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