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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

This paper presents a concise mathematical framework for investigating both feed-forward and backward process, during the training to learn model weights, of an artificial neural network (ANN). Inspired from the idea of the two-step rule…

Neural and Evolutionary Computing · Computer Science 2023-05-02 Ahmed Boughammoura

Backpropagation algorithm is the cornerstone for neural network analysis. Paper extends it for training any derivatives of neural network's output with respect to its input. By the dint of it feedforward networks can be used to solve or…

Neural and Evolutionary Computing · Computer Science 2017-12-13 V. I. Avrutskiy

The back-propagation algorithm is widely used for learning in artificial neural networks. A challenge in machine learning is to create models that generalize to new data samples not seen in the training data. Recently, a common flaw in…

Machine Learning · Statistics 2016-04-07 Arild Nøkland

The back-propagation (BP) algorithm has been considered the de-facto method for training deep neural networks. It back-propagates errors from the output layer to the hidden layers in an exact manner using the transpose of the feedforward…

Neural and Evolutionary Computing · Computer Science 2018-05-01 Hongyin Luo , Jie Fu , James Glass

The Forward-Forward (FF) learning algorithm provides a bottom-up alternative to backpropagation (BP) for training neural networks, relying on a layer-wise "goodness" function with well-designed negative samples for contrastive learning.…

Machine Learning · Computer Science 2025-11-11 Zhichao Zhu , Yang Qi , Hengyuan Ma , Wenlian Lu , Jianfeng Feng

The long-held assumption that backpropagation (BP) is essential for state-of-the-art performance is challenged by this work. We present rigorous, hardware-validated evidence that the Mono-Forward (MF) algorithm, a backpropagation-free…

Machine Learning · Computer Science 2025-11-04 Przemysław Spyra , Witold Dzwinel

Supervised learning in artificial neural networks typically relies on backpropagation, where the weights are updated based on the error-function gradients and sequentially propagated from the output layer to the input layer. Although this…

Neural and Evolutionary Computing · Computer Science 2023-06-06 Giorgia Dellaferrera , Gabriel Kreiman

Backward propagation of errors (backpropagation) is a method to minimize objective functions (e.g., loss functions) of deep neural networks by identifying optimal sets of weights and biases. Imposing constraints on weight precision is often…

Machine Learning · Computer Science 2021-10-26 Guhyun Kim , Doo Seok Jeong

In federated learning (FL), clients with limited resources can disrupt the training efficiency. A potential solution to this problem is to leverage a new learning procedure that does not rely on backpropagation (BP). We present a novel…

Machine Learning · Computer Science 2023-09-06 Seonghwan Park , Dahun Shin , Jinseok Chung , Namhoon Lee

In this paper, we present a new supervised learning algorithm that is based on the Hebbian learning algorithm in an attempt to offer a substitute for back propagation along with the gradient descent for a more biologically plausible method.…

Neural and Evolutionary Computing · Computer Science 2020-01-07 Rafi Qumsieh

The de facto algorithm for training the back pass of a feedforward neural network is backpropagation (BP). The use of almost-everywhere differentiable activation functions made it efficient and effective to propagate the gradient backwards…

Neural and Evolutionary Computing · Computer Science 2022-06-14 John Waldo

Forward gradient learning computes a noisy directional gradient and is a biologically plausible alternative to backprop for learning deep neural networks. However, the standard forward gradient algorithm, when applied naively, suffers from…

Machine Learning · Computer Science 2023-03-03 Mengye Ren , Simon Kornblith , Renjie Liao , Geoffrey Hinton

After the tremendous development of neural networks trained by backpropagation, it is a good time to develop other algorithms for training neural networks to gain more insights into networks. In this paper, we propose a new algorithm for…

Machine Learning · Computer Science 2020-07-01 Benyamin Ghojogh , Fakhri Karray , Mark Crowley

Artificial Intelligence algorithms have been steadily increasing in popularity and usage. Deep Learning, allows neural networks to be trained using huge datasets and also removes the need for human extracted features, as it automates the…

Neural and Evolutionary Computing · Computer Science 2020-05-11 Vasco Lopes , Paulo Fazendeiro

A new learning algorithm proposed by Brandt and Lin for neural network [1], [2] has been shown to be mathematically equivalent to the conventional back-propagation learning algorithm, but has several advantages over the backpropagation…

Neural and Evolutionary Computing · Computer Science 2022-02-28 Feng Lin

In a physical neural system, backpropagation is faced with a number of obstacles including: the need for labeled data, the violation of the locality learning principle, the need for symmetric connections, and the lack of modularity.…

Machine Learning · Computer Science 2021-07-23 Mohammadamin Tavakoli , Peter Sadowski , Pierre Baldi

The rising computational and energy demands of deep neural networks (DNNs), driven largely by backpropagation (BP), challenge sustainable AI development. This paper rigorously investigates three BP-free training methods: the Forward-Forward…

Machine Learning · Computer Science 2026-01-15 Przemysław Spyra

Modern deep-learning systems are specialized to problem settings in which training occurs once and then never again, as opposed to continual-learning settings in which training occurs continually. If deep-learning systems are applied in a…

Machine Learning · Computer Science 2024-04-11 Shibhansh Dohare , J. Fernando Hernandez-Garcia , Parash Rahman , A. Rupam Mahmood , Richard S. Sutton

Speculative backpropagation has emerged as a promising technique to accelerate the training of neural networks by overlapping the forward and backward passes. Leveraging speculative weight updates when error gradients fall within a specific…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-18 Sed Centeno , Christopher Sprague , Arnab A Purkayastha , Ray Simar , Neeraj Magotra