Tight Verification of Probabilistic Robustness in Bayesian Neural Networks

TL;DR

This paper presents two novel algorithms for computing tight probabilistic robustness guarantees in Bayesian Neural Networks, addressing the challenge of parameter space search and polynomial terms, outperforming existing methods on benchmarks.

Contribution

Introduces two algorithms that provide tighter probabilistic robustness bounds for BNNs, compatible with existing verification techniques, and demonstrates their effectiveness on standard datasets.

Findings

Algorithms compute bounds up to 40% tighter than state-of-the-art.

Effective search of parameter space using iterative expansion and gradients.

Applicable to standard verification algorithms for BNNs.

Abstract

We introduce two algorithms for computing tight guarantees on the probabilistic robustness of Bayesian Neural Networks (BNNs). Computing robustness guarantees for BNNs is a significantly more challenging task than verifying the robustness of standard Neural Networks (NNs) because it requires searching the parameters' space for safe weights. Moreover, tight and complete approaches for the verification of standard NNs, such as those based on Mixed-Integer Linear Programming (MILP), cannot be directly used for the verification of BNNs because of the polynomial terms resulting from the consecutive multiplication of variables encoding the weights. Our algorithms efficiently and effectively search the parameters' space for safe weights by using iterative expansion and the network's gradient and can be used with any verification algorithm of choice for BNNs. In addition to proving that our algorithms compute tighter bounds than the SoA, we also evaluate our algorithms against the SoA on standard benchmarks, such as MNIST and CIFAR10, showing that our algorithms compute bounds up to 40% tighter than the SoA.