Energy landscapes for machine learning

Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular potential energy landscapes can be applied to these machine learning landscapes to gain new insight into the solution space involved in training and the nature of the corresponding predictions. In particular, we can define quantities analogous to molecular structure, thermodynamics, and kinetics, and relate these emergent properties to the structure of the underlying landscape. This Perspective aims to describe these analogies with examples from recent applications, and suggest avenues for new interdisciplinary research.This research was funded by EPSRC grant EP/I001352/1, the Gates Cambridge Trust, and the ERC. DM was in the Department of Applied and Computational Mathematics and Statistics when this work was performed, and his current affiliation is Department of Systems, United Technologies Research Center, East Hartford, CT, USA