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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

In this paper, we propose a generic algorithm to train machine learning-based subgrid parametrizations online, i.e., with \textit{a posteriori} loss functions, but for non-differentiable numerical solvers. The proposed approach leverages a…

Computational Physics · Physics 2026-01-14 Hugo Frezat , Ronan Fablet , Guillaume Balarac , Julien Le Sommer

Biological neural networks are equipped with an inherent capability to continuously adapt through online learning. This aspect remains in stark contrast to learning with error backpropagation through time (BPTT) applied to recurrent neural…

Machine Learning · Computer Science 2020-10-09 Thomas Bohnstingl , Stanisław Woźniak , Wolfgang Maass , Angeliki Pantazi , Evangelos Eleftheriou

Backpropagation (BP) is the standard algorithm for training the deep neural networks that power modern artificial intelligence including large language models. However, BP is energy inefficient and unlikely to be implemented by the brain.…

Machine Learning · Computer Science 2025-10-30 Francesco Innocenti

Real-time recurrent learning (RTRL) for sequence-processing recurrent neural networks (RNNs) offers certain conceptual advantages over backpropagation through time (BPTT). RTRL requires neither caching past activations nor truncating…

Machine Learning · Computer Science 2024-02-29 Kazuki Irie , Anand Gopalakrishnan , Jürgen Schmidhuber

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…

Machine Learning · Computer Science 2021-03-01 Kyongmin Yeo , Dylan E. C. Grullon , Fan-Keng Sun , Duane S. Boning , Jayant R. Kalagnanam

Gradient descent has been a central training principle for artificial neural networks from the early beginnings to today's deep learning networks. The most common implementation is the backpropagation algorithm for training feed-forward…

Machine Learning · Computer Science 2020-06-09 Stefan Jaeger

Recurrent Neural Networks (RNNs) are widely used for online regression due to their ability to generalize nonlinear temporal dependencies. As an RNN model, Long-Short-Term-Memory Networks (LSTMs) are commonly preferred in practice, as these…

Machine Learning · Computer Science 2021-06-01 N. Mert Vural , Fatih Ilhan , Selim F. Yilmaz , Salih Ergüt , Suleyman S. Kozat

Large scale deep learning provides a tremendous opportunity to improve the quality of content recommendation systems by employing both wider and deeper models, but this comes at great infrastructural cost and carbon footprint in modern data…

Machine Learning · Computer Science 2020-10-22 Mao Ye , Dhruv Choudhary , Jiecao Yu , Ellie Wen , Zeliang Chen , Jiyan Yang , Jongsoo Park , Qiang Liu , Arun Kejariwal

Network pruning is an effective method to reduce the computational expense of over-parameterized neural networks for deployment on low-resource systems. Recent state-of-the-art techniques for retraining pruned networks such as weight…

Machine Learning · Computer Science 2021-05-10 Duong H. Le , Binh-Son Hua

Learning in a non-stationary environment is an inevitable problem when applying machine learning algorithm to real world environment. Learning new tasks without forgetting the previous knowledge is a challenge issue in machine learning. We…

Machine Learning · Computer Science 2018-11-07 Honglin Li , Frieder Ganz , Shirin Enshaeifar , Payam Barnaghi

Empowered by the backpropagation (BP) algorithm, deep neural networks have dominated the race in solving various cognitive tasks. The restricted training pattern in the standard BP requires end-to-end error propagation, causing large memory…

Machine Learning · Computer Science 2022-05-17 Wenzhe Guo , Mohammed E Fouda , Ahmed M. Eltawil , Khaled N. Salama

The discovery of the backpropagation algorithm ranks among one of the most important moments in the history of machine learning, and has made possible the training of large-scale neural networks through its ability to compute gradients at…

Quantum Physics · Physics 2025-10-08 Joseph Bowles , David Wierichs , Chae-Yeun Park

We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…

Machine Learning · Computer Science 2024-10-11 Semih Cayci , Atilla Eryilmaz

The brain cortex, which processes visual, auditory and sensory data in the brain, is known to have many recurrent connections within its layers and from higher to lower layers. But, in the case of machine learning with neural networks, it…

Machine Learning · Computer Science 2020-10-22 Sebastian Sanokowski

Backpropagation with gradient descent is a common optimization strategy employed by most neural network architectures in machine learning. However, finding optimal hyperparameters to guide training has proven challenging. While it is widely…

Machine Learning · Computer Science 2026-05-20 Vy Bui , Hang Yu , Karthik Kantipudi , Ziv Yaniv , Stefan Jaeger

With increasing scale in model and dataset size, the training of deep neural networks becomes a massive computational burden. One approach to speed up the training process is Selective Backprop. For this approach, we perform a forward pass…

Machine Learning · Computer Science 2023-12-11 Lukas Balles , Cedric Archambeau , Giovanni Zappella

In the last decades, due to the huge technological growth observed, it has become increasingly common that a collection of temporal data rapidly accumulates in vast amounts. This provides an opportunity for extracting valuable information…

Machine Learning · Computer Science 2023-02-22 Felipe Elorrieta , Lucas Osses , Matias Cáceres , Susana Eyheramendy , Wilfredo Palma

Spiking Neural Networks (SNNs) are promising energy-efficient models for neuromorphic computing. For training the non-differentiable SNN models, the backpropagation through time (BPTT) with surrogate gradients (SG) method has achieved high…

Neural and Evolutionary Computing · Computer Science 2023-08-08 Qingyan Meng , Mingqing Xiao , Shen Yan , Yisen Wang , Zhouchen Lin , Zhi-Quan Luo

Natural gradient descent is a principled method for adapting the parameters of a statistical model on-line using an underlying Riemannian parameter space to redefine the direction of steepest descent. The algorithm is examined via methods…

Disordered Systems and Neural Networks · Physics 2009-10-31 Magnus Rattray , David Saad