Provably Tightest Linear Approximation for Robustness Verification of Sigmoid-like Neural Networks

TL;DR

This paper introduces a theoretically grounded, provably tight approximation method for verifying the robustness of sigmoid-like neural networks, significantly improving the precision of robustness bounds compared to existing heuristics.

Contribution

It proposes a network-wise tightness concept and develops two efficient algorithms that provide the tightest approximations, enhancing verification accuracy.

Findings

Up to 251.28% improvement in robustness bounds

More precise verification on convolutional networks

Outperforms state-of-the-art approximation methods

Abstract

The robustness of deep neural networks is crucial to modern AI-enabled systems and should be formally verified. Sigmoid-like neural networks have been adopted in a wide range of applications. Due to their non-linearity, Sigmoid-like activation functions are usually over-approximated for efficient verification, which inevitably introduces imprecision. Considerable efforts have been devoted to finding the so-called tighter approximations to obtain more precise verification results. However, existing tightness definitions are heuristic and lack theoretical foundations. We conduct a thorough empirical analysis of existing neuron-wise characterizations of tightness and reveal that they are superior only on specific neural networks. We then introduce the notion of network-wise tightness as a unified tightness definition and show that computing network-wise tightness is a complex non-convex optimization problem. We bypass the complexity from different perspectives via two efficient, provably tightest approximations. The results demonstrate the promising performance achievement of our approaches over state of the art: (i) achieving up to 251.28% improvement to certified lower robustness bounds; and (ii) exhibiting notably more precise verification results on convolutional networks.