Phases in a class of associative memories via hidden neurons
Associative memory in the Hopfield network is attractor dynamics in a disordered many-body system, and higher-order and exponential extensions turn its retrieval update into softmax attention. The polynomial and exponential regimes have been analyzed by different methods, with no common architecture in which to ask what fixes the storage scale. In this paper we study the bipartite architecture of Krotov and Hopfield, which we call the class $H$, whose model is fixed by a Lagrangian for each layer, taking the hidden neurons as the order parameter of retrieval. At polynomial load the replica method yields the replica-symmetric phase diagrams and closed-form capacities, and the crosstalk mom...
| Authors | Toshihiro Ota, Masato Taki |
|---|---|
| Primary category | cs.LG |
| Published | 10 September 2026 |
| Last updated at source | 10 September 2026 |
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