Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Replacing neural networks by optimal analytical predictors for the
  detection of phase transitions   Identifying phase transitions and classifying phases of matter is central to
understanding the properties and behavior of a broad range of material systems.
In recent years, machine-learning (ML) techniques have been successfully
applied to perform such tasks in a data-driven manner. However, the success of
this approach notwithstanding, we still lack a clear understanding of ML
methods for detecting phase transitions, particularly of those that utilize
neural networks (NNs). In this work, we derive analytical expressions for the
optimal output of three widely used NN-based methods for detecting phase
transitions. These optimal predictions correspond to the output obtained in the
limit of perfectly trained and sufficiently large NNs. The inner workings of
the considered methods are revealed through the explicit dependence of the
optimal output on the input data. By evaluating the analytical expressions, we
can identify phase transitions from data without training NNs. Our theoretical
results are supported by extensive numerical simulations covering, e.g.,
topological, quantum, and many-body localization phase transitions. We expect
similar analyses to provide a deeper understanding of other classification
tasks in condensed matter physics.

25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio