Clip-and-Verify: Linear Constraint-Driven Domain Clipping for Accelerating Neural Network Verification

TL;DR

This paper introduces Clip-and-Verify, a scalable linear constraint-driven framework that accelerates neural network verification by tightening bounds and reducing subproblems in branch-and-bound procedures, achieving state-of-the-art results.

Contribution

The work presents novel algorithms leveraging linear constraints for efficient input space reduction and bound improvement, scalable to large networks without external solvers.

Findings

96% reduction in subproblems during branch-and-bound

State-of-the-art verified accuracy achieved

Effective integration with existing verifiers like α,β-CROWN

Abstract

State-of-the-art neural network (NN) verifiers demonstrate that applying the branch-and-bound (BaB) procedure with fast bounding techniques plays a key role in tackling many challenging verification properties. In this work, we introduce the linear constraint-driven clipping framework, a class of scalable and efficient methods designed to enhance the efficacy of NN verifiers. Under this framework, we develop two novel algorithms that efficiently utilize linear constraints to 1) reduce portions of the input space that are either verified or irrelevant to a subproblem in the context of branch-and-bound, and 2) directly improve intermediate bounds throughout the network. The process novelly leverages linear constraints that often arise from bound propagation methods and is general enough to also incorporate constraints from other sources. It efficiently handles linear constraints using a specialized GPU procedure that can scale to large neural networks without the use of expensive external solvers. Our verification procedure, Clip-and-Verify, consistently tightens bounds across multiple benchmarks and can significantly reduce the number of subproblems handled during BaB. We show that our clipping algorithms can be integrated with BaB-based verifiers such as $\alpha,\beta$-CROWN, utilizing either the split constraints in activation-space BaB or the output constraints that denote the unverified input space. We demonstrate the effectiveness of our procedure on a broad range of benchmarks where, in some instances, we witness a 96% reduction in the number of subproblems during branch-and-bound, and also achieve state-of-the-art verified accuracy across multiple benchmarks. Clip-and-Verify is part of the $\alpha,\beta$-CROWN verifier (http://abcrown.org), the VNN-COMP 2025 winner. Code available at https://github.com/Verified-Intelligence/Clip_and_Verify.