Susceptibilities for Neural Networks Learning from Physical Data

Neural networks that are trained on data arising from a physical system must somehow learn regularities induced by the underlying physical laws. In this setting, concepts from statistical physics provide powerful tools for analysing how physical laws influence the learning process. In this paper we explain how susceptibilities --- which measure the response of a neural network to perturbations of a parameter of the data distribution --- can be applied when learning from physical data. We show that such susceptibilities can identify the conditions under which specific input features are most informative for learning, guiding data selection, a prediction we validate experimentally. For distributions lacking a natural parameter, we propose introducing one via an arbitrary scalar function of the physical state, and demonstrate that susceptibilities track the emergence of specific capabilities (such as collision detection) during training.