Description
"Probabilistic Safety for Bayesian Neural Networks
Matthew Wicker (University of Oxford)*; Luca Laurenti (University of Oxford); Andrea Patane (University of Oxford); Marta Kwiatkowska (Oxford University)
- 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."