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This paper proposes a fractional order gradient method for the backward propagation of convolutional neural networks. To overcome the problem that fractional order gradient method cannot converge to real extreme point, a simplified…

Optimization and Control · Mathematics 2020-01-07 Dian Sheng , Yiheng Wei , Yuquan Chen , Yong Wang

The backpropagation algorithm is an invaluable tool for training artificial neural networks; however, because of a weight sharing requirement, it does not provide a plausible model of brain function. Here, in the context of a two-layer…

Neural and Evolutionary Computing · Computer Science 2020-12-01 Siavash Golkar , David Lipshutz , Yanis Bahroun , Anirvan M. Sengupta , Dmitri B. Chklovskii

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

The Forward-Forward (FF) algorithm presents a compelling, bio-inspired alternative to backpropagation. However, while efficient in training, it has a computationally prohibitive inference process that requires a separate forward pass for…

Machine Learning · Computer Science 2026-05-04 Shalini Sarode , Brian Moser , Joachim Folz , Federico Raue , Tobias Nauen , Stanislav Frolov , Andreas Dengel

Back-propagation algorithm is one of the most widely used and popular techniques to optimize the feed forward neural network training. Nature inspired meta-heuristic algorithms also provide derivative-free solution to optimize complex…

Neural and Evolutionary Computing · Computer Science 2012-09-13 Sudarshan Nandy , Partha Pratim Sarkar , Achintya Das

Modern machine learning models are able to outperform humans on a variety of non-trivial tasks. However, as the complexity of the models increases, they consume significant amounts of power and still struggle to generalize effectively to…

Machine Learning · Computer Science 2023-12-13 Thomas Dooms , Ing Jyh Tsang , Jose Oramas

While backpropagation (BP) is the mainstream approach for gradient computation in neural network training, its heavy reliance on the chain rule of differentiation constrains the designing flexibility of network architecture and training…

Machine Learning · Computer Science 2023-10-16 Jinyang Jiang , Zeliang Zhang , Chenliang Xu , Zhaofei Yu , Yijie Peng

Gradient-based optimization has been a cornerstone of machine learning that enabled the vast advances of Artificial Intelligence (AI) development over the past decades. However, this type of optimization requires differentiation, and with…

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 Forward-Forward (FF) algorithm was recently proposed as a local learning method to address the limitations of backpropagation (BP), offering biological plausibility along with memory-efficient and highly parallelized computational…

Neural and Evolutionary Computing · Computer Science 2024-08-28 Yujie Wu , Siyuan Xu , Jibin Wu , Lei Deng , Mingkun Xu , Qinghao Wen , Guoqi Li

We propose an algorithm capable of identifying and eliminating irrelevant layers of a neural network during the early stages of training. In contrast to weight or filter-level pruning, layer pruning reduces the harder to parallelize…

Machine Learning · Computer Science 2024-06-10 Valentin Frank Ingmar Guenter , Athanasios Sideris

Neural networks have been able to achieve groundbreaking accuracy at tasks conventionally considered only doable by humans. Using stochastic gradient descent, optimization in many dimensions is made possible, albeit at a relatively high…

Machine Learning · Computer Science 2017-07-17 Hirsh R. Agarwal , Andrew Huang

Iterative approximation methods using backpropagation enable the optimization of neural networks, but they remain computationally expensive, especially when used at scale. This paper presents an efficient alternative for optimizing neural…

Machine Learning · Computer Science 2023-11-14 Jake Ryland Williams , Haoran Zhao

Perforated Backpropagation is a neural network optimization technique based on modern understanding of the computational importance of dendrites within biological neurons. This paper explores further experiments from the original…

Machine Learning · Computer Science 2025-06-03 Rorry Brenner , Evan Davis , Rushi Chaudhari , Rowan Morse , Jingyao Chen , Xirui Liu , Zhaoyi You , Laurent Itti

Recently, several studies proposed methods to utilize some classes of optimization problems in designing deep neural networks to encode constraints that conventional layers cannot capture. However, these methods are still in their infancy…

Machine Learning · Computer Science 2020-06-16 Younghan Jeon , Minsik Lee , Jin Young Choi

Neural networks (NN) have demonstrated remarkable capabilities in various tasks, but their computation-intensive nature demands faster and more energy-efficient hardware implementations. Optics-based platforms, using technologies such as…

The backpropagation of error algorithm used to train deep neural networks has been fundamental to the successes of deep learning. However, it requires sequential backward updates and non-local computations, which make it challenging to…

Neural and Evolutionary Computing · Computer Science 2022-02-22 Beren Millidge , Tommaso Salvatori , Yuhang Song , Rafal Bogacz , Thomas Lukasiewicz

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

We propose the predictive forward-forward (PFF) algorithm for conducting credit assignment in neural systems. Specifically, we design a novel, dynamic recurrent neural system that learns a directed generative circuit jointly and…

Machine Learning · Computer Science 2023-04-04 Alexander Ororbia , Ankur Mali

Federated learning (FL) has emerged as a widely adopted paradigm for enabling edge learning with distributed data while ensuring data privacy. However, the traditional FL with deep neural networks trained via backpropagation can hardly meet…

Machine Learning · Computer Science 2025-11-05 Jierui Zhang , Jianhao Huang , Kaibin Huang