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Artificial neural networks are most commonly trained with the back-propagation algorithm, where the gradient for learning is provided by back-propagating the error, layer by layer, from the output layer to the hidden layers. A recently…

Machine Learning · Statistics 2016-12-22 Arild Nøkland

The gradients used to train neural networks are typically computed using backpropagation. While an efficient way to obtain exact gradients, backpropagation is computationally expensive, hinders parallelization, and is biologically…

Machine Learning · Computer Science 2026-01-14 Katharina Flügel , Daniel Coquelin , Marie Weiel , Charlotte Debus , Achim Streit , Markus Götz

The algorithm of brain learning and memory is still undetermined. The backpropagation algorithm of artificial neural networks was thought not suitable for brain cortex, and there is a lack of algorithm for memory engram. We designed a brain…

Neural and Evolutionary Computing · Computer Science 2020-10-29 Yifei Mao

In this paper, we provide an in-depth study of Stochastic Backpropagation (SBP) when training deep neural networks for standard image classification and object detection tasks. During backward propagation, SBP calculates the gradients by…

Computer Vision and Pattern Recognition · Computer Science 2022-10-04 Jun Fang , Mingze Xu , Hao Chen , Bing Shuai , Zhuowen Tu , Joseph Tighe

The ubiquitous backpropagation algorithm requires sequential updates through the network introducing a locking problem. In addition, back-propagation relies on the transpose of forward weight matrices to compute updates, introducing a…

Machine Learning · Computer Science 2023-10-31 David Kappel , Khaleelulla Khan Nazeer , Cabrel Teguemne Fokam , Christian Mayr , Anand Subramoney

Many attempts took place to improve the adaptive filters that can also be useful to improve backpropagation (BP). Normalized least mean squares (NLMS) is one of the most successful algorithms derived from Least mean squares (LMS). However,…

Machine Learning · Computer Science 2021-01-05 Naeem Paeedeh , Kamaledin Ghiasi-Shirazi

Despite considerable theoretical progress in the training of neural networks viewed as a multi-agent system of neurons, particularly concerning biological plausibility and decentralized training, their applicability to real-world problems…

Neural and Evolutionary Computing · Computer Science 2023-10-17 Arshia Soltani Moakhar , Mohammad Azizmalayeri , Hossein Mirzaei , Mohammad Taghi Manzuri , Mohammad Hossein Rohban

Backpropagation (BP) is a core component of the contemporary deep learning incarnation of neural networks. Briefly, BP is an algorithm that exploits the computational architecture of neural networks to efficiently evaluate the gradient of a…

Machine Learning · Statistics 2021-07-21 Dirk Ostwald , Franziska Usée

The development of the back-propagation algorithm represents a landmark in neural networks. We provide an approach that conducts the back-propagation again to reverse the traditional back-propagation process to optimize the input loss at…

Machine Learning · Computer Science 2022-02-15 Weiming Xiong , Ruoyu Yang

Backpropagation (BP) remains the dominant and most successful method for training parameters of deep neural network models. However, BP relies on two computationally distinct phases, does not provide a satisfactory explanation of biological…

Machine Learning · Computer Science 2025-11-12 Sander Dalm , Marcel van Gerven , Nasir Ahmad

Standard neural network based on general back propagation learning using delta method or gradient descent method has some great faults like poor optimization of error-weight objective function, low learning rate, instability .This paper…

Neural and Evolutionary Computing · Computer Science 2012-12-20 Mriganka Chakraborty , Arka Ghosh

The study of Newton's method in complex-valued neural networks faces many difficulties. In this paper, we derive Newton's method backpropagation algorithms for complex-valued holomorphic multilayer perceptrons, and investigate the…

Complex Variables · Mathematics 2014-06-23 Diana Thomson La Corte , Yi Ming Zou

The development of biologically-plausible learning algorithms is important for understanding learning in the brain, but most of them fail to scale-up to real-world tasks, limiting their potential as explanations for learning by real brains.…

Neural and Evolutionary Computing · Computer Science 2022-02-01 Maxence Ernoult , Fabrice Normandin , Abhinav Moudgil , Sean Spinney , Eugene Belilovsky , Irina Rish , Blake Richards , Yoshua Bengio

The concept of a recently proposed Forward-Forward learning algorithm for fully connected artificial neural networks is applied to a single multi output perceptron for classification. The parameters of the system are trained with respect to…

Machine Learning · Computer Science 2023-04-07 K. Fredrik Karlsson

As deep learning applications continue to deploy increasingly large artificial neural networks, the associated high energy demands are creating a need for alternative neuromorphic approaches. Optics and photonics are particularly compelling…

Optics · Physics 2025-08-19 Nicola Dal Cin , Florian Marquardt , Clara C. Wanjura

The Forward-Forward algorithm is an alternative learning method which consists of two forward passes rather than a forward and backward pass employed by backpropagation. Forward-Forward networks employ layer local loss functions which are…

Machine Learning · Computer Science 2025-04-16 Reece Adamson

Training deep neural networks (DNNs) efficiently is a challenge due to the associated highly nonconvex optimization. The backpropagation (backprop) algorithm has long been the most widely used algorithm for gradient computation of…

Machine Learning · Statistics 2018-03-28 Tim Tsz-Kit Lau , Jinshan Zeng , Baoyuan Wu , Yuan Yao

Current artificial neural networks are trained with parameters encoded as floating point numbers that occupy lots of memory space at inference time. Due to the increase in the size of deep learning models, it is becoming very difficult to…

Machine Learning · Computer Science 2024-08-09 Ben Crulis , Barthelemy Serres , Cyril de Runz , Gilles Venturini

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

In modern neural networks like Transformers, linear layers require significant memory to store activations during backward pass. This study proposes a memory reduction approach to perform backpropagation through linear layers. Since the…

Machine Learning · Computer Science 2022-02-04 Daniel Bershatsky , Aleksandr Mikhalev , Alexandr Katrutsa , Julia Gusak , Daniil Merkulov , Ivan Oseledets