@inproceedings{
alfarano2024global,
title={Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers},
author={Alberto Alfarano and Francois Charton and Amaury Hayat},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=kOMrm4ZJ3m}
}
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.
Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers
Alberto Alfarano Francois Charton Amaury Hayat