mlsanityData to 7 Oct 2026

Rigor with Machine Learning from Field Theory to the Poincar'e Conjecture

arXiv 2402.13321 ↗First posted 20 Feb 2024hep-th cs.LGcited by 12

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Abstract (arXiv)

Machine learning techniques are increasingly powerful, leading to many breakthroughs in the natural sciences, but they are often stochastic, error-prone, and blackbox. How, then, should they be utilized in fields such as theoretical physics and pure mathematics that place a premium on rigor and understanding? In this Perspective we discuss techniques for obtaining rigor in the natural sciences with machine learning. Non-rigorous methods may lead to rigorous results via conjecture generation or verification by reinforcement learning. We survey applications of these techniques-for-rigor ranging from string theory to the smooth 4d Poincar'e conjecture in low-dimensional topology. One can also imagine building direct bridges between machine learning theory and either mathematics or theoretical physics. As examples, we describe a new approach to field theory motivated by neural network theory, and a theory of Riemannian metric flows induced by neural network gradient descent, which encompasses Perelman's formulation of the Ricci flow that was utilized to resolve the 3d Poincar'e conjecture.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 36 of its 85 references that are in the map. First posted on arXiv 20 Feb 2024.

Builds on

36 of 85 references.

References · 36

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24 more
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Built on by

Cited by year

Citing papers per year: 2024: 7; 2025: 5.

12 papers.

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  3. 2024A Triumvirate of AI Driven Theoretical Discoverycited by 5
  4. 2024Deep Learning as Ricci Flowcited by 4
  5. 2024TASI Lectures on Physics for Machine Learningcited by 4
  6. 2024Learning BPS Spectra and the Gap Conjecturecited by 3
  7. 2025On knot detection via picture recognitioncited by 2
  8. 2024Learning 3-Manifold Triangulationscited by 1
  9. 2025On the Learnability of Knot Invariants: Representation, Predictability, and Neural Similaritycited by 0
  10. 2025Colored Jones Polynomials and the Volume Conjecturecited by 0
  11. 2025Deep Learning based discovery of Integrable Systemscited by 0
  12. 2025Computations and ML for surjective rational mapscited by 0