# Gaussian Smoothing in Saliency Maps: The Stability-Fidelity Trade-Off in Neural Network Interpretability

arXiv: https://arxiv.org/abs/2411.05837 · HTML: https://mlsanity.com/paper/2411.05837/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 47 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [Improving Deep Learning Interpretability by Saliency Guided Training](https://mlsanity.com/paper/2111.14338/) (2021)
- [Certifiably Robust Interpretation in Deep Learning](https://mlsanity.com/paper/1905.12105/) (2019)
- [Why are Saliency Maps Noisy? Cause of and Solution to Noisy Saliency Maps](https://mlsanity.com/paper/1902.04893/) (2019)
- [How Good is your Explanation? Algorithmic Stability Measures to Assess the Quality of Explanations for Deep Neural Networks](https://mlsanity.com/paper/2009.04521/) (2020)
- [Scientific Inference With Interpretable Machine Learning: Analyzing Models to Learn About Real-World Phenomena](https://mlsanity.com/paper/2206.05487/) (2022)
- [Stein's Lemma for the Reparameterization Trick with Exponential Family Mixtures](https://mlsanity.com/paper/1910.13398/) (2019)
- [Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training](https://mlsanity.com/paper/2404.04647/) (2024)
- [MoreauGrad: Sparse and Robust Interpretation of Neural Networks via Moreau Envelope](https://mlsanity.com/paper/2302.05294/) (2023)

## Built on by (most cited first, 1 of 1)

- [Pushing the (Decision) Boundaries: Dynamically Calibrating Differentially Private Noise to Explainability in Federated Learning](https://mlsanity.com/paper/2609.03851/) (2026)

## Abstract (arXiv)

Saliency maps have been widely used to interpret the decisions of neural network classifiers and discover phenomena from their learned functions. However, standard gradient-based maps are frequently observed to be highly sensitive to the randomness of training data and the stochasticity in the training process. In this work, we study the role of Gaussian smoothing in the well-known Smooth-Grad algorithm in the stability of the gradient-based maps to the randomness of training samples. We extend the algorithmic stability framework to gradient-based interpretation maps and prove bounds on the stability error of standard Simple-Grad, Integrated-Gradients, and Smooth-Grad saliency maps. Our theoretical results suggest the role of Gaussian smoothing in boosting the stability of gradient-based maps to the randomness of training settings. On the other hand, we analyze the faithfulness of the Smooth-Grad maps to the original Simple-Grad and show the lower fidelity under a more intense Gaussian smoothing. We support our theoretical results by performing several numerical experiments on standard image datasets. Our empirical results confirm our hypothesis on the fidelity-stability trade-off in the application of Gaussian smoothing to gradient-based interpretation maps.