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Two novel phenomena for unidirectionally coupled 3-cell Hopfield neural networks (HNNs) are investigated. The first one is the persistence of chaos, which means the permanency of sensitivity and infinitely many unstable periodic…

Adaptation and Self-Organizing Systems · Physics 2024-03-13 Mehmet Onur Fen , Fatma Tokmak Fen

We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatio-temporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatio-temporal…

Disordered Systems and Neural Networks · Physics 2009-11-07 Masahiko Yoshioka

Representation learning from complex data typically involves models with a large number of parameters, which in turn require large amounts of data samples. In neural network models, model complexity grows with the number of inputs to each…

Machine Learning · Computer Science 2026-03-03 Carlos Stein Brito

As well known, Hebb's learning traces its origin in Pavlov's Classical Conditioning, however, while the former has been extensively modelled in the past decades (e.g., by Hopfield model and countless variations on theme), as for the latter…

Disordered Systems and Neural Networks · Physics 2022-07-05 Elena Agliari , Miriam Aquaro , Adriano Barra , Alberto Fachechi , Chiara Marullo

We study the stable phases of an attractor neural network model, with binary units, for hippocampal place cells encoding 1D or 2D spatial maps or environments. Using statistical mechanics tools we show that, below critical values for the…

Statistical Mechanics · Physics 2013-06-26 Rémi Monasson , Sophie Rosay

A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable $S_x = \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable…

Disordered Systems and Neural Networks · Physics 2009-11-07 Motohiro Kemuriyama , Tetsuo Matsui , Kazuhiko Sakakibara

We show how a Hopfield network with modifiable recurrent connections undergoing slow Hebbian learning can extract the underlying geometry of an input space. First, we use a slow/fast analysis to derive an averaged system whose dynamics…

Neurons and Cognition · Quantitative Biology 2011-02-02 Mathieu N. Galtier , Olivier D. Faugeras , Paul C. Bressloff

A memristor is a nonlinear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To enhance the memory property, we should use…

Dynamical Systems · Mathematics 2022-07-07 Leila Eftekhari , Mohammad M. Amirian

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

Memory effects, sometimes, can not be neglected. In the framework of continuous time random walk, memory effect is modeled by the correlated waiting times. In this paper, we derive the two-point probability distribution of the stochastic…

Statistical Mechanics · Physics 2019-01-23 Yao Chen , Xudong Wang , Weihua Deng

In this paper, we derive a new model of synaptic plasticity, based on recent algorithms for reinforcement learning (in which an agent attempts to learn appropriate actions to maximize its long-term average reward). We show that these direct…

Machine Learning · Computer Science 2019-11-19 Peter L. Bartlett , Jonathan Baxter

Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As…

Disordered Systems and Neural Networks · Physics 2011-11-09 Pan Zhang , Yong Chen

A fundamental aspect of learning in biological neural networks is the plasticity property which allows them to modify their configurations during their lifetime. Hebbian learning is a biologically plausible mechanism for modeling the…

Neural and Evolutionary Computing · Computer Science 2021-03-16 Anil Yaman , Giovanni Iacca , Decebal Constantin Mocanu , Matt Coler , George Fletcher , Mykola Pechenizkiy

We study the efficiency of synchronization in ensembles of identical coupled stochastic oscillator systems. By deriving a chemical Langevin equation, we measure the rate at which the systems synchronize. The rate at which the difference in…

Subcellular Processes · Quantitative Biology 2015-04-03 G. Reenaroy Devi , R. K. Brojen Singh , Ram Ramaswamy

The Dense Associative Memory generalizes the Hopfield network by allowing for sharper interaction functions. This increases the capacity of the network as an autoassociative memory as nearby learned attractors will not interfere with one…

Neural and Evolutionary Computing · Computer Science 2024-09-24 Hayden McAlister , Anthony Robins , Lech Szymanski

Recent works have highlighted the need for a new dynamical paradigm in the modeling of brain function and evolution. Specifically, these models should incorporate non-constant and asymmetric synaptic weights $T_{ij}$ in the neuron-neuron…

Neurons and Cognition · Quantitative Biology 2025-11-03 Franco Cardin , Alberto Lovison , Amos Maritan , Aram Megighian

We study the effect of competition between short-term synaptic depression and facilitation on the dynamical properties of attractor neural networks, using Monte Carlo simulation and a mean field analysis. Depending on the balance between…

Neurons and Cognition · Quantitative Biology 2007-05-23 J. J. Torres , J. M. Cortes , J. Marro , H. J. Kappen

We introduce a model of generalized Hebbian learning and retrieval in oscillatory neural networks modeling cortical areas such as hippocampus and olfactory cortex. Recent experiments have shown that synaptic plasticity depends on spike…

Disordered Systems and Neural Networks · Physics 2007-05-23 Silvia Scarpetta , Zhaoping Li , John Hertz

Hippocampal place and time cells encode spatial and temporal aspects of experience. Both have the same neural substrate, but have been modeled as having different functions and mechanistic origins, place cells as continuous attractors, and…

Neurons and Cognition · Quantitative Biology 2026-04-02 Qiaorong S. Yu , Zhaoze Wang , Vijay Balasubramanian

Neural populations exhibit latent dynamical structures that drive time-evolving spiking activities, motivating the search for models that capture both intrinsic network dynamics and external unobserved influences. In this work, we introduce…

Machine Learning · Computer Science 2026-03-11 Yue Song , T. Anderson Keller , Yisong Yue , Pietro Perona , Max Welling