Abstract.
We study the Hopfield model at temperature 1, when thenumber M(N) of patterns grows a bit slower than N. We reach a goodunderstanding of the model whenever M(N)≤N/(log N)11. For example, we show that if M(N)→∞, for two typical configurations σ 1, σ 2, (∑ i ≤ N σ1 i σ2 i )2 is close to NM(N).
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Received: 15 December 1999 / Revised version: 8 December 2000 / Published online: 23 August 2001
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Talagrand, M. On the Hopfield model at the critical temperature. Probab Theory Relat Fields 121, 237–268 (2001). https://doi.org/10.1007/PL00008804
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DOI: https://doi.org/10.1007/PL00008804
Keywords
- Critical Temperature
- Typical Configuration
- Hopfield Model