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We review several of the most widely used techniques for training recurrent neural networks to approximate dynamical systems, then describe a novel algorithm for this task. The algorithm is based on an earlier theoretical result that…

Neural and Evolutionary Computing · Computer Science 2016-06-09 Adam Trischler , Gabriele MT D'Eleuterio

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

Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the…

Methodology · Statistics 2024-05-02 Andrew McInerney , Kevin Burke

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

The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically-coupled McCulloch-Pitts neurons interact to perform emergent computation. Although previous researchers have…

Adaptation and Self-Organizing Systems · Physics 2015-06-09 Christopher Hillar , Ngoc M. Tran

We consider the problem of neural association for a network of non-binary neurons. Here, the task is to first memorize a set of patterns using a network of neurons whose states assume values from a finite number of integer levels. Later,…

Neural and Evolutionary Computing · Computer Science 2013-02-18 Amir Hesam Salavati , K. Raj Kumar , Amin Shokrollahi

Introduction: Machine learning provides fundamental tools both for scientific research and for the development of technologies with significant impact on society. It provides methods that facilitate the discovery of regularities in data and…

Machine Learning · Computer Science 2019-03-12 Andrea Ceni , Peter Ashwin , Lorenzo Livi

The effectiveness of recurrent neural networks can be largely influenced by their ability to store into their dynamical memory information extracted from input sequences at different frequencies and timescales. Such a feature can be…

Machine Learning · Computer Science 2020-07-01 Antonio Carta , Alessandro Sperduti , Davide Bacciu

Despite success across diverse tasks, current artificial recurrent network architectures rely primarily on implicit hidden-state memories, limiting their interpretability and ability to model long-range dependencies. In contrast, biological…

Neural and Evolutionary Computing · Computer Science 2025-07-30 Daniel Szelogowski

A model of associative memory is studied, which stores and reliably retrieves many more patterns than the number of neurons in the network. We propose a simple duality between this dense associative memory and neural networks commonly used…

Neural and Evolutionary Computing · Computer Science 2017-03-28 Dmitry Krotov , John J Hopfield

Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the…

Neural and Evolutionary Computing · Computer Science 2014-12-19 Sharat C. Prasad , Piyush Prasad

This paper introduces a neural network model that learns multiple attributes as images and performs associated, sequential recall of the learned memories. Briefly, the model presented here is an associative memory model that extends…

Neural and Evolutionary Computing · Computer Science 2026-03-27 Hiroshi Inazawa

It is widely believed that deep neural networks contain layer specialization, wherein neural networks extract hierarchical features representing edges and patterns in shallow layers and complete objects in deeper layers. Unlike common…

Machine Learning · Computer Science 2022-03-04 Avi Schwarzschild , Arjun Gupta , Amin Ghiasi , Micah Goldblum , Tom Goldstein

Recurrent connections in the visual cortex are thought to aid object recognition when part of the stimulus is occluded. Here we investigate if and how recurrent connections in artificial neural networks similarly aid object recognition. We…

Computer Vision and Pattern Recognition · Computer Science 2019-09-12 Markus Roland Ernst , Jochen Triesch , Thomas Burwick

The brain must robustly store a large number of memories, corresponding to the many events encountered over a lifetime. However, the number of memory states in existing neural network models either grows weakly with network size or recall…

Neurons and Cognition · Quantitative Biology 2017-11-06 Rishidev Chaudhuri , Ila Fiete

Recurrent neural network is a powerful model that learns temporal patterns in sequential data. For a long time, it was believed that recurrent networks are difficult to train using simple optimizers, such as stochastic gradient descent, due…

Neural and Evolutionary Computing · Computer Science 2015-04-20 Tomas Mikolov , Armand Joulin , Sumit Chopra , Michael Mathieu , Marc'Aurelio Ranzato

Humans excel at continually acquiring, consolidating, and retaining information from an ever-changing environment, whereas artificial neural networks (ANNs) exhibit catastrophic forgetting. There are considerable differences in the…

Neural and Evolutionary Computing · Computer Science 2023-04-17 Fahad Sarfraz , Elahe Arani , Bahram Zonooz

Can neural networks learn goal-directed behaviour using similar strategies to the brain, by combining the relationships between the current state of the organism and the consequences of future actions? Recent work has shown that recurrent…

Neurons and Cognition · Quantitative Biology 2021-01-21 Justin Jude , Matthias H. Hennig

Training deep recurrent neural network (RNN) architectures is complicated due to the increased network complexity. This disrupts the learning of higher order abstracts using deep RNN. In case of feed-forward networks training deep…

Computation and Language · Computer Science 2018-08-07 Murali Karthick Baskar , Martin Karafiat , Lukas Burget , Karel Vesely , Frantisek Grezl , Jan Honza Cernocky

Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that…

Disordered Systems and Neural Networks · Physics 2026-02-17 Ramón Nartallo-Kaluarachchi , Renaud Lambiotte , Alain Goriely