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Characterising optical quantum states is essential for the development of quantum technologies. While traditional approaches to perform full quantum state tomography are often experimentally demanding, neuromorphic architectures may provide…

Based on recent work by Gripon and Berrou, we introduce a new model of an associative memory. We show that this model has an efficiency bounded away from 0 and is therefore significantly more effective than the well known Hopfield model. We…

Probability · Mathematics 2014-11-06 Judith Heusel , Matthias Löwe , Franck Vermet

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 dilutely filled $N$-site optical lattice near zero temperature within a high-$Q$ multimode cavity can be mapped to a spin ensemble with tailorable interactions at all length scales. The effective full site to site interaction matrix can…

Quantum Physics · Physics 2017-03-15 Valentin Torggler , Sebastian Krämer , Helmut Ritsch

Quantum-memory models often reduce complex level structures to an idealized $\Lambda$ system, potentially missing nearby levels and unwanted couplings that can qualitatively alter the predicted performance. Here, we study an extension of a…

Quantum Physics · Physics 2026-05-04 Jia-Wei Ji , Christoph Simon

Operation of the array of coupled oscillators underlying the associative memory function is demonstrated for various interconnection schemes (cross-connect, star phase keying and star frequency keying) and various physical implementation of…

Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are…

Neurons and Cognition · Quantitative Biology 2025-09-03 Simone Betteti , Giacomo Baggio , Francesco Bullo , Sandro Zampieri

In this article, we propose a variational inference formulation of auto-associative memories, allowing us to combine perceptual inference and memory retrieval into the same mathematical framework. In this formulation, the prior probability…

Machine Learning · Computer Science 2022-10-18 Louis Annabi , Alexandre Pitti , Mathias Quoy

We have entered the Noisy Intermediate-Scale Quantum Era. A plethora of quantum processor prototypes allow evaluation of potential of the Quantum Computing paradigm in applications to pressing computational problems of the future. Growing…

High Energy Physics - Experiment · Physics 2019-11-14 Illya Shapoval , Paolo Calafiura

Quantum computing allows for the potential of significant advancements in both the speed and the capacity of widely used machine learning techniques. Here we employ quantum algorithms for the Hopfield network, which can be used for pattern…

Quantum Physics · Physics 2018-10-10 Patrick Rebentrost , Thomas R. Bromley , Christian Weedbrook , Seth Lloyd

The modern Hopfield network, proposed by Krotov and Hopfield, is a mathematical generalization of the Hopfield network, which is a basic model of associative memory that employs higher-order interactions. This study introduces an open…

Quantum Physics · Physics 2025-08-21 Takeshi Kimura , Kohtaro Kato

We introduce the Dreaming $L$-directional Associative Memory (DLAM), a multi-layer Hebbian architecture in which off-line dreaming and supervised heteroassociative coupling coexist within a single energy function, placing our approach…

Disordered Systems and Neural Networks · Physics 2026-05-14 Adriano Barra , Fabrizio Durante , Andrea Ladiana , Michela Marra Solazzo

Circuit quantum electrodynamics, consisting of superconducting artificial atoms coupled to on-chip resonators, represents a prime candidate to implement the scalable quantum computing architecture because of the presence of good tunability…

Quantum Physics · Physics 2015-03-03 T. H. Kyaw , S. Felicetti , G. Romero , E. Solano , L. -C. Kwek

Brain-inspired computing aims to mimic cognitive functions like associative memory, the ability to recall complete patterns from partial cues. Memristor technology offers promising hardware for such neuromorphic systems due to its potential…

Machine Learning · Computer Science 2025-05-20 Chengping He , Mingrui Jiang , Keyi Shan , Szu-Hao Yang , Zefan Li , Shengbo Wang , Giacomo Pedretti , Jim Ignowski , Can Li

We show that a coherent network of lasers exhibits emergent neural computing capabilities. The proposed scheme is built on harnessing the collective behavior of laser networks for storing a number of phase patterns as stable fixed points of…

Optics · Physics 2022-04-06 Mohammad-Ali Miri , Vinod Menon

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

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

The Hopfield model provides a paradigmatic framework for associative memory. Its classical implementation, based on the Hebbian learning rule, suffers from catastrophic forgetting: when one attempts storing too many patterns, the network…

Disordered Systems and Neural Networks · Physics 2026-03-11 Enzo Marinari , Saverio Rossi , Francesco Zamponi

In [7] Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory. In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the…

Probability · Mathematics 2017-07-03 Mete Demircigil , Judith Heusel , Matthias Löwe , Sven Upgang , Franck Vermet

We study a class of Hopfield models where the memories are represented by a mixture of Gaussian and binary variables and the neurons are Ising spins. We study the properties of this family of models as the relative weight of the two kinds…

Disordered Systems and Neural Networks · Physics 2022-09-29 Luca Leuzzi , Alberto Patti , Federico Ricci-Tersenghi