arXiv:2607. 19195v1 Announce Type: cross Abstract: Using large deviations theory, we solve and obtain a general expression for the free energy functional for a broad class of associative memories, including dense associative memories.
By Sumedha, Abhishek Singh
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 pol...
The paper investigates associative memory in a bipartite Hopfield–Krotov architecture, termed class H, where hidden neurons serve as the retrieval order parameter. Using the replica method, it derives replica‑symmetric phase diagrams and closed‑form capacities for polynomial load, showing that crosstalk statistics are similar for Ising and spherical visible neurons. With a softmax hidden layer, the load becomes exponential, mapping the thermodynamics onto a random‑energy‑model that exhibits paramagnetic, condensed, and frozen phases, and revealing that heating destabilizes retrieval through quantized attention reassignments while Gaussian patterns remain metastable at all loads.
By Toshihiro Ota, Masato Taki
arXiv:2609.16827v1 Announce Type: new
Abstract: High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit exceptional storage capabilities and robustness. Previous empirica...
By Akira Tamamori
arXiv:2605. 00366v4 Announce Type: replace-cross Abstract: High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit strong storage capabilities, but the dynamical and geometric mechanisms underlying their stability remain poorly understood.
By Akira Tamamori
The paper studies how hierarchical correlations in data can be learned by a dense Hopfield network with polynomial activation. It analytically derives conditions for each level of a hierarchical memory model to be locally stable, meaning they correspond to local energy minima. Using prototype reconstruction as a minimal generalization test, the authors show that only a quasi‑polynomial amount of information is needed to generalize beyond specific memories or groups, and they observe a similar phase diagram for Fashion‑MNIST data.
By Aditya Cowsik, Adithya Sriram