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[WLPK20] Matthew Wicker, Luca Laurenti, Andrea Patane and Marta Kwiatkowska. Probabilistic Safety for Bayesian Neural Networks. In 36th Conference on Uncertainty in Artificial Intelligence (UAI 2020), AUAI Press. August 2020. [pdf] [bib]
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Abstract. We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, 𝑻 βŠ† ℝᡐ, 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.