I got in some quality time with Bernhard Schölkopf (MPI-IS) this weekend, in which we discussed many things related to contemporary machine learning and its overlap with physics. In particular, we discussed the point that the nonlinearities in machine-learning methods (like deep learning) have to be interpretable as nonlinear functions of dimensionless scalars, if the methods are going to be like laws of physics. That is a strong constraint on what can be put into nonlinear functions. We understood part of that in our recent paper, but not all of it. In particular, thinking about units or dimensions in machine learning might be extremely valuable.
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