Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence between algorithmic instability and transition to replica
  symmetry breaking in perceptron learning systems   Binary perceptron is a fundamental model of supervised learning for the
non-convex optimization, which is a root of the popular deep learning. Binary
perceptron is able to achieve a classification of random high-dimensional data
by computing the marginal probabilities of binary synapses. The relationship
between the algorithmic instability and the equilibrium analysis of the model
remains elusive. Here, we establish the relationship by showing that the
instability condition around the algorithmic fixed point is identical to the
instability for breaking the replica symmetric saddle point solution of the
free energy function. Therefore, our analysis would hopefully provide insights
towards other learning systems in bridging the gap between non-convex learning
dynamics and statistical mechanics properties of more complex neural networks.

36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an