Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers

Alberto Alfarano, François Charton, Amaury Hayat
10/10/2024
cs.LG

No official code found. Best implementation: facebookresearch/Lyapunov (81 stars, last commit 2025-01-23).

Abstract

Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global stability of a dynamical system. This problem has no known general solution, and algorithmic solvers only exist for some small polynomial systems. We propose a new method for generating synthetic training samples from random solutions, and show that sequence-to-sequence transformers trained on such datasets perform better than algorithmic solvers and humans on polynomial systems, and can discover new Lyapunov functions for non-polynomial systems.

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facebookresearch/LyapunovCommunity62%

PyTorch original implementation of "Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers" (NeurIPS 2024).

819PythonNov 14, 20241 years agoNOASSERTION

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Cite this paper

@article{alfarano2024global,
  title  = {Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers},
  author = {Alberto Alfarano and François Charton and Amaury Hayat},
  year   = {2024},
  eprint = {2410.08304},
  archivePrefix = {arXiv},
  doi    = {10.48550/arXiv.2410.08304},
  url    = {http://arxiv.org/abs/2410.08304v1},
  journal = {NEURIPS 2024 2024}
}

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