Mining Verdict Boundaries for Neural Network Verification

2026-07-30

AI Summary

This work addresses the inefficiency of traditional branch-and-bound methods in neural network verification, which suffer from sequential layer-by-layer processing that hinders effective exploration of decision boundaries. To overcome this limitation, the authors propose an efficient localization strategy that exploits path monotonicity to parallelize the splitting of multiple ReLU activations and employs exponential search to skip irrelevant subproblems. Furthermore, quantitative information derived from subproblem solutions is leveraged to accurately estimate boundary locations. By breaking free from the constraints of layer-wise processing, the proposed method significantly outperforms existing branch-and-bound approaches on standard benchmarks, drastically reducing the number of subproblems that require exploration while simultaneously improving both verification speed and precision.

Abstract

Branch and Bound (BaB) aims to achieve complete verification of neural networks by adaptively partitioning the problem and applying off-the-shelf verifiers to subproblems. Its problem-splitting history can be represented as a tree, where each subproblem corresponds to a child node. A key problem of BaB lies in searching for the verdict boundaries across all the paths that divide the verified and unverified subproblems. We observe that the existing BaB approach tackles this problem by solving each expensive subproblem sequentially along the tree path as its depth increases, requiring costly bounds propagation at every visited BaB tree node (i.e., subproblem), which is inefficient. To address this issue, we propose effective search approaches that leverage the monotonicity of each path to efficiently and precisely locate the verdict boundary by simultaneously splitting multiple activation functions (e.g., ReLU), rather than processing them one at a time as in the classical approach. Our approach performs an effective exponential search along each path, allowing us to skip many boundary-unrelated subproblems when identifying the verdict boundary. The enhanced version further improves this process by estimating the boundary's position using quantitative information obtained from subproblem solving. We perform experimental evaluation on commonly-used benchmarks to assess our proposed techniques, and compare them with recent BaB-based approaches.

Problem

• Neural Network Verification
• Branch and Bound
• Verdict Boundaries
• ReLU Activation
• Complete Verification

Innovation

• Branch and Bound
• Verdict Boundary
• Monotonicity
• Exponential Search
• Neural Network Verification