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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

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

Equilibrium propagation has been proposed as a biologically plausible alternative to the backpropagation algorithm. The local nature of gradient computations, combined with the use of convergent RNNs to reach equilibrium states, make this…

Neural and Evolutionary Computing · Computer Science 2026-03-19 Sankar Vinayak Elayedam , Gopalakrishnan Srinivasan

An inverse procedure is proposed and tested which aims at recovering the a priori unknown functional and structural information from global signals of living brains activity. To this end we consider a Leaky-Integrate and Fire (LIF) model…

The network reconstruction task aims to estimate a complex system's structure from various data sources such as time series, snapshots, or interaction counts. Recent work has examined this problem in networks whose relationships involve…

Social and Information Networks · Computer Science 2023-12-05 Simon Lizotte , Jean-Gabriel Young , Antoine Allard

Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists…

Statistical Mechanics · Physics 2015-05-19 Adriano Barra , Elena Agliari

We study the synchronous dynamics of the Hopfield model when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. We use a generating functional technique to derive analytical expressions for the order parameters…

Disordered Systems and Neural Networks · Physics 2007-05-23 Manoranjan P. Singh

We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates…

Probability · Mathematics 2024-07-10 Anton Bovier , Frank den Hollander , Saeda Marello , Elena Pulvirenti , Martin Slowik

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

Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those…

Restricted Boltzmann Machines are described by the Gibbs measure of a bipartite spin glass, which in turn corresponds to the one of a generalised Hopfield network. This equivalence allows us to characterise the state of these systems in…

Disordered Systems and Neural Networks · Physics 2018-02-28 Adriano Barra , Giuseppe Genovese , Peter Sollich , Daniele Tantari

In this paper, we study retrievability of admissible cycles and the dynamics of the networks constructed from admissible cycles with the pseudoinverse learning rule. Retrievability of admissible cycles in networks with $C_0>0$ and $\lambda$…

Dynamical Systems · Mathematics 2014-08-22 Chuan Zhang , Gerhard Dangelmayr , Iuliana Oprea

An inverse procedure is developed and tested to recover functional and structural information from global signals of brains activity. The method assumes a leaky-integrate and fire model with excitatory and inhibitory neurons, coupled via a…

The Hopfield network serves as a fundamental energy-based model in machine learning, capturing memory retrieval dynamics through an ordinary differential equation (ODE). The model's output, the equilibrium point of the ODE, is traditionally…

Machine Learning · Computer Science 2024-08-22 Cédric Goemaere , Johannes Deleu , Thomas Demeester

In this work we study numerically the out of equilibrium dynamics of the Hopfield model for associative memory inside its spin-glass phase. Besides its interest as a neural network model it can also be considered as a prototype of fully…

Disordered Systems and Neural Networks · Physics 2009-10-31 M. A. Montemurro , F. A. Tamarit , D. A. Stariolo , S. A. Cannas

The retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks are derived and studied in replica-symmetric mean-field theory generalizing earlier works on either the fully connected or the symmetrical…

Disordered Systems and Neural Networks · Physics 2009-11-07 W. K. Theumann , R. Erichsen

The Hopfield network (HN) is a classical model of associative memory whose dynamics are closely related to the Ising spin system with 2-body interactions. Stored patterns are encoded as minima of an energy function shaped by a Hebbian…

Applied Physics · Physics 2025-09-23 Marco Cafiso , Paolo Paradisi

Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the…

Disordered Systems and Neural Networks · Physics 2024-06-12 Ángel Poc-López , Miguel Aguilera

Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network…

Neurons and Cognition · Quantitative Biology 2016-02-17 Alireza Alemi , Carlo Baldassi , Nicolas Brunel , Riccardo Zecchina

We analyze a variant of the Hopfield model that incorporates an unlearning mechanism based on spin correlations in the high-temperature regime. In the large system limit where extensively many patterns are stored, we employ the replica…

Disordered Systems and Neural Networks · Physics 2026-02-10 Shuta Takeuchi , Takashi Takahashi , Yoshiyuki Kabashima