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Expected Grad-CAM: Towards gradient faithfulness

Vincenzo Buono, Peyman Sheikholharam Mashhadi, Mahmoud Rahat, Prayag Tiwari, Stefan Byttner

TL;DR

This work proposes a gradient-weighted CAM augmentation that tackles both the saturation and sensitivity problem by reshaping the gradient computation, incorporating two well-established and provably approaches: Expected Gradients and kernel smoothing.

Abstract

Although input-gradients techniques have evolved to mitigate and tackle the challenges associated with gradients, modern gradient-weighted CAM approaches still rely on vanilla gradients, which are inherently susceptible to the saturation phenomena. Despite recent enhancements have incorporated counterfactual gradient strategies as a mitigating measure, these local explanation techniques still exhibit a lack of sensitivity to their baseline parameter. Our work proposes a gradient-weighted CAM augmentation that tackles both the saturation and sensitivity problem by reshaping the gradient computation, incorporating two well-established and provably approaches: Expected Gradients and kernel smoothing. By revisiting the original formulation as the smoothed expectation of the perturbed integrated gradients, one can concurrently construct more faithful, localized and robust explanations which minimize infidelity. Through fine modulation of the perturbation distribution it is possible to regulate the complexity characteristic of the explanation, selectively discriminating stable features. Our technique, Expected Grad-CAM, differently from recent works, exclusively optimizes the gradient computation, purposefully designed as an enhanced substitute of the foundational Grad-CAM algorithm and any method built therefrom. Quantitative and qualitative evaluations have been conducted to assess the effectiveness of our method.

Expected Grad-CAM: Towards gradient faithfulness

TL;DR

This work proposes a gradient-weighted CAM augmentation that tackles both the saturation and sensitivity problem by reshaping the gradient computation, incorporating two well-established and provably approaches: Expected Gradients and kernel smoothing.

Abstract

Although input-gradients techniques have evolved to mitigate and tackle the challenges associated with gradients, modern gradient-weighted CAM approaches still rely on vanilla gradients, which are inherently susceptible to the saturation phenomena. Despite recent enhancements have incorporated counterfactual gradient strategies as a mitigating measure, these local explanation techniques still exhibit a lack of sensitivity to their baseline parameter. Our work proposes a gradient-weighted CAM augmentation that tackles both the saturation and sensitivity problem by reshaping the gradient computation, incorporating two well-established and provably approaches: Expected Gradients and kernel smoothing. By revisiting the original formulation as the smoothed expectation of the perturbed integrated gradients, one can concurrently construct more faithful, localized and robust explanations which minimize infidelity. Through fine modulation of the perturbation distribution it is possible to regulate the complexity characteristic of the explanation, selectively discriminating stable features. Our technique, Expected Grad-CAM, differently from recent works, exclusively optimizes the gradient computation, purposefully designed as an enhanced substitute of the foundational Grad-CAM algorithm and any method built therefrom. Quantitative and qualitative evaluations have been conducted to assess the effectiveness of our method.
Paper Structure (18 sections, 23 equations, 15 figures, 8 tables)

This paper contains 18 sections, 23 equations, 15 figures, 8 tables.

Figures (15)

  • Figure 1: Explanatory functions on VGG-16 across samples from ImageNet-1k Russakovsky2014ImageNetChallenge. Our approach produces sharper (less noisy) and higher localized heat maps with lower complexity than existing methods (\ref{['subfig:loc-0']}). \ref{['subfig:loc-1']} shows the coarse heat map with respect to our method and baseline Grad-CAM Selvaraju2016Grad-CAM:Localization.
  • Figure 2: Comparison of attribution maps under internal saturation conditions. \ref{['subfig:saturation-cmp-0']} illustrates the cosine similarity of the target layer's embeddings with respect to the interpolator parameter ($\alpha$) (see Appendix \ref{['sec:internal-saturation']} for more details). \ref{['subfig:saturation-cmp-1']} displays the attribution maps of various methods under saturation conditions. Internal saturation causes the baseline method to under-represent feature importances across saturating ranges. By extracting the top-4 most important features (\ref{['subfig:saturation-cmp-1']}), it is evident that the baseline method fails to capture relevant discriminative regions, resulting in low insertion AUCs (\ref{['subfig:saturation-cmp-1']}) as these regions are not deemed important by the model.
  • Figure 3: Overview of the proposed Expected Grad-CAM method. Given an input image, a target class, and a reference distribution to sample from, the class-discriminative explanation $\hat{e}$ is computed through input kernel smoothing and difference-from-reference comparisons.
  • Figure 4: Comparison of saliencies generated by different gradient- and non-gradient-based methods. \ref{['subfig:noise-cmp-0']} shows the superimposed (top row) and raw coarse saliencies (bottom row) generated by each method. \ref{['subfig:noise-cmp-1']} presents the Infidelity scores Yeh2019OnExplanations (using log-scale) for the different methods. While baseline methods are noisy with low localization, our method produces sharper, more localized explanations, outperforming even non-gradient-based techniques, and resulting in significantly lower infidelity scores (\ref{['subfig:noise-cmp-1']}).
  • Figure 5: Comparison of attribution maps for various methods under normal conditions (\ref{['subfig:qual-eval-1']}) and internal saturation conditions (\ref{['subfig:qual-eval-0']}). Our method (Expected Grad-CAM) provides sharper, more localized, and more stable explanations compared to its direct counterparts, namely Grad-CAMSelvaraju2016Grad-CAM:Localization, Grad-CAM++Chattopadhay2017Grad-CAM++:Networks, Smooth Grad-CAM++Omeiza2019SmoothModels, and Integrated Grad-CAMSattarzadeh2021IntegratedScoring. Additionally, it offers competitive explanations compared to non-gradient and more complex methods through gradient augmentation. For a complete comparison, refer to \ref{['sec:supp-qualitative']}.
  • ...and 10 more figures

Theorems & Definitions (9)

  • Definition 3.1
  • Remark 3.2
  • Remark 3.3
  • Definition 3.4
  • Definition 3.5
  • Definition 3.6
  • Definition 3.7
  • Definition 3.8
  • Definition 3.9