State-of-the-art neural network (NN) verifiers demonstrate that applying the branchand-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 α,β-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 α,β-CROWNverifier, the VNN-COMP 2025 winner.

Recent progress in neural network verification has challenged the notion of a convex barrier, that is, an inherent weakness in the convex relaxation of the output of a neural network. Specifically, there now exists a tight relaxation for verifying the robustness of a neural network to ` input perturbations, as well as efficient primal and dual solvers for the relaxation. Buoyed by this success, we consider the problem of developing similar techniques for verifying robustness to input perturbations within the probability simplex. We prove a somewhat surprising result that, in this case, not only can one design a tight relaxation that overcomes the convex barrier, but the size of the relaxation remains linear in the number of neurons, thereby leading to simpler and more efficient algorithms. We establish the scalability of our overall approach via the specification of `1 robustness for CIFAR-10 and MNIST classification, where our approach improves the state of the art verified accuracy by up to 14.4%. Furthermore, we establish its accuracy on a novel and highly challenging task of verifying the robustness of a multi-modal (text and image) classifier to arbitrary changes in its textual input.

However, many use cases of neural network verification require solving the inverse problem, or over-approximating the set of inputs that lead to certain outputs.

They iteratively modify and resolve linear programs to conduct a depth-first search from any node in the search tree. Existing divers rely on generic decision rules that fail to exploit structural commonality between similar problem instances that often arise in practice.

However, GCP-CROWN currently relies on generic cutting planes ("cuts") generated from external