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Understanding the memory capacity of neural networks remains a challenging problem in implementing artificial intelligence systems. In this paper, we address the notion of capacity with respect to Hopfield networks and propose a dynamic…

Neural and Evolutionary Computing · Computer Science 2017-09-19 Saarthak Sarup , Mingoo Seok

Artificial neural networks are a popular and effective machine learning technique. Great progress has been made parallelizing the expensive training phase of an individual network, leading to highly specialized pieces of hardware, many…

Numerical Analysis · Computer Science 2017-10-03 Jacob B. Schroder

We show how a Hopfield network with modifiable recurrent connections undergoing slow Hebbian learning can extract the underlying geometry of an input space. First, we use a slow/fast analysis to derive an averaged system whose dynamics…

Neurons and Cognition · Quantitative Biology 2011-02-02 Mathieu N. Galtier , Olivier D. Faugeras , Paul C. Bressloff

A fundamental task for artificial intelligence is learning. Deep Neural Networks have proven to cope perfectly with all learning paradigms, i.e. supervised, unsupervised, and reinforcement learning. Nevertheless, traditional deep learning…

Artificial Intelligence · Computer Science 2021-03-03 Decebal Constantin Mocanu , Elena Mocanu , Tiago Pinto , Selima Curci , Phuong H. Nguyen , Madeleine Gibescu , Damien Ernst , Zita A. Vale

Traditionally, distributed machine learning takes the guise of (i) different nodes training the same model (as in federated learning), or (ii) one model being split among multiple nodes (as in distributed stochastic gradient descent). In…

Networking and Internet Architecture · Computer Science 2022-07-07 Francesco Malandrino , Carla Fabiana Chiasserini

Unsupervised learning in a generalized Hopfield associative-memory network is investigated in this work. First, we prove that the (generalized) Hopfield model is equivalent to a semi-restricted Boltzmann machine with a layer of visible…

Neural and Evolutionary Computing · Computer Science 2017-07-26 Huiling Zhen , Shang-Nan Wang , Hai-Jun Zhou

We consider dense, associative neural-networks trained by a teacher (i.e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo…

Disordered Systems and Neural Networks · Physics 2023-08-16 Elena Agliari , Linda Albanese , Francesco Alemanno , Andrea Alessandrelli , Adriano Barra , Fosca Giannotti , Daniele Lotito , Dino Pedreschi

Multi-task learning aims to learn multiple tasks jointly by exploiting their relatedness to improve the generalization performance for each task. Traditionally, to perform multi-task learning, one needs to centralize data from all the tasks…

Machine Learning · Computer Science 2017-06-21 Sulin Liu , Sinno Jialin Pan , Qirong Ho

In this work we approach attractor neural networks from a machine learning perspective: we look for optimal network parameters by applying a gradient descent over a regularized loss function. Within this framework, the optimal…

Machine Learning · Computer Science 2024-02-21 Elena Agliari , Francesco Alemanno , Miriam Aquaro , Alberto Fachechi

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. While sometimes the underlying task relationship structure is known, often the structure needs to be estimated from data…

The demand for artificial intelligence has grown significantly over the last decade and this growth has been fueled by advances in machine learning techniques and the ability to leverage hardware acceleration. However, in order to increase…

Machine Learning · Computer Science 2022-11-28 Joost Verbraeken , Matthijs Wolting , Jonathan Katzy , Jeroen Kloppenburg , Tim Verbelen , Jan S. Rellermeyer

Neural networks are supposed to recognise blurred images (or patterns) of $N$ pixels (bits) each. Application of the network to an initial blurred version of one of $P$ pre-assigned patterns should converge to the correct pattern. In the…

Statistical Mechanics · Physics 2009-11-07 Dietrich Stauffer , Amnon Aharony , Luciano da Fontoura Costa , Joan Adler

The common thread behind the recent Nobel Prize in Physics to John Hopfield and those conferred to Giorgio Parisi in 2021 and Philip Anderson in 1977 is disorder. Quoting Philip Anderson: "more is different". This principle has been…

Disordered Systems and Neural Networks · Physics 2025-10-16 Elena Agliari , Andrea Alessandrelli , Adriano Barra , Martino Salomone Centonze , Federico Ricci-Tersenghi

Multitask learning aims at solving a set of related tasks simultaneously, by exploiting the shared knowledge for improving the performance on individual tasks. Hence, an important aspect of multitask learning is to understand the…

Machine Learning · Computer Science 2019-10-22 Changjian Shui , Mahdieh Abbasi , Louis-Émile Robitaille , Boyu Wang , Christian Gagné

Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…

Machine Learning · Computer Science 2014-10-24 Jingbo Shang , Tianqi Chen , Hang Li , Zhengdong Lu , Yong Yu

Recently, the original storage prescription for the Hopfield model of neural networks -- as well as for its dense generalizations -- has been turned into a genuine Hebbian learning rule by postulating the expression of its Hamiltonian for…

Disordered Systems and Neural Networks · Physics 2024-10-04 Linda Albanese , Adriano Barra , Pierluigi Bianco , Fabrizio Durante , Diego Pallara

We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…

Disordered Systems and Neural Networks · Physics 2012-09-28 Elena Agliari , Lorenzo Asti , Adriano Barra , Raffaella Burioni , Guido Uguzzoni

We present scalable hybrid-parallel algorithms for training large-scale 3D convolutional neural networks. Deep learning-based emerging scientific workflows often require model training with large, high-dimensional samples, which can make…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-07-28 Yosuke Oyama , Naoya Maruyama , Nikoli Dryden , Erin McCarthy , Peter Harrington , Jan Balewski , Satoshi Matsuoka , Peter Nugent , Brian Van Essen

For four decades statistical physics has been providing a framework to analyse neural networks. A long-standing question remained on its capacity to tackle deep learning models capturing rich feature learning effects, thus going beyond the…

Machine Learning · Statistics 2025-12-15 Jean Barbier , Francesco Camilli , Minh-Toan Nguyen , Mauro Pastore , Rudy Skerk

Deep learning models trained on large data sets have been widely successful in both vision and language domains. As state-of-the-art deep learning architectures have continued to grow in parameter count so have the compute budgets and times…