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Related papers: Some rigorous results for the Hopfield Model

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Federated learning is a distributed, privacy-aware learning scenario which trains a single model on data belonging to several clients. Each client trains a local model on its data and the local models are then aggregated by a central party.…

Machine Learning · Computer Science 2020-01-01 Hesham Mostafa

We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. We show that there exists a regime of…

Machine Learning · Computer Science 2012-02-20 Uri Heinemann , Amir Globerson

We show that a straightforward extension of a simple learning model based on the Hebb rule, the previously introduced Association-Reinforcement-Hebb-Rule, can cope with "delayed", unspecific reinforcement also in the case of structured data…

Condensed Matter · Physics 2009-10-31 M. Biehl , R. Kuehn , I. -O. Stamatescu

In forecasting multiple time series, accounting for the individual features of each sequence can be challenging. To address this, modern deep learning methods for time series analysis combine a shared (global) model with local layers,…

Machine Learning · Computer Science 2025-02-14 Luca Butera , Giovanni De Felice , Andrea Cini , Cesare Alippi

This paper continues the study of metastable behaviour in disordered mean field models initiated in [2], [3]. We consider the generalized Hopfield model with finitely many independent patterns $\xi_1,...,\xi_p$ where the patterns have…

Probability · Mathematics 2009-04-27 Mykhaylo Shkolnikov

We study a neural network model in which both neurons and synaptic interactions evolve in time simultaneously. The time evolution of synaptic interactions is described by a Langevin equation including a Hebbian learning term, and a bias…

Biological Physics · Physics 2009-03-12 T. Uezu , K. Abe , S. Miyoshi , M. Okada

We study a new form of federated learning where the clients train personalized local models and make predictions jointly with the server-side shared model. Using this new federated learning framework, the complexity of the central shared…

Machine Learning · Computer Science 2020-03-31 Alekh Agarwal , John Langford , Chen-Yu Wei

The meaning of a word often varies depending on its usage in different domains. The standard word embedding models struggle to represent this variation, as they learn a single global representation for a word. We propose a method to learn…

Computation and Language · Computer Science 2019-10-22 Lahari Poddar , Gyorgy Szarvas , Lea Frermann

We study associative memory of an oscillator neural network with distributed native frequencies. The model is based on the use of the Hebb learning rule with random patterns ($\xi_i^{\mu}=\pm 1$), and the distribution function of native…

Disordered Systems and Neural Networks · Physics 2009-10-31 Michiko Yamana , Masatoshi Shiino , Masahiko Yoshioka

Continual Learning research typically focuses on tackling the phenomenon of catastrophic forgetting in neural networks. Catastrophic forgetting is associated with an abrupt loss of knowledge previously learned by a model when the task, or…

Machine Learning · Computer Science 2022-04-06 MohammadReza Davari , Nader Asadi , Sudhir Mudur , Rahaf Aljundi , Eugene Belilovsky

Representation and learning of long-range dependencies is a central challenge confronted in modern applications of machine learning to sequence data. Yet despite the prominence of this issue, the basic problem of measuring long-range…

Machine Learning · Statistics 2019-06-10 Alexander Greaves-Tunnell , Zaid Harchaoui

We investigate the influence of different kinds of structure on the learning behaviour of a perceptron performing a classification task defined by a teacher rule. The underlying pattern distribution is permitted to have spatial…

Disordered Systems and Neural Networks · Physics 2009-10-31 G. Dirscherl , B. Schottky , U. Krey

Large language models demonstrate remarkable ability in factual recall, yet the fundamental limits of storing and retrieving input--output associations with neural networks remain unclear. We study these limits in a minimal setting: a…

Machine Learning · Statistics 2026-05-12 Alessio Giorlandino , Sebastian Goldt , Antoine Maillard

We extend the existing work on Hopfield network state classification, employing more complex models that remain interpretable, such as densely-connected feed-forward deep neural networks and support vector machines. The states of the…

Machine Learning · Computer Science 2025-03-06 Hayden McAlister , Anthony Robins , Lech Szymanski

We consider Hopfield networks, where neurons interact pair-wise by Hebbian couplings built over $i$. a set of definite patterns (ground truths), $ii$. a sample of labeled examples (supervised setting), $iii$. a sample of unlabeled examples…

Disordered Systems and Neural Networks · Physics 2025-10-16 Elena Agliari , Alberto Fachechi , Domenico Luongo

We propose and analyze a new variation of the so-called {\em exponential Hopfield model}, a recently introduced family of associative neural networks with unprecedented storage capacity. Our construction is based on a cost function defined…

Disordered Systems and Neural Networks · Physics 2025-09-09 Linda Albanese , Andrea Alessandrelli , Adriano Barra , Peter Sollich

It has been observed that neural networks perform poorly when the data or tasks are presented sequentially. Unlike humans, neural networks suffer greatly from catastrophic forgetting, making it impossible to perform life-long learning. To…

Machine Learning · Computer Science 2023-01-31 Longhui Yu , Tianyang Hu , Lanqing Hong , Zhen Liu , Adrian Weller , Weiyang Liu

Recently a daily routine for associative neural networks has been proposed: the network Hebbian-learns during the awake state (thus behaving as a standard Hopfield model), then, during its sleep state, optimizing information storage, it…

Disordered Systems and Neural Networks · Physics 2020-01-29 Elena Agliari , Francesco Alemanno , Adriano Barra , Alberto Fachechi

Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for…

Mathematical Physics · Physics 2017-08-02 Elena Agliari , Adriano Barra , Chiara Longo , Daniele Tantari

With the tremendous success of deep learning in visual tasks, the representations extracted from intermediate layers of learned models, that is, deep features, attract much attention of researchers. Previous empirical analysis shows that…

Computer Vision and Pattern Recognition · Computer Science 2020-03-31 Qi Qian , Juhua Hu , Hao Li