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arXiv · 2401.15092

A note on the capacity of the binary perceptron

Dylan J. Altschuler·Konstantin Tikhomirov
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Abstract

Determining the capacity $α_c$ of the Binary Perceptron is a long-standing problem. Krauth and Mezard (1989) conjectured an explicit value of $α_c$, 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 $α_c$ < .996, while Krauth and Mezard outlined an argument which can be used to show that $α_c$ < .847. The purpose of this expository note is to record a complete proof of the bound $α_c$ < .847. The proof is a conditional first moment method combined with known results on the spherical perceptron

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Dylan J. Altschuler, Konstantin Tikhomirov. 2024-01-22. A note on the capacity of the binary perceptron. https://arxiv.org/abs/2401.15092

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