Explaining the predictions of deep neural nets has been a topic of great interest in the computer vision literature. While several gradient-based interpretation schemes have been proposed to reveal the influential variables in a neural net's prediction, standard gradient-based interpretation frameworks have been commonly observed to lack robustness to input perturbations and flexibility for incorporating prior knowledge of sparsity and group-sparsity structures. In this work, we propose MoreauGrad as an interpretation scheme based on the classifier neural net's Moreau envelope. We demonstrate that MoreauGrad results in a smooth and robust interpretation of a multi-layer neural network and can be efficiently computed through first-order optimization methods. Furthermore, we show that MoreauGrad can be naturally combined with $L_1$-norm regularization techniques to output a sparse or group-sparse explanation which are prior conditions applicable to a wide range of deep learning applications. We empirically evaluate the proposed MoreauGrad scheme on standard computer vision datasets, showing the qualitative and quantitative success of the MoreauGrad approach in comparison to standard gradient-based interpretation methods.

本文提出了一种基于分类器神经网络Moreau包络的MoreauGrad解释方案，可以平滑、稳健地解释多层神经网络，并能与$L_1$-norm正则化技术自然结合，输出适用于各种深度学习应用的稀疏或组稀疏解释，实验证明该方案在计算机视觉数据集上的定性和定量成功高于标准梯度解释方案。

MoreauGrad：通过Moreau包络稀疏且鲁棒地解释神经网络