Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relevance in the Renormalization Group and in Information Theory   The analysis of complex physical systems hinges on the ability to extract the
relevant degrees of freedom from among the many others. Though much hope is
placed in machine learning, it also brings challenges, chief of which is
interpretability. It is often unclear what relation, if any, the architecture-
and training-dependent learned "relevant" features bear to standard objects of
physical theory. Here we report on theoretical results which may help to
systematically address this issue: we establish equivalence between the
information-theoretic notion of relevance defined in the Information Bottleneck
(IB) formalism of compression theory, and the field-theoretic relevance of the
Renormalization Group. We show analytically that for statistical physical
systems described by a field theory the "relevant" degrees of freedom found
using IB compression indeed correspond to operators with the lowest scaling
dimensions. We confirm our field theoretic predictions numerically. We study
dependence of the IB solutions on the physical symmetries of the data. Our
findings provide a dictionary connecting two distinct theoretical toolboxes,
and an example of constructively incorporating physical interpretability in
applications of deep learning in physics.

23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th