Distribution of the threshold for the symmetric perceptron

TL;DR

This paper derives the explicit distribution of the threshold sequence for the symmetric binary perceptron with Gaussian disorder, demonstrating that the critical window remains of constant width, which advances understanding of phase transitions in neural models.

Contribution

It provides the first explicit distribution for the threshold sequence in the symmetric perceptron, revealing the nature of the critical window.

Findings

Critical window is of constant width.

Explicit distribution for the threshold sequence.

Enhanced understanding of phase transitions in neural models.

Abstract

We derive an explicit distribution for the threshold sequence of the symmetric binary perceptron with Gaussian disorder, proving that the critical window is of constant width.