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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

A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield…

Neural and Evolutionary Computing · Computer Science 2022-06-20 Beren Millidge , Tommaso Salvatori , Yuhang Song , Thomas Lukasiewicz , Rafal Bogacz

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

Auto-associative neural networks (e.g., the Hopfield model implementing the standard Hebbian prescription) serve as a foundational framework for pattern recognition and associative memory in statistical mechanics. However, their…

Disordered Systems and Neural Networks · Physics 2025-06-03 Elena Agliari , Andrea Alessandrelli , Adriano Barra , Martino Salomone Centonze , Federico Ricci-Tersenghi

Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological…

Machine Learning · Statistics 2023-11-20 Luca Ambrogioni

Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another…

Disordered Systems and Neural Networks · Physics 2024-02-14 Carlo Lucibello , Marc Mézard

We investigate how feature correlations influence the capacity of Dense Associative Memory (DAM), a Transformer attention-like model. Practical machine learning scenarios involve feature-correlated data and learn representations in the…

Machine Learning · Computer Science 2025-08-05 Stefan Bielmeier , Gerald Friedland

Humans excel at continually acquiring, consolidating, and retaining information from an ever-changing environment, whereas artificial neural networks (ANNs) exhibit catastrophic forgetting. There are considerable differences in the…

Neural and Evolutionary Computing · Computer Science 2023-04-17 Fahad Sarfraz , Elahe Arani , Bahram Zonooz

An important difference between brains and deep neural networks is the way they learn. Nervous systems learn online where a stream of noisy data points are presented in a non-independent, identically distributed (non-i.i.d.) way. Further,…

Neural and Evolutionary Computing · Computer Science 2023-07-28 Nick Alonso , Jeff Krichmar

It has been shown that a neural network model recently proposed to describe basic memory performance is based on a ternary/binary coding/decoding algorithm which leads to a new neural network assembly memory model (NNAMM) providing…

Artificial Intelligence · Computer Science 2007-05-23 Petro M. Gopych

Dense Associative Memories (DenseAMs) are generalizations of Hopfield networks, which have superior information storage capacity and can store training data points (memories) at local minima of the energy landscape. When the amount of…

Machine Learning · Computer Science 2026-03-18 Bao Pham , Gabriel Raya , Matteo Negri , Mohammed J. Zaki , Luca Ambrogioni , Dmitry Krotov

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been…

Machine Learning · Computer Science 2023-06-07 Bishwajit Saha , Dmitry Krotov , Mohammed J. Zaki , Parikshit Ram

In this study we introduce a novel energy functional for long-sequence memory, building upon the framework of dense Hopfield networks which achieves exponential storage capacity through higher-order interactions. Building upon earlier work…

Machine Learning · Computer Science 2025-07-03 Ahmed Farooq

Despite recent progress in memory augmented neural network (MANN) research, associative memory networks with a single external memory still show limited performance on complex relational reasoning tasks. Especially the content-based…

Machine Learning · Computer Science 2021-08-30 Taewon Park , Inchul Choi , Minho Lee

In neuroscience, classical Hopfield networks are the standard biologically plausible model of long-term memory, relying on Hebbian plasticity for storage and attractor dynamics for recall. In contrast, memory-augmented neural networks in…

Neurons and Cognition · Quantitative Biology 2021-10-28 Danil Tyulmankov , Ching Fang , Annapurna Vadaparty , Guangyu Robert Yang

This article delves into the Hopfield neural network model, drawing inspiration from biological neural systems. The exploration begins with an overview of the model's foundations, incorporating insights from mechanical statistics to deepen…

Disordered Systems and Neural Networks · Physics 2024-10-29 Matteo Silvestri

The Hopfield network model and its generalizations were introduced as a model of associative, or content-addressable, memory. They were widely investigated both as an unsupervised learning method in artificial intelligence and as a model of…

Neurons and Cognition · Quantitative Biology 2024-12-10 Marco Cafiso , Paolo Paradisi

The innate capacity of humans and other animals to learn a diverse, and often interfering, range of knowledge and skills throughout their lifespan is a hallmark of natural intelligence, with obvious evolutionary motivations. In parallel,…

Machine Learning · Computer Science 2021-12-30 David McCaffary

Learning to remember long sequences remains a challenging task for recurrent neural networks. Register memory and attention mechanisms were both proposed to resolve the issue with either high computational cost to retain memory…

Artificial Intelligence · Computer Science 2017-10-04 Wei Zhang , Bowen Zhou

Heretofore, neural networks with external memory are restricted to single memory with lossy representations of memory interactions. A rich representation of relationships between memory pieces urges a high-order and segregated relational…

Machine Learning · Computer Science 2020-06-12 Hung Le , Truyen Tran , Svetha Venkatesh