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In this paper we study robust synchronization of time-fractional Hopfield neural networks with memristive couplings and Hebbian learning rules. This new model of artificial neural networks exhibits strong memory and long-range…

Analysis of PDEs · Mathematics 2025-10-27 Yuncheng You

A Hopfield network is an auto-associative, distributive model of neural memory storage and retrieval. A form of error-correcting code, the Hopfield network can learn a set of patterns as stable points of the network dynamic, and retrieve…

Neurons and Cognition · Quantitative Biology 2014-07-24 Ila Fiete , David J. Schwab , Ngoc M. Tran

Hebbian learning of excitatory synapses plays a central role in storing activity patterns in associative memory models. Furthermore, interstimulus Hebbian learning associates multiple items in the brain by converting temporal correlation to…

Neurons and Cognition · Quantitative Biology 2019-08-21 Tatsuya Haga , Tomoki Fukai

"Dreaming" enables agents to learn from imagined experiences, enabling more robust and sample-efficient learning of world models. In this work, we consider innovations to the state-of-the-art Dreamer model using probabilistic methods that…

Machine Learning · Computer Science 2026-03-06 Gavin Wong

The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically-coupled McCulloch-Pitts neurons interact to perform emergent computation. Although previous researchers have…

Adaptation and Self-Organizing Systems · Physics 2015-06-09 Christopher Hillar , Ngoc M. Tran

Sequential learning involves learning tasks in a sequence, and proves challenging for most neural networks. Biological neural networks regularly conquer the sequential learning challenge and are even capable of transferring knowledge both…

Neural and Evolutionary Computing · Computer Science 2025-03-06 Hayden McAlister , Anthony Robins , Lech Szymanski

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

Modeling self-organization of neural networks for unsupervised learning using Hebbian and anti-Hebbian plasticity has a long history in neuroscience. Yet, derivations of single-layer networks with such local learning rules from principled…

Neurons and Cognition · Quantitative Biology 2017-12-22 Cengiz Pehlevan , Anirvan Sengupta , Dmitri B. Chklovskii

In this paper, we introduce Hebbian learning as a novel method for swarm robotics, enabling the automatic emergence of heterogeneity. Hebbian learning presents a biologically inspired form of neural adaptation that solely relies on local…

Neural and Evolutionary Computing · Computer Science 2025-07-17 Fuda van Diggelen , Tugay Alperen Karagüzel , Andres Garcia Rincon , A. E. Eiben , Dario Floreano , Eliseo Ferrante

Recent work has shown that biologically plausible Hebbian learning can be integrated with backpropagation learning (backprop), when training deep convolutional neural networks. In particular, it has been shown that Hebbian learning can be…

Computer Vision and Pattern Recognition · Computer Science 2020-12-23 Gabriele Lagani , Giuseppe Amato , Fabrizio Falchi , Claudio Gennaro

We consider Hopfield networks, where neurons interact pair-wise by Hebbian couplings built over $i$. a set of definite patterns (ground truths), $ii$. a sample of labeled examples (supervised setting), $iii$. a sample of unlabeled examples…

Disordered Systems and Neural Networks · Physics 2025-10-16 Elena Agliari , Alberto Fachechi , Domenico Luongo

A normative approach called Similarity Matching was recently introduced for deriving and understanding the algorithmic basis of neural computation focused on unsupervised problems. It involves deriving algorithms from computational…

Neural and Evolutionary Computing · Computer Science 2023-10-02 Yanis Bahroun , Dmitri B. Chklovskii , Anirvan M. Sengupta

The Little-Hopfield network is an auto-associative computational model of neural memory storage and retrieval. This model is known to robustly store collections of randomly generated binary patterns as stable-states of the network dynamics.…

Neurons and Cognition · Quantitative Biology 2015-04-30 Christopher Hillar , Ngoc Tran , Kilian Koepsell

Thanks to the availability of large scale digital datasets and massive amounts of computational power, deep learning algorithms can learn representations of data by exploiting multiple levels of abstraction. These machine learning methods…

Disordered Systems and Neural Networks · Physics 2018-10-01 Alberto Testolin , Michele Piccolini , Samir Suweis

We test four fast mean field type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low temperature regime, the simulated annealing…

Disordered Systems and Neural Networks · Physics 2013-05-29 Haiping Huang

Memory is a key component of biological neural systems that enables the retention of information over a huge range of temporal scales, ranging from hundreds of milliseconds up to years. While Hebbian plasticity is believed to play a pivotal…

Neural and Evolutionary Computing · Computer Science 2022-05-24 Thomas Limbacher , Ozan Özdenizci , Robert Legenstein

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

A number of studies have concluded that dreaming is mostly caused by randomly arriving internal signals because "dream contents are random impulses", and argued that dream sleep is unlikely to play an important part in our intellectual…

Neurons and Cognition · Quantitative Biology 2026-02-05 Qi Zhang

We present a biologically detailed extension of the classical Hopfield/Marr auto-associative memory model for CA3, implementing ten populations (two asymmetric pyramidal subtypes, eight GABAergic interneuron classes), forty-seven…

Neural and Evolutionary Computing · Computer Science 2026-04-23 Daniele Corradetti , Renato Corradetti

The Self-Optimization (SO) model can be considered as the third operational mode of the classical Hopfield Network, leveraging the power of associative memory to enhance optimization performance. Moreover, it has been argued to express…

Neural and Evolutionary Computing · Computer Science 2025-11-06 Natalya Weber , Christian Guckelsberger , Tom Froese
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