Achieving Explainability in a Visual Hard Attention Model through Content Prediction

1 INTRODUCTION . Though deep convolution networks achieve state of the art performance on the image classification task , it is difficult to explain which input regions affected the output . A technique called visual hard attention provides this explanation by design . The hard attention model sequentially attends small but informative subregions of the input called glimpses to make predictions . While the attention mechanism explains the task-specific decisions , the attention policies learned by the model remain unexplainable . For example , one can not explain the attention policy of a caption generation model that correctly predicts the word ‘ frisbee ’ while looking at a region far from an actual frisbee ( Xu et al . ( 2015 ) ) . The majority of hard attention models first analyze a complete image to locate the task-relevant subregions and then attend to these locations to make predictions ( Ba et al . ( 2014 ) ; Elsayed et al . ( 2019 ) ) . However , in practice , we often do not have access to the entire scene , and we gradually attend to the important subregions to collect task-specific information . At each step in the process , we decide the next attention-worthy location based on the partial observations collected so far . The explainable attention policies are more desirable under such partial observability . Pioneering work by Mnih et al . ( 2014 ) presents a model that functions under partial observability but their attention policies are not explainable . They train their model with the REINFORCE algorithm ( Williams ( 1992 ) ) , which is challenging to optimize . Moreover , the model ’ s performance is affected adversely if the parameterization of the attention policy is not optimal . For example , an object classification model with unimodal Gaussian policy learns to attend the background region in the middle of the two objects ( Sermanet et al . ( 2014 ) ) . This paper develops a hard-attention model with an explainable attention policy for classifying images through a series of partial observations . We formulate the problem of hard attention as a Bayesian Optimal Experiment Design ( BOED ) . A recurrent model finds an optimal location that gains maximum expected information about the class label and attends to this location . To estimate expected information gain ( EIG ) under partial observability , the model predicts content of the un- seen regions based on the regions observed so far . Using the knowledge gained by attending various locations in an image , the model predicts the class label . To the best of our knowledge , ours is the first hard attention model that is entirely explainable under partial observability . Our main contributions are as follows . First , our attention policies are explainable by design . One can explain that the model attends a specific location because it expects the corresponding glimpse to maximize the expected information gain . Second , the model does not rely on the complete image to predict the attention locations and provides good performance under partial observability . Third , the training objective is differentiable and can be optimized using standard gradient backpropagation . We train the model using discriminative and generative objectives to predict the label and the image content , respectively . Fourth , our attention policy is non-parametric and can be implicitly multi-modal . 2 RELATED WORKS . A hard attention model prioritizes task-relevant regions to extract meaningful features from an input . Early attempts to model attention employed image saliency as a priority map . High priority regions were selected using methods such as winner-take-all ( Koch & Ullman ( 1987 ) ; Itti et al . ( 1998 ) ; Itti & Koch ( 2000 ) ) , searching by throwing out all features but the one with minimal activity ( Ahmad ( 1992 ) ) , and dynamic routing of information ( Olshausen et al . ( 1993 ) ) . Few used graphical models to model visual attention . Rimey & Brown ( 1991 ) used augmented hidden Markov models to model attention policy . Larochelle & Hinton ( 2010 ) used a Restricted Boltzmann Machine ( RBM ) with third-order connections between attention location , glimpse , and the representation of a scene . Motivated by this , Zheng et al . ( 2015 ) proposed an autoregressive model to compute exact gradients , unlike in an RBM . Tang et al . ( 2014 ) used an RBM as a generative model and searched for informative locations using the Hamiltonian Monte Carlo algorithm . Many used reinforcement learning to train attention models . Paletta et al . ( 2005 ) used Q-learning with the reward that measures the objectness of the attended region . Denil et al . ( 2012 ) estimated rewards using particle filters and employed a policy based on the Gaussian Process and the upper confidence bound . Butko & Movellan ( 2008 ) modeled attention as a partially observable Markov decision process and used a policy gradient algorithm for learning . Later , Butko & Movellan ( 2009 ) extended this approach to multiple objects . Recently , the machine learning community use the REINFORCE policy gradient algorithm to train hard attention models ( Mnih et al . ( 2014 ) ; Ba et al . ( 2014 ) ; Xu et al . ( 2015 ) ; Elsayed et al . ( 2019 ) ) . Among these , only Elsayed et al . ( 2019 ) claims explainability by design . Other works use EMstyle learning procedure ( Ranzato ( 2014 ) ) , wake-sleep algorithm ( Ba et al . ( 2015 ) ) , a voting based region selection ( Alexe et al . ( 2012 ) ) , and differentiable models ( Gregor et al . ( 2015 ) ; Jaderberg et al . ( 2015 ) ; Eslami et al . ( 2016 ) ) . Among the recent models , Ba et al . ( 2014 ) ; Ranzato ( 2014 ) ; Ba et al . ( 2015 ) look at the lowresolution gist of an input at the beginning , and Xu et al . ( 2015 ) ; Elsayed et al . ( 2019 ) ; Gregor et al . ( 2015 ) ; Jaderberg et al . ( 2015 ) ; Eslami et al . ( 2016 ) consume the whole image to predict the locations to attend . In contrast , our model does not look at the entire image at low resolution or otherwise . Moreover , our attention policies are explainable . We can apply our model in a wide range of scenarios where explainable predictions are desirable for the partially observable images . 3 MODEL . In this paper , we consider a recurrent attention model that sequentially captures glimpses from an image x and predicts a label y . The model runs for time t = 0 to T − 1 . It uses a recurrent net to maintain a hidden state ht−1 that summarizes glimpses observed until time t − 1 . At time t , it predicts coordinates lt based on the hidden state ht−1 and captures a square glimpse gt centered at lt in an image x , i.e . gt = g ( x , lt ) . It uses gt and lt to update the hidden state to ht and predicts the label y based on the updated state ht . 3.1 ARCHITECTURE . As shown in Figure 1 ( a ) , our model comprises the following three building blocks . A recurrent feature aggregator ( F and R ) maintains a hidden state ht . A classifier ( C ) predicts the class probabilities p ( y|ht ) . A normalizing flow-based variational autoencoder ( S and D ) predicts a complete image given the hidden state ht ; a flow-based encoder S predicts the posterior of a latent variable z from ht , and a decoderD predicts a complete image from z . The BOED , as discussed in section 3.2 , uses the predicted image to find an optimal location to attend at the next time-step . To distinguish the predicted image from the actual image , let us call the former x̃ . Henceforth , we crown any quantity derived from the predicted image x̃ with a ( ˜ ) . Next , we provide details about the three building blocks of the model , followed by a discussion of the BOED in the context of hard attention . 3.1.1 A RECURRENT FEATURE AGGREGATOR . Given a glimpse gt and its location lt , a feed-forward module extracts features ft = F ( gt , lt ) , and a recurrent network updates a hidden state to ht = R ( ht−1 , ft ) . Following Mnih et al . ( 2014 ) , we define F ( gt , lt ) = BN ( LeakyReLU ( Fg ( gt ) + Fl ( lt ) ) ) where Fg and Fl are deep networks , and R ( ht−1 , ft ) = LN ( LeakyReLU ( Linear ( ht−1 ) +Linear ( ft ) ) ) . Here , BN is a BatchNorm layer ( Ioffe & Szegedy ( 2015 ) ) and LN is a LayerNorm layer ( Ba et al . ( 2016 ) ) . 3.1.2 A CLASSIFIER . At each time-step t , a linear classifier predicts the distribution p ( y|ht ) = C ( ht ) from a hidden state ht . As the goal of the model is to predict a label y for an image x , we learn a distribution p ( y|ht ) by minimizing KL [ p ( y|x ) ||p ( y|ht ) ] . Optimization of this KL divergence is equivalent to the minimization of the following cross-entropy loss . LCE ( t ) = −p ( y|x ) log ( p ( y|ht ) ) ( 1 ) 3.1.3 A PARTIAL VARIATIONAL AUTOENCODER . We adapt a variational autoencoder ( VAE ) to predict the complete image x from the hidden state ht . A VAE learns a joint distribution between the image x and the latent variable z given ht , p ( x , z|ht ) = p ( x|z ) p ( z|ht ) . An amortized encoder infers the posterior q ( z|x , ht ) , which is an approximation of the true posterior p ( z|x , ht ) , and a decoder infers the likelihood p ( x|z ) . The training of VAE requires optimizing the Evidence Lower Bound ( ELBO ) , which involves calculating KL [ q ( z|x , ht ) ||p ( z|ht ) ] ( Kingma & Welling ( 2013 ) ) . As the hard attention model does not observe the complete image x , it can not estimate q ( z|x , ht ) . Hence , we can not incorporate the standard VAE directly into a hard attention framework . At the time t , we separate an image x into two parts , ot — the set of regions observed up to t , and ut — the set of regions as yet unobserved . Ma et al . ( 2018 ) observed that in a VAE , ot and ut are conditionally independent given z , i.e . p ( x|z ) = p ( ut|z ) p ( ot|z ) . They predict ut independently from the sample z ∼ q ( z|ot ) , while learning the approximate posterior q ( z|ot ) by optimizing the ELBO on log ( p ( ot ) ) . They refer to the resultant VAE as a Partial VAE . Recall that the hidden state ht calculated by our attention model is a summary of the glimpses observed up to t , which is equivalent to ot , the set of observed regions . Hence , we can write q ( z|ot ) as q ( z|ht ) in the ELBO of the Partial VAE . LPVAE ( t ) = Eq ( z|ot ) log ( p ( ot|z ) ) −KL [ q ( z|ot ) ||p ( z ) ] = Eq ( z|ht ) log ( p ( ot|z ) ) −KL [ q ( z|ht ) ||p ( z ) ] ( 2 ) In a Partial VAE , p ( x , z|ht ) = p ( ut|z ) p ( ot|z ) p ( z|ht ) . We implement a decoder D that predicts the complete image given the sample z ∼ q ( z|ht ) . Let mt be a binary mask with value 1 for the pixels observed by the model up to t and 0 otherwise ; hence , ot = mt x , where is an element-wise multiplication . We write the log-likelihood in equation 2 using the mask mt as follows . log ( p ( ot|z ) ) = −0.5 ∑ |mt D ( z ) −mt x|2 = −0.5 ∑ mt |D ( z ) − x|2 ( 3 ) In equation 2 , the prior p ( z ) is a Gaussian distribution with zero mean and unit variance . To obtain expressive posterior q ( z|ht ) , we use normalizing flows ( Kingma et al . ( 2016 ) ) . As an explicit inversion of the flows is not required , we use auto-regressive Neural Spline Flows ( NSF ) ( Durkan et al . ( 2019 ) ) and efficiently implement them using a single feed-forward network with masked weights as in De Cao et al . ( 2019 ) . Between the two flow layers , we flip the input ( Dinh et al . ( 2016 ) ) and normalize it using ActNorm ( Kingma & Dhariwal ( 2018 ) ) . In Figure 1 ( a ) , the flow-based encoder S infers the posterior q ( z|ht ) = S ( ht ) . As mentioned earlier , we refer to the prediction from the Partial VAE as x̃ . The BOED uses x̃ to find an optimal location to attend . 1

Summary: This paper proposed a new hard attention model for the image classification. They designed hard attention mechanism as a bayesian optimal experimental setting. Compare to other hard attention model, the policies of proposed hard attention can be explainable and differentiable, which is non-parametric. They evaluated their model to four different image classification dataset and their model outperformed than other baseline models.