# The Effect of Prior Lipschitz Continuity on the Adversarial Robustness of Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2101.02689 · HTML: https://mlsanity.com/paper/2101.02689/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 39 references that are in the map.
- First posted on arXiv 7 Jan 2021.

## Builds on (most cited first, 29 of 29)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Wild Patterns: Ten Years After the Rise of Adversarial Machine Learning](https://mlsanity.com/paper/1712.03141/) (2017)
- [Feature Denoising for Improving Adversarial Robustness](https://mlsanity.com/paper/1812.03411/) (2018)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Detecting Adversarial Samples from Artifacts](https://mlsanity.com/paper/1703.00410/) (2017)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Functional Variational Bayesian Neural Networks](https://mlsanity.com/paper/1903.05779/) (2019)
- [When NAS Meets Robustness: In Search of Robust Architectures against Adversarial Attacks](https://mlsanity.com/paper/1911.10695/) (2019)
- [Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network](https://mlsanity.com/paper/1810.01279/) (2018)
- [ME-Net: Towards Effective Adversarial Robustness with Matrix Estimation](https://mlsanity.com/paper/1905.11971/) (2019)
- [Adversarial Attacks Against Medical Deep Learning Systems](https://mlsanity.com/paper/1804.05296/) (2018)
- [Robustness of Bayesian Neural Networks to Gradient-Based Attacks](https://mlsanity.com/paper/2002.04359/) (2020)
- [Probabilistic Safety for Bayesian Neural Networks](https://mlsanity.com/paper/2004.10281/) (2020)
- [Provable robustness against all adversarial lp-perturbations for p≥ 1](https://mlsanity.com/paper/1905.11213/) (2019)
- [Statistical Guarantees for the Robustness of Bayesian Neural Networks](https://mlsanity.com/paper/1903.01980/) (2019)
- [Intriguing Properties of Adversarial Examples](https://mlsanity.com/paper/1711.02846/) (2017)
- [Bayesian Learning-Based Adaptive Control for Safety Critical Systems](https://mlsanity.com/paper/1910.02325/) (2019)
- [The Limitations of Model Uncertainty in Adversarial Settings](https://mlsanity.com/paper/1812.02606/) (2018)
- [Comment on "Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network"](https://mlsanity.com/paper/1907.00895/) (2019)
- [Adversarial Robustness Guarantees for Classification with Gaussian Processes](https://mlsanity.com/paper/1905.11876/) (2019)

## Built on by (most cited first, 3 of 3)

- [A Primer on Bayesian Neural Networks: Review and Debates](https://mlsanity.com/paper/2309.16314/) (2023)
- [Attacking Bayes: On the Adversarial Robustness of Bayesian Neural Networks](https://mlsanity.com/paper/2404.19640/) (2024)
- [Lipschitz bounds for integral kernels](https://mlsanity.com/paper/2604.02887/) (2026)

## Abstract (arXiv)

It is desirable, and often a necessity, for machine learning models to be robust against adversarial attacks. This is particularly true for Bayesian models, as they are well-suited for safety-critical applications, in which adversarial attacks can have catastrophic outcomes. In this work, we take a deeper look at the adversarial robustness of Bayesian Neural Networks (BNNs). In particular, we consider whether the adversarial robustness of a BNN can be increased by model choices, particularly the Lipschitz continuity induced by the prior. Conducting in-depth analysis on the case of i.i.d., zero-mean Gaussian priors and posteriors approximated via mean-field variational inference, we find evidence that adversarial robustness is indeed sensitive to the prior variance.