Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910644433846272 |
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| author | Alfarano, Alberto Charton, François Hayat, Amaury |
| author_facet | Alfarano, Alberto Charton, François Hayat, Amaury |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers Alfarano, Alberto Charton, François Hayat, Amaury Machine Learning 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. |
| title | Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2410.08304 |