Learning Lookahead Lemmas for Neural Network Verification

2026-07-31

AI Summary

This work addresses the limited efficiency and scalability of branch-and-bound methods in neural network verification by proposing an in-processing framework grounded in lookahead reasoning. By deriving novel lemmas over unstable ReLU nodes, the approach constructs an implication graph to intelligently prune the search space and activate Boolean cutting planes. Notably, it introduces for the first time a lookahead lemma-learning mechanism into neural network verification, effectively integrating implication-based reasoning with cutting plane generation. When integrated into the Marabou and α-β-CROWN verifiers, the method significantly enhances performance on standard benchmarks, proving up to 34% more instances unsatisfiable compared to the base solvers.

Abstract

State-of-the-art neural network verifiers use the branch-and-bound procedure as their core solving mechanism. We introduce an inprocessing framework for neural network verification driven by the lookahead procedure. Under this framework, lookahead derives new lemmas over the phases of unstable ReLUs, which are collected into an implication graph that is used to prune the search space and vivify boolean cuts. We instantiate the framework in two state-of-the-art verifiers, Marabou and $α$-$β$-CROWN, and demonstrate that it improves performance in both, proving up to 34% more instances unsatisfiable.

Problem

• neural network verification
• branch-and-bound
• ReLU phases
• search space pruning
• lookahead

Innovation

• lookahead lemmas
• neural network verification
• branch-and-bound
• implication graph
• ReLU phase pruning