Efficient Verification of Neural Control Barrier Functions with Smooth Nonlinear Activations
For researchers in formal verification of neural networks in control, this provides a more efficient verification method for neural control barrier functions with smooth nonlinear activations.
The authors propose LightCROWN, a method that computes tighter Jacobian bounds for neural control barrier functions with nonlinear activations, improving verification success rates up to 100% and enhancing speed and scalability on systems like inverted pendulum, Dubins car, and planar quadrotor.
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.