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Lifelong learning and adaptability are two defining aspects of biological agents. Modern reinforcement learning (RL) approaches have shown significant progress in solving complex tasks, however once training is concluded, the found…

Neural and Evolutionary Computing · Computer Science 2022-04-20 Elias Najarro , Sebastian Risi

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

We study bi-directional associative neural networks that, exposed to noisy examples of an extensive number of random archetypes, learn the latter (with or without the presence of a teacher) when the supplied information is enough: in this…

Disordered Systems and Neural Networks · Physics 2023-07-18 Martino Salomone Centonze , Ido Kanter , Adriano Barra

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

In the present paper, an effort has been made for storing and recalling images with Hopfield Neural Network Model of auto-associative memory. Images are stored by calculating a corresponding weight matrix. Thereafter, starting from an…

Neural and Evolutionary Computing · Computer Science 2011-05-03 C. Ramya , G. Kavitha , Dr. K. S. Shreedhara

Cognitive ageing seems to be a story of global degradation. As one ages there are a number of physical, chemical and biological changes that take place. Therefore it is logical to assume that the brain is no exception to this phenomenon.…

Adaptation and Self-Organizing Systems · Physics 2014-08-07 Sakyasingha Dasgupta

Understanding the memory capacity of neural networks remains a challenging problem in implementing artificial intelligence systems. In this paper, we address the notion of capacity with respect to Hopfield networks and propose a dynamic…

Neural and Evolutionary Computing · Computer Science 2017-09-19 Saarthak Sarup , Mingoo Seok

We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of…

Machine Learning · Computer Science 2024-06-04 Jerry Yao-Chieh Hu , Thomas Lin , Zhao Song , Han Liu

Hebbian learning is a key principle underlying learning in biological neural networks. We relate a Hebbian spike-timing-dependent plasticity rule to noisy gradient descent with respect to a non-convex loss function on the probability…

Machine Learning · Computer Science 2026-01-14 Niklas Dexheimer , Sascha Gaudlitz , Johannes Schmidt-Hieber

Hopfield networks using Hebbian learning suffer from limited storage capacity. While supervised methods like Linear Logistic Regression (LLR) offer some improvement, kernel methods like Kernel Logistic Regression (KLR) significantly enhance…

Machine Learning · Computer Science 2025-08-26 Akira Tamamori

Humans and other animals learn to extract general concepts from sensory experience without extensive teaching. This ability is thought to be facilitated by offline states like sleep where previous experiences are systemically replayed.…

Neurons and Cognition · Quantitative Biology 2022-02-21 Nicolas Deperrois , Mihai A. Petrovici , Walter Senn , Jakob Jordan

Developmental approaches to neural architecture search grow functional networks from compact genomes through self-organisation, but the resulting networks operate with fixed post-growth weights. We characterise Hebbian and anti-Hebbian…

Robotics · Computer Science 2026-04-08 Sergii Medvid , Andrii Valenia , Mykola Glybovets

We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to…

Disordered Systems and Neural Networks · Physics 2009-11-10 D. Bolle , Th. M. Nieuwenhuizen , I. Perez Castillo , T. Verbeiren

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

Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic…

Dynamical Systems · Mathematics 2016-03-23 Pascal Chossat , Martin Krupa

Recurrent neural networks (RNNs) trained using Equilibrium Propagation (EP), a biologically plausible training algorithm, have demonstrated strong performance in various tasks such as image classification and reinforcement learning.…

Machine Learning · Computer Science 2025-08-21 Yoshimasa Kubo , Jean Erik Delanois , Maxim Bazhenov

Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…

Neural and Evolutionary Computing · Computer Science 2023-05-10 Thomas F Burns , Tomoki Fukai

In this article we intoduce a novel stochastic Hebb-like learning rule for neural networks that is neurobiologically motivated. This learning rule combines features of unsupervised (Hebbian) and supervised (reinforcement) learning and is…

Disordered Systems and Neural Networks · Physics 2009-11-11 Frank Emmert-Streib

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

During the first part of life, the brain develops while it learns through a process called synaptogenesis. The neurons, growing and interacting with each other, create synapses. However, eventually the brain prunes those synapses. While…

Neural and Evolutionary Computing · Computer Science 2023-04-04 Andrea Ferigo , Giovanni Iacca
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