Capacity threshold for the Ising perceptron

We show that the capacity of the Ising perceptron is with high probability upper bounded by the constant $\alpha \approx 0.833$ conjectured by Krauth and Mézard, under the condition that an explicit two-variable function $S(\lambda_1,\lambda_2)$ is maximized at (1,0). The earlier work of Ding and Sun proves the matching lower bound subject to a similar numerical condition, and together these results give a conditional proof of the conjecture of Krauth and Mézard. In this talk I will present the main ideas of this proof, assuming no background in statistical physics.

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