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

arXiv: https://arxiv.org/abs/2512.11087 · HTML: https://mlsanity.com/paper/2512.11087/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 83 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Builds on (most cited first, 30 of 49)

- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [Efficient Formal Safety Analysis of Neural Networks](https://mlsanity.com/paper/1809.08098/) (2018)
- [Branch and Bound for Piecewise Linear Neural Network Verification](https://mlsanity.com/paper/1909.06588/) (2019)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [A Dual Approach to Scalable Verification of Deep Networks](https://mlsanity.com/paper/1803.06567/) (2018)
- [A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networks](https://mlsanity.com/paper/1902.08722/) (2019)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [General Cutting Planes for Bound-Propagation-Based Neural Network Verification](https://mlsanity.com/paper/2208.05740/) (2022)
- [Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming](https://mlsanity.com/paper/1903.01287/) (2019)
- [Maximum Resilience of Artificial Neural Networks](https://mlsanity.com/paper/1705.01040/) (2017)
- [Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Bound](https://mlsanity.com/paper/2205.00263/) (2022)
- [Marabou 2.0: A Versatile Formal Analyzer of Neural Networks](https://mlsanity.com/paper/2401.14461/) (2024)
- [PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximations](https://mlsanity.com/paper/2103.03638/) (2021)
- [The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Results](https://mlsanity.com/paper/2109.00498/) (2021)
- [Training for Faster Adversarial Robustness Verification via Inducing ReLU Stability](https://mlsanity.com/paper/1809.03008/) (2018)
- [Enabling certification of verification-agnostic networks via memory-efficient semidefinite programming](https://mlsanity.com/paper/2010.11645/) (2020)
- [The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verification](https://mlsanity.com/paper/2006.14076/) (2020)
- [Neural Network Verification with Branch-and-Bound for General Nonlinearities](https://mlsanity.com/paper/2405.21063/) (2024)
- [Improved Branch and Bound for Neural Network Verification via Lagrangian Decomposition](https://mlsanity.com/paper/2104.06718/) (2021)
- [Scaling Polyhedral Neural Network Verification on GPUs](https://mlsanity.com/paper/2007.10868/) (2020)
- [The Fifth International Verification of Neural Networks Competition (VNN-COMP 2024): Summary and Results](https://mlsanity.com/paper/2412.19985/) (2024)

## Built on by (most cited first, 9 of 9)

- [IoUCert: Robustness Verification for Anchor-based Object Detectors](https://mlsanity.com/paper/2603.03043/) (2026)
- [Bridging Control with Neural Network Verifier alpha-beta-CROWN: A Tutorial](https://mlsanity.com/paper/2605.26577/) (2026)
- [Lookahead Branching for Neural Network Verification](https://mlsanity.com/paper/2607.17290/) (2026)
- [ZonoGPT: Towards An Abstract Domain for Verifying Large GPT Models](https://mlsanity.com/paper/2609.34457/) (2026)
- [On the Extreme Variance of Certified Local Robustness Across Model Seeds](https://mlsanity.com/paper/2601.13303/) (2026)
- [Verified SHAP: Provable Bounds for Exact Shapley Values of Neural Networks](https://mlsanity.com/paper/2605.24084/) (2026)
- [Rethinking Evaluation Paradigms in IBP-based Certified Training](https://mlsanity.com/paper/2606.02134/) (2026)
- [Learning Lookahead Lemmas for Neural Network Verification](https://mlsanity.com/paper/2607.29051/) (2026)
- [CLAD: Constrained Abstract Domain for Neural Network Verification](https://mlsanity.com/paper/2609.34628/) (2026)

## Abstract (arXiv)

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/ClipandVerify.