# Geometric deep learning approach to knot theory

arXiv: https://arxiv.org/abs/2305.16808 · HTML: https://mlsanity.com/paper/2305.16808/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 14 references that are in the map.
- First posted on arXiv 26 May 2023.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [Learning knot invariants across dimensions](https://mlsanity.com/paper/2112.00016/) (2021)
- [Graph Neural Networks and 3-Dimensional Topology](https://mlsanity.com/paper/2305.05966/) (2023)
- [An application of neural networks to a problem in knot theory and group theory (untangling braids)](https://mlsanity.com/paper/2206.05373/) (2022)

## Built on by (most cited first, 1 of 1)

- [The Gordian Knot for VLMs: Diagrammatic Knot Reasoning as a Hard Benchmark](https://mlsanity.com/paper/2605.09900/) (2026)

## Abstract (arXiv)

In this paper, we introduce a novel way to use geometric deep learning for knot data by constructing a functor that takes knots to graphs and using graph neural networks. We will attempt to predict several knot invariants with this approach. This approach demonstrates high generalization capabilities.