Efficient Verification of Neural Control Barrier Functions with Smooth Nonlinear Activations

2026-05-08

AI Summary

This work addresses the limited scalability of formal verification for Neural Control Barrier Functions (NCBFs) when employing smooth nonlinear activation functions such as tanh, a limitation stemming from the overly conservative linear relaxations used in existing methods. To overcome this, the paper introduces LightCROWN, a novel approach that leverages the analytical properties of activation functions to compute substantially tighter bounds on Jacobian matrices, thereby significantly reducing conservatism within the CROWN verification framework. Empirical evaluations demonstrate that LightCROWN achieves up to 100% verification success rates on benchmark nonlinear control systems—including the inverted pendulum, Dubins car, and planar quadrotor—while simultaneously enhancing both computational efficiency and scalability.

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.

Problem

• neural control barrier functions
• formal verification
• nonlinear activations
• Jacobian bounds
• CROWN

Innovation

• Neural Control Barrier Functions
• Formal Verification
• CROWN
• Jacobian Bounds
• Nonlinear Activations