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The FABRIC Strategy for Verifying Neural Feedback Systems

arXiv:2603.08964v1 Announce Type: new Abstract: Forward reachability analysis is a dominant approach for verifying reach-avoid specifications in neural feedback systems, i.e., dynamical systems controlled by neural networks, and a number of directions have been proposed and studied. In contrast, far less attention has been given to backward reachability analysis for these systems, in part because of the limited scalability of known techniques. In this work, we begin to address this gap by introducing new algorithms for computing both over- and underapproximations of backward reachable sets for nonlinear neural feedback systems. We also describe and implement an integration of these backward reachability techniques with existing ones for forward analysis. We call the resulting algorithm Forward and Backward Reachability Integration for Certification (FaBRIC). We evaluate our algorithms on a representative set of benchmarks and show that they significantly outperform the prior state of

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I. Samuel Akinwande, Sydney M. Katz, Mykel J. Kochenderfer, Clark Barrett · · 1 min read · 16 views
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arXiv:2603.08964v1 Announce Type: new Abstract: Forward reachability analysis is a dominant approach for verifying reach-avoid specifications in neural feedback systems, i.e., dynamical systems controlled by neural networks, and a number of directions have been proposed and studied. In contrast, far less attention has been given to backward reachability analysis for these systems, in part because of the limited scalability of known techniques. In this work, we begin to address this gap by introducing new algorithms for computing both over- and underapproximations of backward reachable sets for nonlinear neural feedback systems. We also describe and implement an integration of these backward reachability techniques with existing ones for forward analysis. We call the resulting algorithm Forward and Backward Reachability Integration for Certification (FaBRIC). We evaluate our algorithms on a representative set of benchmarks and show that they significantly outperform the prior state of the art.

Executive Summary

This article presents a novel strategy, called FaBRIC, for verifying neural feedback systems using a combination of forward and backward reachability analysis. The authors introduce new algorithms for computing over- and underapproximations of backward reachable sets for nonlinear neural feedback systems. The proposed approach significantly outperforms the prior state of the art on a set of benchmarks. The integration of forward and backward reachability analysis has the potential to improve the reliability and efficiency of neural feedback systems. The article contributes to the ongoing efforts to develop more robust and scalable techniques for verifying complex dynamical systems. The results and methods presented in this article will be of interest to researchers and practitioners working on neural control systems and formal verification.

Key Points

  • ▸ The authors introduce a novel strategy for verifying neural feedback systems using forward and backward reachability analysis.
  • ▸ New algorithms are proposed for computing over- and underapproximations of backward reachable sets.
  • ▸ The integration of forward and backward reachability analysis outperforms the prior state of the art on benchmarks.

Merits

Scalability

The proposed approach addresses the limited scalability of known backward reachability techniques, enabling the analysis of complex neural feedback systems.

Robustness

The use of over- and underapproximations of backward reachable sets improves the robustness of the verification process by providing a more comprehensive understanding of system behavior.

Efficiency

The integration of forward and backward reachability analysis significantly improves the efficiency of the verification process, enabling the analysis of larger and more complex systems.

Demerits

Computational Complexity

The proposed algorithms may still be computationally intensive, limiting their applicability to large-scale systems or systems with high-dimensional state spaces.

Assumptions

The authors assume that the neural feedback systems can be modeled using a specific type of dynamical system, which may not be applicable to all types of neural networks.

Expert Commentary

The article presents a significant contribution to the field of formal verification of neural networks and control systems. The proposed approach addresses a long-standing challenge in the field and has the potential to improve the reliability and efficiency of neural feedback systems. The results and methods presented in this article will be of interest to researchers and practitioners working on neural control systems and formal verification. However, the proposed algorithms may still be computationally intensive, and further research is needed to address this limitation.

Recommendations

  • ✓ Future research should focus on developing more efficient algorithms for backward reachability analysis, particularly for large-scale systems or systems with high-dimensional state spaces.
  • ✓ The proposed approach should be extended to other types of neural networks and control systems, including those with non-linear dynamics or uncertain parameters.

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