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We present a Hopfield-like autoassociative network for memories representing examples of concepts. Each memory is encoded by two activity patterns with complementary properties. The first is dense and correlated across examples within…

Neurons and Cognition · Quantitative Biology 2023-08-28 Louis Kang , Taro Toyoizumi

The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according the Hebb rule from the set of memorized patterns which are treated as distorted copies of the…

Disordered Systems and Neural Networks · Physics 2007-05-23 Leonid B. Litinskii

Many models used in artificial intelligence and cognitive science rely on multi-element patterns stored in "slots" - dedicated storage locations - in a digital computer. As biological brains likely lack slots, we consider how they might…

Neural and Evolutionary Computing · Computer Science 2025-11-07 Shaunak Bhandarkar , James L. McClelland

A general scheme to realize a perceptron for hardware neural networks is presented, where multiple interconnections are achieved by a superposition of Schrodinger waves. Spatially patterned potentials process information by coupling…

Disordered Systems and Neural Networks · Physics 2015-06-22 T. Espinosa-Ortega , T. C. H. Liew

Artificial neural networks have diverged far from their early inspiration in neurology. In spite of their technological and commercial success, they have several shortcomings, most notably the need for a large number of training examples…

Neural and Evolutionary Computing · Computer Science 2019-12-04 J. Campbell Scott , Thomas F. Hayes , Ahmet S. Ozcan , Winfried W. Wilcke

Content-addressable memories such as Modern Hopfield Networks (MHN) have been studied as mathematical models of auto-association and storage/retrieval in the human declarative memory, yet their practical use for large-scale content storage…

Machine Learning · Computer Science 2024-11-01 Satyananda Kashyap , Niharika S. D'Souza , Luyao Shi , Ken C. L. Wong , Hongzhi Wang , Tanveer Syeda-Mahmood

Associative memory is a fundamental function in the brain. Here, we generalize the standard associative memory model to include long-range Hebbian interactions at the learning stage, corresponding to a large synaptic integration window. In…

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

Associative memory has been a prominent candidate for the computation performed by the massively recurrent neocortical networks. Attractor networks implementing associative memory have offered mechanistic explanation for many cognitive…

Neural and Evolutionary Computing · Computer Science 2022-09-07 Naresh Balaji Ravichandran , Anders Lansner , Pawel Herman

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

A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable $S_x = \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable…

Disordered Systems and Neural Networks · Physics 2009-11-07 Motohiro Kemuriyama , Tetsuo Matsui , Kazuhiko Sakakibara

Associative memory or content-addressable memory is an important component function in computer science and information processing, and at the same time a key concept in cognitive and computational brain science. Many different neural…

Neural and Evolutionary Computing · Computer Science 2026-05-05 Anders Lansner , Andreas Knoblauch , Naresh B Ravichandran , Pawel Herman

This paper look at how the Hopfield neural network can be used to store and recall patterns constructed from natural language sentences. As a pattern recognition and storage tool, the Hopfield neural network has received much attention.…

cmp-lg · Computer Science 2008-02-03 Nigel Collier

The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore…

Neurons and Cognition · Quantitative Biology 2007-06-19 Benoit Siri , Mathias Quoy , Bruno Delord , Bruno Cessac , Hugues Berry

We study a class of Hopfield models where the memories are represented by a mixture of Gaussian and binary variables and the neurons are Ising spins. We study the properties of this family of models as the relative weight of the two kinds…

Disordered Systems and Neural Networks · Physics 2022-09-29 Luca Leuzzi , Alberto Patti , Federico Ricci-Tersenghi

We consider $L$-directional associative memories, composed of $L$ Hopfield networks, displaying imitative Hebbian intra-network interactions and anti-imitative Hebbian inter-network interactions, where couplings are built over a set of…

Disordered Systems and Neural Networks · Physics 2025-04-11 Elena Agliari , Andrea Alessandrelli , Paulo Duarte Mourao , Alberto Fachechi

We introduce a simple cellular-network model to explain the capacity of the plants as memory devices. Following earlier observations (Bose \cite{Bose} and others), we regard the plant as a network in which each of the elements (plant cells)…

Disordered Systems and Neural Networks · Physics 2009-11-10 Jun-ichi Inoue , Bikas K. Chakrabarti

This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…

Optimization and Control · Mathematics 2024-03-25 Veronica Centorrino , Francesco Bullo , Giovanni Russo

We propose a new self-organizing mechanism behind the emergence of memory in which temporal sequences of stimuli are transformed into spatial activity patterns. In particular, the memory emerges despite the absence of temporal correlations…

Disordered Systems and Neural Networks · Physics 2009-11-07 Konstantin Klemm , Preben Alstrom

Recent research has established a connection between modern Hopfield networks (HNs) and transformer attention heads, with guarantees of exponential storage capacity. However, these models still face challenges scaling storage efficiently.…

Machine Learning · Computer Science 2025-04-11 Saul Santos , António Farinhas , Daniel C. McNamee , André F. T. Martins

Codifying memories is one of the fundamental problems of modern Neuroscience. The functional mechanisms behind this phenomenon remain largely unknown. Experimental evidence suggests that some of the memory functions are performed by…

Neurons and Cognition · Quantitative Biology 2022-05-17 Ivan Y. Tyukin , Alexander N. Gorban , Carlos Calvo , Julia Makarova , Valeri A. Makarov