Probabilistic Safety for Bayesian Neural Networks

2020/04/21 by Matthew Wicker, Luca Laurenti, Wicker, Matthew +5 · 1 citation
Computer Science · Engineering · #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #Fault Detection and Control Systems #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms

paper · pdf · doi:10.48550/arxiv.2004.10281

openalex publication_date 2020/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study probabilistic safety for BayesianNeural Networks (BNNs) under adversarial in-put perturbations. Given a compact set of input points,T⊆Rm, we study the probability w.r.t. the BNN posterior that all the pointsinTare mapped to the same region S in theoutput space. In particular, this can be usedto evaluate the probability that a network sam-pled from the BNN is vulnerable to adversarialattacks. We rely on relaxation techniques from non-convex optimization to develop a methodfor computing a lower bound on probabilis-tic safety for BNNs, deriving explicit procedures for the case of interval and linear function propagation techniques. We apply ourmethods to BNNs trained on a regression task,airborne collision avoidance, and MNIST, empirically showing that our approach allows oneto certify probabilistic safety of BNNs withthousands of neurons.

Citations

• Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
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• Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning
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Cited by

• Provably Safe Model Updates

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