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The Hopfield model provides a mathematically idealized yet insightful framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired four decades of extensive research on learning and…

Neurons and Cognition · Quantitative Biology 2025-05-14 Simone Betteti , Giacomo Baggio , Francesco Bullo , Sandro Zampieri

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…

In this paper we present a simple microscopic stochastic model describing short term plasticity within a large homogeneous network of interacting neurons. Each neuron is represented by its membrane potential and by the residual calcium…

Probability · Mathematics 2020-01-29 Antonio Galves , Eva Löcherbach , Christophe Pouzat , Errico Presutti

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

We study a fully connected Hopfield-type associative memory network with online activity-dependent synaptic plasticity, where neural states and synaptic couplings coevolve during retrieval. Using the generating-functional formalism, we…

Disordered Systems and Neural Networks · Physics 2026-05-22 Yoshinori Hara , Yoshiyuki Kabashima

Short-term plasticity (STP) is a mechanism that stores decaying memories in synapses of the cerebral cortex. In computing practice, STP has been used, but mostly in the niche of spiking neurons, even though theory predicts that it is the…

Neural and Evolutionary Computing · Computer Science 2023-08-03 Hector Garcia Rodriguez , Qinghai Guo , Timoleon Moraitis

Synaptic memory is considered to be the main element responsible for learning and cognition in humans. Although traditionally non-volatile long-term plasticity changes have been implemented in nanoelectronic synapses for neuromorphic…

Emerging Technologies · Computer Science 2017-12-20 Abhronil Sengupta , Kaushik Roy

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

In the mammalian brain newly acquired memories depend on the hippocampus for maintenance and recall, but over time these functions are taken over by the neocortex through a process called systems consolidation. However, reactivation of a…

Neurons and Cognition · Quantitative Biology 2019-03-29 Peter Helfer , Thomas R. Shultz

In the mammalian nervous system, various synaptic plasticity rules act, either individually or synergistically, and over wide-ranging timescales to dictate the processes that enable learning and memory formation. To mimic biological…

Disordered Systems and Neural Networks · Physics 2021-06-11 Syed Ghazi Sarwat , Benedikt Kersting , Timoleon Moraitis , Vara Prasad Jonnalagadda , Abu Sebastian

In this work we study, analytically and employing Monte Carlo simulations, the influence of the competition between several activity-dependent synaptic processes, such as short-term synaptic facilitation and depression, on the maximum…

Neurons and Cognition · Quantitative Biology 2010-07-23 Jorge F. Mejias , Joaquin J. Torres

Precise spatio-temporal patterns of neuronal action potentials underly e.g. sensory representations and control of muscle activities. However, it is not known how the synaptic efficacies in the neuronal networks of the brain adapt such that…

Neurons and Cognition · Quantitative Biology 2015-02-24 Christian Albers , Maren Westkott , Klaus Pawelzik

The distinct timescales of synaptic plasticity and neural activity dynamics play an important role in the brain's learning and memory systems. Activity-dependent plasticity reshapes neural circuit architecture, determining spontaneous and…

Neurons and Cognition · Quantitative Biology 2023-06-30 Heather L Cihak , Zachary P Kilpatrick

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

A growing body of research indicates that structural plasticity mechanisms are crucial for learning and memory consolidation. Starting from a simple phenomenological model, we exploit a mean-field approach to develop a theoretical framework…

Neurons and Cognition · Quantitative Biology 2024-06-19 Gianmarco Tiddia , Luca Sergi , Bruno Golosio

Learning and memory relies on synapses changing their strengths in response to neural activity. However there is a substantial gap between the timescales of neural electrical dynamics (1-100 ms) and organism behaviour during learning…

Neurons and Cognition · Quantitative Biology 2023-08-08 Cian O'Donnell

Biological neurons and their in-silico emulations for neuromorphic artificial intelligence (AI) use extraordinarily energy-efficient mechanisms, such as spike-based communication and local synaptic plasticity. It remains unclear whether…

Neural and Evolutionary Computing · Computer Science 2021-06-17 Timoleon Moraitis , Abu Sebastian , Evangelos Eleftheriou

Associative memory models such as the Hopfield network and its dense generalizations with higher-order interactions exhibit a "blackout catastrophe" -- a discontinuous transition where stable memory states abruptly vanish when the number of…

Disordered Systems and Neural Networks · Physics 2026-03-24 David G. Clark

Sleep is thought to support memory consolidation and the recovery of optimal energetic regime by reorganizing synaptic connectivity, yet how plasticity across hierarchical brain circuits contributes to abstraction and energy efficiency…

Working memory often appears to exceed its basic span by organizing items into compact representations called chunks. Chunking can be learned over time for familiar inputs; however, it can also arise spontaneously for novel stimuli. Such…

Neurons and Cognition · Quantitative Biology 2025-09-19 Weishun Zhong , Mikhail Katkov , Misha Tsodyks
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