Shortcut learning in geometric knot classification
This work addresses the problem of shortcut learning in geometric knot classification for researchers in low-dimensional topology and applied fields like protein folding, though it is incremental as it focuses on data and methodology improvements rather than a new model.
The paper investigated how machine learning models use non-topological shortcuts to classify geometric knots, revealing hidden features in training data from Molecular Dynamics simulations. It provided a dataset and code to eliminate these shortcuts, aiming to improve future ML approaches to knot classification.
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.