mlsanityData to 7 Oct 2026

Searching for ribbons with machine learning

arXiv 2304.09304 ↗First posted 18 Apr 2023math.GT cs.LGcited by 11

Not on the map. Why?

Abstract (arXiv)

We apply Bayesian optimization and reinforcement learning to a problem in topology: the question of when a knot bounds a ribbon disk. This question is relevant in an approach to disproving the four-dimensional smooth Poincar'e conjecture; using our programs, we rule out many potential counterexamples to the conjecture. We also show that the programs are successful in detecting many ribbon knots in the range of up to 70 crossings.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 4 of its 37 references that are in the map. First posted on arXiv 18 Apr 2023.

Builds on

4 of 37 references.

References · 4

  1. 2015Trust Region Policy Optimizationcited by 2,503
  2. 2016Asynchronous Methods for Deep Reinforcement Learningcited by 2,218
  3. 2020Learning to Unknotcited by 40
  4. 2021The signature and cusp geometry of hyperbolic knotscited by 8

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 4; 2025: 2; 2026: 3.

11 papers.

  1. 2023Neural Network Field Theories: Non-Gaussianity, Actions, and Localitycited by 21
  2. 2024Rigor with Machine Learning from Field Theory to the Poincar'e Conjecturecited by 12
  3. 2024Can Transformers Do Enumerative Geometry?cited by 8
  4. 2023Graph Neural Networks and 3-Dimensional Topologycited by 4
  5. 2026Flow-based Extremal Mathematical Structure Discoverycited by 3
  6. 2024Learning 3-Manifold Triangulationscited by 1
  7. 2024Deep Learning Evidence for Global Optimality of Gerver's Sofacited by 0
  8. 2025On the Learnability of Knot Invariants: Representation, Predictability, and Neural Similaritycited by 0
  9. 2025Deep Learning based discovery of Integrable Systemscited by 0
  10. 2026Shortcut learning in geometric knot classificationcited by 0
  11. 2026A penalised Saito functional for heuristic search of free line arrangementscited by 0