# Shortcut learning in geometric knot classification

arXiv: https://arxiv.org/abs/2602.17350 · HTML: https://mlsanity.com/paper/2602.17350/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 19 Feb 2026.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [A Review of Feature Selection Methods Based on Mutual Information](https://mlsanity.com/paper/1509.07577/) (2015)
- [Learning knot invariants across dimensions](https://mlsanity.com/paper/2112.00016/) (2021)
- [Searching for ribbons with machine learning](https://mlsanity.com/paper/2304.09304/) (2023)
- [Variational autoencoders understand knot topology](https://mlsanity.com/paper/2504.04179/) (2025)

## Abstract (arXiv)

Classifying the topology of closed curves is a central problem in low dimensional topology with applications beyond mathematics spanning protein folding, polymer physics and even magnetohydrodynamics. The central problem is how to determine whether two embeddings of a closed arc are equivalent under ambient isotopy. Given the striking ability of neural networks to solve complex classification tasks, it is therefore natural to ask if the knot classification problem can be tackled using Machine Learning (ML). In this paper, we investigate generic shortcut methods employed by ML to solve the knot classification challenge and specifically discover hidden non-topological features in training data generated through Molecular Dynamics simulations of polygonal knots that are used by ML to arrive to positive classifications results. We then provide a rigorous foundation for future attempts to tackle the knot classification challenge using ML by developing a publicly-available (i) dataset, that aims to remove the potential of non-topological feature classification and (ii) code, that can generate knot embeddings that faithfully explore chosen geometric state space with fixed knot topology. We expect that our work will accelerate the development of ML models that can solve complex geometric knot classification challenges.