Data-Driven Certification of Neural Networks With Random Input Noise

Methods to certify the robustness of neural networks in presence input uncertainty are vital safety-critical settings. Most certification methods literature designed for adversarial or worst-case inputs, but researchers have recently shown a need that consider random noise. In this article, we examine setting where inputs subject noise coming from an arbitrary probability distribution. We propose method lower-bounds network outputs safe. This bound is cast as chance-constrained optimization problem, which then reformulated using input–output samples make constraints tractable. develop sufficient conditions resulting be convex, well on number needed hold with overwhelming probability. Case studies synthetic, MNIST, and CIFAR-10 experimentally demonstrate able against various regimes over larger regions than prior state-of-the-art techniques.