Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The committee machine: Computational to statistical gaps in learning a
  two-layers neural network   Heuristic tools from statistical physics have been used in the past to locate
the phase transitions and compute the optimal learning and generalization
errors in the teacher-student scenario in multi-layer neural networks. In this
contribution, we provide a rigorous justification of these approaches for a
two-layers neural network model called the committee machine. We also introduce
a version of the approximate message passing (AMP) algorithm for the committee
machine that allows to perform optimal learning in polynomial time for a large
set of parameters. We find that there are regimes in which a low generalization
error is information-theoretically achievable while the AMP algorithm fails to
deliver it, strongly suggesting that no efficient algorithm exists for those
cases, and unveiling a large computational gap.

14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg