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In neural network's Literature, Hebbian learning traditionally refers to the procedure by which the Hopfield model and its generalizations store archetypes (i.e., definite patterns that are experienced just once to form the synaptic…

Disordered Systems and Neural Networks · Physics 2024-02-21 Francesco Alemanno , Miriam Aquaro , Ido Kanter , Adriano Barra , Elena Agliari

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

The Hebbian unlearning algorithm, i.e. an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron. We…

Disordered Systems and Neural Networks · Physics 2022-03-15 Marco Benedetti , Enrico Ventura , Enzo Marinari , Giancarlo Ruocco , Francesco Zamponi

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

This paper introduces a novel unsupervised learning paradigm inspired by Gerald Edelman's theory of neuronal group selection ("Neural Darwinism"). The presented automaton learns to recognize arbitrary symbols (e.g., letters of an alphabet)…

Neural and Evolutionary Computing · Computer Science 2023-12-01 Mario Stepanik

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

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

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

Unsupervised learning of hidden representations has been one of the most vibrant research directions in machine learning in recent years. In this work we study the brain-like Bayesian Confidence Propagating Neural Network (BCPNN) model,…

Neural and Evolutionary Computing · Computer Science 2021-04-19 Naresh Balaji Ravichandran , Anders Lansner , Pawel Herman

Networks in machine learning offer examples of complex high-dimensional dynamical systems reminiscent of biological systems. Here, we study the learning dynamics of Generalized Hopfield networks, which permit a visualization of internal…

Disordered Systems and Neural Networks · Physics 2023-12-07 Nacer Eddine Boukacem , Allen Leary , Robin Thériault , Felix Gottlieb , Madhav Mani , Paul François

The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we…

Disordered Systems and Neural Networks · Physics 2023-05-01 Matteo Negri , Clarissa Lauditi , Gabriele Perugini , Carlo Lucibello , Enrico Malatesta

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

We present a nonparametric interpretation for deep learning compatible modern Hopfield models and utilize this new perspective to debut efficient variants. Our key contribution stems from interpreting the memory storage and retrieval…

Machine Learning · Statistics 2025-06-10 Jerry Yao-Chieh Hu , Bo-Yu Chen , Dennis Wu , Feng Ruan , Han Liu

Statistical mechanics has made significant contributions to the study of biological neural systems by modeling them as recurrent networks of interconnected units with adjustable interactions. Several algorithms have been proposed to…

Disordered Systems and Neural Networks · Physics 2024-03-06 Enrico Ventura

Unsupervised deep learning is one of the most powerful representation learning techniques. Restricted Boltzman machine, sparse coding, regularized auto-encoders, and convolutional neural networks are pioneering building blocks of deep…

Machine Learning · Computer Science 2014-01-06 Xiao-Lei Zhang

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 an unsupervised learning framework for decomposing images into layers of automatically discovered object models. Contrary to recent approaches that model image layers with autoencoder networks, we represent them as explicit…

Computer Vision and Pattern Recognition · Computer Science 2021-08-24 Tom Monnier , Elliot Vincent , Jean Ponce , Mathieu Aubry

Unsupervised learning methods have a soft inspiration in cognition models. To this day, the most successful unsupervised learning methods revolve around clustering samples in a mathematical space. In this paper we propose a primitive-based,…

Artificial Intelligence · Computer Science 2025-07-04 Alfredo Ibias , Hector Antona , Guillem Ramirez-Miranda , Enric Guinovart , Eduard Alarcon

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

Among the performance-enhancing procedures for Hopfield-type networks that implement associative memory, Hebbian Unlearning (or dreaming) strikes for its simplicity and its clear biological interpretation. Yet, it does not easily lend…

Disordered Systems and Neural Networks · Physics 2023-08-28 Marco Benedetti , Louis Carillo , Enzo Marinari , Marc Mèzard
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