Scalable Verification of Neural Control Barrier Functions Using Linear Bound Propagation

2025-11-09

AI Summary

Neural control barrier functions (Neural CBFs) face scalability bottlenecks in safety verification for nonlinear control systems, as existing methods suffer from high computational complexity and fail to scale to large networks. Method: This paper proposes an efficient verification framework based on linear bound propagation (LBP), integrating McCormick relaxations with gradient-bound estimation to analytically derive tight upper and lower bounds on the CBF safety condition. It further introduces a parallelizable, adaptive refinement strategy to substantially reduce conservatism. The framework supports common activation functions (e.g., ReLU, tanh) and control-affine systems. Results: Experiments demonstrate successful safety verification of Neural CBFs with up to ∼1,000 neurons across multiple nonlinear dynamical systems. The method achieves 10–100× speedup over prior approaches and significantly outperforms state-of-the-art methods in certified verification success rate.

Technology Category

• Natural Language Processing: Safety and Robustness
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Control barrier functions (CBFs) are a popular tool for safety certification of nonlinear dynamical control systems. Recently, CBFs represented as neural networks have shown great promise due to their expressiveness and applicability to a broad class of dynamics and safety constraints. However, verifying that a trained neural network is indeed a valid CBF is a computational bottleneck that limits the size of the networks that can be used. To overcome this limitation, we present a novel framework for verifying neural CBFs based on piecewise linear upper and lower bounds on the conditions required for a neural network to be a CBF. Our approach is rooted in linear bound propagation (LBP) for neural networks, which we extend to compute bounds on the gradients of the network. Combined with McCormick relaxation, we derive linear upper and lower bounds on the CBF conditions, thereby eliminating the need for computationally expensive verification procedures. Our approach applies to arbitrary control-affine systems and a broad range of nonlinear activation functions. To reduce conservatism, we develop a parallelizable refinement strategy that adaptively refines the regions over which these bounds are computed. Our approach scales to larger neural networks than state-of-the-art verification procedures for CBFs, as demonstrated by our numerical experiments.

Problem

• Verifying neural control barrier functions efficiently for nonlinear systems
• Overcoming computational bottlenecks in neural network safety certification
• Scaling verification to larger networks using linear bound propagation

Innovation

• Uses linear bound propagation for neural networks
• Extends LBP to compute neural network gradient bounds
• Employs adaptive refinement strategy to reduce conservatism