Robustness Analysis of Neural Networks via Efficient Partitioning with Applications in Control Systems

Abstract

Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds on NN output sets (given an input set) provides a measure of confidence associated with the NN decisions and is essential to deploy NNs on safety-critical systems. Recent works approximate the propagation of sets through nonlinear activations or partition the uncertainty set to provide a guaranteed outer bound on the set of possible NN outputs. However, the bound looseness causes excessive conservatism and/or the computation is too slow for online analysis. This paper unifies propagation and partition approaches to provide a family of robustness analysis algorithms that give tighter bounds than existing works for the same amount of computation time (or reduced computational effort for a desired accuracy level). Moreover, we provide new partitioning techniques that are aware of their current bound estimates and desired boundary shape (e.g., lower bounds, weighted ∞-ball, convex hull), leading to further improvements in the computationtightness tradeoff. The paper demonstrates the tighter bounds and reduced conservatism of the proposed robustness analysis framework with examples from model-free RL and forward kinematics learning.

Towards Optimal Branching of Linear and Semidefinite Relaxations for Neural Network Robustness Certification

“…However, that method is restricted to splitting box-shaped uncertainty sets in half along coordinate axes. Finally, Everett et al (2020) provides theoretical guarantees for the amount of volume reduction in the outer approximation induced by partitioning, but it only considers axis-aligned gridding of the input space. These recent works demonstrate the increased interest in partition-based certification, and their positive results are evidence that partitioning yields tightened approximations with only a modest increase in computational overhead.…”