# Searching for ribbons with machine learning

arXiv: https://arxiv.org/abs/2304.09304 · HTML: https://mlsanity.com/paper/2304.09304/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 37 references that are in the map.
- First posted on arXiv 18 Apr 2023.

## Builds on (most cited first, 4 of 4)

- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [The signature and cusp geometry of hyperbolic knots](https://mlsanity.com/paper/2111.15323/) (2021)

## Built on by (most cited first, 12 of 12)

- [Neural Network Field Theories: Non-Gaussianity, Actions, and Locality](https://mlsanity.com/paper/2307.03223/) (2023)
- [Rigor with Machine Learning from Field Theory to the Poincar'e Conjecture](https://mlsanity.com/paper/2402.13321/) (2024)
- [Can Transformers Do Enumerative Geometry?](https://mlsanity.com/paper/2408.14915/) (2024)
- [Graph Neural Networks and 3-Dimensional Topology](https://mlsanity.com/paper/2305.05966/) (2023)
- [Flow-based Extremal Mathematical Structure Discovery](https://mlsanity.com/paper/2601.18005/) (2026)
- [Learning 3-Manifold Triangulations](https://mlsanity.com/paper/2405.09610/) (2024)
- [Deep Learning Evidence for Global Optimality of Gerver's Sofa](https://mlsanity.com/paper/2407.11106/) (2024)
- [On the Learnability of Knot Invariants: Representation, Predictability, and Neural Similarity](https://mlsanity.com/paper/2502.12243/) (2025)
- [Deep Learning based discovery of Integrable Systems](https://mlsanity.com/paper/2503.10469/) (2025)
- [Shortcut learning in geometric knot classification](https://mlsanity.com/paper/2602.17350/) (2026)
- [A penalised Saito functional for heuristic search of free line arrangements](https://mlsanity.com/paper/2604.02995/) (2026)
- [Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches](https://mlsanity.com/paper/2604.16842/) (2026)

## 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.