# How to beat a Bayesian adversary

arXiv: https://arxiv.org/abs/2407.08678 · HTML: https://mlsanity.com/paper/2407.08678/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 67 references that are in the map.
- First posted on arXiv 11 Jul 2024.

## Builds on (most cited first, 30 of 41)

- [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)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Countering Adversarial Images using Input Transformations](https://mlsanity.com/paper/1711.00117/) (2017)
- [Feature Squeezing: Detecting Adversarial Examples in Deep Neural Networks](https://mlsanity.com/paper/1704.01155/) (2017)
- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examples](https://mlsanity.com/paper/1710.10766/) (2017)
- [On Detecting Adversarial Perturbations](https://mlsanity.com/paper/1702.04267/) (2017)
- [Adversarial Robustness Toolbox v1.0.0](https://mlsanity.com/paper/1807.01069/) (2018)
- [Better Diffusion Models Further Improve Adversarial Training](https://mlsanity.com/paper/2302.04638/) (2023)
- [Adversarial Training and Robustness for Multiple Perturbations](https://mlsanity.com/paper/1904.13000/) (2019)
- [Wasserstein Adversarial Examples via Projected Sinkhorn Iterations](https://mlsanity.com/paper/1902.07906/) (2019)
- [Adversarial Robustness Against the Union of Multiple Perturbation Models](https://mlsanity.com/paper/1909.04068/) (2019)
- [Segment and Complete: Defending Object Detectors against Adversarial Patch Attacks with Robust Patch Detection](https://mlsanity.com/paper/2112.04532/) (2021)
- [Diffusion-Based Adversarial Sample Generation for Improved Stealthiness and Controllability](https://mlsanity.com/paper/2305.16494/) (2023)
- [ME-Net: Towards Effective Adversarial Robustness with Matrix Estimation](https://mlsanity.com/paper/1905.11971/) (2019)
- [Probabilistically Robust Learning: Balancing Average- and Worst-case Performance](https://mlsanity.com/paper/2202.01136/) (2022)
- [Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learning](https://mlsanity.com/paper/2012.12137/) (2020)
- [PatchZero: Defending against Adversarial Patch Attacks by Detecting and Zeroing the Patch](https://mlsanity.com/paper/2207.01795/) (2022)

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

- [Convergence of the generalization error for deep gradient flow methods for PDEs](https://mlsanity.com/paper/2512.25017/) (2025)

## Abstract (arXiv)

Deep neural networks and other modern machine learning models are often susceptible to adversarial attacks. Indeed, an adversary may often be able to change a model's prediction through a small, directed perturbation of the model's input - an issue in safety-critical applications. Adversarially robust machine learning is usually based on a minmax optimisation problem that minimises the machine learning loss under maximisation-based adversarial attacks. In this work, we study adversaries that determine their attack using a Bayesian statistical approach rather than maximisation. The resulting Bayesian adversarial robustness problem is a relaxation of the usual minmax problem. To solve this problem, we propose Abram - a continuous-time particle system that shall approximate the gradient flow corresponding to the underlying learning problem. We show that Abram approximates a McKean-Vlasov process and justify the use of Abram by giving assumptions under which the McKean-Vlasov process finds the minimiser of the Bayesian adversarial robustness problem. We discuss two ways to discretise Abram and show its suitability in benchmark adversarial deep learning experiments.