Robustness of Bayesian Neural Networks to Gradient-Based Attacks
This addresses the problem of adversarial robustness for safety-critical applications, offering a theoretical and empirical analysis that is incremental in extending robustness insights to BNNs.
The paper tackles the vulnerability of deep learning to adversarial attacks by analyzing Bayesian Neural Networks (BNNs) in the large-data, overparametrized limit, showing that BNN posteriors become robust to gradient-based attacks when data lies on lower-dimensional submanifolds, with experimental support on MNIST and Fashion MNIST datasets demonstrating high accuracy and robustness.
Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, the problem remains open. In this paper, we analyse the geometry of adversarial attacks in the large-data, overparametrized limit for Bayesian Neural Networks (BNNs). We show that, in the limit, vulnerability to gradient-based attacks arises as a result of degeneracy in the data distribution, i.e., when the data lies on a lower-dimensional submanifold of the ambient space. As a direct consequence, we demonstrate that in the limit BNN posteriors are robust to gradient-based adversarial attacks. Experimental results on the MNIST and Fashion MNIST datasets with BNNs trained with Hamiltonian Monte Carlo and Variational Inference support this line of argument, showing that BNNs can display both high accuracy and robustness to gradient based adversarial attacks.