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The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according to the Hebb rule from the set of memorized patterns which are treated as distorted copies of the…

Disordered Systems and Neural Networks · Physics 2009-10-31 Leonid B. Litinskii

A recurrent neural network model storing multiple spatial maps, or ``charts'', is analyzed. A network of this type has been suggested as a model for the origin of place cells in the hippocampus of rodents. The extremely diluted and fully…

Disordered Systems and Neural Networks · Physics 2009-10-31 Francesco P. Battaglia , Alessandro Treves

This paper presents a neural network model (associative memory model) for memory and recall of images. In this model, only a single neuron can memorize multi-images and when that neuron is activated, it is possible to recall all the…

Neural and Evolutionary Computing · Computer Science 2025-10-09 Hiroshi Inazawa

A set of fixed points of the Hopfield type neural network is under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…

Disordered Systems and Neural Networks · Physics 2007-05-23 Leonid B. Litinsky

Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…

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

We introduce a model of generalized Hebbian learning and retrieval in oscillatory neural networks modeling cortical areas such as hippocampus and olfactory cortex. Recent experiments have shown that synaptic plasticity depends on spike…

Disordered Systems and Neural Networks · Physics 2007-05-23 Silvia Scarpetta , Zhaoping Li , John Hertz

For the Hopfield model with the Hebb connection matrix we investigate the case of $p$ memorized patterns that are distorted copies of the same {\it standard}. In other words, we try to simulate that learning always takes place by means of…

Disordered Systems and Neural Networks · Physics 2007-05-23 L. B. Litinskii

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

The organizational principles behind the connectivity of a complex network are known to influence its behavior. In this work we investigate, using the Hopfield model, the influence of the network architecture on the performance for…

Disordered Systems and Neural Networks · Physics 2007-05-23 E. P. Rodrigues , M. S. Barbosa , L. da F. Costa

The brain is targeted for processing temporal sequence information. It remains largely unclear how the brain learns to store and retrieve sequence memories. Here, we study how recurrent networks of binary neurons learn sequence attractors…

Neural and Evolutionary Computing · Computer Science 2024-04-04 Yao Lu , Si Wu

In this work we introduce a multi-species generalization of the Hopfield model for associative memory, where neurons are divided into groups and both inter-groups and intra-groups pair-wise interactions are considered, with different…

Disordered Systems and Neural Networks · Physics 2018-07-11 Elena Agliari , Danila Migliozzi , Daniele Tantari

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

Hopfield networks are an attractive choice for solving many types of computational problems because they provide a biologically plausible mechanism. The Self-Optimization (SO) model adds to the Hopfield network by using a biologically…

Adaptation and Self-Organizing Systems · Physics 2024-03-06 Natalya Weber , Werner Koch , Ozan Erdem , Tom Froese

Associative memories in the brain receive and store patterns of activity registered by the sensory neurons, and are able to retrieve them when necessary. Due to their importance in human intelligence, computational models of associative…

Machine Learning · Computer Science 2021-09-17 Tommaso Salvatori , Yuhang Song , Yujian Hong , Simon Frieder , Lei Sha , Zhenghua Xu , Rafal Bogacz , Thomas Lukasiewicz

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

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

Evolution and its intelligence element present thrill and challenges in its exploration. Yet, how species have memory, retrieve them and maintain continuity are the fundamental questions. Most of the phenomenon can only be hypothesised by…

Neurons and Cognition · Quantitative Biology 2024-07-09 Anil Kumar Sharma , Asha Sharma

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

We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…

Analysis of PDEs · Mathematics 2020-09-03 Delphine Salort , Nicolas Torres

Information processing in certain neuronal networks in the brain can be considered as a map of binary vectors, where ones (spikes) and zeros (no spikes) of input neurons are transformed into spikes and no spikes of output neurons. A simple…

Neurons and Cognition · Quantitative Biology 2013-12-05 Andrey Olypher , Jean Vaillant