Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers

TL;DR

This paper introduces a GPU-accelerated method for neural network verification using LiRPA, achieving significant speedups over traditional LP-based methods by combining bound tightening and minimal LP usage.

Contribution

The paper presents a novel approach that replaces LP with LiRPA in branch-and-bound for neural network verification, enabling efficient GPU implementation and improved performance.

Findings

Order of magnitude speedup on GPU compared to LP-based methods

Effective use of LiRPA with bound tightening and batch splits

Enables complete neural network verification efficiently

Abstract

Formal verification of neural networks (NNs) is a challenging and important problem. Existing efficient complete solvers typically require the branch-and-bound (BaB) process, which splits the problem domain into sub-domains and solves each sub-domain using faster but weaker incomplete verifiers, such as Linear Programming (LP) on linearly relaxed sub-domains. In this paper, we propose to use the backward mode linear relaxation based perturbation analysis (LiRPA) to replace LP during the BaB process, which can be efficiently implemented on the typical machine learning accelerators such as GPUs and TPUs. However, unlike LP, LiRPA when applied naively can produce much weaker bounds and even cannot check certain conflicts of sub-domains during splitting, making the entire procedure incomplete after BaB. To address these challenges, we apply a fast gradient based bound tightening procedure combined with batch splits and the design of minimal usage of LP bound procedure, enabling us to effectively use LiRPA on the accelerator hardware for the challenging complete NN verification problem and significantly outperform LP-based approaches. On a single GPU, we demonstrate an order of magnitude speedup compared to existing LP-based approaches.