Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clustering of solutions in the symmetric binary perceptron   The geometrical features of the (non-convex) loss landscape of neural network
models are crucial in ensuring successful optimization and, most importantly,
the capability to generalize well. While minimizers' flatness consistently
correlates with good generalization, there has been little rigorous work in
exploring the condition of existence of such minimizers, even in toy models.
Here we consider a simple neural network model, the symmetric perceptron, with
binary weights. Phrasing the learning problem as a constraint satisfaction
problem, the analogous of a flat minimizer becomes a large and dense cluster of
solutions, while the narrowest minimizers are isolated solutions. We perform
the first steps toward the rigorous proof of the existence of a dense cluster
in certain regimes of the parameters, by computing the first and second moment
upper bounds for the existence of pairs of arbitrarily close solutions.
Moreover, we present a non rigorous derivation of the same bounds for sets of
$y$ solutions at fixed pairwise distances.

14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin