Capacity threshold for the Ising perceptron
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915252706213888 |
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| author | Huang, Brice |
| author_facet | Huang, Brice |
| contents | We show that the capacity of the Ising perceptron is with high probability upper bounded by the constant $α_\star \approx 0.833$ conjectured by Krauth and Mézard, under the condition that an explicit two-variable function $\mathscr{S}_*(λ_1,λ_2)$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_18902 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Capacity threshold for the Ising perceptron Huang, Brice Probability Disordered Systems and Neural Networks Mathematical Physics We show that the capacity of the Ising perceptron is with high probability upper bounded by the constant $α_\star \approx 0.833$ conjectured by Krauth and Mézard, under the condition that an explicit two-variable function $\mathscr{S}_*(λ_1,λ_2)$ 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. |
| title | Capacity threshold for the Ising perceptron |
| topic | Probability Disordered Systems and Neural Networks Mathematical Physics |
| url | https://arxiv.org/abs/2404.18902 |