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arXiv · 2605.03992

HyParLyVe: Hyperplane Partitioning for Neural Lyapunov Verification

Jesse Wayment·Brian Yarbrough·Jingbo Wang·Shreyas Sundaram·Philip E. Paré
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Abstract

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.

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Jesse Wayment, Brian Yarbrough, Jingbo Wang, Shreyas Sundaram, Philip E. Paré. 2026-05-05. HyParLyVe: Hyperplane Partitioning for Neural Lyapunov Verification. https://arxiv.org/abs/2605.03992

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