Pith. sign in

REVIEW 2 cited by

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

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2410.08304 v1 pith:JO4WUZPR submitted 2024-10-10 cs.LG

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

classification cs.LG
keywords lyapunovmathematicsproblemsystemsalgorithmicfunctionsgloballong-standing
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original 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.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Reconstructing conformal field theoretical compositions with Transformers

    hep-th 2026-05 unverdicted novelty 7.0

    Transformers reconstruct the constituent RCFTs in tensor-product theories from low-energy spectra, reaching 98% accuracy on WZW models and generalizing to larger central charges with few out-of-domain examples.

  2. Generating Special Triangulations with Transformers

    hep-th 2026-06 unverdicted novelty 6.0

    Transformers generate new FRSTs of 4D reflexive polytopes across size ranges and self-improve by retraining on their own outputs.