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:2603. 26217v2 Announce Type: replace-cross Abstract: Generalized Hopfield models with higher-order or exponential interaction terms are known to have substantially larger storage capacities than the classical quadratic model.
By Matthias L\"owe, Franck Vermet
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 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
arXiv:2511. 02584v2 Announce Type: replace-cross Abstract: Associative memory, traditionally modeled by Hopfield networks, enables the retrieval of previously stored patterns from partial or noisy cues.
By Mark Bl\"umel, Andreas C. Schneider, Valentin Neuhaus, David A. Ehrlich, Marcel Graetz, Michael Wibral, Abdullah Makkeh, Viola Priesemann
The paper investigates when language diffusion models, specifically Uniform-based Discrete Diffusion Models (UDDMs), shift from memorizing training data to generalizing to new data. It shows that UDDMs act as associative memories, forming basins of attraction around stored examples without requiring an explicit energy function. By measuring token recovery and conditional entropy, the authors identify a sharp transition governed by training set size, where memorization (vanishing entropy) gives way to generalization (finite entropy).
By Bao Pham, Mohammed J. Zaki, Luca Ambrogioni, Dmitry Krotov, Matteo Negri
arXiv:2609.35948v1 Announce Type: cross
Abstract: Geometry does more than constrain an associative memory: curvature determines what it remembers and which states it creates. We develop intrinsic den...
By Krishnakumar Balasubramanian, Zhaoyang Shi
arXiv:2606. 24543v1 Announce Type: new Abstract: Large Language Models (LLMs) are traditionally viewed as autoregressive generators.
By Kanishk Awadhiya
arXiv:2605. 05066v2 Announce Type: replace-cross Abstract: We identify and prove a fundamental trade-off governing long-sequence models: no model can simultaneously achieve (i) per-step computation independent of sequence length (Efficiency), (ii) state size independent of sequence length (Compactness), and (iii) the ability to recall a number of historical facts proportional to sequence length (Recall).
By Yan Zhou
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
arXiv:2606. 31819v1 Announce Type: new Abstract: This work introduces a new computational theory of mind grounded in set theory and hyperdimensional computing.
By Peter Overmann
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