Perceptual Regularization: Visualizing and Learning Generalizable Representations

A deployable machine learning model relies on a good representation . A desirable criteria for a good representation is to be interpretable by humans . We propose a technique termed perceptual regularization that enables visualization of the latent representation . By visualizing the learned representation , we are also able to understand the attention of a model , obtaining visual evidence that supervised networks learn task-specific representations . Moreover our method provides a direct visualization of the effect that adversarial attacks have on the internal representation of a deep network . We show how this can be used to systematically perform latent space interpolation to modify semantic features . 1 INTRODUCTION . Deep neural networks are known to be vulnerable , small changes known as adversarial attacks can completely change the model ’ s prediction ( Szegedy et al. , 2014 ; Nguyen et al. , 2015 ; Kurakin et al. , 2017 ) . There is a rapidly growing body of work on how to perform effective adversarial attacks , and how to defend against them ( Papernot et al. , 2017 ; Madry et al. , 2017 ; Athalye et al. , 2018 ) . On the one hand , adversarial examples are named as such because they as able to trick a deep network using changes imperceptible to humans . On the other hand , the model makes predictions based on its internal representation ( i.e . what the model perceives ) which may be very different from human perception . Indeed , the existence of adversarial examples is evidence that human perception and machine perception are misaligned , and the internal representation of a model and a human differ significantly . The motivating question we would like to address is : are adversarial examples really adversarial examples from the model ’ s perspective ? In order to get insight of this question , we extend an existing visualization technique from Dosovitskiy & Brox ( 2016b ) ; Johnson et al . ( 2016 ) ; Dosovitskiy & Brox ( 2016a ) , stacking a decoder head on top of the model ’ s latent representation with the aim of providing a human interpretable reconstruction , see Figure 1 . In particular , we train the decoder jointly with the network , terming the resultant objective function perceptual regularization . A similar strategy has also been explored in Sabour et al . ( 2017 ) ; Qin et al . ( 2019 ) for Capsule networks , and exploiting semi-supervised ( unlabeled ) data in Lasserre et al . ( 2006 ) ; Grabner et al . ( 2007 ) ; Larochelle & Bengio ( 2008 ) ; Le et al . ( 2018 ) . One of the key insights we bring in our work is that a simple decoder head term is all that is needed to yield significant visual insight into a range of questions about the representations learned by deep networks . Visualization is an active research area , with various standard techniques such as saliency maps Simonyan et al . ( 2014 ) among others Zeiler & Fergus ( 2014 ) ; Mahendran & Vedaldi ( 2015 ) ; Springenberg et al . ( 2015 ) ; Zhou et al . ( 2016 ) being used to visualize representations by inverting them . However , reconstructing the original input from the representation is computationally expensive . An alternative way is to introduce a forward decoder from latent space to image space , aiming to globally invert the representation . This technique has been used in Dosovitskiy & Brox ( 2016b ) ; Johnson et al . ( 2016 ) ; Dosovitskiy & Brox ( 2016a ) and our method follows this line of work . The main contributions of this paper are : • Extending the existing visualization method as a regularization method for jointly learning a visualization for deep representations . • Using this method to visualize how the attention of a model focuses only on aspects that are relevant for prediction . More generally we give promising evidence to suggest that our visualization method is of interest for model diagnostics and interpretability . • Using this visualization method to shed light on what effect adversarial attacks have on a model . • Using adversarial attacks to identify direction vectors in the latent space that correspond to certain semantic features . We show that the decoder network can then be used to synthesize images with modified semantic features . 2 PERCEPTUAL REGULARIZATION . We begin by introducing perceptual regularization . Consider a deep image classification model such as AlexNet ( Krizhevsky et al. , 2012 ) , VGG-Net ( Simonyan & Zisserman , 2015 ) , or ResNet ( He et al. , 2016 ) . It usually consists of two stages : several convolutional layers , followed by dense layers . The convolution layers can be viewed as a feature extraction process which we denote by F , transforming images from the input space X into a latent space Z . The dense layers C : Z → Y act as a classifier on the latent space . In order to regularize and visualize the latent representation , we introduce a decoder D : Z → X on top of the latent space Z which we jointly train with the classification model . The architecture is shown in Figure 1 . More precisely , we denote the classification model by H = C ◦ F and term the reconstruction P = D ◦ F a perception of the model . The regularization strategy we introduce is to jointly trainH and P together by minimizing min P , H EX , Y [ ` ( H ( X ) , Y ) ︸ ︷︷ ︸ classification loss +λ ‖X − P ( X ) ‖2︸ ︷︷ ︸ reconstruction loss ] . ( Perceptual regularization ) The first term is the standard classification loss and we take ` to be the cross-entropy loss throughout the paper . The regularization term is the ` 2 reconstruction loss scaled by a hyper-parameter λ > 0 . Intuitively , the decoder tries to reconstruct the original image based on the same information the classifier uses for prediction . In particular , if the feature map F preserves all the information from the input , the perception should be able to perfectly recover X . Conversely , if a lot of information has been thrown away , then we will get a poor reconstruction and the regularization loss will be high . Therefore , our regularization biases the learned representation to maintain more information about the input compared to vanilla supervised learning . This will be useful if one would like to reuse the learned features later for other tasks . Notice that the regularization term vanishes when P is the identity mapping , in which case the feature map F is bijective . This can happen when the model is very powerful and therefore able to memorize any dataset . However , this situation is less interesting in the sense that a good representation should efficiently compress the information . This idea has been clearly understood with the information bottleneck objective , for which it is known that F ( X ) approximates the minimal sufficient statistic for Y given X ( Shamir et al. , 2010 ) . Therefore , to constrain the expressiveness of the feature map , we impose a bottleneck structure in the network architecture . More precisely , the dimension of the latent space Z is made significantly smaller than the dimension of the input space X . This enforces the feature map to compress information and makes it very unlikely to be bijective . As well as regularizing the model , perceptual regularization also provides a natural way to visualize the latent space . In particular , the perception P is designed to decode the feature map F , which is very useful for model understanding . In the next three sections we begin to explore the insights that can be drawn using perceptual regularization . 3 VISUALIZING FEATURES LEARNED BY A DEEP NETWORK . Extensive research have been conducted on attention-based models in object recognition and image captioning Bahdanau et al . ( 2014 ) ; Karpathy & Fei-Fei ( 2015 ) ; Ba et al . ( 2015 ) ; Gregor et al . ( 2015 ) ; Xu et al . ( 2015 ) ; Jaderberg et al . ( 2015 ) ; He et al . ( 2017 ) , where the attention mechanism is explicitly introduced as a spatial map highlighting image regions . A second application of perceptual regularization is to visualize what a classifier ’ s attention focuses on . In particular , if a model is trained to predict the object in the middle of an image , it is commonly believed that the learned representation “ overfits ” to the training task by focusing only on the central part of the image . This can be a cause of negative transfer - when reusing a learned representation for a new task actually hurts performance ( Pan & Yang , 2009 ; Kuzborskij & Orabona , 2013 ) . We show our visualization method can help understand when a representation will cause negative transfer . All experimental details , including architecture and hyper-parameters are given in full in the appendix . 3.1 THE ATTENTION PROBLEM . It has long been intuitively understood that the representations in the final layers of a supervised deep network will only focus on aspects of the data relevant to its prediction task ( Long et al. , 2015 ; Yosinski et al. , 2014 ; Alain & Bengio , 2017 ) . In this section we demonstrate on the SVHN dataset ( Netzer et al. , 2011 ) that this phenomenon of focused attention can be visualized using perceptual regularization . The SVHN dataset consists of images of house numbers and the task is to predict the number in the center of the image . In particular , an image could contain multiple numbers but the label is given according to the middle one . A natural question is : will a supervised model learn a representation that remembers numbers that are not in the center ? To answer this question , we train a CNN with perceptual regularization and then use perception to visualize the attention of the model , i.e . given any input X , we visualize P ( X ) . As shown in Figure 2 , our visualization technique shows that the model learns a representation that focuses on the middle of the image , and forgets what is at the edges of the image . This provides additional evidence to support the observation that a supervised model learns a representation specific to its prediction task . This is fine if there is only one task of interest , but makes transferring features between tasks problematic . For example , in our case , the representation would be completely ineffective for identifying the digit on the left or right hand sides . 3.2 PERCEPTUAL REGULARIZATION TO CONTROL ATTENTION . The cause of this restricted attention problem is the guidance given by the labels . In this section , we demonstrate that perceptual regularization can be useful to reduce the problem of overfitting learned features to the training task . In particular , our method allows for a smooth interpolation between supervised learning and unsupervised learning . In the extreme case , when λ→ 0 , we recover the standard supervised learning setting , and when λ → ∞ we recover the classical auto-encoder objective . Hence , the parameter λ can control how much information we would like our model ’ s representation to keep . We run experiments on the SVHN dataset by varying the regularization parameter λ . We keep the architecture fixed ( see Appendix B.3 for more details ) . Figure 3 shows different regimes of features for different values of λ . There are four main regimes : • Tiny ( λ < 10−4 , Figure 3 ( a ) ) : Since λ is extremely small the contribution to the loss from the decoder branch is so negligible that there is not much incentive to learn a good decoder and the visualization breaks down . • Delicate ( 10−4 < λ < 10−2 , Figure 3 ( b ) ) : A good decoder is learned and the bias injected into the learned feature map by the regularization term is small . The number in the center is well reconstructed , but the edges of the image are not and the colors are missing . It is in this regime that we are able to see the restricted attention of a classifier . • Intermediate ( 10−2 < λ < 1 , Figure 3 ( c ) ) : We obtain more faithful reconstructions compared to the “ delicate ” regime . In particular , the numbers at the edges are reasonably reconstructed but colors are still not well captured . • Large ( λ > 1 , Figure 3 ( d ) ) : The decoder is very good , both numbers and colors are recovered . The regularization has had a significant effect on the nature of the learned features . Since these features retain much more information than for smaller λ they are more likely to transfer well to new unseen tasks . Clearly the choice of λ heavily affects the features learned by the model . The larger λ is , the more information is preserved in the features : small values of λ only preserve the number in the middle of the image , intermediate values can also reconstruct the boundary of the image , and only for large λ is the input ’ s precise color correctly reconstructed . It is also important to note that the accuracy on the supervised task decreases as λ increases , but at a relatively slow rate . This is to be expected . In the limit λ→∞ there is no longer any incentive to perform good classification , only reconstruction . An interesting future direction will be to understand why certain features are harder to learn than others , for instance , in our example why the color is recovered later than numbers along the edges . It is important to note that perceptual regularization introduces an inductive bias towards learning representations that retain a lot of information about the original input , which are different from what is learned without it . If one wanted to avoid this bias then one idea is to learn the feature map first , then learn the visualization decoder separately , with the feature map frozen . This strategy works reasonably well when the network ’ s size is small . But , as the network gets more complicated it becomes computationally difficult to decode the feature map . Hence , as an alternative solution , we train the decoder jointly with the feature map . What we have shown is that although the bias induced by the regularization is an apparent drawback , it can in fact be turned into a strength by using λ to control the behavior of the feature map . Finally , the specific values of λ quoted are meant only to serve as a very rough guide about trends . Making the magnitude of the reconstruction loss and classification loss comparable is often effective to locate the “ delicate ” λ .

Summary: Claims: The authors present perceptual regularization as a method for learning a visualization of deep representations for promoting interpretability and understanding of vulnerability to adversarial attacks. Second, they show their method can explain negative transfer to new tasks. Finally, they show that the representations learned with this regularization method transfer to unseen tasks better than without the reconstruction regularization.