# MoreauGrad: Sparse and Robust Interpretation of Neural Networks via Moreau Envelope

arXiv: https://arxiv.org/abs/2302.05294 · HTML: https://mlsanity.com/paper/2302.05294/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 8 Jan 2023.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [Object Detection with Deep Learning: A Review](https://mlsanity.com/paper/1807.05511/) (2018)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [Deep Learning for Medical Image Analysis](https://mlsanity.com/paper/1708.08987/) (2017)
- [Real Time Image Saliency for Black Box Classifiers](https://mlsanity.com/paper/1705.07857/) (2017)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Fooling Neural Network Interpretations via Adversarial Model Manipulation](https://mlsanity.com/paper/1902.02041/) (2019)
- [Structured Adversarial Attack: Towards General Implementation and Better Interpretability](https://mlsanity.com/paper/1808.01664/) (2018)
- [There and Back Again: Revisiting Backpropagation Saliency Methods](https://mlsanity.com/paper/2004.02866/) (2020)
- [Interpretable and Fine-Grained Visual Explanations for Convolutional Neural Networks](https://mlsanity.com/paper/1908.02686/) (2019)
- [On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradient](https://mlsanity.com/paper/1803.06573/) (2018)
- [Certifiably Robust Interpretation in Deep Learning](https://mlsanity.com/paper/1905.12105/) (2019)
- [Building Reliable Explanations of Unreliable Neural Networks: Locally Smoothing Perspective of Model Interpretation](https://mlsanity.com/paper/2103.14332/) (2021)

## Built on by (most cited first, 5 of 5)

- [Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training](https://mlsanity.com/paper/2404.04647/) (2024)
- [MoreauPruner: Robust Pruning of Large Language Models against Weight Perturbations](https://mlsanity.com/paper/2406.07017/) (2024)
- [Gaussian Smoothing in Saliency Maps: The Stability-Fidelity Trade-Off in Neural Network Interpretability](https://mlsanity.com/paper/2411.05837/) (2024)
- [A Super-pixel-based Approach to the Stable Interpretation of Neural Networks](https://mlsanity.com/paper/2412.14509/) (2024)
- [On the Fragility of AI-Based Channel Decoders under Small Channel Perturbations](https://mlsanity.com/paper/2602.01582/) (2026)

## Abstract (arXiv)

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 L1-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.