Related papers: Probabilistic Safety for Bayesian Neural Networks

Probabilistic Safety for Bayesian Neural Networks

URL: http://arxiv.org/abs/2004.10281v2
Date: Fri, 19 Jun 2020 02:06:15 GMT
Title: Probabilistic Safety for Bayesian Neural Networks
Authors: Matthew Wicker, Luca Laurenti, Andrea Patane, Marta Kwiatkowska
Abstract summary: We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. In particular, we evaluate that a network sampled from the BNN is vulnerable to adversarial attacks. We apply our methods to BNNs trained on a task airborne avoidance, empirically showing that our approach allows one to certify probabilistic safety of BNNs with millions of parameters.
Score: 22.71265211510824
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, $T \subseteq \mathbb{R}^m$, we study the probability w.r.t. the BNN posterior that all the points in $T$ are mapped to the same region $S$ in the output space. In particular, this can be used to evaluate the probability that a network sampled from the BNN is vulnerable to adversarial attacks. We rely on relaxation techniques from non-convex optimization to develop a method for computing a lower bound on probabilistic safety for BNNs, deriving explicit procedures for the case of interval and linear function propagation techniques. We apply our methods to BNNs trained on a regression task, airborne collision avoidance, and MNIST, empirically showing that our approach allows one to certify probabilistic safety of BNNs with millions of parameters.

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