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Dense Associative Memory (DAM) generalizes Hopfield networks through higher-order interactions and achieves storage capacity that scales as $O(N^{n-1})$ under suitable pattern separation conditions. Existing dynamical analyses primarily…

Machine Learning · Computer Science 2026-04-15 Madhava Gaikwad

I introduce a novel associative memory model named Correlated Dense Associative Memory (CDAM), which integrates both auto- and hetero-association in a unified framework for continuous-valued memory patterns. Employing an arbitrary graph…

Neural and Evolutionary Computing · Computer Science 2024-06-04 Thomas F Burns

Deep neural networks (DNN) trained in a supervised way suffer from two known problems. First, the minima of the objective function used in learning correspond to data points (also known as rubbish examples or fooling images) that lack…

Machine Learning · Computer Science 2018-11-27 Dmitry Krotov , John J Hopfield

Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its…

Disordered Systems and Neural Networks · Physics 2025-10-29 Kazushi Mimura , Jun'ichi Takeuchi , Yuto Sumikawa , Yoshiyuki Kabashima , Anthony C. C. Coolen

Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require…

Machine Learning · Computer Science 2024-11-01 Benjamin Hoover , Duen Horng Chau , Hendrik Strobelt , Parikshit Ram , Dmitry Krotov

Sequential learning involves learning tasks in a sequence, and proves challenging for most neural networks. Biological neural networks regularly conquer the sequential learning challenge and are even capable of transferring knowledge both…

Neural and Evolutionary Computing · Computer Science 2025-03-06 Hayden McAlister , Anthony Robins , Lech Szymanski

Protocol-dependent states in structural glasses can encode a disordered, yet retrievable memory. While training such materials is typically done via a global drive, such as external shear, in dense active matter the driving is instead local…

Soft Condensed Matter · Physics 2024-04-05 Elisabeth Agoritsas , Peter K. Morse

Modern Hopfield Neural Networks (HNNs), also known as Dense Associative Memories (DAMs), enhance the performance of simple recurrent neural networks by leveraging the nonlinearities in their energy functions. They have broad applications in…

Optics · Physics 2026-01-12 Khalid Musa , Santosh Kumar , Michael Katidis , Yu-Ping Huang

The Dense Associative Memory generalizes the Hopfield network by allowing for sharper interaction functions. This increases the capacity of the network as an autoassociative memory as nearby learned attractors will not interfere with one…

Neural and Evolutionary Computing · Computer Science 2024-09-24 Hayden McAlister , Anthony Robins , Lech Szymanski

Lack of memory (locality in time) is a major limitation of almost all present time-dependent density functional approximations. By using semiclassical dynamics to compute correlation effects within a density-matrix functional approach, we…

Chemical Physics · Physics 2015-05-18 A. K. Rajam , I. Raczkowska , N. T. Maitra

Heretofore, neural networks with external memory are restricted to single memory with lossy representations of memory interactions. A rich representation of relationships between memory pieces urges a high-order and segregated relational…

Machine Learning · Computer Science 2020-06-12 Hung Le , Truyen Tran , Svetha Venkatesh

Dense Associative Memory (DAM) models generalize the classical Hopfield model by incorporating n-body or exponential interactions that greatly enhance storage capacity. While the criticality of DAM models has been largely investigated,…

Adaptation and Self-Organizing Systems · Physics 2026-01-19 Marco Cafiso , Paolo Paradisi

Dense Associative Memory (DAM) models have been attracting renewed attention since they were shown to be robust to adversarial examples and closely related to cutting edge machine learning paradigms, such as the attention mechanism and…

Machine Learning · Computer Science 2026-01-27 Robin Thériault , Daniele Tantari

The primate heteromodal cortex presents an evident functional modularity at a mesoscopic level, with physiological and anatomical evidence pointing to it as likely substrate of long-term memory. In order to investigate some of its…

Neurons and Cognition · Quantitative Biology 2021-12-09 Carlo Fulvi Mari

Dense Associative Memory (DenseAM) is a promising family of AI architectures that is represented by a neural network performing temporal dynamics on an energy landscape. While hyperparameter transfer methods are well-studied for…

Machine Learning · Computer Science 2026-05-12 Roi Holtzman , Dmitry Krotov , Boris Hanin

We study various models of associative memories with sparse information, i.e. a pattern to be stored is a random string of $0$s and $1$s with about $\log N$ $1$s, only. We compare different synaptic weights, architectures and retrieval…

Probability · Mathematics 2016-06-27 Vincent Gripon , Judith Heusel , Matthias Löwe , Franck Vermet

Deep clustering - joint representation learning and latent space clustering - is a well studied problem especially in computer vision and text processing under the deep learning framework. While the representation learning is generally…

Computer Vision and Pattern Recognition · Computer Science 2026-01-06 Bishwajit Saha , Dmitry Krotov , Mohammed J. Zaki , Parikshit Ram

Conversion of temporal to spatial correlations in the cortex is one of the most intriguing functions in the brain. The learning at synapses triggering the correlation conversion can take place in a wide integration window, whose influence…

Disordered Systems and Neural Networks · Physics 2021-12-21 Zijian Jiang , Jianwen Zhou , Tianqi Hou , K. Y. Michael Wong , Haiping Huang

Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another…

Disordered Systems and Neural Networks · Physics 2024-02-14 Carlo Lucibello , Marc Mézard

Neuron models of associative memory provide a new and prospective technology for reliable date storage and patterns recognition. However, even when the patterns are uncorrelated, the efficiency of most known models of associative memory is…

Disordered Systems and Neural Networks · Physics 2007-05-23 B. V. Kryzhanovsky , L. B. Litinskii , A. Fonarev
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