# Bayesian Adversarial Spheres: Bayesian Inference and Adversarial Examples in a Noiseless Setting

arXiv: https://arxiv.org/abs/1811.12335 · HTML: https://mlsanity.com/paper/1811.12335/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2018.

## Built on by (most cited first, 8 of 8)

- [A Primer on Bayesian Neural Networks: Review and Debates](https://mlsanity.com/paper/2309.16314/) (2023)
- [Bayesian Inference with Certifiable Adversarial Robustness](https://mlsanity.com/paper/2102.05289/) (2021)
- [On the Robustness of Bayesian Neural Networks to Adversarial Attacks](https://mlsanity.com/paper/2207.06154/) (2022)
- [Adversarial Robustness Certification for Bayesian Neural Networks](https://mlsanity.com/paper/2306.13614/) (2023)
- [Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformers](https://mlsanity.com/paper/2603.09453/) (2026)
- [Mitigating Closed-model Adversarial Examples with Bayesian Neural Modeling for Enhanced End-to-End Speech Recognition](https://mlsanity.com/paper/2202.08532/) (2022)
- [Attacking Bayes: On the Adversarial Robustness of Bayesian Neural Networks](https://mlsanity.com/paper/2404.19640/) (2024)
- [Random Projections for Improved Adversarial Robustness](https://mlsanity.com/paper/2102.09230/) (2021)

## Abstract (arXiv)

Modern deep neural network models suffer from adversarial examples, i.e. confidently misclassified points in the input space. It has been shown that Bayesian neural networks are a promising approach for detecting adversarial points, but careful analysis is problematic due to the complexity of these models. Recently Gilmer et al. (2018) introduced adversarial spheres, a toy set-up that simplifies both practical and theoretical analysis of the problem. In this work, we use the adversarial sphere set-up to understand the properties of approximate Bayesian inference methods for a linear model in a noiseless setting. We compare predictions of Bayesian and non-Bayesian methods, showcasing the advantages of the former, although revealing open challenges for deep learning applications.