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State-of-the-art backpropagation-free learning methods employ local error feedback to direct iterative optimisation via gradient descent. Here, we examine the more restrictive setting where retrograde communication from neuronal outputs is…

Machine Learning · Computer Science 2025-12-19 Robert O'Shea , Bipin Rajendran

Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights. Recent work has improved the training stability of…

Machine Learning · Computer Science 2026-05-25 Francesco Innocenti , El Mehdi Achour , Rafal Bogacz

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

Relieving the reliance of neural network training on a global back-propagation (BP) has emerged as a notable research topic due to the biological implausibility and huge memory consumption caused by BP. Among the existing solutions, local…

Machine Learning · Computer Science 2024-06-11 Yibo Yang , Xiaojie Li , Motasem Alfarra , Hasan Hammoud , Adel Bibi , Philip Torr , Bernard Ghanem

Despite being the cornerstone of deep learning, backpropagation is criticized for its inherent sequentiality, which can limit the scalability of very deep models. Such models faced convergence issues due to vanishing gradient, later…

Machine Learning · Computer Science 2025-04-01 Erwan Fagnou , Paul Caillon , Blaise Delattre , Alexandre Allauzen

The ever-growing size of training datasets enhances the generalization capability of modern machine learning models but also incurs exorbitant computational costs. Existing data pruning approaches aim to accelerate training by removing…

Computer Vision and Pattern Recognition · Computer Science 2025-07-01 Dongyue Wu , Zilin Guo , Jialong Zuo , Nong Sang , Changxin Gao

In the evolving landscape of natural language processing (NLP), fine-tuning pre-trained Large Language Models (LLMs) with first-order (FO) optimizers like SGD and Adam has become standard. Yet, as LLMs grow {in size}, the substantial memory…

Physics intelligence and digital twins often require rapid and repeated performance evaluation of various engineering systems (e.g. robots, autonomous vehicles, semiconductor chips) to enable (almost) real-time actions or decision making.…

Machine Learning · Computer Science 2026-02-10 Yequan Zhao , Xinling Yu , Xian Xiao , Zhixiong Chen , Ziyue Liu , Geza Kurczveil , Raymond G. Beausoleil , Sijia Liu , Zheng Zhang

Most downstream adaptation methods tune all or part of the parameters of pre-trained models (PTMs) through gradient descent, where the tuning cost increases linearly with the growth of the model size. By contrast, gradient-free methods only…

Computation and Language · Computer Science 2022-10-17 Tianxiang Sun , Zhengfu He , Hong Qian , Yunhua Zhou , Xuanjing Huang , Xipeng Qiu

We study the problem of training neural networks with quantized parameters. Learning low-precision quantized parameters by enabling computation of gradients via the Straight-Through Estimator (STE) can be challenging. While the STE enables…

Machine Learning · Computer Science 2025-10-29 Ningfeng Yang , Tor M. Aamodt

Neural network learning is usually time-consuming since backpropagation needs to compute full gradients and backpropagate them across multiple layers. Despite its success of existing works in accelerating propagation through sparseness, the…

Machine Learning · Computer Science 2020-10-28 Zhiyuan Zhang , Pengcheng Yang , Xuancheng Ren , Qi Su , Xu Sun

Motivated by the potential for parallel implementation of batch-based algorithms and the accelerated convergence achievable with approximated second order information a limited memory version of the BFGS algorithm has been receiving…

Machine Learning · Computer Science 2023-03-07 Federico Zocco , Seán McLoone

Brain-inspired neuromorphic computing with spiking neural networks (SNNs) is a promising energy-efficient computational approach. However, successfully training SNNs in a more biologically plausible and neuromorphic-hardware-friendly way is…

Neural and Evolutionary Computing · Computer Science 2024-07-18 Mingqing Xiao , Qingyan Meng , Zongpeng Zhang , Di He , Zhouchen Lin

Forward-mode automatic differentiation (FmAD) and zero-order (ZO) optimization have been proposed as memory-efficient alternatives to backpropagation (BP) for gradient computation, especially in low-resource settings. However, their…

Machine Learning · Computer Science 2025-06-30 Kunjal Panchal , Sunav Choudhary , Yuriy Brun , Hui Guan

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

Backpropagation (BP) of errors is the backbone training algorithm for artificial neural networks (ANNs). It updates network weights through gradient descent to minimize a loss function representing the mismatch between predictions and…

Machine Learning · Statistics 2025-08-13 Davide Casnici , Charlotte Frenkel , Justin Dauwels

Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…

Optimization and Control · Mathematics 2021-08-10 Tom Tirer , Raja Giryes

Backpropagation (BP) is widely used for calculating gradients in deep neural networks (DNNs). Applied often along with stochastic gradient descent (SGD) or its variants, BP is considered as a de-facto choice in a variety of machine learning…

Machine Learning · Computer Science 2024-01-11 Ziang Li , Yiwen Guo , Haodi Liu , Changshui Zhang

The backpropagation of error algorithm (BP) is impossible to implement in a real brain. The recent success of deep networks in machine learning and AI, however, has inspired proposals for understanding how the brain might learn across…

Machine Learning · Computer Science 2018-11-21 Sergey Bartunov , Adam Santoro , Blake A. Richards , Luke Marris , Geoffrey E. Hinton , Timothy Lillicrap

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