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

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 $α,β$-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 $α,β$-CROWN verifier (http://abcrown.org), the VNN-COMP 2025 winner. Code available at https://github.com/Verified-Intelligence/Clip_and_Verify.

CoSDA: Continual Source-Free Domain Adaptation

Without access to the source data, source-free domain adaptation (SFDA) transfers knowledge from a source-domain trained model to target domains. Recently, SFDA has gained popularity due to the need to protect the data privacy of the source domain, but it suffers from catastrophic forgetting on the source domain due to the lack of data. To systematically investigate the mechanism of catastrophic forgetting, we first reimplement previous SFDA approaches within a unified framework and evaluate them on four benchmarks. We observe that there is a trade-off between adaptation gain and forgetting loss, which motivates us to design a consistency regularization to mitigate forgetting. In particular, we propose a continual source-free domain adaptation approach named CoSDA, which employs a dual-speed optimized teacher-student model pair and is equipped with consistency learning capability. Our experiments demonstrate that CoSDA outperforms state-of-the-art approaches in continuous adaptation. Notably, our CoSDA can also be integrated with other SFDA methods to alleviate forgetting.