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Associative memory or content addressable memory is an important component function in computer science and information processing and is a key concept in cognitive and computational brain science. Many different neural network…

Neural and Evolutionary Computing · Computer Science 2025-02-19 Anders Lansner , Naresh B Ravichandran , Pawel Herman

We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning…

Chaotic Dynamics · Physics 2008-04-07 Benoit Siri , Hugues Berry , Bruno Cessac , Bruno Delord , Mathias Quoy

This paper targets the problem of encoding information into binary cell assemblies. Spiking neural networks and k-winners-take-all models are two common approaches, but the first is hard to use for information processing and the second is…

Neural and Evolutionary Computing · Computer Science 2021-08-03 Viacheslav Osaulenko , Danylo Ulianych

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

Artificial neural networks have successfully tackled a large variety of problems by training extremely deep networks via back-propagation. A direct application of back-propagation to spiking neural networks contains biologically implausible…

Neural and Evolutionary Computing · Computer Science 2021-11-29 Kyle Daruwalla , Mikko Lipasti

The research presented in this paper advances the integration of Hebbian learning into Convolutional Neural Networks (CNNs) for image processing, systematically exploring different architectures to build an optimal configuration, adhering…

Neural and Evolutionary Computing · Computer Science 2026-05-05 Julian Jimenez Nimmo , Esther Mondragon

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

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 demonstrate that our recently introduced stochastic Hebb-like learning rule is capable of learning the problem of timing in general network topologies generated by an algorithm of Watts and Strogatz. We compare our results with a…

Disordered Systems and Neural Networks · Physics 2007-05-23 Frank Emmert-Streib

This paper introduces and evaluates a novel training method for neural networks: Dual Variable Learning Rates (DVLR). Building on insights from behavioral psychology, the dual learning rates are used to emphasize correct and incorrect…

Machine Learning · Computer Science 2021-02-11 Elizabeth Liner , Risto Miikkulainen

Hopfield networks are an attractive choice for solving many types of computational problems because they provide a biologically plausible mechanism. The Self-Optimization (SO) model adds to the Hopfield network by using a biologically…

Adaptation and Self-Organizing Systems · Physics 2024-03-06 Natalya Weber , Werner Koch , Ozan Erdem , Tom Froese

In this paper reinforcement learning with binary vector actions was investigated. We suggest an effective architecture of the neural networks for approximating an action-value function with binary vector actions. The proposed architecture…

Neural and Evolutionary Computing · Computer Science 2015-12-07 Naoto Yoshida

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

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

Determining the memory capacity of two layer neural networks with $m$ hidden neurons and input dimension $d$ (i.e., $md+2m$ total trainable parameters), which refers to the largest size of general data the network can memorize, is a…

Machine Learning · Computer Science 2024-07-25 Liam Madden , Christos Thrampoulidis

Neural networks are supposed to recognise blurred images (or patterns) of $N$ pixels (bits) each. Application of the network to an initial blurred version of one of $P$ pre-assigned patterns should converge to the correct pattern. In the…

Statistical Mechanics · Physics 2009-11-07 Dietrich Stauffer , Amnon Aharony , Luciano da Fontoura Costa , Joan Adler

In this paper, we introduce a new type of generalized neural network where neurons and synapses maintain multiple states. We show that classical gradient-based backpropagation in neural networks can be seen as a special case of a two-state…

Machine Learning · Computer Science 2021-06-15 Mark Sandler , Max Vladymyrov , Andrey Zhmoginov , Nolan Miller , Andrew Jackson , Tom Madams , Blaise Aguera y Arcas

We investigate from a computational perspective the efficiency of the Willshaw synaptic update rule in the context of familiarity discrimination, a binary-answer, memory-related task that has been linked through psychophysical experiments…

Neurons and Cognition · Quantitative Biology 2012-08-01 João Sacramento , Andreas Wichert

Krotov and Hopfield (2021) proposed a biologically plausible two-layer associative memory network with memory storage capacity exponential in the number of visible neurons. However, the capacity was only linear in the number of hidden…

Neurons and Cognition · Quantitative Biology 2026-03-11 Mohadeseh Shafiei Kafraj , Dmitry Krotov , Peter E. Latham

Local learning rules in biological neural networks (BNNs) are commonly referred to as Hebbian learning. [26] links a biologically motivated Hebbian learning rule to a specific zeroth-order optimization method. In this work, we study a…

Statistics Theory · Mathematics 2023-11-08 Johannes Schmidt-Hieber , Wouter M Koolen