Storage capacity of the zero-margin Ising perceptron

For the zero-margin Ising perceptron, determine the limiting constraint capacity. The target is M_N/N→α★≈0.8330786 in probability for Gaussian and fixed standardized subgaussian disorder, including Bernoulli. The route requires the full Ding–Sun and Huang conditions, including curvature and endpoint clauses.

Why it matters and what counts as progress

Why it matters: It asks whether the Krauth–Mézard predicted threshold follows after the remaining analytic conditions are discharged and universality is applied.

What counts as progress: Discharge all curvature, endpoint and universality conditions needed for the predicted capacity; establish the probability limit for each covered disorder law.

How the problem developed

1989 · Conjecture [1]
Werner Krauth and Marc Mézard Used replica calculations to predict a zero-margin storage capacity near 0.833 for networks with binary weights.
23 Feb 2025 · Conditional lower bound [2]
Jian Ding and Nike Sun Proved the predicted capacity as a lower bound subject to an explicit numerical condition.
13 Jul 2026 · Proof claim [3]
Yitzchak Shmalo Reported interval-arithmetic verification of the remaining sign conditions, yielding convergence in probability to the predicted capacity for Gaussian and fixed standardized subgaussian disorder.

AI contribution

The storage capacity of the Ising perceptron: verification of the outstanding numerical conditions

Yitzchak Shmalo

Shmalo's paper verifies Ding–Sun Condition 1.2, including curvature and endpoint clauses, and Huang Condition 1.3 for the zero-margin Ising perceptron. Combining these with prior conditional and universality theorems yields M_N/N→α★≈0.8330786 in probability for Gaussian and fixed standardized subgaussian disorder, including Bernoulli.

AI involvementAI-autonomous

ImportanceMajor

Technical verificationPartial

Human understandingFew