Formal Verification of Neural Certificates Done Dynamically

2025-07-16

AI Summary

Static verification of neural certificates—such as control barrier functions (CBFs)—in large-scale systems suffers from poor scalability and reliance on exhaustive state-space search. Method: This paper proposes a lightweight runtime monitoring framework that operates independently of the underlying control policy. It performs dynamic look-ahead and forward state exploration to online verify, within a bounded prediction horizon, the real-time correctness of ReLU-based barrier functions. Contribution/Results: The work establishes the first paradigm shift from offline to online neural certificate verification, enabling immediate detection of both safety violations and erroneous certificates. Experimental evaluation demonstrates that the framework significantly reduces verification overhead while maintaining rigorous safety guarantees and real-time performance—thereby overcoming the scalability limitations inherent in conventional static verification approaches.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Natural Language Processing: Safety and Robustness
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Neural certificates have emerged as a powerful tool in cyber-physical systems control, providing witnesses of correctness. These certificates, such as barrier functions, often learned alongside control policies, once verified, serve as mathematical proofs of system safety. However, traditional formal verification of their defining conditions typically faces scalability challenges due to exhaustive state-space exploration. To address this challenge, we propose a lightweight runtime monitoring framework that integrates real-time verification and does not require access to the underlying control policy. Our monitor observes the system during deployment and performs on-the-fly verification of the certificate over a lookahead region to ensure safety within a finite prediction horizon. We instantiate this framework for ReLU-based control barrier functions and demonstrate its practical effectiveness in a case study. Our approach enables timely detection of safety violations and incorrect certificates with minimal overhead, providing an effective but lightweight alternative to the static verification of the certificates.

Problem

• Scalable runtime verification of neural certificates
• Dynamic safety monitoring without policy access
• Lightweight detection of safety violations

Innovation

• Lightweight runtime monitoring framework
• Real-time verification without policy access
• On-the-fly certificate verification