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

TL;DR

SEEV introduces a novel framework that enhances the efficiency of verifying neural control barrier functions with ReLU networks by reducing activation regions and employing tight over-approximations, enabling faster safety verification.

Contribution

The paper presents a new synthesis and verification framework that significantly reduces computational costs in verifying ReLU neural barrier functions for safety.

Findings

Verification efficiency is significantly improved.

Maintains barrier function quality across benchmarks.

Reduces activation regions at the safety boundary.

Abstract

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.