RETHINKING THE ROLE OF GRADIENT-BASED ATTRI-BUTION METHODS FOR MODEL INTERPRETABILITY

Abstract

Current methods for the interpretability of discriminative deep neural networks commonly rely on the model's input-gradients, i.e., the gradients of the output logits w.r.t. the inputs. The common assumption is that these input-gradients contain information regarding p θ (y | x), the model's discriminative capabilities, thus justifying their use for interpretability. However, in this work we show that these input-gradients can be arbitrarily manipulated as a consequence of the shiftinvariance of softmax without changing the discriminative function. This leaves an open question: if input-gradients can be arbitrary, why are they highly structured and explanatory in standard models? We investigate this by re-interpreting the logits of standard softmax-based classifiers as unnormalized log-densities of the data distribution and show that input-gradients can be viewed as gradients of a class-conditional density model p θ (x | y) implicit within the discriminative model. This leads us to hypothesize that the highly structured and explanatory nature of input-gradients may be due to the alignment of this class-conditional model p θ (x | y) with that of the ground truth data distribution p data (x | y). We test this hypothesis by studying the effect of density alignment on gradient explanations. To achieve this density alignment, we use an algorithm called score-matching, and propose novel approximations to this algorithm to enable training large-scale models. Our experiments show that improving the alignment of the implicit density model with the data distribution enhances gradient structure and explanatory power while reducing this alignment has the opposite effect. This also leads us to conjecture that unintended density alignment in standard neural network training may explain the highly structured nature of input-gradients observed in practice. Overall, our finding that input-gradients capture information regarding an implicit generative model implies that we need to re-think their use for interpreting discriminative models.

1. INTRODUCTION

Input-gradients, or gradients of outputs w.r.t. inputs, are commonly used for the interpretation of deep neural networks (Simonyan et al., 2013) . For image classification tasks, an input pixel with a larger input-gradient magnitude is attributed a higher 'importance' value, and the resulting maps are observed to agree with human intuition regarding which input pixels are important for the task at hand (Adebayo et al., 2018) . Quantitative studies (Samek et al., 2016; Shrikumar et al., 2017) also show that these importance estimates are meaningful in predicting model response to larger structured perturbations. These results suggest that input-gradients do indeed capture relevant information regarding the underlying model. However in this work, we show that input-gradients can be arbitrarily manipulated using the shift-invariance of softmax without changing the underlying discriminative model, which calls into question the reliability of input-gradient based attribution methods for interpreting arbitrary black-box models. Given that input-gradients can be arbitrarily structured, the reason for their highly structured and explanatory nature in standard pre-trained models is puzzling. Why are input-gradients relatively well-

