Efficient Verification of Neural Control Barrier Functions with Smooth Nonlinear Activations

TL;DR

This paper introduces LightCROWN, a method that improves the efficiency and success rate of verifying neural control barrier functions with nonlinear activations by computing tighter Jacobian bounds.

Contribution

LightCROWN provides a novel approach to tighten Jacobian bounds in CROWN-based verification, enhancing scalability and success rates for neural control barrier functions with nonlinear activations.

Findings

LightCROWN achieves up to 100% verification success rate.

It improves speed and scalability over existing methods.

Applicable to complex nonlinear control systems.

Abstract

Formal verification of neural control barrier functions (NCBFs) remains challenging, especially for neural networks with nonlinear activations like \(\tanh\). Existing CROWN-based methods rely on conservative linear relaxations for Jacobian bounds, limiting scalability. We propose LightCROWN, which computes tighter Jacobian bounds by exploiting the analytical properties of activation functions. Experiments on nonlinear control systems including the inverted pendulum, Dubins car, and planar quadrotor demonstrate that LightCROWN improves verification success rates up to 100\%, while enhancing speed and scalability. Our approach provides a generalizable improvement for CROWN-based frameworks, enabling more efficient verification of complex NCBFs. The code can be found at github.com/Autonomous-Systems-and-Control-Lab/verify-neural-CBF.