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We derive a well-defined renormalized version of mutual information thatallows to estimate the dependence between continuous random variables in theimportant case when one is deterministically dependent on the other. This isthe situation relevant for feature extraction, where the goal is to produce alow-dimensional effective description of a high-dimensional system. Ourapproach enables the discovery of collective variables in physical systems,thus adding to the toolbox of artificial scientific discovery, while alsoaiding the analysis of information flow in artificial neural networks.

Renormalized Mutual Information for Artificial Scientific Discovery