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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2605.03992 |
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| _version_ | 1866915981529448448 |
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| author | Wayment, Jesse Yarbrough, Brian Wang, Jingbo Sundaram, Shreyas Paré, Philip E. |
| author_facet | Wayment, Jesse Yarbrough, Brian Wang, Jingbo Sundaram, Shreyas Paré, Philip E. |
| contents | This work introduces HyParLyVe (Hyperplane Partitioned Lyapunov Verifier), a novel algorithm for sound and complete verification of neural Lyapunov candidates by interpreting shallow ReLU networks as hyperplane arrangements. This perspective reduces positive definiteness verification to a finite set of vertex evaluations, and the decrease condition to a bounded optimization problem over each region. We formally prove correctness of the proposed verification procedures and demonstrate that HyParLyVe achieves significant speedups over state-of-the-art methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03992 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | HyParLyVe: Hyperplane Partitioning for Neural Lyapunov Verification Wayment, Jesse Yarbrough, Brian Wang, Jingbo Sundaram, Shreyas Paré, Philip E. Systems and Control This work introduces HyParLyVe (Hyperplane Partitioned Lyapunov Verifier), a novel algorithm for sound and complete verification of neural Lyapunov candidates by interpreting shallow ReLU networks as hyperplane arrangements. This perspective reduces positive definiteness verification to a finite set of vertex evaluations, and the decrease condition to a bounded optimization problem over each region. We formally prove correctness of the proposed verification procedures and demonstrate that HyParLyVe achieves significant speedups over state-of-the-art methods. |
| title | HyParLyVe: Hyperplane Partitioning for Neural Lyapunov Verification |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2605.03992 |