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Catastrophic forgetting/interference is a critical problem for lifelong learning machines, which impedes the agents from maintaining their previously learned knowledge while learning new tasks. Neural networks, in particular, suffer plenty…

Neural and Evolutionary Computing · Computer Science 2019-03-15 Soheil Kolouri , Nicholas Ketz , Xinyun Zou , Jeffrey Krichmar , Praveen Pilly

The Hopfield model describes a neural network that stores memories using all-to-all-coupled spins. Memory patterns are recalled under equilibrium dynamics. Storing too many patterns breaks the associative recall process because frustration…

Associative memory, a form of content-addressable memory, facilitates information storage and retrieval in many biological and physical systems. In statistical mechanics models, associative memory at equilibrium is represented through…

Disordered Systems and Neural Networks · Physics 2022-03-08 Agnish Kumar Behera , Madan Rao , Srikanth Sastry , Suriyanarayanan Vaikuntanathan

Classical autoassociative memory models have been central to understanding emergent computations in recurrent neural circuits across diverse biological contexts. However, they typically neglect neuromodulatory agents that are known to…

Neurons and Cognition · Quantitative Biology 2025-12-17 Daiki Goto , Hector Manuel Lopez Rios , Monika Scholz , Suriyanarayanan Vaikuntanathan

Dense Associative Memories or modern Hopfield networks permit storage and reliable retrieval of an exponentially large (in the dimension of feature space) number of memories. At the same time, their naive implementation is non-biological,…

Neurons and Cognition · Quantitative Biology 2021-04-29 Dmitry Krotov , John Hopfield

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

Neural networks are susceptible to catastrophic forgetting. They fail to preserve previously acquired knowledge when adapting to new tasks. Inspired by human associative memory system, we propose a brain-like approach that imitates the…

Computer Vision and Pattern Recognition · Computer Science 2021-03-26 Yi Gu , Jie Li , Yuting Gao , Ruoxin Chen , Chentao Wu , Feiyang Cai , Chao Wang , Zirui Zhang

In this work we study numerically the out of equilibrium dynamics of the Hopfield model for associative memory inside its spin-glass phase. Besides its interest as a neural network model it can also be considered as a prototype of fully…

Disordered Systems and Neural Networks · Physics 2009-10-31 M. A. Montemurro , F. A. Tamarit , D. A. Stariolo , S. A. Cannas

Autoassociative networks were proposed in the 80's as simplified models of memory function in the brain, using recurrent connectivity with hebbian plasticity to store patterns of neural activity that can be later recalled. This type of…

Disordered Systems and Neural Networks · Physics 2011-11-10 Emilio Kropff , Alessandro Treves

We introduce a Hopfield-type associative memory in which effective connectivity is multiplicatively modulated by astrocytic gains evolving under an entropy-regularized replicator equation. The coupled neuron-astrocyte dynamics admit a…

Data Analysis, Statistics and Probability · Physics 2026-04-29 Arnau Vivet , Alex Arenas

In Hopfield-type associative memory models, memories are stored in the connectivity matrix and can be retrieved subsequently thanks to the collective dynamics of the network. In these models, the retrieval of a particular memory can be…

Neurons and Cognition · Quantitative Biology 2025-10-21 Marco Benedetti , Nicolas Brunel , Enzo Marinari , Ulises Pereira Obilinovic

Energy-based probabilistic models learned by maximizing the likelihood of the data are limited by the intractability of the partition function. A widely used workaround is to maximize the pseudo-likelihood, which replaces the global…

Statistical Mechanics · Physics 2026-03-31 Francesco D'Amico , Dario Bocchi , Luca Maria Del Bono , Saverio Rossi , Matteo Negri

Lifelong learning capabilities are crucial for artificial autonomous agents operating on real-world data, which is typically non-stationary and temporally correlated. In this work, we demonstrate that dynamically grown networks outperform…

Neural and Evolutionary Computing · Computer Science 2018-12-03 German I. Parisi , Xu Ji , Stefan Wermter

In "Large Associative Memory Problem in Neurobiology and Machine Learning," Dmitry Krotov and John Hopfield introduced a general technique for the systematic construction of neural ordinary differential equations with non-increasing energy…

Neurons and Cognition · Quantitative Biology 2025-02-27 Vladimir Fanaskov , Ivan Oseledets

Attractor networks are an influential theory for memory storage in brain systems. This theory has recently been challenged by the observation of strong temporal variability in neuronal recordings during memory tasks. In this work, we study…

Neurons and Cognition · Quantitative Biology 2021-12-02 Ulises Pereira-Obilinovic , Johnatan Aljadeff , Nicolas Brunel

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

Unlike the brain, artificial neural networks, including state-of-the-art deep neural networks for computer vision, are subject to "catastrophic forgetting": they rapidly forget the previous task when trained on a new one. Neuroscience…

Neural and Evolutionary Computing · Computer Science 2021-06-09 Axel Laborieux , Maxence Ernoult , Tifenn Hirtzlin , Damien Querlioz

We analyze continuous Hopfield associative memories augmented by additional, rapid short-term associative synaptic plasticity. Through the cavity method, we determine the boundary between the retrieval and forgetting, or spin-glass phase,…

Neurons and Cognition · Quantitative Biology 2026-02-10 Martina Del Gaudio , Federico Ghimenti , Surya Ganguli

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

Associative memory and probabilistic modeling are two fundamental topics in artificial intelligence. The first studies recurrent neural networks designed to denoise, complete and retrieve data, whereas the second studies learning and…

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