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A ternary/binary data coding algorithm and conditions under which Hopfield networks implement optimal convolutional or Hamming decoding algorithms has been described. Using the coding/decoding approach (an optimal Binary Signal Detection…

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

On the basis of convolutional (Hamming) version of recent Neural Network Assembly Memory Model (NNAMM) for intact two-layer autoassociative Hopfield network optimal receiver operating characteristics (ROCs) have been derived analytically. A…

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

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

The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…

Neural and Evolutionary Computing · Computer Science 2018-10-30 Alberto Fachechi , Elena Agliari , Adriano Barra

Dense Associative Memories or Modern Hopfield Networks have many appealing properties of associative memory. They can do pattern completion, store a large number of memories, and can be described using a recurrent neural network with a…

Neural and Evolutionary Computing · Computer Science 2021-07-29 Dmitry Krotov

Associative memory architectures are designed for memorization but also offer, through their retrieval method, a form of generalization to unseen inputs: stored memories can be seen as prototypes from this point of view. Focusing on Modern…

Machine Learning · Computer Science 2023-11-14 Matan Abudy , Nur Lan , Emmanuel Chemla , Roni Katzir

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

Associative memory models are content-addressable memory systems fundamental to biological intelligence and are notable for their high interpretability. However, existing models evaluate the quality of retrieval based on proximity, which…

Machine Learning · Computer Science 2025-11-26 Shurong Wang , Yuqi Pan , Zhuoyang Shen , Meng Zhang , Hongwei Wang , Guoqi Li

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

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

We present a Hopfield-like autoassociative network for memories representing examples of concepts. Each memory is encoded by two activity patterns with complementary properties. The first is dense and correlated across examples within…

Neurons and Cognition · Quantitative Biology 2023-08-28 Louis Kang , Taro Toyoizumi

We present an algorithm to store binary memories in a Hopfield neural network using minimum probability flow, a recent technique to fit parameters in energy-based probabilistic models. In the case of memories without noise, our algorithm…

Adaptation and Self-Organizing Systems · Physics 2015-05-21 Christopher Hillar , Jascha Sohl-Dickstein , Kilian Koepsell

The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological…

Disordered Systems and Neural Networks · Physics 2022-04-19 Miriam Aquaro , Francesco Alemanno , Ido Kanter , Fabrizio Durante , Elena Agliari , Adriano Barra

Dense Associative Memories or modern Hopfield networks permit storage and reliable retrieval of an exponentially large (in the dimension of feature space) number of memories. At the same time, their naive implementation is non-biological,…

Neurons and Cognition · Quantitative Biology 2021-04-29 Dmitry Krotov , John Hopfield

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 the problem of learning associative memory -- a system which is able to retrieve a remembered pattern based on its distorted or incomplete version. Attractor networks provide a sound model of associative memory: patterns are stored…

Machine Learning · Statistics 2021-04-21 Sergey Bartunov , Jack W Rae , Simon Osindero , Timothy P Lillicrap

We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical…

Disordered Systems and Neural Networks · Physics 2009-10-31 Masaki Nomura , Toshio Aoyagi

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

Associative memory retrieves complete patterns from partial or corrupted inputs and constitutes a primitive form of generative inference. Classical Hopfield networks (CHN) provide a canonical framework for associative memory but suffer from…

Sequence memory is an essential attribute of natural and artificial intelligence that enables agents to encode, store, and retrieve complex sequences of stimuli and actions. Computational models of sequence memory have been proposed where…

Neural and Evolutionary Computing · Computer Science 2023-11-06 Hamza Tahir Chaudhry , Jacob A. Zavatone-Veth , Dmitry Krotov , Cengiz Pehlevan
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