Probabilistic Safety for Bayesian Neural Networks

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.

UAI 2020; 13 pages, 5 figures, 1 table

References in corpus (13)

• What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?
• Wild Patterns: Ten Years After the Rise of Adversarial Machine Learning
• Safe Model-based Reinforcement Learning with Stability Guarantees
• Formal Security Analysis of Neural Networks using Symbolic Intervals
• On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models
• Understanding Measures of Uncertainty for Adversarial Example Detection
• A Simple Baseline for Bayesian Uncertainty in Deep Learning
• Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network
• Guaranteeing Safety for Neural Network-Based Aircraft Collision Avoidance Systems
• Reachability Analysis of Deep Neural Networks with Provable Guarantees
• Adversarial Phenomenon in the Eyes of Bayesian Deep Learning
• Robustness of Bayesian Neural Networks to Gradient-Based Attacks
• Verification of deep probabilistic models