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The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…

Dynamical Systems · Mathematics 2026-04-06 Hans-Peter Beise

Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks…

Disordered Systems and Neural Networks · Physics 2017-11-23 Dong-Ling Deng , Xiaopeng Li , S. Das Sarma

The stability and convergence of the neural networks are the fundamental characteristics in the Hopfield type networks. Since time delay is ubiquitous in most physical and biological systems, more attention is being made for the delayed…

Neural and Evolutionary Computing · Computer Science 2010-02-08 A. K. Ojha , Dushmanta Mallick , C. Mallick

In this paper, the commensurate fractional-order variant of an Hopfield neuronal network is analyzed. The system is integrated with the ABM method for fractional-order equations. Beside the standard stability analysis of equilibria, the…

Numerical Analysis · Mathematics 2021-07-28 Marius-F. Danca

Algorithms for associative memory typically rely on a network of many connected units. The prototypical example is the Hopfield model, whose generalizations to the quantum realm are mainly based on open quantum Ising models. We propose a…

Quantum Physics · Physics 2023-05-17 Adrià Labay-Mora , Roberta Zambrini , Gian Luca Giorgi

Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…

Pattern Formation and Solitons · Physics 2025-07-22 Andrew L. Krause , Václav Klika , Edgardo Villar-Sepúlveda , Alan R. Champneys , Eamonn A. Gaffney

We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural…

Disordered Systems and Neural Networks · Physics 2009-11-10 B. Wemmenhove , N. S. Skantzos

To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world and scale-free topologies. The random net is the most…

Disordered Systems and Neural Networks · Physics 2009-11-10 Patrick N. Mcgraw , Michael Menzinger

Cortical populations of neurons develop sparse representations adapted to the statistics of the environment. While existing synaptic plasticity models reproduce some of the observed receptive-field properties, a major obstacle is the…

Neurons and Cognition · Quantitative Biology 2022-09-16 Carlos Stein N. Brito , Wulfram Gerstner

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines, a class of neural network models that uses synaptic…

Neural and Evolutionary Computing · Computer Science 2016-12-16 Emre O. Neftci , Bruno U. Pedroni , Siddharth Joshi , Maruan Al-Shedivat , Gert Cauwenberghs

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

Hebbian learning is a biological principle that intuitively describes how neurons adapt their connections through repeated stimuli. However, when applied to machine learning, it suffers serious issues due to the unconstrained updates of the…

Machine Learning · Computer Science 2025-10-23 Shikuang Deng , Jiayuan Zhang , Yuhang Wu , Ting Chen , Shi Gu

We complement our previous work [arxiv: 0707.0565] with the full (non diluted) solution describing the stable states of an attractor network that stores correlated patterns of activity. The new solution provides a good fit of simulations of…

Disordered Systems and Neural Networks · Physics 2007-07-23 Emilio Kropff

We consider two models of Hopfield-like associative memory with $q$-valued neurons: Potts-glass neural network (PGNN) and parametrical neural network (PNN). In these models neurons can be in more than two different states. The models have…

Disordered Systems and Neural Networks · Physics 2007-05-23 B. V. Kryzhanovsky , L. B. Litinskii , A. L. Mikaelian

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

We investigate the maximum number of embedded patterns in the two-dimensional Hopfield model. The grand state energies of two specific network states, namely, the energies of the pure-ferromagnetic state and the state of specific one stored…

Disordered Systems and Neural Networks · Physics 2009-11-07 Shinsuke Koyama

The network embedding task is to represent the node in the network as a low-dimensional vector while incorporating the topological and structural information. Most existing approaches solve this problem by factorizing a proximity matrix,…

Machine Learning · Computer Science 2022-09-01 Yuchen Liang , Dmitry Krotov , Mohammed J. Zaki

The full dynamics of a synchronous recurrent neural network model with Ising binary units and a Hebbian learning rule with a finite self-interaction is studied in order to determine the stability to synaptic and stochastic noise of…

Disordered Systems and Neural Networks · Physics 2009-11-13 F. L. Metz , W. K. Theumann

An Ashkin-Teller neural network, allowing for two types of neurons is considered in the case of low loading as a function of the strength of the respective couplings between these neurons. The storage and retrieval of embedded patterns…

Disordered Systems and Neural Networks · Physics 2009-10-31 D. Bolle , P. Kozlowski

Feedback-rich neural architectures can regenerate earlier representations and inject temporal context, making them a natural setting for strictly local synaptic plasticity. Existing literature raises doubt about whether a minimal,…

Neural and Evolutionary Computing · Computer Science 2026-02-03 Josh Li , Fow-sen Choa