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[2602.17350] Shortcut learning in geometric knot classification
Summary
This paper explores the application of machine learning to classify geometric knots, addressing the challenge of identifying equivalent embeddings of closed curves.
Why It Matters
Understanding knot classification has implications beyond mathematics, impacting fields like protein folding and polymer physics. This research provides a foundation for future machine learning models to tackle complex classification tasks by focusing on topological features.
Key Takeaways
- Machine learning can potentially solve knot classification problems.
- The study identifies non-topological features in training data that affect classification outcomes.
- A publicly available dataset and code are provided to facilitate future research.
- The research aims to enhance the accuracy of geometric knot classification using ML.
- Applications extend to various scientific fields, including biology and physics.
Computer Science > Machine Learning arXiv:2602.17350 (cs) [Submitted on 19 Feb 2026] Title:Shortcut learning in geometric knot classification Authors:Djordje Mihajlovic, Davide Michieletto View a PDF of the paper titled Shortcut learning in geometric knot classification, by Djordje Mihajlovic and Davide Michieletto View PDF HTML (experimental) Abstract: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 explor...