From classification to models: When do SVMs discover physical features?

The complexity of glasses makes it challenging to explain their dynamics. Machine Learning (ML) in recent years has emerged as a promising tool to understand glassy dynamics, predicting rearrangements of particles in the glass with a high degree of accuracy. It also helped in discovering the link between structural features of the glass and the rearrangement dynamics. Support Vector Machine (SVM) was one of the first ML methods to discover such a non-trivial relationship. Specifically, an SVM model hyper-parameter, the distance from the separating hyperplane, was found to be linearly related to the Arrhenius energy, which governed the rearrangement process. Here we investigate under which conditions SVM can discover such relevant physical quantities in glassy systems. We study a toy glass model with known energy where an SVM is trained to predict the system dynamics based on a large array of structural features. We demonstrate analytically that the distance from the inferred separating hyperplane becomes linearly related to Arrhenius energy under some conditions, which we investigate. This is a step towards understanding when ML can discover new physics.