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Résumé |
Identifying the relevant degrees of freedom is key to developing an effective
theory. RG provides a framework for this, but its practical execution in
unfamiliar systems is difficult. Machine learning (ML) approaches, on the other
hand, though promising, lack formal interpretability: it is often unclear what
relation the discovered, architecture-dependent, "relevant" features bear to
objects of physical theory. I will present results addressing both issues. We
develop a fast algorithm, the RSMI-NE, employing recent results in ML-based
estimation of information-theoretic quantities to identify the most relevant field
theory operators in a statistical system. Information about the phase diagram,
correlations and symmetries (also emergent) can be obtained, which we validate on
the example of the interacting dimer model. I will also discuss formal results
underlying the algorithm: we establish an equivalence between the information-
theoretic relevance defined in the Information Bottleneck (IB) approach of
compression theory, and the field-theoretic relevance of the RG. We show
analytically that for statistical physical systems the "relevant" degrees of
freedom found using IB (and RSMI-NE) indeed correspond to operators with the
lowest scaling dimensions, providing a dictionary connecting two distinct
theoretical toolboxes, and paving the way to automated theory building in more
complex settings. |
