A note on the capacity of the binary perceptron
Probability
2024-01-30 v1 Discrete Mathematics
Machine Learning
Machine Learning
Abstract
Determining the capacity of the Binary Perceptron is a long-standing problem. Krauth and Mezard (1989) conjectured an explicit value of , approximately equal to .833, and a rigorous lower bound matching this prediction was recently established by Ding and Sun (2019). Regarding the upper bound, Kim and Roche (1998) and Talagrand (1999) independently showed that < .996, while Krauth and Mezard outlined an argument which can be used to show that < .847. The purpose of this expository note is to record a complete proof of the bound < .847. The proof is a conditional first moment method combined with known results on the spherical perceptron
Cite
@article{arxiv.2401.15092,
title = {A note on the capacity of the binary perceptron},
author = {Dylan J. Altschuler and Konstantin Tikhomirov},
journal= {arXiv preprint arXiv:2401.15092},
year = {2024}
}