mlsanityData to 7 Oct 2026

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

arXiv 2410.08304 ↗First posted 10 Oct 2024cs.LGcited by 29

On the map: LLM reasoning → Mathematical reasoning

Abstract (arXiv)

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.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 17 of its 44 references that are in the map. First posted on arXiv 10 Oct 2024.

Builds on

17 of 44 references.

Closest ancestors · 1

Same direction, newest first

  1. 2020Generative Language Modeling for Automated Theorem Proving7 Sep

Other references · 16

  1. 2017Attention Is All You Needcited by 59,932
  2. 2022Large Language Models Are Human-Level Prompt Engineerscited by 1,020
  3. 2019Deep Learning for Symbolic Mathematicscited by 266
  4. 2022HyperTree Proof Search for Neural Theorem Provingcited by 192
  5. 2021Neural Symbolic Regression that Scalescited by 185
  6. 2020Neural Lyapunov Controlcited by 142
  7. 2021Investigating the Limitations of Transformers with Simple Arithmetic Taskscited by 136
  8. 2023Length Generalization in Arithmetic Transformerscited by 64
  9. 2021Constructions in combinatorics via neural networkscited by 46
  10. 2016Robustness of Control Barrier Functions for Safety Critical Controlcited by 29
  11. 2020It's Not What Machines Can Learn, It's What We Cannot Teachcited by 29
  12. 2022SALSA: Attacking Lattice Cryptography with Transformerscited by 28
4 more
  1. 2023Fossil 2.0: Formal Certificate Synthesis for the Verification and Control of Dynamical Modelscited by 15
  2. 2019Formalising perfectoid spacescited by 7
  3. 2024Formally Verified Physics-Informed Neural Control Lyapunov Functionscited by 4
  4. 2015Classical Converse Theorems in Lyapunov's Second Methodcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 14; 2026: 11.

29 papers.

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  1. 2024Formal Mathematical Reasoning: A New Frontier in AIcited by 80
  2. 2024PatternBoost: Constructions in Mathematics with a Little Help from AIcited by 32
  3. 2024AIGS: Generating Science from AI-Powered Automated Falsificationcited by 17
  4. 2025Auto-Formulating Dynamic Programming Problems with Large Language Modelscited by 15
  5. 2026LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematicscited by 7
  6. 2025CayleyPy RL: Pathfinding and Reinforcement Learning on Cayley Graphscited by 5
  7. 2025Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformerscited by 5
  8. 2024Learning Interpretable Network Dynamics via Universal Neural Symbolic Regressioncited by 4
  9. 2025Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?cited by 4
  10. 2026The Agentic Researcher: A Practical Guide to AI-Assisted Research in Mathematics and Machine Learningcited by 4
  11. 2025Geometric Generality of Transformer-Based Gr"obner Basis Computationcited by 3
  12. 2026Flow-based Extremal Mathematical Structure Discoverycited by 3
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  1. 2025Local Look-Ahead Guidance via Verifier-in-the-Loop for Automated Theorem Provingcited by 2
  2. 2025From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithmcited by 2
  3. 2026Can Neural Networks Learn Small Algebraic Worlds? An Investigation Into the Group-theoretic Structures Learned By Narrow Models Trained To Predict Group Operationscited by 2
  4. 2025Analytical Lyapunov Function Discovery: An RL-based Generative Approachcited by 1
  5. 2025Int2Int: a framework for mathematics with transformerscited by 1
  6. 2025Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applicationscited by 1
  7. 2025Discovering Learning-Friendly Generation Orders for Sequential Computationcited by 1
  8. 2025CayleyPy Growth: Efficient growth computations and hundreds of new conjectures on Cayley graphs (Brief version)cited by 1
  9. 2025CALT: A Library for Computer Algebra with Transformercited by 0
  10. 2025Learning Moderately Input-Sensitive Functions: A Case Study in QR Code Decodingcited by 0
  11. 2026Breaking the Data Barrier in Learning Symbolic Computation: A Case Study on Variable Ordering Suggestion for Cylindrical Algebraic Decompositioncited by 0
  12. 2026Approximating Matrix Functions with Deep Neural Networks and Transformerscited by 0
  13. 2026Reconstructing conformal field theoretical compositions with Transformerscited by 0
  14. 2026Learning Large-Scale Modular Addition with an Auxiliary Moduluscited by 0
  15. 2026Mapping Uncharted Symmetries: Machine Discovery in Combinatoricscited by 0
  16. 2026Learning First Integrals via Backward-Generated Data and Guided Reinforcement Learningcited by 0
  17. 2026Generating Special Triangulations with Transformerscited by 0

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  1. 2023Learning Lyapunov-Stable Polynomial Dynamical Systems through Imitation
  2. 2026Iteris: Agentic Research Loops for Computational Mathematics
  3. 2022Transformers Learn Shortcuts to Automata
  4. 2025Scalable Learning of High-Dimensional Demonstrations with Composition of Linear Parameter Varying Dynamical Systems
  5. 2024On Foundation Models for Dynamical Systems from Purely Synthetic Data
  6. 2026Stability and Generalization in Looped Transformers
  7. 2023Algebraic Dynamical Systems in Machine Learning
  8. 2023Learning a Stable Dynamic System with a Lyapunov Energy Function for Demonstratives Using Neural Networks