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Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an…

Biological Physics · Physics 2021-06-07 Oskar H Schnaack , Luca Peliti , Armita Nourmohammad

Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its…

Disordered Systems and Neural Networks · Physics 2025-10-29 Kazushi Mimura , Jun'ichi Takeuchi , Yuto Sumikawa , Yoshiyuki Kabashima , Anthony C. C. Coolen

The Hopfield model is a pioneering neural network model with associative memory retrieval. The analytical solution of the model in mean field limit revealed that memories can be retrieved without any error up to a finite storage capacity of…

Disordered Systems and Neural Networks · Physics 2017-10-31 Do-Hyun Kim , Jinha Park , B. Kahng

Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require…

Machine Learning · Computer Science 2024-11-01 Benjamin Hoover , Duen Horng Chau , Hendrik Strobelt , Parikshit Ram , Dmitry Krotov

We generalize the standard Hopfield model to the case when a weight is assigned to each input pattern. The weight can be interpreted as the frequency of the pattern occurrence at the input of the network. In the framework of the statistical…

Disordered Systems and Neural Networks · Physics 2012-05-07 Iakov Karandashev , Boris Kryzhanovsky , Leonid Litinskii

Associative memory, a form of content-addressable memory, facilitates information storage and retrieval in many biological and physical systems. In statistical mechanics models, associative memory at equilibrium is represented through…

Disordered Systems and Neural Networks · Physics 2022-03-08 Agnish Kumar Behera , Madan Rao , Srikanth Sastry , Suriyanarayanan Vaikuntanathan

The Hopfield model describes a neural network that stores memories using all-to-all-coupled spins. Memory patterns are recalled under equilibrium dynamics. Storing too many patterns breaks the associative recall process because frustration…

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

While Hopfield networks are known as paradigmatic models for memory storage and retrieval, modern artificial intelligence systems mainly stand on the machine learning paradigm. We show that it is possible to formulate a teacher-student…

Disordered Systems and Neural Networks · Physics 2024-01-02 Francesco Alemanno , Luca Camanzi , Gianluca Manzan , Daniele Tantari

Content-addressable memories such as Modern Hopfield Networks (MHN) have been studied as mathematical models of auto-association and storage/retrieval in the human declarative memory, yet their practical use for large-scale content storage…

Machine Learning · Computer Science 2024-11-01 Satyananda Kashyap , Niharika S. D'Souza , Luyao Shi , Ken C. L. Wong , Hongzhi Wang , Tanveer Syeda-Mahmood

Neural networks are supposed to recognise blurred images (or patterns) of $N$ pixels (bits) each. Application of the network to an initial blurred version of one of $P$ pre-assigned patterns should converge to the correct pattern. In the…

Statistical Mechanics · Physics 2009-11-07 Dietrich Stauffer , Amnon Aharony , Luciano da Fontoura Costa , Joan Adler

Associative memories are structures that store data in such a way that it can later be retrieved given only a part of its content -- a sort-of error/erasure-resilience property. They are used in applications ranging from caches and memory…

Information Theory · Computer Science 2013-04-23 Vincent Gripon , Michael Rabbat

Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This…

Neural and Evolutionary Computing · Computer Science 2017-09-05 V. I. Gritsenko , D. A. Rachkovskij , A. A. Frolov , R. Gayler , D. Kleyko , E. Osipov

To improve the storage capacity of the Hopfield model, we develop a version of the dreaming algorithm that perpetually reinforces the patterns to be stored (as in the Hebb rule), and erases the spurious memories (as in dreaming algorithms).…

Disordered Systems and Neural Networks · Physics 2025-06-03 Ludovica Serricchio , Dario Bocchi , Claudio Chilin , Raffaele Marino , Matteo Negri , Chiara Cammarota , Federico Ricci-Tersenghi

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

The standard model of memory consolidation foresees that memories are initially recorded in the hippocampus, while features that capture higher-level generalisations of data are created in the cortex, where they are stored for a possibly…

Neurons and Cognition · Quantitative Biology 2017-06-20 Alessandro Fontana

Being hit by a ball is usually not a pleasant experience. While a ball may not be fatal, other objects can be. To protect themselves, many organisms, from humans to insects, have developed neuronal mechanisms to signal approaching objects…

Neurons and Cognition · Quantitative Biology 2025-03-17 Matthias S. Keil

In this paper, we propose a deep convolutional neural network for learning the embeddings of images in order to capture the notion of visual similarity. We present a deep siamese architecture that when trained on positive and negative pairs…

Computer Vision and Pattern Recognition · Computer Science 2019-01-14 Rishab Sharma , Anirudha Vishvakarma

We consider the class of Hopfield models of associative memory with activation function $F$ and state space $\{-1,1\}^N$, where each vertex of the cube describes a configuration of $N$ binary neurons. $M$ randomly chosen configurations,…

Probability · Mathematics 2025-04-08 Véronique Gayrard

In existing image classification systems that use deep neural networks, the knowledge needed for image classification is implicitly stored in model parameters. If users want to update this knowledge, then they need to fine-tune the model…

Computer Vision and Pattern Recognition · Computer Science 2022-08-01 Kengo Nakata , Youyang Ng , Daisuke Miyashita , Asuka Maki , Yu-Chieh Lin , Jun Deguchi