# On knot detection via picture recognition

arXiv: https://arxiv.org/abs/2510.06284 · HTML: https://mlsanity.com/paper/2510.06284/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 54 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 11 of 11)

- [CvT: Introducing Convolutions to Vision Transformers](https://mlsanity.com/paper/2103.15808/) (2021)
- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [Disentangling a Deep Learned Volume Formula](https://mlsanity.com/paper/2012.03955/) (2020)
- [Learning knot invariants across dimensions](https://mlsanity.com/paper/2112.00016/) (2021)
- [Rigor with Machine Learning from Field Theory to the Poincar'e Conjecture](https://mlsanity.com/paper/2402.13321/) (2024)
- [Big Data Approaches to Knot Theory: Understanding the Structure of the Jones Polynomial](https://mlsanity.com/paper/1912.10086/) (2019)
- [Big data approach to Kazhdan-Lusztig polynomials](https://mlsanity.com/paper/2412.01283/) (2024)
- [Mapper-type algorithms for complex data and relations](https://mlsanity.com/paper/2109.00831/) (2021)
- [Big data comparison of quantum invariants](https://mlsanity.com/paper/2503.15810/) (2025)
- [Monoidal categories, representation gap and cryptography](https://mlsanity.com/paper/2201.01805/) (2022)
- [On detection probabilities of link invariants](https://mlsanity.com/paper/2509.05574/) (2025)

## Built on by (most cited first, 2 of 2)

- [RL unknotter, hard unknots and unknotting number](https://mlsanity.com/paper/2603.07955/) (2026)
- [The Gordian Knot for VLMs: Diagrammatic Knot Reasoning as a Hard Benchmark](https://mlsanity.com/paper/2605.09900/) (2026)

## Abstract (arXiv)

Our goal is to one day take a photo of a knot and have a phone automatically recognize it. In this expository work, we explain a strategy to approximate this goal, using a mixture of modern machine learning methods (in particular convolutional neural networks and transformers for image recognition) and traditional algorithms (to compute quantum invariants like the Jones polynomial). We present simple baselines that predict crossing number directly from images, showing that even lightweight CNN and transformer architectures can recover meaningful structural information. The longer-term aim is to combine these perception modules with symbolic reconstruction into planar diagram (PD) codes, enabling downstream invariant computation for robust knot classification. This two-stage approach highlights the complementarity between machine learning, which handles noisy visual data, and invariants, which enforce rigorous topological distinctions.