Capacity threshold for the Ising perceptron
| Autor: | Huang, Brice |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We show that the capacity of the Ising perceptron is with high probability upper bounded by the constant $\alpha_\star \approx 0.833$ conjectured by Krauth and M\'ezard, under the condition that an explicit two-variable function $\mathscr{S}_\star(\lambda_1,\lambda_2)$ 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 M\'ezard. Comment: 76 pages, 2 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|