# SEEV: Synthesis with Efficient Exact Verification for ReLU Neural Barrier Functions

arXiv: https://arxiv.org/abs/2410.20326 · HTML: https://mlsanity.com/paper/2410.20326/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2024.

## Built on by (most cited first, 7 of 7)

- [CP-NCBF: A Conformal Prediction-based Approach to Synthesize Verified Neural Control Barrier Functions](https://mlsanity.com/paper/2503.17395/) (2025)
- [Formal Verification of Neural Certificates Done Dynamically](https://mlsanity.com/paper/2507.11987/) (2025)
- [OTI: A Model-free and Visually Interpretable Measure of Image Attackability](https://mlsanity.com/paper/2601.17536/) (2026)
- [Robustness Certificates for Neural Networks Against Data Poisoning and Evasion Attacks](https://mlsanity.com/paper/2512.20865/) (2025)
- [Conformal Reachability for Safe Control in Unknown Environments](https://mlsanity.com/paper/2602.03799/) (2026)
- [Set-Based Training of Neural Barrier Certificates for Safety Verification of Dynamical Systems](https://mlsanity.com/paper/2605.02526/) (2026)
- [k-Inductive Neural Barrier Certificates for Unknown Nonlinear Dynamics](https://mlsanity.com/paper/2605.20108/) (2026)

## Abstract (arXiv)

Neural Control Barrier Functions (NCBFs) have shown significant promise in enforcing safety constraints on nonlinear autonomous systems. State-of-the-art exact approaches to verifying safety of NCBF-based controllers exploit the piecewise-linear structure of ReLU neural networks, however, such approaches still rely on enumerating all of the activation regions of the network near the safety boundary, thus incurring high computation cost. In this paper, we propose a framework for Synthesis with Efficient Exact Verification (SEEV). Our framework consists of two components, namely (i) an NCBF synthesis algorithm that introduces a novel regularizer to reduce the number of activation regions at the safety boundary, and (ii) a verification algorithm that exploits tight over-approximations of the safety conditions to reduce the cost of verifying each piecewise-linear segment. Our simulations show that SEEV significantly improves verification efficiency while maintaining the CBF quality across various benchmark systems and neural network structures. Our code is available at https://github.com/HongchaoZhang-HZ/SEEV.