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In this paper, we investigate the associative memory in recurrent neural networks, based on the model of evolving neural networks proposed by Nolfi, Miglino and Parisi. Experimentally developed network has highly asymmetric synaptic weights…

adap-org · Physics 2008-02-03 Sh. Fujita , H. Nishimura

The Hopfield model provides a paradigmatic framework for associative memory. Its classical implementation, based on the Hebbian learning rule, suffers from catastrophic forgetting: when one attempts storing too many patterns, the network…

Disordered Systems and Neural Networks · Physics 2026-03-11 Enzo Marinari , Saverio Rossi , Francesco Zamponi

We consider nonequilibrium transport in a simple chain of identical mechanical cells in which particles move around. In each cell, there is a rotating disc, with which these particles interact, and this is the only interaction in the model.…

Statistical Mechanics · Physics 2008-07-15 Jean-Pierre Eckmann , Carlos Mejia-Monasterio , Emmanuel Zabey

In neuroscience, classical Hopfield networks are the standard biologically plausible model of long-term memory, relying on Hebbian plasticity for storage and attractor dynamics for recall. In contrast, memory-augmented neural networks in…

Neurons and Cognition · Quantitative Biology 2021-10-28 Danil Tyulmankov , Ching Fang , Annapurna Vadaparty , Guangyu Robert Yang

Humans learn and form memories in stochastic environments. Auto-associative memory systems model these processes by storing patterns and later recovering them from corrupted versions. Here, memories are learned by associating each pattern…

Systems and Control · Electrical Eng. & Systems 2026-04-02 Qin He , Jing Shuang Li

A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield…

Neural and Evolutionary Computing · Computer Science 2022-06-20 Beren Millidge , Tommaso Salvatori , Yuhang Song , Thomas Lukasiewicz , Rafal Bogacz

Associative Memories like the famous Hopfield Networks are elegant models for describing fully recurrent neural networks whose fundamental job is to store and retrieve information. In the past few years they experienced a surge of interest…

Machine Learning · Computer Science 2025-10-06 Dmitry Krotov , Benjamin Hoover , Parikshit Ram , Bao Pham

Statistical mechanics has made significant contributions to the study of biological neural systems by modeling them as recurrent networks of interconnected units with adjustable interactions. Several algorithms have been proposed to…

Disordered Systems and Neural Networks · Physics 2024-03-06 Enrico Ventura

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered…

Adaptation and Self-Organizing Systems · Physics 2009-11-10 Luis G. Morelli , Guillermo Abramson , Marcelo N. Kuperman

Generalized Hopfield models with higher-order or exponential interaction terms are known to have substantially larger storage capacities than the classical quadratic model. On the other hand, associative memories for sparse patterns, such…

Probability · Mathematics 2026-03-30 Matthias Löwe , Franck Vermet

Manuscript symbols can be stored, recognized and retrieved from an entropic digital memory that is associative and distributed but yet declarative; memory retrieval is a constructive operation, memory cues to objects not contained in the…

Machine Learning · Computer Science 2022-10-12 Rafael Morales , Noé Hernández , Ricardo Cruz , Victor D. Cruz , Luis A. Pineda

We study analytically and numerically a Hopfield fully-connected network with $d$-dimensional vector spins. These networks are models of associative memory that generalize the standard Hopfield with Ising spins, where $P$ examples are…

Disordered Systems and Neural Networks · Physics 2026-02-17 Flavio Nicoletti , Francesco D'Amico , Matteo Negri

As a mathematical model of associative memories, the Hopfield model was now well-established and a lot of studies to reveal the pattern-recalling process have been done from various different approaches. As well-known, a single neuron is…

Disordered Systems and Neural Networks · Physics 2015-05-27 Jun-ichi Inoue

We report on both analytical and numerical results concerning stochastic Hopfield--like neural automata exhibiting the following (biologically inspired) features: (1) Neurons and synapses evolve in time as in contact with respective baths…

Statistical Mechanics · Physics 2007-05-23 J. J. Torres , J. Marro , P. L. Garrido , J. M. Cortes , F. Ramos , M. A. Munoz

This paper is concerned with correlation functions of stochastic systems with memory, a prominent example being a molecule or colloid moving through a complex (e.g., viscoelastic) fluid environment. Analytical investigations of such systems…

Soft Condensed Matter · Physics 2021-02-24 Timo J. Doerries , Sarah A. M. Loos , Sabine H. L. Klapp

Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an…

Biological Physics · Physics 2021-06-07 Oskar H Schnaack , Luca Peliti , Armita Nourmohammad

I review and expand the model of quantum associative memory that I have recently proposed. In this model binary patterns of n bits are stored in the quantum superposition of the appropriate subset of the computational basis of n qbits.…

Quantum Physics · Physics 2007-05-23 Carlo A. Trugenberger

Using the Hopfield model as a benchmark case, the present work focuses on the investigation of partially annealed associative neural networks, wherein neural dynamics is coupled to slowly evolving patterns within the…

Disordered Systems and Neural Networks · Physics 2026-05-12 Linda Albanese , Andrea Alessandrelli , Adriano Barra , Silvio Franz , Federico Ricci-Tersenghi

To improve the storage capacity of the Hopfield model, we develop a version of the dreaming algorithm that perpetually reinforces the patterns to be stored (as in the Hebb rule), and erases the spurious memories (as in dreaming algorithms).…

Disordered Systems and Neural Networks · Physics 2025-06-03 Ludovica Serricchio , Dario Bocchi , Claudio Chilin , Raffaele Marino , Matteo Negri , Chiara Cammarota , Federico Ricci-Tersenghi

We study the functioning of associative memory on three-level quantum elements, qutrites represented by spins with S = 1. The recording of patterns into the superposition of quantum states and their recall are carried out by adiabatic…

Quantum Physics · Physics 2019-06-21 V. E. Zobov , I. S. Pichkovskiy
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