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:2609.16805v1 Announce Type: new
Abstract: High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit a "Ridge of Optimization" characterized by extreme stability and a...
By Akira Tamamori
arXiv:2507.10383v5 Announce Type: replace-cross
Abstract: Recurrent neural networks are canonical models of biological memory. In these models, memories are represented by distributed patterns of neu...
By Uri Cohen, M\'at\'e Lengyel
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:2602. 14885v2 Announce Type: replace-cross Abstract: Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that restricts network dynamics to gradient-like flows.
By Ram\'on Nartallo-Kaluarachchi, Renaud Lambiotte, Alain Goriely