Of Good Demons and Bad Angels: Guaranteeing Safe Control under Finite Precision
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908473033228288 |
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| author | Teuber, Samuel Lohar, Debasmita Beckert, Bernhard |
| author_facet | Teuber, Samuel Lohar, Debasmita Beckert, Bernhard |
| contents | As neural networks (NNs) become increasingly prevalent in safety-critical neural network-controlled cyber-physical systems (NNCSs), formally guaranteeing their safety becomes crucial. For these systems, safety must be ensured throughout their entire operation, necessitating infinite-time horizon verification. To verify the infinite-time horizon safety of NNCSs, recent approaches leverage Differential Dynamic Logic (dL). However, these dL-based guarantees rely on idealized, real-valued NN semantics and fail to account for roundoff errors introduced by finite-precision implementations. This paper bridges the gap between theoretical guarantees and real-world implementations by incorporating robustness under finite-precision perturbations -- in sensing, actuation, and computation -- into the safety verification. We model the problem as a hybrid game between a good Demon, responsible for control actions, and a bad Angel, introducing perturbations. This formulation enables formal proofs of robustness w.r.t. a given (bounded) perturbation. Leveraging this bound, we employ state-of-the-art mixed-precision fixed-point tuners to synthesize sound and efficient implementations, thus providing a complete end-to-end solution. We evaluate our approach on case studies from the automotive and aeronautics domains, producing efficient NN implementations with rigorous infinite-time horizon safety guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Of Good Demons and Bad Angels: Guaranteeing Safe Control under Finite Precision Teuber, Samuel Lohar, Debasmita Beckert, Bernhard Systems and Control Artificial Intelligence Machine Learning Logic in Computer Science As neural networks (NNs) become increasingly prevalent in safety-critical neural network-controlled cyber-physical systems (NNCSs), formally guaranteeing their safety becomes crucial. For these systems, safety must be ensured throughout their entire operation, necessitating infinite-time horizon verification. To verify the infinite-time horizon safety of NNCSs, recent approaches leverage Differential Dynamic Logic (dL). However, these dL-based guarantees rely on idealized, real-valued NN semantics and fail to account for roundoff errors introduced by finite-precision implementations. This paper bridges the gap between theoretical guarantees and real-world implementations by incorporating robustness under finite-precision perturbations -- in sensing, actuation, and computation -- into the safety verification. We model the problem as a hybrid game between a good Demon, responsible for control actions, and a bad Angel, introducing perturbations. This formulation enables formal proofs of robustness w.r.t. a given (bounded) perturbation. Leveraging this bound, we employ state-of-the-art mixed-precision fixed-point tuners to synthesize sound and efficient implementations, thus providing a complete end-to-end solution. We evaluate our approach on case studies from the automotive and aeronautics domains, producing efficient NN implementations with rigorous infinite-time horizon safety guarantees. |
| title | Of Good Demons and Bad Angels: Guaranteeing Safe Control under Finite Precision |
| topic | Systems and Control Artificial Intelligence Machine Learning Logic in Computer Science |
| url | https://arxiv.org/abs/2507.22760 |