Abstract
We derive a well-defined renormalized version of mutual information that allows us to estimate the dependence between continuous random variables in the important case when one is deterministically dependent on the other. This is the situation relevant for feature extraction, where the goal is to produce a low-dimensional effective description of a high-dimensional system. Our approach enables the discovery of collective variables in physical systems, thus adding to the toolbox of artificial scientific discovery, while also aiding the analysis of information flow in artificial neural networks.
Highlights
Introduction.—One of the most useful general concepts in the analysis of physical systems is the notion of collective coordinates
Our approach enables the discovery of collective variables in physical systems, adding to the toolbox of artificial scientific discovery, while aiding the analysis of information flow in artificial neural networks
Future frameworks of artificial scientific discovery [2,3,4,5] will have to rely on general approaches like this, adding to the rapidly developing toolbox of machine learning for physics [6,7,8]
Summary
Introduction.—One of the most useful general concepts in the analysis of physical systems is the notion of collective coordinates. We derive a well-defined renormalized version of mutual information that allows us to estimate the dependence between continuous random variables in the important case when one is deterministically dependent on the other.
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