MNIST dataset the capsule model is able to detect all targeted and untargeted PGD attacks. Both the CNN-R and the CNN-CR models are able to detect the black box attacks as well, but with a relatively higher undetected rate. A table of these results can be seen in Table 7 in the Appendix.
+
+# 5.2 CORRUPTION ATTACKS
+
+Recent work has argued that improving the robustness of neural networks to $\ell _ { p }$ norm bounded adversarial attacks should not come at the expense of increasing error rates under distributional shifts that do not affect human classification rates and are likely to be encountered in the “realworld” (Gilmer et al., 2018a). For example, if an image is corrupted due to adverse weather, lighting, or occlusion, we might hope that our model can continue to provide reliable predictions or detect the distributional shift. We can test our detection method on its ability to detect these distributional shifts by making use of the Corrupted MNIST dataset (Mu & Gilmer, 2019). This data set contains many visual transformations of MNIST that do not seem to affect human performance, but nevertheless are strongly misclassified by state-of-the-art MNIST models. Our three models can almost always detect these distributional shifts (in all corruptions CapsNets have either a small undetected rate or an undetected rate of 0). The error rate (the proportion of misclassified input) and undetected rate of three test models on the Corrupted MNIST dataset is shown in Table 2. Please refer to Figure 7 and Figure 8 in the Appendix for visualization of Corrupted MNIST.
+
+# 5.3 RECONSTRUCTIVE ATTACKS
+
+Thus far we have only evaluated previously-defined attacks. Following the suggestion in (Carlini & Wagner, 2017a) that detection methods need to show effectiveness towards defense-aware attacks, we introduce an attack specifically designed to take into account our defense mechanism. In order to construct adversarial examples that cannot be detected by the network, we propose a two-stage optimization method to generate a “reconstructive attack”.
+
+Table 3: Success rate and the worst case undetected rate of white-box targeted and untargeted reconstructive attacks. $S _ { t } / R _ { t }$ is shown for targeted attacks and $S _ { u } / R _ { u }$ is presented for untargeted attacks. The worst case undetected rate is reported via tuning the hyperparameter $\beta$ in Eqn 1 and Eqn 2. The best defense models are shown in bold (smaller success rate and undetected rate is better). All the numbers are shown in $\%$ . A full table with more attacks can be seen in Table 6 in Appendix.   
+
+<table><tr><td></td><td colspan="2">MNIST</td><td colspan="2">FASHION</td><td colspan="2">SVHN</td></tr><tr><td></td><td>Targeted R-PGD</td><td>Untargeted R-PGD</td><td>Targeted R-PGD</td><td>Untargeted R-PGD</td><td>Targeted R-PGD</td><td>Untargeted R-PGD</td></tr><tr><td>CapsNet</td><td>50.7/33.7</td><td>88.1/37.9</td><td>53.7/29.8</td><td>84.9/75.5</td><td>82.0/79.2</td><td>98.9/97.5</td></tr><tr><td>CNN+CR</td><td>98.6/68.1</td><td>99.4/87.7</td><td>89.8/84.4</td><td>91.5/86.0</td><td>99.0/97.9</td><td>99.9/99.5</td></tr><tr><td>CNN+R</td><td>95.5/71.2</td><td>95.1/70.5</td><td>94.6/88.4</td><td>98.9/90.0</td><td>99.5/99.3</td><td>100.0/99.9</td></tr></table>
+
+![](images/dcef3ee1e045e15cdcffd265fc6c139d590570c97f184c878a84ea161f509e47.jpg)  
+Figure 2: The undetected rate of the white-box targeted defense-aware R-PGD attack versus the False Positive Rate on the MNIST, Fashion-MNIST and SVHN datasets.
+
+Untargeted Reconstructive Attacks To construct untargeted reconstructive attacks, we first update the perturbation based on the gradient of the cross-entropy loss function following a standard FGSM attack (Goodfellow et al., 2014), that is:
+
+$$
+\delta \gets \mathrm { c l i p } _ { \epsilon } ( \delta + c \cdot \beta \cdot \mathrm { s i g n } ( \nabla _ { \delta } \ell _ { n e t } ( f ( x + \delta ) , y ) ) ) ,
+$$
+
+where $\ell _ { n e t } ( f ( \cdot ) , y )$ is the cross-entropy loss function, $\epsilon$ is the $\ell _ { \infty }$ bound for our attacks, $c$ is a hyperparameter controlling the step size in each iteration and $\beta$ is a hyperparameter which balances the importance of the cross-entropy loss and the reconstruction loss (explained further below). In the second stage, we focus on constraining the reconstructed image from the newly predicted label to have a small reconstruction distance by updating $\delta$ according to
+
+$$
+\delta \gets \mathrm { c l i p } _ { \epsilon } ( \delta - c \cdot ( 1 - \beta ) \cdot \mathrm { s i g n } ( \nabla _ { \delta } ( \| r ( v _ { f ( x + \delta ) } ) - ( x + \delta ) \| _ { 2 } ) ) ) ,
+$$
+
+where $r \big ( v _ { f ( x + \delta ) } \big )$ is the class-conditional reconstruction based on the predicted label $f ( x + \delta )$ in a CapsNet or $\mathrm { C N N + C R }$ network. The $\delta$ used here is the optimized $\delta$ from the first stage. $\| r ( v _ { f ( x + \delta ) } ) -$ $( x + \delta ) \| _ { 2 }$ is the $\ell _ { 2 }$ reconstruction distance between the reconstructed image and the input image. Since the $\mathrm { C N N + R }$ network does not use the class conditional reconstruction, we simply use the reconstructed image without the masking mechanism. According to Eqn 1 and Eqn 2, we can see that $\beta$ balances the importance between the success rate of attacks and the reconstruction distance. This hyperparameter was tuned for each model and each dataset in order to create the strongest attacks. The success rate and undetected rate change as this parameter, which is shown in Figure 9 in Appendix.
+
+Targeted Reconstructive Attacks We perform a similar two-stage optimization to construct targeted reconstructive attacks, by defining a target label and attempting to maximize the classification probability of this label, and minimize the reconstruction error from corresponding capsule. Because the targeted label is given, another way to construct targeted reconstructive attacks is to combine these two stages into one stage via minimizing the loss function $\ell = \boldsymbol { \beta } \cdot \ell _ { n e t } ( f ( x + \delta ) , y ) + ( 1 - \beta ) \cdot \| \boldsymbol { r } ( v _ { f ( x + \delta ) } ) - ( x + \delta ) \| _ { 2 }$ . We implemented both of these targeted reconstructive attacks and found that the two-stage version is a stronger attack. Therefore, all the Reconstructive Attack experiments performed in this paper are based on two-stage optimization.
+
+![](images/3305f2537867e2d22b33557a43922ed39ef464bb4d5a47f2d33130e838f37e08.jpg)  
+Figure 3: The defense-aware R-PGD attack is tested on the CIFAR-10 dataset with $\epsilon _ { \infty } = 8 / 2 5 5$ . Left: The undetected rate of white-box/black-box defense-aware R-PGD versus the Fasle Positive Rate for the clean examples. The test model is our CapsNet. Right: The undetected rate of white-box defense-aware R-PGD versus the Fasle Positive Rate for the clean examples. The test model is our CapsNet using class-conditional reconstruction, “CapsNet All” using all capsule information, and the DeepCaps (Rajasegaran et al., 2019) using class-independent capsule information.
+
+We build our reconstructive attack based on the standard PGD attack, denoted as R-PGD, and test the performance of our detection models against this reconstructive attack in a white-box setting (white-box Reconstructive FGSM and BIM are reported in Table 6 in the Appendix). Comparing Table 1 and Table 3, we can see that the Reconstructive Attack is significantly less successful at changing the models prediction (lower success rates than the standard attack). However, this attack is more successful at fooling our detection method. For all attacks and datasets the capsule model has the lowest attack success rate and the lowest undetected rate. We report results for black-box R-PGD attacks in Table 7 in the Appendix, which suggest similar conclusions.
+
+In addition, we report the undetected rate of the white-box targeted defense-aware R-PGD attack versus the False Positive Rate on the MNIST, Fashion-MNIST and SVHN datasets in Figure 2. We can clearly see that the undetected rate of the defense-aware attack against CapsNet is significantly smaller than the CNN-based networks, which suggests that CapsNets are more robust against adversarial attacks. Furthermore, CNN with class-conditional reconstruction $\mathrm { C N N + C R }$ ) has smaller undetected rate at the same False Positive Rate compared to the CNN without class-conditional reconstruction $( \mathrm { C N N + R } )$ , which suggests the class-conditional information is helpful in our models to improve the robustness against adversarial attacks.
+
+# 5.4 CIFAR-10 DATASET
+
+In order to show that our method based on CapsNet is capable to scale up to more complex datasets, we test our detection method with a deeper reconstruction network on CIFAR-10 (Krizhevsky, 2009). The classification accuracy on the clean test dataset is $9 2 . 2 \%$ . In addition, we display the undetected rate of the white-box/black-box defense-aware R-PGD attack against CapsNets versus the False Positive Rate in Figure 3 (Left), where we can see a significant drop of the undetected rate of black-box R-PGD compared to the white-box setting. This indicates the CapsNets greatly reduce the attack transferability and the threat of black-box attacks.
+
+Class-conditional Information To investigate the effectiveness of the class-conditional information in the reconstruction network, we compare our CapsNet based on (Sabour et al., 2017) with the other two variants of CapsNets: “CapsNet All” and “DeepCaps” (Rajasegaran et al., 2019). In “CapsNet All”, we remove the masking mechanism in the CapsNet and use all the capsules to do the reconstruction. In “DeepCaps”, we extract the winning-capsule information as a single vector and used it as the input for the reconstruction network instead of using a masking mechanism to mask out the losing capsules information. In this way, the class information in DeepCaps is more explicitly fed into the reconstruction network. As shown in Figure 3 (right), our CapsNet has the best detection performance (the lowest undetected rate at the same False Positive Rate) compared to the other two
+
+![](images/c56b33d8cdce5d8097eb9eb90e235535bcc6ffb5b8dd0841e9a8552d776d4812.jpg)
+
+![](images/1c871acd5f931848f081ff2f41686870d3b7f5acb5a9b95c3c7d55a07d452d6a.jpg)  
+Figure 4: This diagram visualizes the adversarial success rates for each source/target pair for targeted R-PGD attacks on Fashion-MNIST with $\epsilon _ { \infty } = 2 5 / 2 5 5$ . The size of the box at position x, y represents the success rate of adversarially perturbing inputs of class $\mathbf { X }$ to be classified as class y. We can see that there is significantly higher variance for the CapsNet model than for the two CNN models.   
+Figure 5: These are randomly sampled (not cherry picked) successful and undetected adversarial attacks created by R-PGD with a target class of 0 for each model on the SVHN dataset $\epsilon _ { \infty } = 2 5 / 2 5 5 )$ . We can see that for the capsule model, many of the attacks are not “adversarial” as they resemble members of the target class.
+
+Capsule models. “DeepCaps” performs slightly worse than our “CapsNet” and “CapsNet All” has the worst detection performance. Therefore, we conclude that the class-conditional information used in the reconstruction network increases the model’s robustness to adversarial attack. This also holds true to CNN-based networks because $\mathrm { C N N + C R }$ has a better detection performance than $\mathrm { C N N + R }$ , shown in Figure 2.
+
+# 6 VISUAL COHERENCE OF THE RECONSTRUCTIVE ATTACK
+
+The great success of CapsNet over CNN-based models motivates us to further diagnose the generated adversarial examples for CapsNets. If our true aim in adversarial robustness research is to create models that make predictions based on reasonable and human-observable features, then we would prefer models that are more likely to misclassify a “shirt” as a “t-shirt” (in the case of FashionMNIST) than to misclassify a “bag” as a “sweater”. For a model to behave ideally, the success of an adversarial perturbation would be related to the visual similarity between the source and the target class. By visualizing a matrix of adversarial success rates between each pair of classes (shown in Figure 4), we can see that for the capsule model there is a great variance between the source and target class pairs and that the success rate of attacks is highly related to the visual similarity of the classes. However, this is not the case for either of the other two CNN-based models.
+
+Thus far we have treated all attacks as equal. However, a key component of an adversarial example is that it is visually similar to the source image, and that it does not resemble the adversarial target class. The adversarial research community makes use of a small epsilon bound as a mechanism for ensuring that the resultant adversarial attacks are visually unchanged from the source image. For standard attacks against CNN-based models this heuristic is sufficient, because taking gradient steps in the image space in order to have a network misclassify an image normally results in something visually similar to the source image. But this is not the case for adversarial attacks against CapsNets. As shown in Figure 5, when we use R-PGD to attack the CapsNet, many of the resultant attacks resemble members of the target class. In this way, they stop being “adversarial”. As such, an attack detection method which does not detect them as adversarial is arguably behaving correctly. This puts the previously undetected rates presented earlier in a new light, and illustrates a difficulty in the evaluation of adversarial attacks and defenses. In addition, it should be noted that this phenomenon rarely occurs in a standard convolutional neural network, which suggests that the features captured by CapsNet are more aligned with human perception.
+
+# 7 DISCUSSION
+
+Our detection mechanism relies on a similarity metric (i.e. a measure of reconstruction error) between the reconstruction and the input. This metric is required both during training in order to train the reconstruction network and during test time in order to flag adversarial examples. In the four datasets we have evaluated, the distance between examples roughly correlates with semantic similarity. However, this may not be the case for images in more complex datasets such as the SUN dataset (Xiao et al., 2010) and ImageNet (Deng et al., 2009), in which two images may be similar in terms of semantic content but nevertheless have significant $\ell _ { 2 }$ distance. A better similarity metric (Theis et al., 2015; Zhang et al., 2018) can be further explored to extend our methods to more complex problems. Furthermore our reconstruction network is trained on a hidden representation of one class but is trained to reconstruct the entire input. In datasets without distractors or backgrounds, this is not a problem. But in the case of ImageNet, in which the object responsible for the classification is not the only object in the image, attempting to reconstruct the entire input from a class encoding seems misguided.
+
+# 8 CONCLUSION
+
+We have presented a class-conditional reconstruction-based detection method that does not rely on a specific predefined adversarial attack. We have shown that by reconstructing the input from the internal class-conditional representation, our system is able to accurately detect black-box and white-box FGSM, BIM, PGD, and CW attacks. We then proposed a new attack to beat our defense - the Reconstructive Attack - in which the adversary optimizes not only the classification loss but also minimizes the reconstruction loss. We showed that this attack was able to fool our detection mechanism but with a much smaller success rate than a standard attack.
+
+Compared to CNN-based models, we showed that the CapsNet was able to detect adversarial examples with greater accuracy on all the datasets we explored. To further explain the success of CapsNet, we qualitatively showed that the success of the reconstructive attack was highly related to the visual similarity between the target class and the source class for the CapsNet. In addition, we showed that images generated by this reconstructive attack to attack the CapsNet are not typically adversarial, i.e. many of the resultant attacks resemble members of the target class even with a small $\ell _ { \infty }$ norm bound. These are not the case for the CNN-based models. The extensive qualitative studies indicate that the capsule model relies on visual features similar to those used by humans. We believe this is a step towards solving the true problem posed by adversarial examples.
+
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+
+# APPENDIX
+
+# A NETWORK ARCHITECTURES
+
+Figure 6 shows the architecute of the capsule network, the CNN reconstruction model and the CNN conditional reconstruction model used for experiments on MNIST, FashionMNIST and SVHN dataset. MNIST and Fashion MNIST have exactly the same architectures while we use larger models for SVHN. Note that the only difference between the CNN reconstruction $( \mathrm { C N N + R } )$ ) and the CNN conditional reconstruction $\mathbf { \left( C N N + C R \right) }$ ) is the masking procedure on the input to the reconstruction network based on the predicted class. All three models have the same number of parameters.
+
+![](images/6f3aa886fbab5409364bc7abf70efda9eeffe18088432df460c2b265abe5aae5.jpg)  
+Figure 6: The architecture for the CapsNet, $\mathrm { C N N + R }$ and $\mathrm { C N N + C R }$ model used for our experiments on MNIST (LeCun et al., 1998), FashionMNIST (Xiao et al., 2017), and SVHN (Netzer et al., 2011).
+
+# B TEST MODELS
+
+The error rate of each test model used in the paper are presented in Table 4. We ensure that they have similar performance.
+
+Table 4: Error rate of each model when the input are clean test images in each dataset.   
+
+<table><tr><td>Dataset</td><td>CapsNet</td><td>CNN+CR</td><td>CNN+R</td></tr><tr><td>MNIST</td><td>0.6%</td><td>0.7%</td><td>0.6%</td></tr><tr><td>FashionMNIST</td><td>9.6%</td><td>9.5%</td><td>9.3%</td></tr><tr><td>SVHN</td><td>10.7%</td><td>9.3%</td><td>9.5%</td></tr></table>
+
+# C IMPLEMENTATION DETAILS
+
+For all the $\ell _ { \infty }$ based adversarial examples, the $\ell _ { \infty }$ norm of the perturbations is bound by $\epsilon$ , which is set to 0.3, 0.1, 0.1 for MNIST, Fashion MNIST and SVHN dataset respectively following previous work (Madry et al., 2017; Song et al., 2017). In FGSM based attacks, the step size $c$ is 0.05. In BIM-based (Kurakin et al., 2016) and PGD-based (Madry et al., 2017) attacks, the step size $c$ is 0.01 for all the datasets and the number of iterations are 1000, 500 and 200 for MNIST, Fashion MNIST and SVHN dataset respectively. We choose a sufficiently large number of iterations to ensure the attacks has converged.
+
+We use the publicly released code from the authors of (Carlini & Wagner, 2017b) to perform the CW attack for our models. The number of iterations are set to 1000 for all three datasets.
+
+# D WHITE BOX STANDARD ATTACKS
+
+The results of four white box standard attacks on the three datasets are shown in Table 5.
+
+Table 5: Success rate and undetected rate of white-box targeted and untargeted attacks. In the table, $S _ { t } / R _ { t }$ is shown for targeted attacks and $S _ { u } / R _ { u }$ is presented for untargeted attacks.   
+
+<table><tr><td rowspan="2">Networks</td><td colspan="4">Targeted (%) FGSM</td><td colspan="4">Untargeted (%) BIM</td></tr><tr><td>BIM</td><td></td><td>PGD</td><td>CW</td><td>FGSM</td><td></td><td>PGD</td><td>CW</td></tr><tr><td colspan="9">MNIST Dataset</td></tr><tr><td>CapsNet CNN+CR</td><td>3/0</td><td>82/0</td><td>86/0</td><td>99/2</td><td>11/0</td><td>99/0</td><td>99/0</td><td>100/19</td></tr><tr><td></td><td>16/0</td><td>93/0</td><td>95/0</td><td>89/8</td><td>85/0</td><td>100/0</td><td>100/0</td><td>100/28</td></tr><tr><td>CNN+R</td><td>37/0</td><td>100/0</td><td>100/0</td><td>100/47</td><td>64/0</td><td>100/0</td><td>100/0</td><td>100/63</td></tr><tr><td colspan="9">FASHION I MNISTDataset</td></tr><tr><td>CapsNet</td><td>715</td><td>54/9</td><td>55/10</td><td>100/26</td><td>35/29</td><td>86/50</td><td>87/51</td><td>100/68</td></tr><tr><td>CNN+CR</td><td>19/13</td><td>89/28</td><td>89/28</td><td>87/37</td><td>74/33</td><td>100/25</td><td>100/24</td><td>100/72</td></tr><tr><td>CNN+R</td><td>23/16</td><td>98/19</td><td>98/19</td><td>99/81</td><td>62/48</td><td>100/35</td><td>100/34</td><td>100/87</td></tr><tr><td colspan="9"> SVHN Dataset</td></tr><tr><td>CapsNet</td><td>22/20</td><td>83/45</td><td>84/46</td><td>100/90</td><td>74/67</td><td>99/70</td><td>99/68</td><td>100/94</td></tr><tr><td>CNN+CR CNN+R</td><td>24/23</td><td>99/90</td><td>99/90</td><td>99/93</td><td>87/82</td><td>100/90</td><td>100/89</td><td>100/90</td></tr><tr><td></td><td>26/24</td><td>100/86</td><td>100/86</td><td>100/94</td><td>88/82</td><td>100/92</td><td>100/92</td><td>100/95</td></tr></table>
+
+# E VISUALIZATION OF CORRUPTED MNIST DATASET
+
+Visualization of examples from Corrupted MNIST dataset (Mu & Gilmer, 2019) and the corresponding reconstructed images for each model are shown in Figure 7 and Figure 8.
+
+![](images/113b8f9ba68153f1165873917ce1cb3e89bb1e0528c4555e0ccba41783c0db7b.jpg)  
+Figure 7: Examples of Corrupted MNIST and the reconstructed image for each model. A red box represent that this input is flagged as an adversarial example while a green box represent this input has been misclassified and not been detected.
+
+![](images/588b2318b9774d1400fcd7cd32007fea6caf4a90beedb123af99676430103c5a.jpg)  
+Figure 8: Examples of Corrupted MNIST and the reconstructed image for each model. A red box represents that this input is flagged as an adversarial example while a green box represents that this input has been misclassified and not been detected.
+
+# F RECONSTRUCTIVE ATTACKS
+
+The results of Reconstructive FGSM, BIM and PGD on the three datasets are reported in Table 6.
+
+Table 6: Success rate and the worst case undetected rate of white-box targeted and untargeted reconstructive attacks. Below $S _ { t } / R _ { t }$ is shown for targeted attacks and $S _ { u } \bar { / } R _ { u }$ is presented for untargeted attacks.   
+
+<table><tr><td>Networks</td><td>R-FGSM</td><td>Targeted (%) R-BIM</td><td>R-PGD</td><td>R-FGSM</td><td>Untargeted (%) R-BIM</td><td>R-PGD</td></tr><tr><td colspan="7">MNIST Dataset</td></tr><tr><td>CapsNet</td><td>1.8/0.3</td><td>51.0/33.8</td><td>50.7/33.7</td><td>6.1/1.0</td><td>84.5/35.1</td><td>88.1/37.9</td></tr><tr><td>CNN+CR</td><td>7.6/0.5</td><td>98.0/68.1</td><td>98.6/68.1</td><td>41.7/3.2</td><td>96.5/86.8</td><td>99.4/87.7</td></tr><tr><td>CNN+R</td><td>16.9/3.3</td><td>86.3/65.9</td><td>95.5/71.2</td><td>25.9/8.1</td><td>82.9/67.8</td><td>95.1/70.5</td></tr><tr><td colspan="7">FASHION MNIST Dataset</td></tr><tr><td>CapsNet</td><td>6.5/5.8</td><td>53.3/28.4</td><td>53.7/29.8</td><td>33.3/29.9</td><td>85.3/75.9</td><td>84.9/75.5</td></tr><tr><td>CNN+CR</td><td>17.7/14.0</td><td>80.3/72.4</td><td>78.1/72.0</td><td>68.0/57.3</td><td>89.8/84.4</td><td>91.5/86.0</td></tr><tr><td>CNN+R</td><td>19.4/17.6</td><td>95.2/88.8</td><td>94.6/88.4</td><td>58.6/53.5</td><td>98.8/90.1</td><td>98.9/90.0</td></tr><tr><td colspan="7">SVHN Dataset</td></tr><tr><td>CapsNet</td><td>21.6/21.2</td><td>81.1/78.3</td><td>82.0/79.2</td><td>71.6/68.3</td><td>98.9/97.5</td><td>98.9/97.5</td></tr><tr><td>CNN+CR</td><td>24.2/22.6</td><td>98.5/97.6</td><td>99.0/97.9</td><td>86.0/82.3</td><td>99.9/99.5</td><td>99.9/99.5</td></tr><tr><td>CNN+R</td><td>26.6/25.8</td><td>99.6/99.4</td><td>99.5/99.3</td><td>87.1/84.5</td><td>100.0/99.9</td><td>100.0/99.9</td></tr></table>
+
+Figure 9 shows the plot of success rate and undetected rate versus the hyperparameter $\beta$ which balances the importance between attacking the classifier and fooling the detection mechanism in the targeted reconstructive PGD attacks on the MNIST dataset.
+
+![](images/8cddf9af8747c1350afc7e1fe0895c9b076be39b8d08daf81bdc3d2b1b2b77bc.jpg)  
+Figure 9: An example shows the plot of the success rate in (a) and undetected rate in (b) of targeted reconstructive PGD attack vesus the hyperparameter beta $\beta$ for each model on the MNIST test set. We set the max $\ell _ { \infty }$ norm $\epsilon = 0 . 3$ to create the attacks.
+
+# G BLACK BOX ATTACKS
+
+Table 7: Success rate and undetected rate of black-box targeted and untargeted attacks. In the table, $S _ { t } / R _ { t }$ is shown for targeted attacks and $S _ { u } / R _ { u }$ is presented for untargeted attacks. All the numbers are shown in $\%$ .   
+H VISUALIZATION OF ADVERSARIAL EXAMPLES AND RECONSTRUCTIONS   
+
+<table><tr><td colspan="8">MNIST Dataset</td></tr><tr><td>Targeted</td><td>CapsNet</td><td>CNN-CR</td><td>CNN-R</td><td>Untargeted</td><td>CapsNet</td><td>CNN-CR</td><td>CNN-R</td></tr><tr><td>PGD</td><td>1.5/0.0</td><td>7.8/0.0</td><td>7.4/0.0</td><td>PGD</td><td>8.5/0.0</td><td>32.6/0.0</td><td>27.6/0.0</td></tr><tr><td>R-PGD</td><td>4.2/1.0</td><td>18.3/11.0</td><td>11.3/4.8</td><td>R-PGD</td><td>10.4/2.4</td><td>42.7/24.9</td><td>25.2/8.9</td></tr></table>
+
+![](images/aacb183a4b1c4b86994c64eeb29370a753b73b8b45173db8b6994c9ba0e6df58.jpg)  
+Figure 10: The source clean image is presented in the first row with its reconstruction in the second row. For each model, the top row are the targeted adversarial examples and the bottom are the corresponding reconstruction image when the input are the PGD on the MNIST (left), R-PGD on the Fashion-MNIST (middle), CW on the SVHN (right).
+
+![](images/fb94341a4962dca46a6f2333f57b7519edbf866a127592d898866fe8f696c2a4.jpg)  
+Figure 11: These are randomly sampled (not cherry picked) inputs (top row) and the result of adversarially perturbing them with targeted R-PGD against the CapsNet model (other rows). Many of these attacks are not successful. Note the visual similarity between many of the attacks and the target class.

parse/train/Skgy464Kvr/Skgy464Kvr_content_list.json

@@ -0,0 +1,1674 @@
+[
+    {
+        "type": "text",
+        "text": "DETECTING AND DIAGNOSING ADVERSARIALIMAGES WITH CLASS-CONDITIONAL CAPSULERECONSTRUCTIONS",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yao Qin∗   \nUC San Diego   \nyaq007@eng.ucsd.edu ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Nicholas Frosst∗ Google Brain frosst@google.com ",
+        "bbox": [
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+            195,
+            558,
+            238
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Sara Sabour   \nGoogle Brain   \nsasabour@google.com   \nColin Raffel   \nGoogle Brain   \ncraffel@google.com ",
+        "bbox": [
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+            238
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Garrison Cottrell UC San Diego gary@eng.ucsd.edu ",
+        "bbox": [
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+            258,
+            557,
+            301
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Geoffrey Hinton   \nGoogle Brain   \ngeoffhinton@google.com ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
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+            352
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Adversarial examples raise questions about whether neural network models are sensitive to the same visual features as humans. In this paper, we first detect adversarial examples or otherwise corrupted images based on a class-conditional reconstruction of the input. To specifically attack our detection mechanism, we propose the Reconstructive Attack which seeks both to cause a misclassification and a low reconstruction error. This reconstructive attack produces undetected adversarial examples but with much smaller success rate. Among all these attacks, we find that CapsNets always perform better than convolutional networks. Then, we diagnose the adversarial examples for CapsNets and find that the success of the reconstructive attack is highly related to the visual similarity between the source and target class. Additionally, the resulting perturbations can cause the input image to appear visually more like the target class and hence become non-adversarial. This suggests that CapsNets use features that are more aligned with human perception and have the potential to address the central issue raised by adversarial examples. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            587,
+            336,
+            602
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Adversarial examples (Szegedy et al., 2013) are inputs that are designed by an adversary to cause a machine learning system to make a misclassification. A series of studies on adversarial attacks have shown that it is easy to cause misclassifications using visually imperceptible changes to an image under $\\ell _ { p }$ -norm based similarity metrics (Goodfellow et al., 2014; Kurakin et al., 2016; Madry et al., 2017; Carlini & Wagner, 2017b; Goodfellow et al., 2018). Since the discovery of adversarial examples, there has been a constant “arms race” between better attacks and better defenses. Many new defenses have been proposed (Song et al., 2017; Gong et al., 2017; Grosse et al., 2017; Metzen et al., 2017), only to be broken shortly thereafter (Carlini & Wagner, 2017a; Athalye et al., 2018). Hinton et al. (2018) showed that capsule models are more robust to simple adversarial attacks than CNNs but Michels et al. (2019) showed that this is not the case for all attacks. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The cycle of attacks and defenses motivates us to rethink both how we can improve the general robustness of neural networks as well as the high-level motivation for this pursuit. One potential path forward is to detect adversarial inputs, instead of attempting to accurately classify them (Schott et al., 2018; Roth et al., 2019). Recent work (Jetley et al., 2018; Gilmer et al., 2018b) argue that adversarial examples can exist within the data distribution, which implies that detecting adversarial examples based on an estimate of the data distribution alone might be insufficient. Instead, in this paper we develop methods for detecting adversarial examples by making use of class-conditional reconstruction networks. These sub-networks, first proposed by Sabour et al. (2017) as part of a Capsule Network (CapsNet), allow a model to produce a reconstruction of its input based on the identity and instantiation parameters of the winning capsule. Interestingly, we find that reconstructing an input from the capsule corresponding to the correct class results in a much lower reconstruction error than reconstructing the input from capsules corresponding to incorrect classes, as shown in Figure 1(a). Motivated by this, we propose using the reconstruction sub-network in a CapsNet as an attack-independent detection mechanism. Specifically, we reconstruct a given input from the pose parameters of the winning capsule and then detect adversarial examples by comparing the difference between the reconstruction distributions for natural and adversarial (or otherwise corrupted) images. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/a2c6adf0cf1f639c8b0fccf3ed956f8e21c832df077bcabef2310e41920598be.jpg",
+        "image_caption": [
+            "Figure 1: (a) The histogram of $\\ell _ { 2 }$ distances between the input and the reconstruction using the correct capsule or other capsules in CapsNet on the real MNIST images. Notice the stark difference between the distributions of reconstructions of the capsule corresponding to the correct class and other capsules. (b) The histograms of $\\ell _ { 2 }$ distances between the reconstruction and the input for real and adversarial images for the three models explored in this paper on the MNIST dataset. We use PGD (Madry et al., 2017) with the $\\ell _ { \\infty }$ bound $\\epsilon = 0 . 3$ to create the attacks. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We extend this detection mechanism to standard convolutional neural networks (CNNs) and show its effectiveness against black box and white box attacks on three image datasets; MNIST, FashionMNIST and SVHN. We show that capsule models achieve the strongest attack detection rates and accuracy on these attacks. We then test our method against a stronger attack, the Reconstructive Attack, specifically designed to attack our detection mechanism by generating adversarial examples with a small reconstruction error. With this attack we are able to create undetected adversarial examples, but we show that this attack is less successful in fooling the classifier than a non-reconstructive attack. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Among all these attacks, we find CapsNets perform the best in detecting adversarial examples. To explain the success of CapsNets over CNNs, we further diagnose the adversarial examples for CapsNets and find that 1) the success of the targeted reconstructive attack is highly dependent on the visual similarity between the source image and the target class. 2) many of the resultant attacks resemble members of the target class and so cease to be “adversarial” – i.e., they may also be misclassified by humans. These findings suggest that CapsNets with class conditional reconstructions have the potential to address the real issue with adversarial examples – networks should make predictions based on the same properties of the image that people use rather than using features that can be manipulated by an imperceptible adversarial attack. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In summary, our main contributions are: ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• We propose a class-conditional capsule reconstruction based detection method to detect standard white-box/black-box adversarial examples on three datasets. This detection mechanism is attack-agnostic and is successfully extended to standard convolutional neural networks. We test our detection mechanism on the corrupted MNIST dataset and show that it can work as a general out-of-distribution detector.   \n• A stronger reconstructive attack is specifically designed to attack our detection mechanism but becomes less successful in fooling the classifier.   \n• We perform extensive qualitative studies to explain the superior performance of CapsNets in detecting adversarial examples compared to CNNs. The results suggest that the features captured by CapsNets are more aligned with human perception. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            863,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Adversarial examples were first introduced in (Biggio et al., 2013; Szegedy et al., 2013), where a given image was modified by following the gradient of a classifier’s output with respect to the image’s pixels. Goodfellow et al. (2014) then developed the more efficient Fast Gradient Sign method (FGSM), which can change the label of the input image $X$ with a similarly imperceptible perturbation that is constructed by taking an $\\epsilon$ step in the direction of the gradient. Later, the Basic Iterative Method (BIM) (Kurakin et al., 2016) and Projected Gradient Descent (Madry et al., 2017) can generate stronger attacks improved on FGSM by taking multiple steps in the direction of the gradient. In addition, Carlini & Wagner (2017b) proposed another iterative optimization-based method to construct strong adversarial examples with small perturbations. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "An early approach to reducing vulnerability to adversarial examples was proposed by (Goodfellow et al., 2014), where a network was trained on both clean images and adversarially perturbed ones. Since then, there has been a constant “arms race” between better attacks and better defenses; Kurakin et al. (2018) provide an overview of this field. However, many defenses against adversarial examples have been demonstrated to be an effect of “obfuscated gradients” and can be further circumvented under the white-box setting (Athalye et al., 2018). ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Another line of work attempts to circumvent adversarial examples by detecting them with a separatelytrained classifier (Gong et al., 2017; Grosse et al., 2017; Metzen et al., 2017) or using statistical properties (Hendrycks & Gimpel, 2016; Li & Li, 2017; Feinman et al., 2017; Grosse et al., 2017). However, many of these approaches were subsequently shown to be flawed (Carlini & Wagner, 2017a; Athalye et al., 2018). The most recent work in detecting adversarial examples (Roth et al., 2019) that has a $9 9 \\%$ true positive rate on CIFAR-10 dataset (Krizhevsky, 2009) has also been fully bypassed by later work (Hosseini et al., 2019) which decreased the true positive rate to less than $2 \\%$ . ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Similar to our work, Schott et al. (2018) also investigated the effectiveness of a class-conditional generative model as a defense mechanism for MNIST digits. However, we differ in some important ways. Their model is in some ways the opposite of ours - they first attempt to generate the input, and then make a classification on the resulting generated images, whereas our method attempts to first classify the input, making use of an otherwise unchanged capsule classification model, and then generates the input from a high level representation. As such, our method does not increase the computational overhead of classifying the input, compared to the approach of Schott et al. (2018). In addition, the work of Schott et al. (2018) is only applied to MNIST, so our results on the more complex datasets represent an improvement. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 PRELIMINARIES ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Adversarial Examples Given a clean test image $x$ , its corresponding label $y$ , and a classifier $f ( \\cdot )$ which predicts a class label given an input, we refer to $x ^ { \\prime } = x + \\delta$ as an adversarial example if it is able to fool the classifier into making a wrong prediction $f ( x ^ { \\prime } ) \\neq f ( x ) = y .$ . The small adversarial perturbation $\\delta$ (where “small” is measured under some norm) causes the adversarial example $x ^ { \\prime }$ to appear visually similar to the clean image $x$ but to be classified differently. In the unrestricted case where we only require that $f ( x ^ { \\prime } ) \\neq y$ , we refer to $x ^ { \\prime }$ as an “untargeted adversarial example”. A more powerful attack is to generate a “targeted adversarial example”: instead of simply fooling the classifier to make a wrong prediction, we force the classifier to predict some targeted label $f ( x ^ { \\prime } ) = t \\neq y$ . In this paper, the target label $t$ is selected uniformly at random as any label which is not the ground-truth correct label. As is standard practice in the literature, in this paper we test our detection mechanism on three $\\ell _ { \\infty }$ norm based attacks (fast gradient sign method (FGSM) (Goodfellow et al., 2014), the basic iterative method (BIM) (Kurakin et al., 2016), projected gradient descent (PGD) (Madry et al., 2017)) and one $\\ell _ { 2 }$ norm based attack (Carlini-Wagner (CW) (Carlini & Wagner, 2017b)). ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Capsule Networks Capsule Networks (CapsNets) are an alternative architecture for neural networks (Sabour et al., 2017; Hinton et al., 2018). In this work we make use of the CapsNet architecture detailed by (Sabour et al., 2017). Unlike a standard neural network which is made up of layers of scalar-valued units, CapsNets are made up of layers of capsules, that output a vector or matrix. Intuitively, just as one can think of the activation of a unit in a normal neural network as the presence of a feature in the input, the activation of a capsule can be thought of as both the presence of a feature and the pose parameters that represent attributes of that feature. A top-level capsule in a classification network therefore outputs both a classification and pose parameters that represent the instance of that class in the input. This high level representation allows us to train a reconstruction network. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Threat Model In this paper, we test our detection mechanism against both white-box and black-box attacks. For white-box attacks, the adversary has full access to the model as well as its parameters. In particular, the adversary is allowed to compute the gradient through the model to generate adversarial examples. To perform black-box attacks, the adversary is allowed to know the network architecture but not its parameters. Therefore, we retrain a substitute model that has the same architecture as the target model and generate adversarial examples by attacking the substitute model. Then we transfer these attacks to the target model. For $\\ell _ { \\infty }$ based attacks, we always control the $\\ell _ { \\infty }$ norm of the adversarial perturbation to be within a relatively small bound $\\epsilon _ { \\infty }$ , specific to each dataset. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4 DETECTING ADVERSARIAL IMAGES BY RECONSTRUCTION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To detect adversarial images, we make use of the reconstruction network proposed in (Sabour et al., 2017), which takes pose parameters $v$ as input and outputs the reconstructed image $r ( v )$ . The reconstruction network is simply a fully connected neural network with two ReLU hidden layers with 512 and 1024 units respectively, with a sigmoid output with the same dimensionality as the dataset. The reconstruction network is trained to minimize the $\\ell _ { 2 }$ distance between the input image and the reconstructed image. This same network architecture is used for all the models and datasets we explore. The only difference is what is given to the reconstruction network as input. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1 MODELS ",
+        "text_level": 1,
+        "bbox": [
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+            386,
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+            398
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "CapsNet The reconstruction network of the CapsNet is class-conditional: It takes in the pose parameters of all the class capsules and masks all values to 0 except for the pose parameters of the predicted class. We use this reconstruction network for detecting adversarial attacks by measuring the Euclidean distance between the input and a class conditional reconstruction. Specifically, for any given input $x$ , the CapsNet outputs a prediction $f ( x )$ as well as the pose parameters $v$ for all classes. The reconstruction network takes in the pose parameters and then selects the pose parameter corresponding to the predicted class, denoted as $v _ { f ( x ) }$ , to generate a reconstruction $r ( v _ { f ( x ) } )$ . Then we compute the $\\ell _ { 2 }$ reconstruction distance $d ( \\boldsymbol { x } ) = \\| r ( \\boldsymbol { v } _ { f ( \\boldsymbol { x } ) } ) , \\boldsymbol { x } \\| _ { 2 }$ between the reconstructed image and the input image, and compare it with a pre-defined detection threshold $\\theta$ (described below in Section 4.2). If the reconstruction distance ${ \\bar { d } } ( x )$ is higher than the detection threshold $\\theta$ , we flag the input as an adversarial example. Figure 1 (b) shows an example of histograms of reconstruction distances for natural images and typical adversarial examples. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$\\mathbf { C N N + C R }$ Although our strategy is inspired by the reconstruction networks used in CapsNets, the strategy can be extended to standard convolutional neural networks (CNNs). We create a similar architecture, CNN with conditional reconstruction $( \\mathrm { C N N + C R } )$ ), by dividing the penultimate hidden layer of a CNN into groups corresponding to each class. The sum of each neuron group serves as the logit for that particular class and the group itself serves the same purpose as the pose parameters in the CapsNet. We use the same masking mechanism as Sabour et al. (2017) to select the pose parameter corresponding to the predicted label $v _ { f ( x ) }$ and generate the reconstruction based on the selected pose parameters. In this way we extend the class-conditional reconstruction network to standard CNNs. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$\\mathbf { C N N + R }$ We can also create a more na¨ıve implementation of our strategy by simply computing the reconstruction from the activations in the entire penultimate layer without any masking mechanism. We call this model the $\\mathrm { \" C N N { + } R } \\mathrm { \" }$ model. In this way we are able to study the effect of conditioning on the predicted class. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2 DETECTION THRESHOLD ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We find the threshold $\\theta$ for detecting adversarial inputs by measuring the reconstruction error between a validation input image and its reconstruction. If the distance between the input and the reconstruction is above the chosen threshold $\\theta$ , we classify the data as adversarial. Choosing the detection threshold $\\theta$ involves a trade-off between false positive and false negative detection rates. The optimal threshold depends on the probability of the system being attacked. Such a trade-off is discussed by Gilmer et al. (2018a). In our experiments we don’t tune this parameter and simply set it as the 95th percentile of validation distances. This means our false positive rate on real validation data is $5 \\%$ . ",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/bb51bc9d056a4282faaabb131c54b737429353105bb0f24c4a86b4eb52b64c94.jpg",
+        "table_caption": [
+            "Table 1: Success Rate / Undetected Rate of white-box targeted and untargeted attacks on the MNIST dataset. In the table, $S _ { t } / R _ { t }$ is shown for targeted attacks and $S _ { u } / R _ { u }$ is presented for untargeted attacks. A smaller success rate and undetected rate means a stronger defense model. Full results for FashionMNIST and SVHN can be seen in Table 5 in the Appendix. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Networks</td><td colspan=\"4\">Targeted (%)</td><td colspan=\"4\">Untargeted (%)</td></tr><tr><td>FGSM</td><td>BIM</td><td>PGD</td><td>CW</td><td>FGSM</td><td>BIM</td><td>PGD</td><td>CW</td></tr><tr><td>CapsNet</td><td>3/0</td><td>82/0</td><td>86/0</td><td>99/2</td><td>11/0</td><td>99/0</td><td>99/0</td><td>100/19</td></tr><tr><td>CNN+CR</td><td>16/0</td><td>93/0</td><td>95/0</td><td>89/8</td><td>85/0</td><td>100/0</td><td>100/0</td><td>100/28</td></tr><tr><td>CNN+R</td><td>37/0</td><td>100/0</td><td>100/0</td><td>100/47</td><td>64/0</td><td>100/0</td><td>100/0</td><td>100/63</td></tr></table>",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3 EVALUATION METRICS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "We use Success Rate to measure the success of attacks. For targeted attacks, the success rate $S _ { t }$ is defined as the proportion of inputs which are classified as the target class, $\\begin{array} { r } { S _ { t } = \\frac { 1 } { N } \\sum _ { i } ^ { N } ( f ( x _ { i } ^ { \\prime } ) = } \\end{array}$ $t _ { i }$ ), while the success rate for untargeted attacks is defined as the proportion of inputs which are misclassified, $\\begin{array} { r } { S _ { u } ~ = ~ \\frac { 1 } { N } \\sum _ { i } ^ { N } ( f ( x _ { i } ^ { \\prime } ) ~ \\neq ~ y _ { i } ) } \\end{array}$ . Previous work (Carlini & Wagner, $2 0 1 7 \\mathrm { a }$ ; Hosseini et al., 2019) used the True Positive Rate to measure the proportion of adversarial examples that are detected, which alone is insufficient to measure the ability of different detection mechanism because the unsuccessful adversarial examples do not have to be detected. Therefore, in this paper, we propose to use the Undetected Rate: the proportion of attacks that are successful and undetected to evaluate the detection mechanism. For targeted attacks, the undetected rate is defined as $\\begin{array} { r } { R _ { t } = \\frac { 1 } { N } \\sum _ { i } ^ { N } ( f ( x _ { i } ^ { \\prime } ) = t _ { i } ) \\cap ( d ( x _ { i } ^ { \\prime } ) \\leq \\theta ) } \\end{array}$ , where $d ( \\cdot )$ computes the reconstruction distance of the input and $\\theta$ denotes the detection threshold introduced in Section 4.2. Similarly, the undetected rate for untargeted attacks Ru can be defined as Ru = 1N PNi (f (x0i) 6= yi) ∩ (d(x0i) ≤ θ). The smaller undetected rate can also be used to evaluate the attacks (higher is better). We also plot the Undetected Rate vs. False Positive Rate curve to compare the detection performance between different models, where False Positive Rate is defined as the proportion of clean examples that are misclassified as the adversarial example by the detection method. ",
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+    {
+        "type": "text",
+        "text": "4.4 TEST MODELS AND DATASETS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In all experiments, all three models (CapsNet, $\\mathrm { C N N + R }$ , and $\\mathbf { C N N + C R }$ ) have the same number of parameters and were trained with Adam (Kingma & Ba, 2014) for the same number of epochs. In general, all models achieved similar test accuracy. We did not do an exhaustive hyperparameter search on these models, instead we chose hyperparameters that allowed each model to perform roughly equivalently on the test sets. We run experiments on three datasets: MNIST (LeCun et al., 1998), FashionMNIST (Xiao et al., 2017), and SVHN (Netzer et al., 2011). The test error rate for each model on these three datasets, as well as details of the model architectures, can be seen in Section A and Section B in the Appendix. ",
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+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "We first demonstrate how reconstruction networks can detect standard white and black-box attacks in addition to naturally corrupted images. Then, we introduce the “reconstructive attack”, which is specifically designed to circumvent our defense and show that it is a more powerful attack in this setting. Based on this finding, we qualitatively study the kind of misclassifications caused by the reconstructive attack and argue that they suggest that CapsNets learn features that are better aligned with human perception. ",
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+    {
+        "type": "text",
+        "text": "5.1 STANDARD ATTACKS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "White Box We present the success and undetected rates for several targeted and untargeted attacks on MNIST (Table 1), FashionMNIST, and SVHN (Table 5 presented in the Appendix). Our method is able to accurately detect many attacks with very low undetected rates. Capsule models almost always have the lowest undetected rates out of our three models. It is worth noting that this method performs best with the simplest dataset, MNIST, and that the highest undetected rates are found with the Carlini-Wagner attack on the SVHN dataset. This illustrates both the strength of this attack and a shortcoming of our defense, namely that our detection mechanism relies on $\\ell _ { 2 }$ image distance as a proxy for visual similarity, and in the case of higher dimensional color datasets such as SVHN, this proxy is less meaningful. ",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/f218de5b2efe49ccc7d48696fe5a88aa1c44078c6e5449572608fa16ac44faa4.jpg",
+        "table_caption": [
+            "Table 2: Error Rate/Undetected Rate on the Corrupted MNIST dataset. A smaller error rate and undetected rate means a better defense model. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Corruption</td><td>Clean</td><td>Gaussian Noise</td><td>Gaussian Blur</td><td>Line</td><td>Dotted Line</td><td>Elastic Transform</td></tr><tr><td>CapsNet</td><td>0.6/0.2</td><td>12.1/0.0</td><td>10.3/4.1</td><td>19.6/0.1</td><td>4.3/0.0</td><td>11.3/0.8</td></tr><tr><td>CNN+CR</td><td>0.7/0.3</td><td>9.8/0.0</td><td>6.7/4.2</td><td>17.6/0.1</td><td>4.2/0.0</td><td>11.1/1.1</td></tr><tr><td>CNN+R</td><td>0.6/0.4</td><td>6.7/0.0</td><td>8.9/6.4</td><td>18.9/0.1</td><td>3.1/0.0</td><td>12.2/2.1</td></tr><tr><td>Corruption</td><td>Saturate</td><td>JPEG</td><td>Quantize</td><td>Sheer</td><td>Spatter</td><td>Rotate</td></tr><tr><td>CapsNet</td><td>3.5/0.0</td><td>0.8/0.4</td><td>0.7/0.1</td><td>1.6/0.4</td><td>1.9/0.2</td><td>6.5/2.2</td></tr><tr><td>CNN+CR</td><td>1.5/0.0</td><td>0.8/0.5</td><td>0.9/0.1</td><td>2.1/0.4</td><td>1.8/0.4</td><td>6.1/1.6</td></tr><tr><td>CNN+R</td><td>1.2/0.0</td><td>0.7/0.5</td><td>0.7/0.2</td><td>2.2/0.7</td><td>1.8/0.4</td><td>6.5/3.4</td></tr><tr><td>Corruption</td><td>Contrast</td><td>Inverse</td><td>Canny Edge</td><td>Fog</td><td>Frost</td><td>Zigzag</td></tr><tr><td>CapsNet</td><td>92.0/0.0</td><td>91.0/0.0</td><td>21.5/0.0</td><td>83.7/0.0</td><td>70.6/0.0</td><td>16.9/0.0</td></tr><tr><td>CNN+CR</td><td>72.0/32.6</td><td>78.1/0.0</td><td>34.6/0.0</td><td>66.0/0.5</td><td>37.6/0.0</td><td>18.4/0.0</td></tr><tr><td>CNN+R</td><td>73.4/49.4</td><td>88.1/0.0</td><td>23.4/0.0</td><td>65.6/0.1</td><td>36.2/0.0</td><td>17.5/0.0</td></tr></table>",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Black Box We also tested our detection mechanism results on black box attacks. Given the low undetected rates in the white-box settings, it is not surprising that our detection method is able to detect black box attacks as well. In fact, on the MNIST dataset the capsule model is able to detect all targeted and untargeted PGD attacks. Both the CNN-R and the CNN-CR models are able to detect the black box attacks as well, but with a relatively higher undetected rate. A table of these results can be seen in Table 7 in the Appendix. ",
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+    {
+        "type": "text",
+        "text": "5.2 CORRUPTION ATTACKS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recent work has argued that improving the robustness of neural networks to $\\ell _ { p }$ norm bounded adversarial attacks should not come at the expense of increasing error rates under distributional shifts that do not affect human classification rates and are likely to be encountered in the “realworld” (Gilmer et al., 2018a). For example, if an image is corrupted due to adverse weather, lighting, or occlusion, we might hope that our model can continue to provide reliable predictions or detect the distributional shift. We can test our detection method on its ability to detect these distributional shifts by making use of the Corrupted MNIST dataset (Mu & Gilmer, 2019). This data set contains many visual transformations of MNIST that do not seem to affect human performance, but nevertheless are strongly misclassified by state-of-the-art MNIST models. Our three models can almost always detect these distributional shifts (in all corruptions CapsNets have either a small undetected rate or an undetected rate of 0). The error rate (the proportion of misclassified input) and undetected rate of three test models on the Corrupted MNIST dataset is shown in Table 2. Please refer to Figure 7 and Figure 8 in the Appendix for visualization of Corrupted MNIST. ",
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+    {
+        "type": "text",
+        "text": "5.3 RECONSTRUCTIVE ATTACKS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Thus far we have only evaluated previously-defined attacks. Following the suggestion in (Carlini & Wagner, 2017a) that detection methods need to show effectiveness towards defense-aware attacks, we introduce an attack specifically designed to take into account our defense mechanism. In order to construct adversarial examples that cannot be detected by the network, we propose a two-stage optimization method to generate a “reconstructive attack”. ",
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+    {
+        "type": "table",
+        "img_path": "images/794580c3a59f4efe6805071bd40e40c4d6ae7ed3b575737ebb0ebed4af3e1052.jpg",
+        "table_caption": [
+            "Table 3: Success rate and the worst case undetected rate of white-box targeted and untargeted reconstructive attacks. $S _ { t } / R _ { t }$ is shown for targeted attacks and $S _ { u } / R _ { u }$ is presented for untargeted attacks. The worst case undetected rate is reported via tuning the hyperparameter $\\beta$ in Eqn 1 and Eqn 2. The best defense models are shown in bold (smaller success rate and undetected rate is better). All the numbers are shown in $\\%$ . A full table with more attacks can be seen in Table 6 in Appendix. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"2\">MNIST</td><td colspan=\"2\">FASHION</td><td colspan=\"2\">SVHN</td></tr><tr><td></td><td>Targeted R-PGD</td><td>Untargeted R-PGD</td><td>Targeted R-PGD</td><td>Untargeted R-PGD</td><td>Targeted R-PGD</td><td>Untargeted R-PGD</td></tr><tr><td>CapsNet</td><td>50.7/33.7</td><td>88.1/37.9</td><td>53.7/29.8</td><td>84.9/75.5</td><td>82.0/79.2</td><td>98.9/97.5</td></tr><tr><td>CNN+CR</td><td>98.6/68.1</td><td>99.4/87.7</td><td>89.8/84.4</td><td>91.5/86.0</td><td>99.0/97.9</td><td>99.9/99.5</td></tr><tr><td>CNN+R</td><td>95.5/71.2</td><td>95.1/70.5</td><td>94.6/88.4</td><td>98.9/90.0</td><td>99.5/99.3</td><td>100.0/99.9</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/dcef3ee1e045e15cdcffd265fc6c139d590570c97f184c878a84ea161f509e47.jpg",
+        "image_caption": [
+            "Figure 2: The undetected rate of the white-box targeted defense-aware R-PGD attack versus the False Positive Rate on the MNIST, Fashion-MNIST and SVHN datasets. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Untargeted Reconstructive Attacks To construct untargeted reconstructive attacks, we first update the perturbation based on the gradient of the cross-entropy loss function following a standard FGSM attack (Goodfellow et al., 2014), that is: ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/6228cf9c9c7a1599000bae98cd134f862f82265e11fdb8160b0ca0e1569495a8.jpg",
+        "text": "$$\n\\delta \\gets \\mathrm { c l i p } _ { \\epsilon } ( \\delta + c \\cdot \\beta \\cdot \\mathrm { s i g n } ( \\nabla _ { \\delta } \\ell _ { n e t } ( f ( x + \\delta ) , y ) ) ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where $\\ell _ { n e t } ( f ( \\cdot ) , y )$ is the cross-entropy loss function, $\\epsilon$ is the $\\ell _ { \\infty }$ bound for our attacks, $c$ is a hyperparameter controlling the step size in each iteration and $\\beta$ is a hyperparameter which balances the importance of the cross-entropy loss and the reconstruction loss (explained further below). In the second stage, we focus on constraining the reconstructed image from the newly predicted label to have a small reconstruction distance by updating $\\delta$ according to ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/713bed1386dadf1c21eec2199825c694d4885206c4c76c90963fa4c13c68d8d3.jpg",
+        "text": "$$\n\\delta \\gets \\mathrm { c l i p } _ { \\epsilon } ( \\delta - c \\cdot ( 1 - \\beta ) \\cdot \\mathrm { s i g n } ( \\nabla _ { \\delta } ( \\| r ( v _ { f ( x + \\delta ) } ) - ( x + \\delta ) \\| _ { 2 } ) ) ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where $r \\big ( v _ { f ( x + \\delta ) } \\big )$ is the class-conditional reconstruction based on the predicted label $f ( x + \\delta )$ in a CapsNet or $\\mathrm { C N N + C R }$ network. The $\\delta$ used here is the optimized $\\delta$ from the first stage. $\\| r ( v _ { f ( x + \\delta ) } ) -$ $( x + \\delta ) \\| _ { 2 }$ is the $\\ell _ { 2 }$ reconstruction distance between the reconstructed image and the input image. Since the $\\mathrm { C N N + R }$ network does not use the class conditional reconstruction, we simply use the reconstructed image without the masking mechanism. According to Eqn 1 and Eqn 2, we can see that $\\beta$ balances the importance between the success rate of attacks and the reconstruction distance. This hyperparameter was tuned for each model and each dataset in order to create the strongest attacks. The success rate and undetected rate change as this parameter, which is shown in Figure 9 in Appendix. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Targeted Reconstructive Attacks We perform a similar two-stage optimization to construct targeted reconstructive attacks, by defining a target label and attempting to maximize the classification probability of this label, and minimize the reconstruction error from corresponding capsule. Because the targeted label is given, another way to construct targeted reconstructive attacks is to combine these two stages into one stage via minimizing the loss function $\\ell = \\boldsymbol { \\beta } \\cdot \\ell _ { n e t } ( f ( x + \\delta ) , y ) + ( 1 - \\beta ) \\cdot \\| \\boldsymbol { r } ( v _ { f ( x + \\delta ) } ) - ( x + \\delta ) \\| _ { 2 }$ . We implemented both of these targeted reconstructive attacks and found that the two-stage version is a stronger attack. Therefore, all the Reconstructive Attack experiments performed in this paper are based on two-stage optimization. ",
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+    {
+        "type": "image",
+        "img_path": "images/3305f2537867e2d22b33557a43922ed39ef464bb4d5a47f2d33130e838f37e08.jpg",
+        "image_caption": [
+            "Figure 3: The defense-aware R-PGD attack is tested on the CIFAR-10 dataset with $\\epsilon _ { \\infty } = 8 / 2 5 5$ . Left: The undetected rate of white-box/black-box defense-aware R-PGD versus the Fasle Positive Rate for the clean examples. The test model is our CapsNet. Right: The undetected rate of white-box defense-aware R-PGD versus the Fasle Positive Rate for the clean examples. The test model is our CapsNet using class-conditional reconstruction, “CapsNet All” using all capsule information, and the DeepCaps (Rajasegaran et al., 2019) using class-independent capsule information. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "We build our reconstructive attack based on the standard PGD attack, denoted as R-PGD, and test the performance of our detection models against this reconstructive attack in a white-box setting (white-box Reconstructive FGSM and BIM are reported in Table 6 in the Appendix). Comparing Table 1 and Table 3, we can see that the Reconstructive Attack is significantly less successful at changing the models prediction (lower success rates than the standard attack). However, this attack is more successful at fooling our detection method. For all attacks and datasets the capsule model has the lowest attack success rate and the lowest undetected rate. We report results for black-box R-PGD attacks in Table 7 in the Appendix, which suggest similar conclusions. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In addition, we report the undetected rate of the white-box targeted defense-aware R-PGD attack versus the False Positive Rate on the MNIST, Fashion-MNIST and SVHN datasets in Figure 2. We can clearly see that the undetected rate of the defense-aware attack against CapsNet is significantly smaller than the CNN-based networks, which suggests that CapsNets are more robust against adversarial attacks. Furthermore, CNN with class-conditional reconstruction $\\mathrm { C N N + C R }$ ) has smaller undetected rate at the same False Positive Rate compared to the CNN without class-conditional reconstruction $( \\mathrm { C N N + R } )$ , which suggests the class-conditional information is helpful in our models to improve the robustness against adversarial attacks. ",
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+    {
+        "type": "text",
+        "text": "5.4 CIFAR-10 DATASET ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In order to show that our method based on CapsNet is capable to scale up to more complex datasets, we test our detection method with a deeper reconstruction network on CIFAR-10 (Krizhevsky, 2009). The classification accuracy on the clean test dataset is $9 2 . 2 \\%$ . In addition, we display the undetected rate of the white-box/black-box defense-aware R-PGD attack against CapsNets versus the False Positive Rate in Figure 3 (Left), where we can see a significant drop of the undetected rate of black-box R-PGD compared to the white-box setting. This indicates the CapsNets greatly reduce the attack transferability and the threat of black-box attacks. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Class-conditional Information To investigate the effectiveness of the class-conditional information in the reconstruction network, we compare our CapsNet based on (Sabour et al., 2017) with the other two variants of CapsNets: “CapsNet All” and “DeepCaps” (Rajasegaran et al., 2019). In “CapsNet All”, we remove the masking mechanism in the CapsNet and use all the capsules to do the reconstruction. In “DeepCaps”, we extract the winning-capsule information as a single vector and used it as the input for the reconstruction network instead of using a masking mechanism to mask out the losing capsules information. In this way, the class information in DeepCaps is more explicitly fed into the reconstruction network. As shown in Figure 3 (right), our CapsNet has the best detection performance (the lowest undetected rate at the same False Positive Rate) compared to the other two ",
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+    {
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+        "image_caption": [],
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+    {
+        "type": "image",
+        "img_path": "images/1c871acd5f931848f081ff2f41686870d3b7f5acb5a9b95c3c7d55a07d452d6a.jpg",
+        "image_caption": [
+            "Figure 4: This diagram visualizes the adversarial success rates for each source/target pair for targeted R-PGD attacks on Fashion-MNIST with $\\epsilon _ { \\infty } = 2 5 / 2 5 5$ . The size of the box at position x, y represents the success rate of adversarially perturbing inputs of class $\\mathbf { X }$ to be classified as class y. We can see that there is significantly higher variance for the CapsNet model than for the two CNN models. ",
+            "Figure 5: These are randomly sampled (not cherry picked) successful and undetected adversarial attacks created by R-PGD with a target class of 0 for each model on the SVHN dataset $\\epsilon _ { \\infty } = 2 5 / 2 5 5 )$ . We can see that for the capsule model, many of the attacks are not “adversarial” as they resemble members of the target class. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Capsule models. “DeepCaps” performs slightly worse than our “CapsNet” and “CapsNet All” has the worst detection performance. Therefore, we conclude that the class-conditional information used in the reconstruction network increases the model’s robustness to adversarial attack. This also holds true to CNN-based networks because $\\mathrm { C N N + C R }$ has a better detection performance than $\\mathrm { C N N + R }$ , shown in Figure 2. ",
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+    {
+        "type": "text",
+        "text": "6 VISUAL COHERENCE OF THE RECONSTRUCTIVE ATTACK ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The great success of CapsNet over CNN-based models motivates us to further diagnose the generated adversarial examples for CapsNets. If our true aim in adversarial robustness research is to create models that make predictions based on reasonable and human-observable features, then we would prefer models that are more likely to misclassify a “shirt” as a “t-shirt” (in the case of FashionMNIST) than to misclassify a “bag” as a “sweater”. For a model to behave ideally, the success of an adversarial perturbation would be related to the visual similarity between the source and the target class. By visualizing a matrix of adversarial success rates between each pair of classes (shown in Figure 4), we can see that for the capsule model there is a great variance between the source and target class pairs and that the success rate of attacks is highly related to the visual similarity of the classes. However, this is not the case for either of the other two CNN-based models. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Thus far we have treated all attacks as equal. However, a key component of an adversarial example is that it is visually similar to the source image, and that it does not resemble the adversarial target class. The adversarial research community makes use of a small epsilon bound as a mechanism for ensuring that the resultant adversarial attacks are visually unchanged from the source image. For standard attacks against CNN-based models this heuristic is sufficient, because taking gradient steps in the image space in order to have a network misclassify an image normally results in something visually similar to the source image. But this is not the case for adversarial attacks against CapsNets. As shown in Figure 5, when we use R-PGD to attack the CapsNet, many of the resultant attacks resemble members of the target class. In this way, they stop being “adversarial”. As such, an attack detection method which does not detect them as adversarial is arguably behaving correctly. This puts the previously undetected rates presented earlier in a new light, and illustrates a difficulty in the evaluation of adversarial attacks and defenses. In addition, it should be noted that this phenomenon rarely occurs in a standard convolutional neural network, which suggests that the features captured by CapsNet are more aligned with human perception. ",
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+        "type": "text",
+        "text": "",
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+    },
+    {
+        "type": "text",
+        "text": "7 DISCUSSION ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Our detection mechanism relies on a similarity metric (i.e. a measure of reconstruction error) between the reconstruction and the input. This metric is required both during training in order to train the reconstruction network and during test time in order to flag adversarial examples. In the four datasets we have evaluated, the distance between examples roughly correlates with semantic similarity. However, this may not be the case for images in more complex datasets such as the SUN dataset (Xiao et al., 2010) and ImageNet (Deng et al., 2009), in which two images may be similar in terms of semantic content but nevertheless have significant $\\ell _ { 2 }$ distance. A better similarity metric (Theis et al., 2015; Zhang et al., 2018) can be further explored to extend our methods to more complex problems. Furthermore our reconstruction network is trained on a hidden representation of one class but is trained to reconstruct the entire input. In datasets without distractors or backgrounds, this is not a problem. But in the case of ImageNet, in which the object responsible for the classification is not the only object in the image, attempting to reconstruct the entire input from a class encoding seems misguided. ",
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+    },
+    {
+        "type": "text",
+        "text": "8 CONCLUSION ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We have presented a class-conditional reconstruction-based detection method that does not rely on a specific predefined adversarial attack. We have shown that by reconstructing the input from the internal class-conditional representation, our system is able to accurately detect black-box and white-box FGSM, BIM, PGD, and CW attacks. We then proposed a new attack to beat our defense - the Reconstructive Attack - in which the adversary optimizes not only the classification loss but also minimizes the reconstruction loss. We showed that this attack was able to fool our detection mechanism but with a much smaller success rate than a standard attack. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Compared to CNN-based models, we showed that the CapsNet was able to detect adversarial examples with greater accuracy on all the datasets we explored. To further explain the success of CapsNet, we qualitatively showed that the success of the reconstructive attack was highly related to the visual similarity between the target class and the source class for the CapsNet. In addition, we showed that images generated by this reconstructive attack to attack the CapsNet are not typically adversarial, i.e. many of the resultant attacks resemble members of the target class even with a small $\\ell _ { \\infty }$ norm bound. These are not the case for the CNN-based models. The extensive qualitative studies indicate that the capsule model relies on visual features similar to those used by humans. We believe this is a step towards solving the true problem posed by adversarial examples. ",
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+    {
+        "type": "text",
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+    {
+        "type": "text",
+        "text": "APPENDIX ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A NETWORK ARCHITECTURES ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            138,
+            446,
+            155
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Figure 6 shows the architecute of the capsule network, the CNN reconstruction model and the CNN conditional reconstruction model used for experiments on MNIST, FashionMNIST and SVHN dataset. MNIST and Fashion MNIST have exactly the same architectures while we use larger models for SVHN. Note that the only difference between the CNN reconstruction $( \\mathrm { C N N + R } )$ ) and the CNN conditional reconstruction $\\mathbf { \\left( C N N + C R \\right) }$ ) is the masking procedure on the input to the reconstruction network based on the predicted class. All three models have the same number of parameters. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/6f3aa886fbab5409364bc7abf70efda9eeffe18088432df460c2b265abe5aae5.jpg",
+        "image_caption": [
+            "Figure 6: The architecture for the CapsNet, $\\mathrm { C N N + R }$ and $\\mathrm { C N N + C R }$ model used for our experiments on MNIST (LeCun et al., 1998), FashionMNIST (Xiao et al., 2017), and SVHN (Netzer et al., 2011). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            187,
+            276,
+            816,
+            625
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B TEST MODELS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            722,
+            326,
+            738
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "The error rate of each test model used in the paper are presented in Table 4. We ensure that they have similar performance. ",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/2837941f8ca1fec5a386ff75986f834dccdd207b51a6fec348b843a1eea28808.jpg",
+        "table_caption": [
+            "Table 4: Error rate of each model when the input are clean test images in each dataset. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>CapsNet</td><td>CNN+CR</td><td>CNN+R</td></tr><tr><td>MNIST</td><td>0.6%</td><td>0.7%</td><td>0.6%</td></tr><tr><td>FashionMNIST</td><td>9.6%</td><td>9.5%</td><td>9.3%</td></tr><tr><td>SVHN</td><td>10.7%</td><td>9.3%</td><td>9.5%</td></tr></table>",
+        "bbox": [
+            174,
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+            901
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "C IMPLEMENTATION DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            439,
+            118
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "For all the $\\ell _ { \\infty }$ based adversarial examples, the $\\ell _ { \\infty }$ norm of the perturbations is bound by $\\epsilon$ , which is set to 0.3, 0.1, 0.1 for MNIST, Fashion MNIST and SVHN dataset respectively following previous work (Madry et al., 2017; Song et al., 2017). In FGSM based attacks, the step size $c$ is 0.05. In BIM-based (Kurakin et al., 2016) and PGD-based (Madry et al., 2017) attacks, the step size $c$ is 0.01 for all the datasets and the number of iterations are 1000, 500 and 200 for MNIST, Fashion MNIST and SVHN dataset respectively. We choose a sufficiently large number of iterations to ensure the attacks has converged. ",
+        "bbox": [
+            174,
+            133,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We use the publicly released code from the authors of (Carlini & Wagner, 2017b) to perform the CW attack for our models. The number of iterations are set to 1000 for all three datasets. ",
+        "bbox": [
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "D WHITE BOX STANDARD ATTACKS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            286,
+            493,
+            303
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "The results of four white box standard attacks on the three datasets are shown in Table 5. ",
+        "bbox": [
+            176,
+            318,
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+            333
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/2fed502df57b4092eb6e8cba7e66178c37ecd2def6dfb7d3c2be8d2b0e7d5879.jpg",
+        "table_caption": [
+            "Table 5: Success rate and undetected rate of white-box targeted and untargeted attacks. In the table, $S _ { t } / R _ { t }$ is shown for targeted attacks and $S _ { u } / R _ { u }$ is presented for untargeted attacks. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Networks</td><td colspan=\"4\">Targeted (%) FGSM</td><td colspan=\"4\">Untargeted (%) BIM</td></tr><tr><td>BIM</td><td></td><td>PGD</td><td>CW</td><td>FGSM</td><td></td><td>PGD</td><td>CW</td></tr><tr><td colspan=\"9\">MNIST Dataset</td></tr><tr><td>CapsNet CNN+CR</td><td>3/0</td><td>82/0</td><td>86/0</td><td>99/2</td><td>11/0</td><td>99/0</td><td>99/0</td><td>100/19</td></tr><tr><td></td><td>16/0</td><td>93/0</td><td>95/0</td><td>89/8</td><td>85/0</td><td>100/0</td><td>100/0</td><td>100/28</td></tr><tr><td>CNN+R</td><td>37/0</td><td>100/0</td><td>100/0</td><td>100/47</td><td>64/0</td><td>100/0</td><td>100/0</td><td>100/63</td></tr><tr><td colspan=\"9\">FASHION I MNISTDataset</td></tr><tr><td>CapsNet</td><td>715</td><td>54/9</td><td>55/10</td><td>100/26</td><td>35/29</td><td>86/50</td><td>87/51</td><td>100/68</td></tr><tr><td>CNN+CR</td><td>19/13</td><td>89/28</td><td>89/28</td><td>87/37</td><td>74/33</td><td>100/25</td><td>100/24</td><td>100/72</td></tr><tr><td>CNN+R</td><td>23/16</td><td>98/19</td><td>98/19</td><td>99/81</td><td>62/48</td><td>100/35</td><td>100/34</td><td>100/87</td></tr><tr><td colspan=\"9\"> SVHN Dataset</td></tr><tr><td>CapsNet</td><td>22/20</td><td>83/45</td><td>84/46</td><td>100/90</td><td>74/67</td><td>99/70</td><td>99/68</td><td>100/94</td></tr><tr><td>CNN+CR CNN+R</td><td>24/23</td><td>99/90</td><td>99/90</td><td>99/93</td><td>87/82</td><td>100/90</td><td>100/89</td><td>100/90</td></tr><tr><td></td><td>26/24</td><td>100/86</td><td>100/86</td><td>100/94</td><td>88/82</td><td>100/92</td><td>100/92</td><td>100/95</td></tr></table>",
+        "bbox": [
+            194,
+            383,
+            803,
+            625
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "E VISUALIZATION OF CORRUPTED MNIST DATASET ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            102,
+            630,
+            118
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Visualization of examples from Corrupted MNIST dataset (Mu & Gilmer, 2019) and the corresponding reconstructed images for each model are shown in Figure 7 and Figure 8. ",
+        "bbox": [
+            174,
+            133,
+            825,
+            162
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/113b8f9ba68153f1165873917ce1cb3e89bb1e0528c4555e0ccba41783c0db7b.jpg",
+        "image_caption": [
+            "Figure 7: Examples of Corrupted MNIST and the reconstructed image for each model. A red box represent that this input is flagged as an adversarial example while a green box represent this input has been misclassified and not been detected. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            176,
+            823,
+            746
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/588b2318b9774d1400fcd7cd32007fea6caf4a90beedb123af99676430103c5a.jpg",
+        "image_caption": [
+            "Figure 8: Examples of Corrupted MNIST and the reconstructed image for each model. A red box represents that this input is flagged as an adversarial example while a green box represents that this input has been misclassified and not been detected. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            102,
+            825,
+            377
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "F RECONSTRUCTIVE ATTACKS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            465,
+            444,
+            482
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "The results of Reconstructive FGSM, BIM and PGD on the three datasets are reported in Table 6. ",
+        "bbox": [
+            173,
+            496,
+            808,
+            512
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "table",
+        "img_path": "images/b2e88745f7ab72ae8f34ba20bdc7076b0dc456606797bbdeaffb501a6f5a850e.jpg",
+        "table_caption": [
+            "Table 6: Success rate and the worst case undetected rate of white-box targeted and untargeted reconstructive attacks. Below $S _ { t } / R _ { t }$ is shown for targeted attacks and $S _ { u } \\bar { / } R _ { u }$ is presented for untargeted attacks. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Networks</td><td>R-FGSM</td><td>Targeted (%) R-BIM</td><td>R-PGD</td><td>R-FGSM</td><td>Untargeted (%) R-BIM</td><td>R-PGD</td></tr><tr><td colspan=\"7\">MNIST Dataset</td></tr><tr><td>CapsNet</td><td>1.8/0.3</td><td>51.0/33.8</td><td>50.7/33.7</td><td>6.1/1.0</td><td>84.5/35.1</td><td>88.1/37.9</td></tr><tr><td>CNN+CR</td><td>7.6/0.5</td><td>98.0/68.1</td><td>98.6/68.1</td><td>41.7/3.2</td><td>96.5/86.8</td><td>99.4/87.7</td></tr><tr><td>CNN+R</td><td>16.9/3.3</td><td>86.3/65.9</td><td>95.5/71.2</td><td>25.9/8.1</td><td>82.9/67.8</td><td>95.1/70.5</td></tr><tr><td colspan=\"7\">FASHION MNIST Dataset</td></tr><tr><td>CapsNet</td><td>6.5/5.8</td><td>53.3/28.4</td><td>53.7/29.8</td><td>33.3/29.9</td><td>85.3/75.9</td><td>84.9/75.5</td></tr><tr><td>CNN+CR</td><td>17.7/14.0</td><td>80.3/72.4</td><td>78.1/72.0</td><td>68.0/57.3</td><td>89.8/84.4</td><td>91.5/86.0</td></tr><tr><td>CNN+R</td><td>19.4/17.6</td><td>95.2/88.8</td><td>94.6/88.4</td><td>58.6/53.5</td><td>98.8/90.1</td><td>98.9/90.0</td></tr><tr><td colspan=\"7\">SVHN Dataset</td></tr><tr><td>CapsNet</td><td>21.6/21.2</td><td>81.1/78.3</td><td>82.0/79.2</td><td>71.6/68.3</td><td>98.9/97.5</td><td>98.9/97.5</td></tr><tr><td>CNN+CR</td><td>24.2/22.6</td><td>98.5/97.6</td><td>99.0/97.9</td><td>86.0/82.3</td><td>99.9/99.5</td><td>99.9/99.5</td></tr><tr><td>CNN+R</td><td>26.6/25.8</td><td>99.6/99.4</td><td>99.5/99.3</td><td>87.1/84.5</td><td>100.0/99.9</td><td>100.0/99.9</td></tr></table>",
+        "bbox": [
+            200,
+            579,
+            795,
+            819
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Figure 9 shows the plot of success rate and undetected rate versus the hyperparameter $\\beta$ which balances the importance between attacking the classifier and fooling the detection mechanism in the targeted reconstructive PGD attacks on the MNIST dataset. ",
+        "bbox": [
+            173,
+            130,
+            825,
+            171
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "image",
+        "img_path": "images/8cddf9af8747c1350afc7e1fe0895c9b076be39b8d08daf81bdc3d2b1b2b77bc.jpg",
+        "image_caption": [
+            "Figure 9: An example shows the plot of the success rate in (a) and undetected rate in (b) of targeted reconstructive PGD attack vesus the hyperparameter beta $\\beta$ for each model on the MNIST test set. We set the max $\\ell _ { \\infty }$ norm $\\epsilon = 0 . 3$ to create the attacks. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            209,
+            188,
+            789,
+            356
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "G BLACK BOX ATTACKS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            439,
+            397,
+            455
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "table",
+        "img_path": "images/8d9300b1d9fd6d1fe19452d4bb5e0e04e77f9f31f811b7a01b95d96f667d1d4e.jpg",
+        "table_caption": [
+            "Table 7: Success rate and undetected rate of black-box targeted and untargeted attacks. In the table, $S _ { t } / R _ { t }$ is shown for targeted attacks and $S _ { u } / R _ { u }$ is presented for untargeted attacks. All the numbers are shown in $\\%$ . ",
+            "H VISUALIZATION OF ADVERSARIAL EXAMPLES AND RECONSTRUCTIONS "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"8\">MNIST Dataset</td></tr><tr><td>Targeted</td><td>CapsNet</td><td>CNN-CR</td><td>CNN-R</td><td>Untargeted</td><td>CapsNet</td><td>CNN-CR</td><td>CNN-R</td></tr><tr><td>PGD</td><td>1.5/0.0</td><td>7.8/0.0</td><td>7.4/0.0</td><td>PGD</td><td>8.5/0.0</td><td>32.6/0.0</td><td>27.6/0.0</td></tr><tr><td>R-PGD</td><td>4.2/1.0</td><td>18.3/11.0</td><td>11.3/4.8</td><td>R-PGD</td><td>10.4/2.4</td><td>42.7/24.9</td><td>25.2/8.9</td></tr></table>",
+        "bbox": [
+            179,
+            512,
+            818,
+            588
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "image",
+        "img_path": "images/aacb183a4b1c4b86994c64eeb29370a753b73b8b45173db8b6994c9ba0e6df58.jpg",
+        "image_caption": [
+            "Figure 10: The source clean image is presented in the first row with its reconstruction in the second row. For each model, the top row are the targeted adversarial examples and the bottom are the corresponding reconstruction image when the input are the PGD on the MNIST (left), R-PGD on the Fashion-MNIST (middle), CW on the SVHN (right). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            650,
+            820,
+            821
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "image",
+        "img_path": "images/fb94341a4962dca46a6f2333f57b7519edbf866a127592d898866fe8f696c2a4.jpg",
+        "image_caption": [
+            "Figure 11: These are randomly sampled (not cherry picked) inputs (top row) and the result of adversarially perturbing them with targeted R-PGD against the CapsNet model (other rows). Many of these attacks are not successful. Note the visual similarity between many of the attacks and the target class. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            220,
+            304,
+            794,
+            655
+        ],
+        "page_idx": 17
+    }
+]

parse/train/Sklgs0NFvr/Sklgs0NFvr.md

@@ -0,0 +1,258 @@
+# LEARNING THE DIFFERENCE THAT MAKES A DIFFERENCE WITH COUNTERFACTUALLY-AUGMENTED DATA
+
+Divyansh Kaushik, Eduard Hovy, Zachary C. Lipton   
+Carnegie Mellon University   
+Pittsburgh PA, USA   
+{dkaushik, hovy, zlipton}@cmu.edu
+
+# ABSTRACT
+
+Despite alarm over the reliance of machine learning systems on so-called spurious patterns, the term lacks coherent meaning in standard statistical frameworks. However, the language of causality offers clarity: spurious associations are due to confounding (e.g., a common cause), but not direct or indirect causal effects. In this paper, we focus on natural language processing, introducing methods and resources for training models less sensitive to spurious patterns. Given documents and their initial labels, we task humans with revising each document so that it (i) accords with a counterfactual target label; (ii) retains internal coherence; and (iii) avoids unnecessary changes. Interestingly, on sentiment analysis and natural language inference tasks, classifiers trained on original data fail on their counterfactually-revised counterparts and vice versa. Classifiers trained on combined datasets perform remarkably well, just shy of those specialized to either domain. While classifiers trained on either original or manipulated data alone are sensitive to spurious features (e.g., mentions of genre), models trained on the combined data are less sensitive to this signal. Both datasets are publicly available1.
+
+# 1 INTRODUCTION
+
+What makes a document’s sentiment positive? What makes a loan applicant creditworthy? What makes a job candidate qualified? When does a photograph truly depict a dolphin? Moreover, what does it mean for a feature to be relevant to such a determination?
+
+Statistical learning offers one framework for approaching these questions. First, we swap out the semantic question for a more readily answerable associative question. For example, instead of asking what conveys a document’s sentiment, we recast the question as which documents are likely to be labeled as positive (or negative)? Then, in this associative framing, we interpret as relevant, those features that are most predictive of the label. However, despite the rapid adoption and undeniable commercial success of associative learning, this framing seems unsatisfying.
+
+Alongside deep learning’s predictive wins, critical questions have piled up concerning spurious patterns, artifacts, robustness, and discrimination, that the purely associative perspective appears ill-equipped to answer. For example, in computer vision, researchers have found that deep neural networks rely on surface-level texture (Jo & Bengio, 2017; Geirhos et al., 2018) or clues in the image’s background to recognize foreground objects even when that seems both unnecessary and somehow wrong: the beach is not what makes a seagull a seagull. And yet, researchers struggle to articulate precisely why models should not rely on such patterns.
+
+In natural language processing (NLP), these issues have emerged as central concerns in the literature on annotation artifacts and societal biases. Across myriad tasks, researchers have demonstrated that models tend to rely on spurious associations (Poliak et al., 2018; Gururangan et al., 2018; Kaushik & Lipton, 2018; Kiritchenko & Mohammad, 2018). Notably, some models for question-answering tasks may not actually be sensitive to the choice of the question (Kaushik & Lipton, 2018), while in Natural Language Inference (NLI), classifiers trained on hypotheses only (vs hypotheses and premises) perform surprisingly well (Poliak et al., 2018; Gururangan et al., 2018). However, papers seldom make clear what, if anything, spuriousness means within the standard supervised learning framework. ML systems are trained to exploit the mutual information between features and a label to make accurate predictions. The standard statistical learning toolkit does not offer a conceptual distinction between spurious and non-spurious associations.
+
+![](images/13256fcaea9ed4a3abaa41f3eb5712d6296f421625d51e2394c40ab84fc7930e.jpg)  
+Figure 1: Pipeline for collecting and leveraging counterfactually-altered data
+
+Causality, however, offers a coherent notion of spuriousness. Spurious associations owe to confounding rather than to a (direct or indirect) causal path. We might consider a factor of variation to be spuriously correlated with a label of interest if intervening upon it would not impact the applicability of the label or vice versa. While our paper does not call upon the mathematical machinery of causality, we draw inspiration from the underlying philosophy to design a new dataset creation procedure in which humans counterfactually revise documents.
+
+Returning to NLP, although we lack automated tools for mapping between raw text and disentangled factors, we nevertheless describe documents in terms of these abstract representations. Moreover, it seems natural to speak of manipulating these factors directly (Hovy, 1987). Consider, for example, the following interventions: (i) Revise the letter to make it more positive; (ii) Edit the second sentence so that it appears to contradict the first. These edits might be thought of as intervening on only those aspects of the text that are necessary to make the counterfactual label applicable.
+
+In this exploratory paper, we design a human-in-the-loop system for counterfactually manipulating documents. Our hope is that by intervening only upon the factor of interest, we might disentangle the spurious and non-spurious associations, yielding classifiers that hold up better when spurious associations do not transport out of domain. We employ crowd workers not to label documents, but rather to edit them, manipulating the text to make a targeted (counterfactual) class applicable. For sentiment analysis, we direct the worker to revise this negative movie review to make it positive, without making any gratuitous changes. We might regard the second part of this directive as a least action principle, ensuring that we perturb only those spans necessary to alter the applicability of the label. For NLI, a 3-class classification task (entailment, contradiction, neutral), we ask the workers to modify the premise while keeping the hypothesis intact, and vice versa, collecting edits corresponding to each of the (two) counterfactual classes. Using this platform, we collect thousands of counterfactually-manipulated examples for both sentiment analysis and NLI, extending the IMDb (Maas et al., 2011) and SNLI (Bowman et al., 2015) datasets, respectively. The result is two new datasets (each an extension of a standard resource) that enable us to both probe fundamental properties of language and train classifiers less reliant on spurious signal.
+
+We show that classifiers trained on original IMDb reviews fail on counterfactually-revised data and vice versa. We further show that spurious correlations in these datasets are even picked up by linear models. However, augmenting the revised examples breaks up these correlations (e.g., genre ceases to be predictive of sentiment). For a Bidirectional LSTM (Graves & Schmidhuber, 2005) trained on IMDb reviews, classification accuracy goes down from $7 9 . 3 \%$ to $5 5 . 7 \%$ when evaluated on original vs revised reviews. The same classifier trained on revised reviews achieves an accuracy of $8 9 . 1 \%$ on revised reviews compared to $6 2 . 5 \%$ on their original counterparts. These numbers go to $8 1 . 7 \%$ and $9 2 . 0 \%$ on original and revised data, respectively, when the classifier is retrained on the combined dataset. Similar patterns are observed for linear classifiers. We discovered that BERT (Devlin et al., 2019) is more resilient to such drops in performance on sentiment analysis.
+
+Additionally, SNLI models appear to rely on spurious associations as identified by Gururangan et al. (2018). Our experiments show that when fine-tuned on original SNLI sentence pairs, BERT fails on pairs with revised premise and vice versa, suffering more than a 30 point drop in accuracy. Fine-tuned on the combined set, BERT’s performance improves significantly across all datasets. Similarly, a Bi-LSTM trained on (original) hypotheses alone can accurately classify $6 9 \%$ of pairs correctly but performs worse than the blind classifier when evaluated on the revised dataset. When trained on hypotheses only from the combined dataset, its performance is not appreciably better than random guessing.
+
+# 2 RELATED WORK
+
+Several papers demonstrate cases where NLP systems appear not to learn what humans consider to be the difference that makes the difference. For example, otherwise state-of-the-art models have been shown to be vulnerable to synthetic transformations such as distractor phrases (Jia & Liang, 2017; Wallace et al., 2019), to misclassify paraphrased task (Iyyer et al., 2018; Pfeiffer et al., 2019) and to fail on template-based modifications (Ribeiro et al., 2018). Glockner et al. (2018) demonstrate that simply replacing words by synonyms or hypernyms, which should not alter the applicable label, nevertheless breaks ML-based NLI systems. Gururangan et al. (2018) and Poliak et al. (2018) show that classifiers correctly classified the hypotheses alone in about $6 9 \%$ of SNLI corpus. They further discover that crowd workers adopted specific annotation strategies and heuristics for data generation. Chen et al. (2016) identify similar issues exist with automatically-constructed benchmarks for question-answering (Hermann et al., 2015). Kaushik & Lipton (2018) discover that reported numbers in question-answering benchmarks could often be achieved by the same models when restricted to be blind either to the question or to the passages. Dixon et al. (2018); Zhao et al. (2018) and Kiritchenko & Mohammad (2018) showed how imbalances in training data lead to unintended bias in the resulting models, and, consequently, potentially unfair applications. Shen et al. (2018) substitute words to test the behavior of sentiment analysis algorithms in the presence of stylistic variation, finding that similar word pairs produce significant differences in sentiment score.
+
+Several papers explore richer feedback mechanisms for classification. Some ask annotators to highlight rationales, spans of text indicative of the label (Zaidan et al., 2007; Zaidan & Eisner, 2008; Poulis & Dasgupta, 2017). For each document, Zaidan et al. remove the rationales to generate contrast documents, learning classifiers to distinguish original documents from their contrasting counterparts. While this feedback is easier to collect than ours, how to leverage it for training deep NLP models, where features are not neatly separated, remains less clear.
+
+Lu et al. (2018) programmatically alter text to invert gender bias and combined the original and manipulated data yielding gender-balanced dataset for learning word embeddings. In the simplest experiments, they swap each gendered word for its other-gendered counterpart. For example, the doctor ran because he is late becomes the doctor ran because she is late. However, they do not substitute names even if they co-refer to a gendered pronoun. Building on their work, Zmigrod et al. (2019) describe a data augmentation approach for mitigating gender stereotypes associated with animate nouns for morphologically-rich languages like Spanish and Hebrew. They use a Markov random field to infer how the sentence must be modified while altering the grammatical gender of particular nouns to preserve morpho-syntactic agreement. In contrast, Maudslay et al. (2019) describe a method for probabilistic automatic in-place substitution of gendered words in a corpus. Unlike Lu et al., they propose an explicit treatment of first names by pre-defining name-pairs for swapping, thus expanding Lu et al.’s list of gendered word pairs significantly.
+
+# 3 DATA COLLECTION
+
+We use Amazon’s Mechanical Turk crowdsourcing platform to recruit editors to revise each document. To ensure high quality of the collected data, we restricted the pool to U.S. residents that had already completed at least $5 0 0 ~ \mathrm { H I T s }$ and had an over $9 7 \%$ HIT approval rate. For each HIT, we conducted pilot tests to identify appropriate compensation per assignment, receive feedback from workers and revise our instructions accordingly. A total of 713 workers contributed throughout the whole process, of which 518 contributed edits reflected in the final datasets.
+
+![](images/ddc33254b6efd758b4b27d1fb01a16d9cab9c2c09c23b87f1555a076f3f96053.jpg)  
+Figure 2: Annotation platform for collecting counterfactually annotated data for sentiment analysis
+
+Table 1: Percentage of inter-editor agreement for counterfactually-revised movie reviews   
+
+<table><tr><td colspan="10">Number of tokens</td></tr><tr><td>Type</td><td>0-50</td><td>51-100</td><td>101-150</td><td>151-200</td><td>201-250</td><td>251-300</td><td>301-329</td><td>Full</td></tr><tr><td>Replacement</td><td>35.6</td><td>25.7</td><td>20.0</td><td>17.2</td><td>15.0</td><td>14.8</td><td>11.6</td><td>19.3</td></tr><tr><td>Insertion</td><td>27.7</td><td>20.8</td><td>14.4</td><td>12.2</td><td>11.0</td><td>11.5</td><td>07.6</td><td>14.3</td></tr><tr><td>Combined</td><td>41.6</td><td>32.7</td><td>26.3</td><td>23.4</td><td>21.6</td><td>20.3</td><td>16.2</td><td>25.5</td></tr></table>
+
+Sentiment Analysis The original IMDb dataset consists of $5 0 k$ reviews divided equally across train and test splits. To keep the task of editing from growing unwieldy, we filter out the longest $20 \%$ of reviews, leaving $2 0 k$ reviews in the train split from which we randomly sample $2 . 5 k$ reviews, enforcing a 50:50 class balance. Following revision by the crowd workers, we partition this dataset into train/validation/test splits containing 1707, 245 and 488 examples, respectively. We present each review to two workers, instructing them to revise the review such that (a) the counterfactual label applies; (b) the document remains coherent; and (c) no unecessary modifications are made.
+
+Over a four week period, we manually inspected each generated review and rejected the ones that were outright wrong (sentiment was still the same or the review was a spam). After review, we rejected roughly $2 \%$ of revised reviews. For 60 original reviews, we did not approve any among the counterfactually-revised counterparts supplied by the workers. To construct the new dataset, we chose one revised review (at random) corresponding to each original review. In qualitative analysis, we identified eight common patterns among the edits (Table 2).
+
+By comparing original reviews to their counterfactually-revised counterparts we gain insight into which aspects are causally relevant. To analyze inter-editor agreement, we mark indices corresponding to replacements and insertions, representing the edits in each original review by a binary vector. Using these representations, we compute the Jaccard similarity between the two reviews (Table 1), finding it to be negatively correlated with the length of the review.
+
+Natural Language Inference Unlike sentiment analysis, SNLI is 3-way classification task, with inputs consisting of two sentences, a premise and a hypothesis and the three possible labels being entailment, contradiction, and neutral. The label is meant to describe the relationship between the facts stated in each sentence. We randomly sampled 1750, 250, and 500 pairs from the train, validation, and test sets of SNLI respectively, constraining the new data to have balanced classes. In one HIT, we asked workers to revise the hypothesis while keeping the premise intact, seeking edits corresponding to each of the two counterfactual classes. We refer to this data as Revised Hypothesis (RH). In another HIT, we asked workers to revise the original premise, while leaving the original hypothesis intact, seeking similar edits, calling it Revised Premise (RP).
+
+Table 2: Most prominent categories of edits performed by humans for sentiment analysis (Original/Revised, in order). Red spans were replaced by Blue spans.   
+
+<table><tr><td>Types of Revisions</td><td>Examples</td></tr><tr><td>Recasting fact as hoped for</td><td>The world of Atlantis,hidden beneath the earth&#x27;s core,is fantastic The world of Atlantis,hidden beneath the earth&#x27;s core is supposed to be fantastic</td></tr><tr><td>Suggesting sarcasm</td><td>thoroughly captivating thriller-drama, taking a deep and real- istic view thoroughly mind numbing “thriller-drama&quot;, taking a “deep&quot;</td></tr><tr><td>Inserting modifiers</td><td>and “realistic”(who are they kidding?) view The presentation of simply Atlantis&#x27; landscape and setting</td></tr><tr><td>Replacing modifiers</td><td>The presentation of Atlantis’ predictable landscape and setting “Election” is a highly fascinating and thoroughly captivating thriller-drama</td></tr><tr><td>Inserting phrases</td><td>“Election” is a highly expected and thoroughly mind numbing &quot;thriller-drama&quot; Although there&#x27;s hardly any action, the ending is still shocking. Although there&#x27;s hardly any action (or reason to continue watch-</td></tr><tr><td>Diminishing via qualifiers</td><td>ing past 10 minutes), the ending is still shocking. which,while usually containing some reminder of harshness,be- come more and more intriguing.</td></tr><tr><td>Differing perspectives</td><td>which,usually containing some reminder of harshness,became only slightly more intriguing. Granted, not all of the story makes full sense, but the film doesn&#x27;t feature any amazing new computer-generated visual effects.</td></tr><tr><td>Changing ratings</td><td>Granted, some of the story makes sense, but the film doesn&#x27;t feature any amazing new computer-generated visual effects. one of the worst ever scenes in a sports movie. 3 stars out of 10. one of the wildest ever scenes in a sports movie. 8 stars out of 10.</td></tr></table>
+
+Following data collection, we employed a different set of workers to verify whether the given label accurately described the relationship between each premise-hypothesis pair. We presented each pair to three workers and performed a majority vote. When all three reviewers were in agreement, we approved or rejected the pair based on their decision, else, we verified the data ourselves. Finally, we only kept premise-hypothesis pairs for which we had valid revised data in both RP and RH, corresponding to both counterfactual labels. As a result, we discarded $\approx 9 \%$ data. RP and RH, each comprised of 3332 pairs in train, 400 in validation, and 800 in test, leading to a total of 6664 pairs in train, 800 in validation, and 1600 in test in the revised dataset. In qualitative analysis, we identified some common patterns among hypothesis and premise edits (Table 3, 4).
+
+We collected all data after IRB approval and measured the time taken to complete each HIT to ensure that all workers were paid more than the federal minimum wage. During our pilot studies, workers spent roughly 5 minutes per revised review, and 4 minutes per revised sentence (for NLI). We paid workers $\$ 0.65$ per revision, and $\$ 0.15$ per verification, totalling $\$ 10778.14$ for the study.
+
+# 4 MODELS
+
+Our experiments rely on the following five models: Support Vector Machines (SVMs), Na¨ıve Bayes (NB) classifiers, Bidirectional Long Short-Term Memory Networks (Bi-LSTMs; Graves & Schmidhuber, 2005), ELMo models with LSTM, and fine-tuned BERT models (Devlin et al., 2019). For brevity, we discuss only implementation details necessary for reproducibility.
+
+Table 3: Analysis of edits performed by humans for NLI hypotheses. P denotes Premise, OH denotes Original Hypothesis, and NH denotes New Hypothesis.   
+
+<table><tr><td>Types of Revisions</td><td>Examples</td></tr><tr><td>Modifying/removing actions</td><td>P: A young dark-haired woman crouches on the banks of a river while washing dishes. OH: A woman washes dishes in the river while camping. (Neu- tral)</td></tr><tr><td>Substituting entities</td><td>NH:A woman washes dishes in the river.(Entailment) P:Students are inside of a lecture hall. OH: Students are indoors. (Entailment)</td></tr><tr><td>Adding details to entities</td><td>NH: Students are on the soccer field. (Contradiction) P:An older man with glasses raises his eyebrows in surprise. OH: The man has no glasses. (Contradiction)</td></tr><tr><td>Inserting relationships</td><td>NH: The man wears bifocals. (Neutral) P:A blond woman speaking to a brunette woman with her arms crossed. OH:A woman is talking to another woman. (Entailment)</td></tr><tr><td>Numerical modifications</td><td>NH: A woman is talking to a family member. (Neutral) P: Several farmers bent over working on the fields while lady with a baby and four other children accompany them. OH:The lady has three children.(Contradiction)</td></tr><tr><td>Using/Removing negation</td><td>NH: The lady has many children. (Entailment) P:An older man with glasses raises his eyebrows in surprise. OH: The man has no glasses. (Contradiction)</td></tr><tr><td>Unrelated hypothesis</td><td>NH: The man wears glasses. (Entailment) P:A female athlete in crimson top and dark blue shorts is run- ning on the street. OH: A woman is sitting on a white couch. (Contradiction)</td></tr></table>
+
+Standard Methods We use scikit-learn (Pedregosa et al., 2011) implementations of SVMs and Na¨ıve Bayes for sentiment analysis. We train these models on TF-IDF bag of words feature representations of the reviews. We identify parameters for both classifiers using grid search conducted over the validation set.
+
+Bi-LSTM When training Bi-LSTMs for sentiment analysis, we restrict the vocabulary to the most frequent $2 0 k$ tokens, replacing out-of-vocabulary tokens by UNK. We fix the maximum input length at 300 tokens and pad smaller reviews. Each token is represented by a randomly-initialized 50-dimensional embedding. Our model consists of a bidirectional LSTM (hidden dimension 50) with recurrent dropout (probability 0.5) and global max-pooling following the embedding layer. To generate output, we feed this (fixed-length) representation through a fully-connected hidden layer with ReLU (Nair & Hinton, 2010) activation (hidden dimension 50), and then a fully-connected output layer with softmax activation. We train all models for a maximum of 20 epochs using Adam (Kingma & Ba, 2015), with a learning rate of $\mathrm { 1 e { - } 3 }$ and a batch size of 32. We apply early stopping when validation loss does not decrease for 5 epochs. We also experimented with a larger Bi-LSTM which led to overfitting. We use the architecture due to Poliak et al. (2018) to evaluate hypothesisonly baselines.2
+
+ELMo-LSTM We compute contextualized word representations (ELMo) using character-based word representations and bidirectional LSTMs (Peters et al., 2018). The module outputs a 1024- dimensional weighted sum of representations from the 3 Bi-LSTM layers used in ELMo. We represent each word by a 128-dimensional embedding concatenated to the resulting 1024-dimensional ELMo representation, leading to a 1152-dimensional hidden representation. Following Batch Normalization, this is passed through an LSTM (hidden size 128) with recurrent dropout (probability
+
+Table 4: Analysis of edits performed by humans for NLI premises. OP denotes Original Premise, NP denotes New Premise, and H denotes Hypothesis.   
+
+<table><tr><td>Types of Revisions</td><td>Examples</td></tr><tr><td>Introducing direct evidence</td><td>OP: Man walking with tall buildings with reflections behind him. (Neutral) NP: Man walking away from his friend, with tall buildings</td></tr><tr><td>Introducing indirect evidence</td><td>with reflections behind him. (Contradiction) H: The man was walking to meet a friend. OP:An Indian man standing on the bank of a river. (Neutral) NP: An Indian man standing with only a camera on the bank of a river. (Contradiction)</td></tr><tr><td>Substituting entities</td><td>H: He is fishing. OP:A young man in front of a grill laughs while pointing at something to his left. (Entailment) NP: A young man in front of a chair laughs while pointing at</td></tr><tr><td>Numerical modifications</td><td>something to his left. (Neutral) H:A man is outside OP:The exhaustion in the woman&#x27;s face while she continues to ride her bicycle in the competition.(Neutral) NP: The exhaustion in the woman&#x27;s face while she continues to ride her bicycle in the competition for people above 7 ft.</td></tr><tr><td>Reducing evidence</td><td>(Entailment) H: A tall person on a bike OP: The girl in yellow shorts and white jacket has a tennis ball in her left pocket. (Entailment) NP: The girl in yellow shorts and white jacket has a tennis ball.</td></tr><tr><td>Using abstractions</td><td>(Neutral) H: A girl with a tennis ball in her pocket. OP: An elderly woman in a crowd pushing a wheelchair. (En- tailment)</td></tr><tr><td>Substituting evidence</td><td>NP: An elderly person in a crowd pushing a wheelchair. (Neu- tral) H: There is an elderly woman in a crowd. OP: A woman is cutting something with scissors. (Entail- ment) NP: A woman is reading something about scissors. (Contra- diction)</td></tr></table>
+
+0.2). The output from this LSTM is then passed to a fully-connected output layer with softmax activation. We train this model for up to 20 epochs with same early stopping criteria as for Bi-LSTM, using the Adam optimizer with a learning rate of $\mathrm { 1 e { - } 3 }$ and a batch size of 32.
+
+BERT We use an off-the-shelf uncased BERT Base model, fine-tuning for each task.3 To account for BERT’s sub-word tokenization, we set the maximum token length is set at 350 for sentiment analysis and 50 for NLI. We fine-tune BERT up to 20 epochs with same early stopping criteria as for Bi-LSTM, using the BERT Adam optimizer with a batch size of 16 (to fit on a Tesla V-100 GPU). We found learning rates of $5 \mathrm { e } { - 5 }$ and $1 \mathrm { e } { - } 5$ to work best for sentiment analysis and NLI respectively.
+
+![](images/dc07cb5d2dccb512e1c308efdaf27a8d1d6129edb1f9b1ad6b4b1d2083e97816.jpg)  
+Figure 3: Most important features learned by an SVM classifier trained on TF-IDF bag of words.
+
+# 5 EXPERIMENTAL RESULTS
+
+Sentiment Analysis We find that for sentiment analysis, linear models trained on the original $1 . 7 k$ reviews achieve $8 0 \%$ accuracy when evaluated on original reviews but only $5 1 \%$ (level of random guessing) on revised reviews (Table 5). Linear models trained on revised reviews achieve $9 1 \%$ accuracy on revised reviews but only $5 8 . 3 \%$ on the original test set. We see similar pattern for Bi-LSTMs where accuracy drops substantially in both directions. Interestingly, while BERT models suffer drops too, they are less pronounced, perhaps a benefit of the exposure to a larger dataset where the spurious patterns may not have held. Classifiers trained on combined datasets perform well on both, often within $\approx 3$ pts of models trained on the same amount of data taken only from the original distribution. Thus, there may be a price to pay for breaking the reliance on spurious associations, but it may not be substantial.
+
+We also conduct experiments to evaluate our sentiment models vis-a-vis their generalization out-ofdomain to new domains. We evaluate models on Amazon reviews (Ni et al., 2019) on data aggregated over six genres: beauty, fashion, appliances, giftcards, magazines, and software, the Twitter sentiment dataset (Rosenthal et al., 2017),4 and Yelp reviews released as part of the Yelp dataset challenge. We show that in almost all cases, models trained on the counterfactually-augmented IMDb dataset perform better than models trained on comparable quantities of original data.
+
+To gain intuition about what is learnable absent the edited spans, we tried training several models on passages where the edited spans have been removed from training set sentences (but not test set). SVM, Na¨ıve Bayes, and Bi-LSTM achieve $5 7 . 8 \%$ , $5 9 . 1 \%$ , $6 0 . 2 \%$ accuracy, respectively, on this task. Notably, these passages are predictive of the (true) label despite being semantially compatible with the counterfactual label. However, BERT performs worse than random guessing.
+
+In one simple demonstration of the benefits of our approach, we note that seemingly irrelevant words such as: romantic, will, my, has, especially, life, works, both, it, its, lives and gives (correlated with positive sentiment), and horror, own, jesus, cannot, even, instead, minutes, your, effort, script, seems and something (correlated with negative sentiment) are picked up as high-weight features by linear models trained on either original or revised reviews as top predictors. However, because humans never edit these during revision owing to their lack of semantic relevance, combining the original and revised datasets breaks these associations and these terms cease to be predictive of sentiment (Fig 4). Models trained on original data but at the same scale as combined data are able to perform slightly better on the original test set but still fail on the revised reviews. All models trained on $1 9 k$ original reviews receive a slight boost in accuracy on revised data (except Na¨ıve Bayes), yet their performance significantly worse compared to specialized models. Retraining models on a combination of the original $1 9 k$ reviews with revised $1 . 7 k$ reviews leads to significant increases in accuracy for all models on classifying revised reviews, while slightly improving the accuracy on classifying the original reviews. This underscores the importance of including counterfactuallyrevised examples in training data.
+
+Natural Language Inference Fine-tuned on $1 . 6 7 k$ original sentence pairs, BERT achieves $7 2 . 2 \%$ accuracy on SNLI dataset but it is only able to accurately classify $3 9 . 7 \%$ sentence pairs from the RP set (Table 7). Fine-tuning BERT on the full SNLI training set ( $5 0 0 k$ sentence pairs) results in similar behavior. Fine-tuning it on RP sentence pairs improves its accuracy to $6 6 . 3 \%$ on RP but causes a drop of roughly 20 pts on SNLI. On RH sentence pairs, this results in an accuracy of $6 7 \%$ on RH and $\bar { 7 } 1 . 9 \%$ on SNLI test set but $4 7 . 4 \%$ on the RP set. To put these numbers in context, each individual hypothesis sentence in RP is associated with two labels, each in the presence of a different premise. A model that relies on hypotheses only would at best perform slightly better than choosing the majority class when evaluated on this dataset. However, fine-tuning BERT on a combination of RP and RH leads to consistent performance on all datasets as the dataset design forces models to look at both premise and hypothesis. Combining original sentences with RP and RH improves these numbers even further. We compare this with the performance obtained by fine-tuning it on $8 . 3 k$ sentence pairs sampled from SNLI training set, and show that while the two perform roughly within 4 pts of each other when evaluated on SNLI, the former outperforms latter on both RP and RH.
+
+Table 5: Accuracy of various models for sentiment analysis trained with various datasets. Orig. denotes original, Rev. denotes revised, and Orig. - Edited denotes the original dataset where the edited spans have been removed.   
+
+<table><tr><td> Training data</td><td colspan="2">SVM</td><td colspan="2">NB</td><td colspan="2">ELMo</td><td colspan="2">Bi-LSTM</td><td colspan="2">BERT</td></tr><tr><td></td><td>0</td><td>R</td><td>0</td><td>R</td><td>0</td><td>R</td><td>0</td><td>R</td><td>0</td><td>R</td></tr><tr><td>Orig. (1.7k)</td><td>80.0</td><td>51.0</td><td>74.9</td><td>47.3</td><td>81.9</td><td>66.7</td><td>79.3</td><td>55.7</td><td>87.4</td><td>82.2</td></tr><tr><td>Rev. (1.7k)</td><td>58.3</td><td>91.2</td><td>50.9</td><td>88.7</td><td>63.8</td><td>82.0</td><td>62.5</td><td>89.1</td><td>80.4</td><td>90.8</td></tr><tr><td>Orig. -Edited</td><td>57.8</td><td>1</td><td>59.1</td><td>1</td><td>50.3</td><td>1</td><td>60.2</td><td>1</td><td>49.2</td><td>1</td></tr><tr><td>Orig. &amp; Rev. (3.4k)</td><td>83.7</td><td>87.3</td><td>86.1</td><td>91.2</td><td>85.0</td><td>92.0</td><td>81.5</td><td>92.0</td><td>88.5</td><td>95.1</td></tr><tr><td>Orig. (3.4k)</td><td>85.1</td><td>54.3</td><td>82.4</td><td>48.2</td><td>82.4</td><td>61.1</td><td>80.4</td><td>59.6</td><td>90.2</td><td>86.1</td></tr><tr><td>Orig. (19k)</td><td>87.8</td><td>60.9</td><td>84.3</td><td>42.8</td><td>86.5</td><td>64.3</td><td>86.3</td><td>68.0</td><td>93.2</td><td>88.3</td></tr><tr><td>Orig. (19k)&amp; Rev.</td><td>87.8</td><td>76.2</td><td>85.2</td><td>48.4</td><td>88.3</td><td>84.6</td><td>88.7</td><td>79.5</td><td>93.2</td><td>93.9</td></tr></table>
+
+Table 6: Accuracy of various sentiment analysis models on out-of-domain data   
+
+<table><tr><td>Training data</td><td>SVM</td><td>NB</td><td>ELMo</td><td>Bi-LSTM</td><td>BERT</td></tr><tr><td></td><td>Accuracy on Amazon Reviews</td><td></td><td></td><td></td><td></td></tr><tr><td>Orig. &amp; Rev. (3.4k)</td><td>77.1</td><td>82.6</td><td>78.4</td><td>82.7</td><td>85.1</td></tr><tr><td>Orig. (3.4k)</td><td>74.7</td><td>66.9</td><td>79.1</td><td>65.9</td><td>80.0</td></tr><tr><td>Accuracy on Semeval 2017 (Twitter)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Orig. &amp; Rev. (3.4k)</td><td>66.5</td><td>73.9</td><td>70.0</td><td>68.7</td><td>82.9</td></tr><tr><td>Orig. (3.4k)</td><td>61.2</td><td>64.6</td><td>69.5</td><td>55.3</td><td>79.3</td></tr><tr><td></td><td>Accuracy </td><td></td><td> on Yelp Reviews</td><td></td><td></td></tr><tr><td>Orig. &amp; Rev. (3.4k)</td><td>87.6</td><td>89.6</td><td>87.2</td><td>86.2</td><td>89.4</td></tr><tr><td>Orig. (3.4k)</td><td>81.8</td><td>77.5</td><td>82.0</td><td>78.0</td><td>85.3</td></tr></table>
+
+Table 7: Accuracy of BERT on NLI with various train and eval sets.   
+
+<table><tr><td>Train/Eval</td><td>Original</td><td>RP</td><td>RH</td><td>RP&amp;RH</td></tr><tr><td>Original (1.67k)</td><td>72.2</td><td>39.7</td><td>59.5</td><td>49.6</td></tr><tr><td>Revised Premise (RP; 3.3k)</td><td>50.6</td><td>66.3</td><td>50.1</td><td>58.2</td></tr><tr><td>Revised Hypothesis (RH; 3.3k)</td><td>71.9</td><td>47.4</td><td>67.0</td><td>57.2</td></tr><tr><td>RP &amp; RH(6.6k)</td><td>64.7</td><td>64.6</td><td>67.8</td><td>66.2</td></tr><tr><td>Original w/RP &amp; RH(8.3k)</td><td>73.5</td><td>64.6</td><td>69.6</td><td>67.1</td></tr><tr><td>Original (8.3k)</td><td>77.8</td><td>44.6</td><td>66.1</td><td>55.4</td></tr><tr><td>Original (500k)</td><td>90.4</td><td>54.3</td><td>74.3</td><td>64.3</td></tr></table>
+
+Table 8: Accuracy of Bi-LSTM classifier trained on hypotheses only   
+
+<table><tr><td>Train/Test</td><td>Original</td><td>RP</td><td>RH</td><td>RP&amp;RH</td></tr><tr><td>Majority class</td><td>34.7</td><td>34.6</td><td>34.6</td><td>34.6</td></tr><tr><td>RP &amp; RH(6.6k)</td><td>32.4</td><td>35.1</td><td>33.4</td><td>34.2</td></tr><tr><td>Original w/RP &amp; RH (8.3k)</td><td>44.0</td><td>25.8</td><td>43.2</td><td>34.5</td></tr><tr><td>Original (8.3k)</td><td>60.2</td><td>20.5</td><td>46.6</td><td>33.6</td></tr><tr><td>Original (500k)</td><td>69.0</td><td>15.4</td><td>53.2</td><td>34.3</td></tr></table>
+
+Table 9: Accuracy of models trained to differentiate between original and revised data   
+
+<table><tr><td>Model</td><td>IMDb</td><td>SNLI/RP</td><td>SNLI/RH</td></tr><tr><td>Majority class</td><td>50.0</td><td>66.7</td><td>66.7</td></tr><tr><td>SVM</td><td>67.4</td><td>46.6</td><td>51.0</td></tr><tr><td>NB</td><td>69.2</td><td>66.7</td><td>66.6</td></tr><tr><td>BERT</td><td>77.3</td><td>64.8</td><td>69.7</td></tr></table>
+
+To further isolate this effect, Bi-LSTM trained on SNLI hypotheses only achieves $6 9 \%$ accuracy on SNLI test set, which drops to $4 4 \%$ if it is retrained on combination of original, RP and RH data (Table 8). Note that this combined dataset consists of five variants of each original premisehypothesis pair. Of these five pairs, three consist of the same hypothesis sentence, each associated with different truth value given the respective premise. Using these hypotheses only would provide conflicting feedback to a classifier during training, thus causing the drop in performance. Further, we notice that the gain of the latter over majority class baseline comes primarily from the original data, as the same model retrained only on RP and RH data experiences a further drop of $1 1 . 6 \%$ in accuracy, performing worse than just choosing the majority class at all times.
+
+One reasonable concern might be that our models would simply distinguish whether an example were from the original or revised dataset and thereafter treat them differently. The fear might be that our models would exhibit a hypersensitivity (rather than insensitivity) to domain. To test the potential for this behavior, we train several models to distinguish between original and revised data (Table 9). BERT identifies original reviews from revised reviews with $7 7 . 3 \%$ accuracy. In case of NLI, BERT and Na¨ıve Bayes perform roughly within 3 pts of the majority class baseline $( 6 6 . 7 \% )$ whereas SVM performs substantially worse.
+
+# 6 CONCLUSION
+
+By leveraging humans not only to provide labels but also to intervene upon the data, revising documents to accord with various labels, we can elucidate the difference that makes a difference. Moreover, we can leverage the augmented data to train classifiers less dependent on spurious associations. Our study demonstrates the promise of leveraging human-in-the-loop feedback to disentangle the spurious and non-spurious associations, yielding classifiers that hold up better when spurious associations do not transport out of domain. Our methods appear useful on both sentiment analysis and NLI, two contrasting tasks. In sentiment analysis, expressions of opinion matter more than stated facts, while in NLI this is reversed. SNLI poses another challenge in that it is a 3-class classification task using two input sentences. In future work, we will extend these techniques, leveraging humans in the loop to build more robust systems for question answering and summarization.
+
+# ACKNOWLEDGEMENTS
+
+The authors are grateful to Amazon AWS and NVIDIA for providing GPUs to conduct the experiments, Salesforce Research and Facebook AI for their generous grants that made the data collection possible, Sina Fazelpour, Sivaraman Balakrishnan, Shruti Rijhwani, Shruti Palaskar, Aishwarya Kamath, Michael Collins, Rajesh Ranganath and Sanjoy Dasgupta for their valuable feedback, and Tzu-Hsiang Lin for his generous help in creating the data collection platform. We also thank Abridge AI, UPMC, the Center for Machine Learning in Health, and the AI Ethics and Governance Fund for their support of our broader research on robust machine learning.
+
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+Jianmo Ni, Jiacheng Li, and Julian McAuley. Justifying recommendations using distantly-labeled reviews and fine-grained aspects. In Empirical Methods in Natural Language Processing and International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), 2019. URL https://www.aclweb.org/anthology/D19-1018.
+
+F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-learn: Machine learning in Python. Journal of Machine Learning Research (JMLR), 12, 2011.
+
+Matthew E Peters, Mark Neumann, Mohit Iyyer, Matt Gardner, Christopher Clark, Kenton Lee, and Luke Zettlemoyer. Deep contextualized word representations. In North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLT), 2018.
+
+Jonas Pfeiffer, Aishwarya Kamath, Iryna Gurevych, and Sebastian Ruder. What do deep networks like to read? arXiv preprint arXiv:1909.04547, 2019.
+
+Adam Poliak, Jason Naradowsky, Aparajita Haldar, Rachel Rudinger, and Benjamin Van Durme. Hypothesis Only Baselines in Natural Language Inference. In Joint Conference on Lexical and Computational Semantics (\*Sem), 2018.
+
+Stefanos Poulis and Sanjoy Dasgupta. Learning with feature feedback: from theory to practice. In Artificial Intelligence and Statistics (AISTATS), 2017.
+
+Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. Semantically equivalent adversarial rules for debugging nlp models. In Association for Computational Linguistics (ACL), 2018.
+
+Sara Rosenthal, Noura Farra, and Preslav Nakov. SemEval-2017 task 4: Sentiment analysis in twitter. In International Workshop on Semantic Evaluation (SemEval), 2017. URL https: //www.aclweb.org/anthology/S17-2088.
+
+Judy Hanwen Shen, Lauren Fratamico, Iyad Rahwan, and Alexander M Rush. Darling or babygirl? investigating stylistic bias in sentiment analysis. 5th Workshop on Fairness, Accountability, and Transparency in Machine Learning (FATML), 2018.
+
+Eric Wallace, Shi Feng, Nikhil Kandpal, Matt Gardner, and Sameer Singh. Universal adversarial triggers for nlp. arXiv preprint arXiv:1908.07125, 2019.
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+Omar Zaidan, Jason Eisner, and Christine Piatko. Using annotator rationales to improve machine learning for text categorization. In North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLT), 2007.
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+Omar F Zaidan and Jason Eisner. Modeling annotators: A generative approach to learning from annotator rationales. In Empirical Methods in Natural Language Processing (EMNLP). Association for Computational Linguistics, 2008.
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+
+Ran Zmigrod, Sebastian J. Mielke, Hanna Wallach, and Ryan Cotterell. Counterfactual data augmentation for mitigating gender stereotypes in languages with rich morphology. In Association for Computational Linguistics (ACL), 2019.
+
+# APPENDIX
+
+Table 10: Most frequent insertions/deletions by human annotators for sentiment analysis.   
+
+<table><tr><td>Revision</td><td>Removed words</td><td>Inserted words</td></tr><tr><td>Positive to Negative</td><td>movie,film,great, like,good,re- ally, would, see,story, love</td><td>movie, film, one, like,bad,would, really,even,story, see</td></tr><tr><td>Negative to Positive</td><td>bad,even,worst, waste,nothing, never,much,would, like, litle</td><td>great, good,best, even, well, amaz- ing,much,many,watch,better</td></tr></table>
+
+Table 11: Most frequent insertions/deletions by human annotators for SNLI.   
+
+<table><tr><td colspan="2">Revision Removed words</td><td>Inserted words</td></tr><tr><td colspan="2">Revising Premise</td><td></td></tr><tr><td>Entailment to Neutral</td><td>woman，walking，man，blue, sitting， men, girl, standing, looking,running</td><td>person, near, child, something, together, people, tall, vehicle, wall, holding</td></tr><tr><td>Neutral to Entailment</td><td>man,street,black,water, little, front,young,playing,woman, two</td><td>waiting,couple,playing,run- ning， getting，making， tall, game, black,happily</td></tr><tr><td>Entailment to Contradiction</td><td>blue,people,standing，girl, front，street，red,young，sit- ting,band</td><td>sitting， standing, inside, young, women, child, red, men, sits,one</td></tr><tr><td>Contradiction to Entailment</td><td>sitting，man，walking，black, blue,people,red，standing, white,street</td><td>man,sitting, sleeping,woman, sits,eating,playing,park, two, standing</td></tr><tr><td>Neutral to Contradiction</td><td>man， woman， people,boy, black，red,standing，young， two,water</td><td>man,woman, boy, men, alone, sitting,girl,dog,three,one</td></tr><tr><td>Contradiction to Neutral</td><td>man, sitting,black,blue,walk-1 ing，red,standing， street， white,street</td><td>man， sitting， woman, peo- ple,person, near, something, something,sits,black</td></tr><tr><td colspan="3">Revising Hypothesis</td></tr><tr><td>Entailment to Neutral</td><td>man, wearing， white, blue, black,shirt,one,young，peo- ple,woman</td><td>people,there,playing，man, person,wearing,outside,two, old, near</td></tr><tr><td>Neutral to Entailment</td><td>white，wearing，shirt,black, blue, man, two, standing, young, red</td><td>playing，wearing，man， two, there,woman，people,men, near,person</td></tr><tr><td>Entailment to Contradiction</td><td>man, wearing， white, blue, black,two,shirt,one,young, people</td><td>people,man, woman, playing, no,inside,person, two,wear- ing,women</td></tr><tr><td>Contradiction to Entailment</td><td>wearing， blue, black, man, white,two,red,shirt,young, one</td><td>people, there,man, two,wear- ing， playing， people,men, woman, outside</td></tr><tr><td>Neutral to Contradiction</td><td>white， man, wearing, shirt, black，blue，two，standing, woman, red</td><td>woman，man,there,playing, two,wearing, one,men,girl, no</td></tr><tr><td>Contradiction to Neutral</td><td>wearing，blue，black,man, white, two,red, sitting,young, standing</td><td>people,playing,man,woman, two,wearing,near, tall,men, old</td></tr></table>
+
+![](images/7cb9700ac11b85a6f7186dd7b2be5724ab8c3d6da2bbcb8cb8bcc5a7c49722da.jpg)  
+Figure 4: Thirty most important features learned by an SVM classifier trained on TF-IDF bag of words.
+
+The blue box contains a text passage and a label. Please edit this text in the textbox below, making a small number of changes such that:
+
+(a) the document remains coherent and (b) the new label (colored) accurately describes the revised passage.
+
+Do not change any portions of the passage unnecessarily.
+
+After modifying the passage and checking it over to make sure that is coherent and matches the label.
+
+(a) Revising IMDb movie reviews
+
+The upper blue box contains Sentence 1. The lower blue box contains Sentence 2. Given that Sentence 1 is True, Sentence 2 (by implication), must either be (a) definitely True, (b) definitely False, or (c) May be True.
+
+You are presented with an initial Sentence 1 and Sentence 2 and the correct initial relationship label (True, False, or May be True).
+
+Please edit Sentence 2 in the textboxes, making a small number of changes such that:
+
+(a) The new sentences are coherent and   
+(b) The target labels (in red) accurately describe the truthfulness of the modified Sentence 2 given the original Sentence 1.
+
+Do not change any portions of the sentence unnecessarily.
+
+After modifying the text and checking it over to make sure that it is coherent and matches the target label.
+
+(b) Revising hypothesis in SNLI
+
+The upper blue box contains Sentence 1. The lower blue box contains Sentence 2. Given that Sentence 1 is True, Sentence 2 (by implication), must either be (a) definitely True, (b) definitely False, or (c) May be True.
+
+You are presented with an initial Sentence 1 and Sentence 2 and the correct initial relationship label (True, False, or May be True).
+
+Please edit Sentence 1 in the textboxes, making a small number of changes such that:
+
+(a) The new sentences are coherent and   
+(b) The target labels (in red) accurately describe the truthfulness of the original Sentence 2 given the modified Sentence 1.
+
+After modifying the text and checking it over to make sure that it is coherent and matches the target label.
+
+(c) Revising premise in SNLI

parse/train/Sklgs0NFvr/Sklgs0NFvr_content_list.json

@@ -0,0 +1,1382 @@
+[
+    {
+        "type": "text",
+        "text": "LEARNING THE DIFFERENCE THAT MAKES A DIFFERENCE WITH COUNTERFACTUALLY-AUGMENTED DATA ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            98,
+            816,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Divyansh Kaushik, Eduard Hovy, Zachary C. Lipton   \nCarnegie Mellon University   \nPittsburgh PA, USA   \n{dkaushik, hovy, zlipton}@cmu.edu ",
+        "bbox": [
+            183,
+            169,
+            553,
+            226
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            262,
+            544,
+            277
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Despite alarm over the reliance of machine learning systems on so-called spurious patterns, the term lacks coherent meaning in standard statistical frameworks. However, the language of causality offers clarity: spurious associations are due to confounding (e.g., a common cause), but not direct or indirect causal effects. In this paper, we focus on natural language processing, introducing methods and resources for training models less sensitive to spurious patterns. Given documents and their initial labels, we task humans with revising each document so that it (i) accords with a counterfactual target label; (ii) retains internal coherence; and (iii) avoids unnecessary changes. Interestingly, on sentiment analysis and natural language inference tasks, classifiers trained on original data fail on their counterfactually-revised counterparts and vice versa. Classifiers trained on combined datasets perform remarkably well, just shy of those specialized to either domain. While classifiers trained on either original or manipulated data alone are sensitive to spurious features (e.g., mentions of genre), models trained on the combined data are less sensitive to this signal. Both datasets are publicly available1. ",
+        "bbox": [
+            233,
+            294,
+            764,
+            501
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            527,
+            336,
+            542
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "What makes a document’s sentiment positive? What makes a loan applicant creditworthy? What makes a job candidate qualified? When does a photograph truly depict a dolphin? Moreover, what does it mean for a feature to be relevant to such a determination? ",
+        "bbox": [
+            176,
+            559,
+            823,
+            601
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Statistical learning offers one framework for approaching these questions. First, we swap out the semantic question for a more readily answerable associative question. For example, instead of asking what conveys a document’s sentiment, we recast the question as which documents are likely to be labeled as positive (or negative)? Then, in this associative framing, we interpret as relevant, those features that are most predictive of the label. However, despite the rapid adoption and undeniable commercial success of associative learning, this framing seems unsatisfying. ",
+        "bbox": [
+            174,
+            608,
+            823,
+            690
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Alongside deep learning’s predictive wins, critical questions have piled up concerning spurious patterns, artifacts, robustness, and discrimination, that the purely associative perspective appears ill-equipped to answer. For example, in computer vision, researchers have found that deep neural networks rely on surface-level texture (Jo & Bengio, 2017; Geirhos et al., 2018) or clues in the image’s background to recognize foreground objects even when that seems both unnecessary and somehow wrong: the beach is not what makes a seagull a seagull. And yet, researchers struggle to articulate precisely why models should not rely on such patterns. ",
+        "bbox": [
+            174,
+            698,
+            825,
+            796
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In natural language processing (NLP), these issues have emerged as central concerns in the literature on annotation artifacts and societal biases. Across myriad tasks, researchers have demonstrated that models tend to rely on spurious associations (Poliak et al., 2018; Gururangan et al., 2018; Kaushik & Lipton, 2018; Kiritchenko & Mohammad, 2018). Notably, some models for question-answering tasks may not actually be sensitive to the choice of the question (Kaushik & Lipton, 2018), while in Natural Language Inference (NLI), classifiers trained on hypotheses only (vs hypotheses and premises) perform surprisingly well (Poliak et al., 2018; Gururangan et al., 2018). However, papers seldom make clear what, if anything, spuriousness means within the standard supervised learning framework. ML systems are trained to exploit the mutual information between features and a label to make accurate predictions. The standard statistical learning toolkit does not offer a conceptual distinction between spurious and non-spurious associations. ",
+        "bbox": [
+            174,
+            803,
+            825,
+            900
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/13256fcaea9ed4a3abaa41f3eb5712d6296f421625d51e2394c40ab84fc7930e.jpg",
+        "image_caption": [
+            "Figure 1: Pipeline for collecting and leveraging counterfactually-altered data "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            269,
+            102,
+            725,
+            265
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            325,
+            823,
+            381
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Causality, however, offers a coherent notion of spuriousness. Spurious associations owe to confounding rather than to a (direct or indirect) causal path. We might consider a factor of variation to be spuriously correlated with a label of interest if intervening upon it would not impact the applicability of the label or vice versa. While our paper does not call upon the mathematical machinery of causality, we draw inspiration from the underlying philosophy to design a new dataset creation procedure in which humans counterfactually revise documents. ",
+        "bbox": [
+            174,
+            388,
+            823,
+            472
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Returning to NLP, although we lack automated tools for mapping between raw text and disentangled factors, we nevertheless describe documents in terms of these abstract representations. Moreover, it seems natural to speak of manipulating these factors directly (Hovy, 1987). Consider, for example, the following interventions: (i) Revise the letter to make it more positive; (ii) Edit the second sentence so that it appears to contradict the first. These edits might be thought of as intervening on only those aspects of the text that are necessary to make the counterfactual label applicable. ",
+        "bbox": [
+            174,
+            479,
+            825,
+            563
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this exploratory paper, we design a human-in-the-loop system for counterfactually manipulating documents. Our hope is that by intervening only upon the factor of interest, we might disentangle the spurious and non-spurious associations, yielding classifiers that hold up better when spurious associations do not transport out of domain. We employ crowd workers not to label documents, but rather to edit them, manipulating the text to make a targeted (counterfactual) class applicable. For sentiment analysis, we direct the worker to revise this negative movie review to make it positive, without making any gratuitous changes. We might regard the second part of this directive as a least action principle, ensuring that we perturb only those spans necessary to alter the applicability of the label. For NLI, a 3-class classification task (entailment, contradiction, neutral), we ask the workers to modify the premise while keeping the hypothesis intact, and vice versa, collecting edits corresponding to each of the (two) counterfactual classes. Using this platform, we collect thousands of counterfactually-manipulated examples for both sentiment analysis and NLI, extending the IMDb (Maas et al., 2011) and SNLI (Bowman et al., 2015) datasets, respectively. The result is two new datasets (each an extension of a standard resource) that enable us to both probe fundamental properties of language and train classifiers less reliant on spurious signal. ",
+        "bbox": [
+            174,
+            570,
+            825,
+            777
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We show that classifiers trained on original IMDb reviews fail on counterfactually-revised data and vice versa. We further show that spurious correlations in these datasets are even picked up by linear models. However, augmenting the revised examples breaks up these correlations (e.g., genre ceases to be predictive of sentiment). For a Bidirectional LSTM (Graves & Schmidhuber, 2005) trained on IMDb reviews, classification accuracy goes down from $7 9 . 3 \\%$ to $5 5 . 7 \\%$ when evaluated on original vs revised reviews. The same classifier trained on revised reviews achieves an accuracy of $8 9 . 1 \\%$ on revised reviews compared to $6 2 . 5 \\%$ on their original counterparts. These numbers go to $8 1 . 7 \\%$ and $9 2 . 0 \\%$ on original and revised data, respectively, when the classifier is retrained on the combined dataset. Similar patterns are observed for linear classifiers. We discovered that BERT (Devlin et al., 2019) is more resilient to such drops in performance on sentiment analysis. ",
+        "bbox": [
+            174,
+            785,
+            825,
+            924
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Additionally, SNLI models appear to rely on spurious associations as identified by Gururangan et al. (2018). Our experiments show that when fine-tuned on original SNLI sentence pairs, BERT fails on pairs with revised premise and vice versa, suffering more than a 30 point drop in accuracy. Fine-tuned on the combined set, BERT’s performance improves significantly across all datasets. Similarly, a Bi-LSTM trained on (original) hypotheses alone can accurately classify $6 9 \\%$ of pairs correctly but performs worse than the blind classifier when evaluated on the revised dataset. When trained on hypotheses only from the combined dataset, its performance is not appreciably better than random guessing. ",
+        "bbox": [
+            174,
+            103,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            242,
+            344,
+            257
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Several papers demonstrate cases where NLP systems appear not to learn what humans consider to be the difference that makes the difference. For example, otherwise state-of-the-art models have been shown to be vulnerable to synthetic transformations such as distractor phrases (Jia & Liang, 2017; Wallace et al., 2019), to misclassify paraphrased task (Iyyer et al., 2018; Pfeiffer et al., 2019) and to fail on template-based modifications (Ribeiro et al., 2018). Glockner et al. (2018) demonstrate that simply replacing words by synonyms or hypernyms, which should not alter the applicable label, nevertheless breaks ML-based NLI systems. Gururangan et al. (2018) and Poliak et al. (2018) show that classifiers correctly classified the hypotheses alone in about $6 9 \\%$ of SNLI corpus. They further discover that crowd workers adopted specific annotation strategies and heuristics for data generation. Chen et al. (2016) identify similar issues exist with automatically-constructed benchmarks for question-answering (Hermann et al., 2015). Kaushik & Lipton (2018) discover that reported numbers in question-answering benchmarks could often be achieved by the same models when restricted to be blind either to the question or to the passages. Dixon et al. (2018); Zhao et al. (2018) and Kiritchenko & Mohammad (2018) showed how imbalances in training data lead to unintended bias in the resulting models, and, consequently, potentially unfair applications. Shen et al. (2018) substitute words to test the behavior of sentiment analysis algorithms in the presence of stylistic variation, finding that similar word pairs produce significant differences in sentiment score. ",
+        "bbox": [
+            174,
+            279,
+            825,
+            513
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Several papers explore richer feedback mechanisms for classification. Some ask annotators to highlight rationales, spans of text indicative of the label (Zaidan et al., 2007; Zaidan & Eisner, 2008; Poulis & Dasgupta, 2017). For each document, Zaidan et al. remove the rationales to generate contrast documents, learning classifiers to distinguish original documents from their contrasting counterparts. While this feedback is easier to collect than ours, how to leverage it for training deep NLP models, where features are not neatly separated, remains less clear. ",
+        "bbox": [
+            174,
+            520,
+            825,
+            603
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Lu et al. (2018) programmatically alter text to invert gender bias and combined the original and manipulated data yielding gender-balanced dataset for learning word embeddings. In the simplest experiments, they swap each gendered word for its other-gendered counterpart. For example, the doctor ran because he is late becomes the doctor ran because she is late. However, they do not substitute names even if they co-refer to a gendered pronoun. Building on their work, Zmigrod et al. (2019) describe a data augmentation approach for mitigating gender stereotypes associated with animate nouns for morphologically-rich languages like Spanish and Hebrew. They use a Markov random field to infer how the sentence must be modified while altering the grammatical gender of particular nouns to preserve morpho-syntactic agreement. In contrast, Maudslay et al. (2019) describe a method for probabilistic automatic in-place substitution of gendered words in a corpus. Unlike Lu et al., they propose an explicit treatment of first names by pre-defining name-pairs for swapping, thus expanding Lu et al.’s list of gendered word pairs significantly. ",
+        "bbox": [
+            174,
+            611,
+            825,
+            777
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 DATA COLLECTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            804,
+            367,
+            820
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We use Amazon’s Mechanical Turk crowdsourcing platform to recruit editors to revise each document. To ensure high quality of the collected data, we restricted the pool to U.S. residents that had already completed at least $5 0 0 ~ \\mathrm { H I T s }$ and had an over $9 7 \\%$ HIT approval rate. For each HIT, we conducted pilot tests to identify appropriate compensation per assignment, receive feedback from workers and revise our instructions accordingly. A total of 713 workers contributed throughout the whole process, of which 518 contributed edits reflected in the final datasets. ",
+        "bbox": [
+            174,
+            840,
+            825,
+            922
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/ddc33254b6efd758b4b27d1fb01a16d9cab9c2c09c23b87f1555a076f3f96053.jpg",
+        "image_caption": [
+            "Figure 2: Annotation platform for collecting counterfactually annotated data for sentiment analysis "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            108,
+            784,
+            354
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/fa994f3ecdd4c176803724f0d50ad0df681e8b2f6fa7a9de9e627eeed717ecb5.jpg",
+        "table_caption": [
+            "Table 1: Percentage of inter-editor agreement for counterfactually-revised movie reviews "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"10\">Number of tokens</td></tr><tr><td>Type</td><td>0-50</td><td>51-100</td><td>101-150</td><td>151-200</td><td>201-250</td><td>251-300</td><td>301-329</td><td>Full</td></tr><tr><td>Replacement</td><td>35.6</td><td>25.7</td><td>20.0</td><td>17.2</td><td>15.0</td><td>14.8</td><td>11.6</td><td>19.3</td></tr><tr><td>Insertion</td><td>27.7</td><td>20.8</td><td>14.4</td><td>12.2</td><td>11.0</td><td>11.5</td><td>07.6</td><td>14.3</td></tr><tr><td>Combined</td><td>41.6</td><td>32.7</td><td>26.3</td><td>23.4</td><td>21.6</td><td>20.3</td><td>16.2</td><td>25.5</td></tr></table>",
+        "bbox": [
+            207,
+            433,
+            790,
+            532
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Sentiment Analysis The original IMDb dataset consists of $5 0 k$ reviews divided equally across train and test splits. To keep the task of editing from growing unwieldy, we filter out the longest $20 \\%$ of reviews, leaving $2 0 k$ reviews in the train split from which we randomly sample $2 . 5 k$ reviews, enforcing a 50:50 class balance. Following revision by the crowd workers, we partition this dataset into train/validation/test splits containing 1707, 245 and 488 examples, respectively. We present each review to two workers, instructing them to revise the review such that (a) the counterfactual label applies; (b) the document remains coherent; and (c) no unecessary modifications are made. ",
+        "bbox": [
+            173,
+            554,
+            825,
+            652
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Over a four week period, we manually inspected each generated review and rejected the ones that were outright wrong (sentiment was still the same or the review was a spam). After review, we rejected roughly $2 \\%$ of revised reviews. For 60 original reviews, we did not approve any among the counterfactually-revised counterparts supplied by the workers. To construct the new dataset, we chose one revised review (at random) corresponding to each original review. In qualitative analysis, we identified eight common patterns among the edits (Table 2). ",
+        "bbox": [
+            174,
+            659,
+            825,
+            743
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "By comparing original reviews to their counterfactually-revised counterparts we gain insight into which aspects are causally relevant. To analyze inter-editor agreement, we mark indices corresponding to replacements and insertions, representing the edits in each original review by a binary vector. Using these representations, we compute the Jaccard similarity between the two reviews (Table 1), finding it to be negatively correlated with the length of the review. ",
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+        "type": "text",
+        "text": "Natural Language Inference Unlike sentiment analysis, SNLI is 3-way classification task, with inputs consisting of two sentences, a premise and a hypothesis and the three possible labels being entailment, contradiction, and neutral. The label is meant to describe the relationship between the facts stated in each sentence. We randomly sampled 1750, 250, and 500 pairs from the train, validation, and test sets of SNLI respectively, constraining the new data to have balanced classes. In one HIT, we asked workers to revise the hypothesis while keeping the premise intact, seeking edits corresponding to each of the two counterfactual classes. We refer to this data as Revised Hypothesis (RH). In another HIT, we asked workers to revise the original premise, while leaving the original hypothesis intact, seeking similar edits, calling it Revised Premise (RP). ",
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+    {
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+        "img_path": "images/4e769c70d1bc14f7b5717141bd16e1f2def9991bc47528537f7ee9b004914cf2.jpg",
+        "table_caption": [
+            "Table 2: Most prominent categories of edits performed by humans for sentiment analysis (Original/Revised, in order). Red spans were replaced by Blue spans. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Types of Revisions</td><td>Examples</td></tr><tr><td>Recasting fact as hoped for</td><td>The world of Atlantis,hidden beneath the earth&#x27;s core,is fantastic The world of Atlantis,hidden beneath the earth&#x27;s core is supposed to be fantastic</td></tr><tr><td>Suggesting sarcasm</td><td>thoroughly captivating thriller-drama, taking a deep and real- istic view thoroughly mind numbing “thriller-drama&quot;, taking a “deep&quot;</td></tr><tr><td>Inserting modifiers</td><td>and “realistic”(who are they kidding?) view The presentation of simply Atlantis&#x27; landscape and setting</td></tr><tr><td>Replacing modifiers</td><td>The presentation of Atlantis’ predictable landscape and setting “Election” is a highly fascinating and thoroughly captivating thriller-drama</td></tr><tr><td>Inserting phrases</td><td>“Election” is a highly expected and thoroughly mind numbing &quot;thriller-drama&quot; Although there&#x27;s hardly any action, the ending is still shocking. Although there&#x27;s hardly any action (or reason to continue watch-</td></tr><tr><td>Diminishing via qualifiers</td><td>ing past 10 minutes), the ending is still shocking. which,while usually containing some reminder of harshness,be- come more and more intriguing.</td></tr><tr><td>Differing perspectives</td><td>which,usually containing some reminder of harshness,became only slightly more intriguing. Granted, not all of the story makes full sense, but the film doesn&#x27;t feature any amazing new computer-generated visual effects.</td></tr><tr><td>Changing ratings</td><td>Granted, some of the story makes sense, but the film doesn&#x27;t feature any amazing new computer-generated visual effects. one of the worst ever scenes in a sports movie. 3 stars out of 10. one of the wildest ever scenes in a sports movie. 8 stars out of 10.</td></tr></table>",
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+        "text": "",
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+        "text": "Following data collection, we employed a different set of workers to verify whether the given label accurately described the relationship between each premise-hypothesis pair. We presented each pair to three workers and performed a majority vote. When all three reviewers were in agreement, we approved or rejected the pair based on their decision, else, we verified the data ourselves. Finally, we only kept premise-hypothesis pairs for which we had valid revised data in both RP and RH, corresponding to both counterfactual labels. As a result, we discarded $\\approx 9 \\%$ data. RP and RH, each comprised of 3332 pairs in train, 400 in validation, and 800 in test, leading to a total of 6664 pairs in train, 800 in validation, and 1600 in test in the revised dataset. In qualitative analysis, we identified some common patterns among hypothesis and premise edits (Table 3, 4). ",
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+        "type": "text",
+        "text": "We collected all data after IRB approval and measured the time taken to complete each HIT to ensure that all workers were paid more than the federal minimum wage. During our pilot studies, workers spent roughly 5 minutes per revised review, and 4 minutes per revised sentence (for NLI). We paid workers $\\$ 0.65$ per revision, and $\\$ 0.15$ per verification, totalling $\\$ 10778.14$ for the study. ",
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+    {
+        "type": "text",
+        "text": "4 MODELS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our experiments rely on the following five models: Support Vector Machines (SVMs), Na¨ıve Bayes (NB) classifiers, Bidirectional Long Short-Term Memory Networks (Bi-LSTMs; Graves & Schmidhuber, 2005), ELMo models with LSTM, and fine-tuned BERT models (Devlin et al., 2019). For brevity, we discuss only implementation details necessary for reproducibility. ",
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+        "table_caption": [
+            "Table 3: Analysis of edits performed by humans for NLI hypotheses. P denotes Premise, OH denotes Original Hypothesis, and NH denotes New Hypothesis. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Types of Revisions</td><td>Examples</td></tr><tr><td>Modifying/removing actions</td><td>P: A young dark-haired woman crouches on the banks of a river while washing dishes. OH: A woman washes dishes in the river while camping. (Neu- tral)</td></tr><tr><td>Substituting entities</td><td>NH:A woman washes dishes in the river.(Entailment) P:Students are inside of a lecture hall. OH: Students are indoors. (Entailment)</td></tr><tr><td>Adding details to entities</td><td>NH: Students are on the soccer field. (Contradiction) P:An older man with glasses raises his eyebrows in surprise. OH: The man has no glasses. (Contradiction)</td></tr><tr><td>Inserting relationships</td><td>NH: The man wears bifocals. (Neutral) P:A blond woman speaking to a brunette woman with her arms crossed. OH:A woman is talking to another woman. (Entailment)</td></tr><tr><td>Numerical modifications</td><td>NH: A woman is talking to a family member. (Neutral) P: Several farmers bent over working on the fields while lady with a baby and four other children accompany them. OH:The lady has three children.(Contradiction)</td></tr><tr><td>Using/Removing negation</td><td>NH: The lady has many children. (Entailment) P:An older man with glasses raises his eyebrows in surprise. OH: The man has no glasses. (Contradiction)</td></tr><tr><td>Unrelated hypothesis</td><td>NH: The man wears glasses. (Entailment) P:A female athlete in crimson top and dark blue shorts is run- ning on the street. OH: A woman is sitting on a white couch. (Contradiction)</td></tr></table>",
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+        "type": "text",
+        "text": "Standard Methods We use scikit-learn (Pedregosa et al., 2011) implementations of SVMs and Na¨ıve Bayes for sentiment analysis. We train these models on TF-IDF bag of words feature representations of the reviews. We identify parameters for both classifiers using grid search conducted over the validation set. ",
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+    {
+        "type": "text",
+        "text": "Bi-LSTM When training Bi-LSTMs for sentiment analysis, we restrict the vocabulary to the most frequent $2 0 k$ tokens, replacing out-of-vocabulary tokens by UNK. We fix the maximum input length at 300 tokens and pad smaller reviews. Each token is represented by a randomly-initialized 50-dimensional embedding. Our model consists of a bidirectional LSTM (hidden dimension 50) with recurrent dropout (probability 0.5) and global max-pooling following the embedding layer. To generate output, we feed this (fixed-length) representation through a fully-connected hidden layer with ReLU (Nair & Hinton, 2010) activation (hidden dimension 50), and then a fully-connected output layer with softmax activation. We train all models for a maximum of 20 epochs using Adam (Kingma & Ba, 2015), with a learning rate of $\\mathrm { 1 e { - } 3 }$ and a batch size of 32. We apply early stopping when validation loss does not decrease for 5 epochs. We also experimented with a larger Bi-LSTM which led to overfitting. We use the architecture due to Poliak et al. (2018) to evaluate hypothesisonly baselines.2 ",
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+    {
+        "type": "text",
+        "text": "ELMo-LSTM We compute contextualized word representations (ELMo) using character-based word representations and bidirectional LSTMs (Peters et al., 2018). The module outputs a 1024- dimensional weighted sum of representations from the 3 Bi-LSTM layers used in ELMo. We represent each word by a 128-dimensional embedding concatenated to the resulting 1024-dimensional ELMo representation, leading to a 1152-dimensional hidden representation. Following Batch Normalization, this is passed through an LSTM (hidden size 128) with recurrent dropout (probability ",
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+    {
+        "type": "table",
+        "img_path": "images/f5646fa09f785d7f5855247b3caf3b93a1592e930ef6ee602007eb932e437688.jpg",
+        "table_caption": [
+            "Table 4: Analysis of edits performed by humans for NLI premises. OP denotes Original Premise, NP denotes New Premise, and H denotes Hypothesis. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Types of Revisions</td><td>Examples</td></tr><tr><td>Introducing direct evidence</td><td>OP: Man walking with tall buildings with reflections behind him. (Neutral) NP: Man walking away from his friend, with tall buildings</td></tr><tr><td>Introducing indirect evidence</td><td>with reflections behind him. (Contradiction) H: The man was walking to meet a friend. OP:An Indian man standing on the bank of a river. (Neutral) NP: An Indian man standing with only a camera on the bank of a river. (Contradiction)</td></tr><tr><td>Substituting entities</td><td>H: He is fishing. OP:A young man in front of a grill laughs while pointing at something to his left. (Entailment) NP: A young man in front of a chair laughs while pointing at</td></tr><tr><td>Numerical modifications</td><td>something to his left. (Neutral) H:A man is outside OP:The exhaustion in the woman&#x27;s face while she continues to ride her bicycle in the competition.(Neutral) NP: The exhaustion in the woman&#x27;s face while she continues to ride her bicycle in the competition for people above 7 ft.</td></tr><tr><td>Reducing evidence</td><td>(Entailment) H: A tall person on a bike OP: The girl in yellow shorts and white jacket has a tennis ball in her left pocket. (Entailment) NP: The girl in yellow shorts and white jacket has a tennis ball.</td></tr><tr><td>Using abstractions</td><td>(Neutral) H: A girl with a tennis ball in her pocket. OP: An elderly woman in a crowd pushing a wheelchair. (En- tailment)</td></tr><tr><td>Substituting evidence</td><td>NP: An elderly person in a crowd pushing a wheelchair. (Neu- tral) H: There is an elderly woman in a crowd. OP: A woman is cutting something with scissors. (Entail- ment) NP: A woman is reading something about scissors. (Contra- diction)</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "0.2). The output from this LSTM is then passed to a fully-connected output layer with softmax activation. We train this model for up to 20 epochs with same early stopping criteria as for Bi-LSTM, using the Adam optimizer with a learning rate of $\\mathrm { 1 e { - } 3 }$ and a batch size of 32. ",
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+        "type": "text",
+        "text": "BERT We use an off-the-shelf uncased BERT Base model, fine-tuning for each task.3 To account for BERT’s sub-word tokenization, we set the maximum token length is set at 350 for sentiment analysis and 50 for NLI. We fine-tune BERT up to 20 epochs with same early stopping criteria as for Bi-LSTM, using the BERT Adam optimizer with a batch size of 16 (to fit on a Tesla V-100 GPU). We found learning rates of $5 \\mathrm { e } { - 5 }$ and $1 \\mathrm { e } { - } 5$ to work best for sentiment analysis and NLI respectively. ",
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+    {
+        "type": "image",
+        "img_path": "images/dc07cb5d2dccb512e1c308efdaf27a8d1d6129edb1f9b1ad6b4b1d2083e97816.jpg",
+        "image_caption": [
+            "Figure 3: Most important features learned by an SVM classifier trained on TF-IDF bag of words. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "5 EXPERIMENTAL RESULTS ",
+        "text_level": 1,
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+        "text": "Sentiment Analysis We find that for sentiment analysis, linear models trained on the original $1 . 7 k$ reviews achieve $8 0 \\%$ accuracy when evaluated on original reviews but only $5 1 \\%$ (level of random guessing) on revised reviews (Table 5). Linear models trained on revised reviews achieve $9 1 \\%$ accuracy on revised reviews but only $5 8 . 3 \\%$ on the original test set. We see similar pattern for Bi-LSTMs where accuracy drops substantially in both directions. Interestingly, while BERT models suffer drops too, they are less pronounced, perhaps a benefit of the exposure to a larger dataset where the spurious patterns may not have held. Classifiers trained on combined datasets perform well on both, often within $\\approx 3$ pts of models trained on the same amount of data taken only from the original distribution. Thus, there may be a price to pay for breaking the reliance on spurious associations, but it may not be substantial. ",
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+    {
+        "type": "text",
+        "text": "We also conduct experiments to evaluate our sentiment models vis-a-vis their generalization out-ofdomain to new domains. We evaluate models on Amazon reviews (Ni et al., 2019) on data aggregated over six genres: beauty, fashion, appliances, giftcards, magazines, and software, the Twitter sentiment dataset (Rosenthal et al., 2017),4 and Yelp reviews released as part of the Yelp dataset challenge. We show that in almost all cases, models trained on the counterfactually-augmented IMDb dataset perform better than models trained on comparable quantities of original data. ",
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+    {
+        "type": "text",
+        "text": "To gain intuition about what is learnable absent the edited spans, we tried training several models on passages where the edited spans have been removed from training set sentences (but not test set). SVM, Na¨ıve Bayes, and Bi-LSTM achieve $5 7 . 8 \\%$ , $5 9 . 1 \\%$ , $6 0 . 2 \\%$ accuracy, respectively, on this task. Notably, these passages are predictive of the (true) label despite being semantially compatible with the counterfactual label. However, BERT performs worse than random guessing. ",
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+    {
+        "type": "text",
+        "text": "In one simple demonstration of the benefits of our approach, we note that seemingly irrelevant words such as: romantic, will, my, has, especially, life, works, both, it, its, lives and gives (correlated with positive sentiment), and horror, own, jesus, cannot, even, instead, minutes, your, effort, script, seems and something (correlated with negative sentiment) are picked up as high-weight features by linear models trained on either original or revised reviews as top predictors. However, because humans never edit these during revision owing to their lack of semantic relevance, combining the original and revised datasets breaks these associations and these terms cease to be predictive of sentiment (Fig 4). Models trained on original data but at the same scale as combined data are able to perform slightly better on the original test set but still fail on the revised reviews. All models trained on $1 9 k$ original reviews receive a slight boost in accuracy on revised data (except Na¨ıve Bayes), yet their performance significantly worse compared to specialized models. Retraining models on a combination of the original $1 9 k$ reviews with revised $1 . 7 k$ reviews leads to significant increases in accuracy for all models on classifying revised reviews, while slightly improving the accuracy on classifying the original reviews. This underscores the importance of including counterfactuallyrevised examples in training data. ",
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+    {
+        "type": "text",
+        "text": "Natural Language Inference Fine-tuned on $1 . 6 7 k$ original sentence pairs, BERT achieves $7 2 . 2 \\%$ accuracy on SNLI dataset but it is only able to accurately classify $3 9 . 7 \\%$ sentence pairs from the RP set (Table 7). Fine-tuning BERT on the full SNLI training set ( $5 0 0 k$ sentence pairs) results in similar behavior. Fine-tuning it on RP sentence pairs improves its accuracy to $6 6 . 3 \\%$ on RP but causes a drop of roughly 20 pts on SNLI. On RH sentence pairs, this results in an accuracy of $6 7 \\%$ on RH and $\\bar { 7 } 1 . 9 \\%$ on SNLI test set but $4 7 . 4 \\%$ on the RP set. To put these numbers in context, each individual hypothesis sentence in RP is associated with two labels, each in the presence of a different premise. A model that relies on hypotheses only would at best perform slightly better than choosing the majority class when evaluated on this dataset. However, fine-tuning BERT on a combination of RP and RH leads to consistent performance on all datasets as the dataset design forces models to look at both premise and hypothesis. Combining original sentences with RP and RH improves these numbers even further. We compare this with the performance obtained by fine-tuning it on $8 . 3 k$ sentence pairs sampled from SNLI training set, and show that while the two perform roughly within 4 pts of each other when evaluated on SNLI, the former outperforms latter on both RP and RH. ",
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+    {
+        "type": "table",
+        "img_path": "images/0edffe5c28acac569cb9dd76b6ab92476a8e5b6fcbd9b4ff8057fb3ed2c803cf.jpg",
+        "table_caption": [
+            "Table 5: Accuracy of various models for sentiment analysis trained with various datasets. Orig. denotes original, Rev. denotes revised, and Orig. - Edited denotes the original dataset where the edited spans have been removed. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td> Training data</td><td colspan=\"2\">SVM</td><td colspan=\"2\">NB</td><td colspan=\"2\">ELMo</td><td colspan=\"2\">Bi-LSTM</td><td colspan=\"2\">BERT</td></tr><tr><td></td><td>0</td><td>R</td><td>0</td><td>R</td><td>0</td><td>R</td><td>0</td><td>R</td><td>0</td><td>R</td></tr><tr><td>Orig. (1.7k)</td><td>80.0</td><td>51.0</td><td>74.9</td><td>47.3</td><td>81.9</td><td>66.7</td><td>79.3</td><td>55.7</td><td>87.4</td><td>82.2</td></tr><tr><td>Rev. (1.7k)</td><td>58.3</td><td>91.2</td><td>50.9</td><td>88.7</td><td>63.8</td><td>82.0</td><td>62.5</td><td>89.1</td><td>80.4</td><td>90.8</td></tr><tr><td>Orig. -Edited</td><td>57.8</td><td>1</td><td>59.1</td><td>1</td><td>50.3</td><td>1</td><td>60.2</td><td>1</td><td>49.2</td><td>1</td></tr><tr><td>Orig. &amp; Rev. (3.4k)</td><td>83.7</td><td>87.3</td><td>86.1</td><td>91.2</td><td>85.0</td><td>92.0</td><td>81.5</td><td>92.0</td><td>88.5</td><td>95.1</td></tr><tr><td>Orig. (3.4k)</td><td>85.1</td><td>54.3</td><td>82.4</td><td>48.2</td><td>82.4</td><td>61.1</td><td>80.4</td><td>59.6</td><td>90.2</td><td>86.1</td></tr><tr><td>Orig. (19k)</td><td>87.8</td><td>60.9</td><td>84.3</td><td>42.8</td><td>86.5</td><td>64.3</td><td>86.3</td><td>68.0</td><td>93.2</td><td>88.3</td></tr><tr><td>Orig. (19k)&amp; Rev.</td><td>87.8</td><td>76.2</td><td>85.2</td><td>48.4</td><td>88.3</td><td>84.6</td><td>88.7</td><td>79.5</td><td>93.2</td><td>93.9</td></tr></table>",
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+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/2796fb07352bd8def1f9773fbae2ef09c489f1270b000701cf7c8ca5897f3db6.jpg",
+        "table_caption": [
+            "Table 6: Accuracy of various sentiment analysis models on out-of-domain data "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Training data</td><td>SVM</td><td>NB</td><td>ELMo</td><td>Bi-LSTM</td><td>BERT</td></tr><tr><td></td><td>Accuracy on Amazon Reviews</td><td></td><td></td><td></td><td></td></tr><tr><td>Orig. &amp; Rev. (3.4k)</td><td>77.1</td><td>82.6</td><td>78.4</td><td>82.7</td><td>85.1</td></tr><tr><td>Orig. (3.4k)</td><td>74.7</td><td>66.9</td><td>79.1</td><td>65.9</td><td>80.0</td></tr><tr><td>Accuracy on Semeval 2017 (Twitter)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Orig. &amp; Rev. (3.4k)</td><td>66.5</td><td>73.9</td><td>70.0</td><td>68.7</td><td>82.9</td></tr><tr><td>Orig. (3.4k)</td><td>61.2</td><td>64.6</td><td>69.5</td><td>55.3</td><td>79.3</td></tr><tr><td></td><td>Accuracy </td><td></td><td> on Yelp Reviews</td><td></td><td></td></tr><tr><td>Orig. &amp; Rev. (3.4k)</td><td>87.6</td><td>89.6</td><td>87.2</td><td>86.2</td><td>89.4</td></tr><tr><td>Orig. (3.4k)</td><td>81.8</td><td>77.5</td><td>82.0</td><td>78.0</td><td>85.3</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/78f6a41482b1cd92018b0bf360766974a27298e38ec7c284e8c359177a5acb3b.jpg",
+        "table_caption": [
+            "Table 7: Accuracy of BERT on NLI with various train and eval sets. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Train/Eval</td><td>Original</td><td>RP</td><td>RH</td><td>RP&amp;RH</td></tr><tr><td>Original (1.67k)</td><td>72.2</td><td>39.7</td><td>59.5</td><td>49.6</td></tr><tr><td>Revised Premise (RP; 3.3k)</td><td>50.6</td><td>66.3</td><td>50.1</td><td>58.2</td></tr><tr><td>Revised Hypothesis (RH; 3.3k)</td><td>71.9</td><td>47.4</td><td>67.0</td><td>57.2</td></tr><tr><td>RP &amp; RH(6.6k)</td><td>64.7</td><td>64.6</td><td>67.8</td><td>66.2</td></tr><tr><td>Original w/RP &amp; RH(8.3k)</td><td>73.5</td><td>64.6</td><td>69.6</td><td>67.1</td></tr><tr><td>Original (8.3k)</td><td>77.8</td><td>44.6</td><td>66.1</td><td>55.4</td></tr><tr><td>Original (500k)</td><td>90.4</td><td>54.3</td><td>74.3</td><td>64.3</td></tr></table>",
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+        "type": "table",
+        "img_path": "images/93c813b03bfb32adf4ff1998bfde73056911c0c728aaaa9f2d08d437102af6b5.jpg",
+        "table_caption": [
+            "Table 8: Accuracy of Bi-LSTM classifier trained on hypotheses only "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Train/Test</td><td>Original</td><td>RP</td><td>RH</td><td>RP&amp;RH</td></tr><tr><td>Majority class</td><td>34.7</td><td>34.6</td><td>34.6</td><td>34.6</td></tr><tr><td>RP &amp; RH(6.6k)</td><td>32.4</td><td>35.1</td><td>33.4</td><td>34.2</td></tr><tr><td>Original w/RP &amp; RH (8.3k)</td><td>44.0</td><td>25.8</td><td>43.2</td><td>34.5</td></tr><tr><td>Original (8.3k)</td><td>60.2</td><td>20.5</td><td>46.6</td><td>33.6</td></tr><tr><td>Original (500k)</td><td>69.0</td><td>15.4</td><td>53.2</td><td>34.3</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/75a9e344e2f41e95143941f26a4bb63575187dd43d9fae1280e4c0d36cb5e216.jpg",
+        "table_caption": [
+            "Table 9: Accuracy of models trained to differentiate between original and revised data "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>IMDb</td><td>SNLI/RP</td><td>SNLI/RH</td></tr><tr><td>Majority class</td><td>50.0</td><td>66.7</td><td>66.7</td></tr><tr><td>SVM</td><td>67.4</td><td>46.6</td><td>51.0</td></tr><tr><td>NB</td><td>69.2</td><td>66.7</td><td>66.6</td></tr><tr><td>BERT</td><td>77.3</td><td>64.8</td><td>69.7</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To further isolate this effect, Bi-LSTM trained on SNLI hypotheses only achieves $6 9 \\%$ accuracy on SNLI test set, which drops to $4 4 \\%$ if it is retrained on combination of original, RP and RH data (Table 8). Note that this combined dataset consists of five variants of each original premisehypothesis pair. Of these five pairs, three consist of the same hypothesis sentence, each associated with different truth value given the respective premise. Using these hypotheses only would provide conflicting feedback to a classifier during training, thus causing the drop in performance. Further, we notice that the gain of the latter over majority class baseline comes primarily from the original data, as the same model retrained only on RP and RH data experiences a further drop of $1 1 . 6 \\%$ in accuracy, performing worse than just choosing the majority class at all times. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "One reasonable concern might be that our models would simply distinguish whether an example were from the original or revised dataset and thereafter treat them differently. The fear might be that our models would exhibit a hypersensitivity (rather than insensitivity) to domain. To test the potential for this behavior, we train several models to distinguish between original and revised data (Table 9). BERT identifies original reviews from revised reviews with $7 7 . 3 \\%$ accuracy. In case of NLI, BERT and Na¨ıve Bayes perform roughly within 3 pts of the majority class baseline $( 6 6 . 7 \\% )$ whereas SVM performs substantially worse. ",
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+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "By leveraging humans not only to provide labels but also to intervene upon the data, revising documents to accord with various labels, we can elucidate the difference that makes a difference. Moreover, we can leverage the augmented data to train classifiers less dependent on spurious associations. Our study demonstrates the promise of leveraging human-in-the-loop feedback to disentangle the spurious and non-spurious associations, yielding classifiers that hold up better when spurious associations do not transport out of domain. Our methods appear useful on both sentiment analysis and NLI, two contrasting tasks. In sentiment analysis, expressions of opinion matter more than stated facts, while in NLI this is reversed. SNLI poses another challenge in that it is a 3-class classification task using two input sentences. In future work, we will extend these techniques, leveraging humans in the loop to build more robust systems for question answering and summarization. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGEMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The authors are grateful to Amazon AWS and NVIDIA for providing GPUs to conduct the experiments, Salesforce Research and Facebook AI for their generous grants that made the data collection possible, Sina Fazelpour, Sivaraman Balakrishnan, Shruti Rijhwani, Shruti Palaskar, Aishwarya Kamath, Michael Collins, Rajesh Ranganath and Sanjoy Dasgupta for their valuable feedback, and Tzu-Hsiang Lin for his generous help in creating the data collection platform. We also thank Abridge AI, UPMC, the Center for Machine Learning in Health, and the AI Ethics and Governance Fund for their support of our broader research on robust machine learning. ",
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+        "type": "text",
+        "text": "APPENDIX ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/4c26af4dc84f8d48660b73f0cd2c08dc0f20685a65ad5e5731734a48927ee41e.jpg",
+        "table_caption": [
+            "Table 10: Most frequent insertions/deletions by human annotators for sentiment analysis. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Revision</td><td>Removed words</td><td>Inserted words</td></tr><tr><td>Positive to Negative</td><td>movie,film,great, like,good,re- ally, would, see,story, love</td><td>movie, film, one, like,bad,would, really,even,story, see</td></tr><tr><td>Negative to Positive</td><td>bad,even,worst, waste,nothing, never,much,would, like, litle</td><td>great, good,best, even, well, amaz- ing,much,many,watch,better</td></tr></table>",
+        "bbox": [
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+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/42bf3a09dc76c9019998b17d1068494ae232bf9cbcad18ec1b7f1f072ceb459a.jpg",
+        "table_caption": [
+            "Table 11: Most frequent insertions/deletions by human annotators for SNLI. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">Revision Removed words</td><td>Inserted words</td></tr><tr><td colspan=\"2\">Revising Premise</td><td></td></tr><tr><td>Entailment to Neutral</td><td>woman，walking，man，blue, sitting， men, girl, standing, looking,running</td><td>person, near, child, something, together, people, tall, vehicle, wall, holding</td></tr><tr><td>Neutral to Entailment</td><td>man,street,black,water, little, front,young,playing,woman, two</td><td>waiting,couple,playing,run- ning， getting，making， tall, game, black,happily</td></tr><tr><td>Entailment to Contradiction</td><td>blue,people,standing，girl, front，street，red,young，sit- ting,band</td><td>sitting， standing, inside, young, women, child, red, men, sits,one</td></tr><tr><td>Contradiction to Entailment</td><td>sitting，man，walking，black, blue,people,red，standing, white,street</td><td>man,sitting, sleeping,woman, sits,eating,playing,park, two, standing</td></tr><tr><td>Neutral to Contradiction</td><td>man， woman， people,boy, black，red,standing，young， two,water</td><td>man,woman, boy, men, alone, sitting,girl,dog,three,one</td></tr><tr><td>Contradiction to Neutral</td><td>man, sitting,black,blue,walk-1 ing，red,standing， street， white,street</td><td>man， sitting， woman, peo- ple,person, near, something, something,sits,black</td></tr><tr><td colspan=\"3\">Revising Hypothesis</td></tr><tr><td>Entailment to Neutral</td><td>man, wearing， white, blue, black,shirt,one,young，peo- ple,woman</td><td>people,there,playing，man, person,wearing,outside,two, old, near</td></tr><tr><td>Neutral to Entailment</td><td>white，wearing，shirt,black, blue, man, two, standing, young, red</td><td>playing，wearing，man， two, there,woman，people,men, near,person</td></tr><tr><td>Entailment to Contradiction</td><td>man, wearing， white, blue, black,two,shirt,one,young, people</td><td>people,man, woman, playing, no,inside,person, two,wear- ing,women</td></tr><tr><td>Contradiction to Entailment</td><td>wearing， blue, black, man, white,two,red,shirt,young, one</td><td>people, there,man, two,wear- ing， playing， people,men, woman, outside</td></tr><tr><td>Neutral to Contradiction</td><td>white， man, wearing, shirt, black，blue，two，standing, woman, red</td><td>woman，man,there,playing, two,wearing, one,men,girl, no</td></tr><tr><td>Contradiction to Neutral</td><td>wearing，blue，black,man, white, two,red, sitting,young, standing</td><td>people,playing,man,woman, two,wearing,near, tall,men, old</td></tr></table>",
+        "bbox": [
+            176,
+            205,
+            823,
+            832
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/7cb9700ac11b85a6f7186dd7b2be5724ab8c3d6da2bbcb8cb8bcc5a7c49722da.jpg",
+        "image_caption": [
+            "Figure 4: Thirty most important features learned by an SVM classifier trained on TF-IDF bag of words. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            240,
+            176,
+            756,
+            789
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "The blue box contains a text passage and a label. Please edit this text in the textbox below, making a small number of changes such that: ",
+        "bbox": [
+            178,
+            202,
+            830,
+            231
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "(a) the document remains coherent and (b) the new label (colored) accurately describes the revised passage. ",
+        "bbox": [
+            179,
+            238,
+            625,
+            266
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Do not change any portions of the passage unnecessarily. ",
+        "bbox": [
+            184,
+            272,
+            552,
+            286
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "After modifying the passage and checking it over to make sure that is coherent and matches the label. ",
+        "bbox": [
+            181,
+            287,
+            828,
+            314
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "(a) Revising IMDb movie reviews ",
+        "bbox": [
+            403,
+            316,
+            606,
+            330
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "The upper blue box contains Sentence 1. The lower blue box contains Sentence 2. Given that Sentence 1 is True, Sentence 2 (by implication), must either be (a) definitely True, (b) definitely False, or (c) May be True. ",
+        "bbox": [
+            179,
+            348,
+            715,
+            392
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "You are presented with an initial Sentence 1 and Sentence 2 and the correct initial relationship label (True, False, or May be True). ",
+        "bbox": [
+            178,
+            397,
+            831,
+            426
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Please edit Sentence 2 in the textboxes, making a small number of changes such that: ",
+        "bbox": [
+            179,
+            433,
+            738,
+            448
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "(a) The new sentences are coherent and   \n(b) The target labels (in red) accurately describe the truthfulness of the modified Sentence 2 given the original Sentence 1. ",
+        "bbox": [
+            178,
+            454,
+            833,
+            496
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Do not change any portions of the sentence unnecessarily. ",
+        "bbox": [
+            179,
+            502,
+            560,
+            516
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "After modifying the text and checking it over to make sure that it is coherent and matches the target label. ",
+        "bbox": [
+            179,
+            517,
+            828,
+            545
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "(b) Revising hypothesis in SNLI ",
+        "bbox": [
+            408,
+            547,
+            601,
+            561
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "The upper blue box contains Sentence 1. The lower blue box contains Sentence 2. Given that Sentence 1 is True, Sentence 2 (by implication), must either be (a) definitely True, (b) definitely False, or (c) May be True. ",
+        "bbox": [
+            179,
+            579,
+            715,
+            622
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "You are presented with an initial Sentence 1 and Sentence 2 and the correct initial relationship label (True, False, or May be True). ",
+        "bbox": [
+            176,
+            627,
+            828,
+            656
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "Please edit Sentence 1 in the textboxes, making a small number of changes such that: ",
+        "bbox": [
+            181,
+            662,
+            740,
+            678
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "(a) The new sentences are coherent and   \n(b) The target labels (in red) accurately describe the truthfulness of the original Sentence 2 given the modified Sentence 1. ",
+        "bbox": [
+            179,
+            684,
+            830,
+            726
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "After modifying the text and checking it over to make sure that it is coherent and matches the target label. ",
+        "bbox": [
+            174,
+            748,
+            833,
+            773
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "(c) Revising premise in SNLI ",
+        "bbox": [
+            416,
+            777,
+            591,
+            791
+        ],
+        "page_idx": 16
+    }
+]