# Stability Guarantees for Feature Attributions with Multiplicative Smoothing

arXiv: https://arxiv.org/abs/2307.05902 · HTML: https://mlsanity.com/paper/2307.05902/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 64 references that are in the map.
- First posted on arXiv 12 Jul 2023.

## Builds on (most cited first, 30 of 54)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [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)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [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)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [Towards Faithfully Interpretable NLP Systems: How should we define and evaluate faithfulness?](https://mlsanity.com/paper/2004.03685/) (2020)
- [ERASER: A Benchmark to Evaluate Rationalized NLP Models](https://mlsanity.com/paper/1911.03429/) (2019)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Interpretation of Neural Networks is Fragile](https://mlsanity.com/paper/1710.10547/) (2017)
- [TweetEval: Unified Benchmark and Comparative Evaluation for Tweet Classification](https://mlsanity.com/paper/2010.12421/) (2020)
- [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AI](https://mlsanity.com/paper/2201.08164/) (2022)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Learning to Explain: An Information-Theoretic Perspective on Model Interpretation](https://mlsanity.com/paper/1802.07814/) (2018)

## Built on by (most cited first, 14 of 14)

- [SmoothLLM: Defending Large Language Models Against Jailbreaking Attacks](https://mlsanity.com/paper/2310.03684/) (2023)
- [Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanations](https://mlsanity.com/paper/2506.08505/) (2025)
- [Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guarantees](https://mlsanity.com/paper/2602.16823/) (2026)
- [Probabilistic Stability Guarantees for Feature Attributions](https://mlsanity.com/paper/2504.13787/) (2025)
- [SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism](https://mlsanity.com/paper/2510.21599/) (2025)
- [Interpretability Can Be Actionable](https://mlsanity.com/paper/2605.11161/) (2026)
- [Sum-of-Parts: Self-Attributing Neural Networks with End-to-End Learning of Feature Groups](https://mlsanity.com/paper/2310.16316/) (2023)
- [Enhancing Model Interpretability with Local Attribution over Global Exploration](https://mlsanity.com/paper/2408.07736/) (2024)
- [Additive Models Explained: A Computational Complexity Approach](https://mlsanity.com/paper/2510.21292/) (2025)
- [Unifying Formal Explanations: A Complexity-Theoretic Perspective](https://mlsanity.com/paper/2602.18160/) (2026)
- [Provably Explaining Neural Additive Models](https://mlsanity.com/paper/2602.17530/) (2026)
- [Missingness Bias Calibration in Feature Attribution Explanations](https://mlsanity.com/paper/2603.04831/) (2026)
- [When LRP Diverges from Leave-One-Out in Transformers](https://mlsanity.com/paper/2510.18810/) (2025)
- [Measuring Explainer Stability via Attribution Separability](https://mlsanity.com/paper/2608.02697/) (2026)

## Abstract (arXiv)

Explanation methods for machine learning models tend not to provide any formal guarantees and may not reflect the underlying decision-making process. In this work, we analyze stability as a property for reliable feature attribution methods. We prove that relaxed variants of stability are guaranteed if the model is sufficiently Lipschitz with respect to the masking of features. We develop a smoothing method called Multiplicative Smoothing (MuS) to achieve such a model. We show that MuS overcomes the theoretical limitations of standard smoothing techniques and can be integrated with any classifier and feature attribution method. We evaluate MuS on vision and language models with various feature attribution methods, such as LIME and SHAP, and demonstrate that MuS endows feature attributions with non-trivial stability guarantees.