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The Forward-Forward (FF) algorithm trains networks layer-by-layer using a local "goodness function," yet sum-of-squares (SoS) has remained the only choice studied. We systematically explore the goodness-function design space and identify a…

Machine Learning · Computer Science 2026-04-20 Talha Ruzgar Akkus , Suayp Talha Kocabay , Kamer Ali Yuksel , Hassan Sawaf

The Forward-Forward (FF) Algorithm has been recently proposed to alleviate the issues of backpropagation (BP) commonly used to train deep neural networks. However, its current formulation exhibits limitations such as the generation of…

Machine Learning · Computer Science 2024-03-29 Andreas Papachristodoulou , Christos Kyrkou , Stelios Timotheou , Theocharis Theocharides

The Forward-Forward (FF) algorithm offers a biologically plausible alternative to backpropagation, enabling neural networks to learn through local updates. However, FF's efficacy relies heavily on the definition of "goodness", which is a…

Machine Learning · Computer Science 2025-11-25 Arya Shah , Vaibhav Tripathi

The Forward-Forward (FF) algorithm offers a promising alternative to backpropagation (BP). Despite advancements in recent FF-based extensions, which have enhanced the original algorithm and adapted it to convolutional neural networks…

Machine Learning · Computer Science 2026-01-26 Qingchun Gong , Robert Bogdan Staszewski , Kai Xu

The Forward-Forward algorithm eliminates backpropagation's memory constraints and biological implausibility through dual forward passes with positive and negative data. However, conventional implementations suffer from critical inter-layer…

Machine Learning · Computer Science 2025-12-23 Salar Beigzad

The aim of this paper is to introduce a new learning procedure for neural networks and to demonstrate that it works well enough on a few small problems to be worth further investigation. The Forward-Forward algorithm replaces the forward…

Machine Learning · Computer Science 2022-12-29 Geoffrey Hinton

The so-called Forward-Forward Algorithm (FFA) has recently gained momentum as an alternative to the conventional back-propagation algorithm for neural network learning, yielding competitive performance across various modeling tasks. By…

Machine Learning · Computer Science 2025-01-10 Erik B. Terres-Escudero , Javier Del Ser , Pablo Garcia Bringas

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

Recent successes in image analysis with deep neural networks are achieved almost exclusively with Convolutional Neural Networks (CNNs), typically trained using the backpropagation (BP) algorithm. In a 2022 preprint, Geoffrey Hinton proposed…

Computer Vision and Pattern Recognition · Computer Science 2025-11-05 Riccardo Scodellaro , Ajinkya Kulkarni , Frauke Alves , Matthias Schröter

The application of deep learning to the area of communications systems has been a growing field of interest in recent years. Forward-forward (FF) learning is an efficient alternative to the backpropagation (BP) algorithm, which is the…

Information Theory · Computer Science 2026-02-17 Daniel Seifert , Onur Günlü , Rafael F. Schaefer

The forward-forward algorithm presents a new method of training neural networks by updating weights during an inference, performing parameter updates for each layer individually. This immediately reduces memory requirements during training…

Machine Learning · Computer Science 2023-06-28 Michael Hopwood

Backpropagation remains the dominant algorithm for training deep neural networks, but it incurs substantial memory overhead and relies on global error propagation, which is often regarded as biologically implausible. The Forward-Forward…

Machine Learning · Computer Science 2026-05-08 James Gong , Bruce Li , Waleed Abdulla

Although backpropagation is widely accepted as a training algorithm for artificial neural networks, researchers are always looking for inspiration from the brain to find ways with potentially better performance. Forward-Forward is a novel…

Computer Vision and Pattern Recognition · Computer Science 2025-12-02 Hossein Aghagolzadeh , Mehdi Ezoji

Agents that operate autonomously benefit from lifelong learning capabilities. However, compatible training algorithms must comply with the decentralized nature of these systems, which imposes constraints on both the parameter counts and the…

Machine Learning · Computer Science 2025-03-28 Xing Chen , Dongshu Liu , Jeremie Laydevant , Julie Grollier

Spiking Neural Networks (SNNs) offer a biologically inspired computational paradigm that emulates neuronal activity through discrete spike-based processing. Despite their advantages, training SNNs with traditional backpropagation (BP)…

Neural and Evolutionary Computing · Computer Science 2025-05-28 Mohammadnavid Ghader , Saeed Reza Kheradpisheh , Bahar Farahani , Mahmood Fazlali

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

Graph neural networks (GNNs) have achieved remarkable success across a wide range of applications, such as recommendation, drug discovery, and question answering. Behind the success of GNNs lies the backpropagation (BP) algorithm, which is…

Machine Learning · Computer Science 2024-04-16 Namyong Park , Xing Wang , Antoine Simoulin , Shuai Yang , Grey Yang , Ryan Rossi , Puja Trivedi , Nesreen Ahmed

Deep neural networks trained with backpropagation have achieved outstanding performance in vision tasks but remain biologically implausible, computationally demanding, and difficult to interpret. The Forward-Forward (FF) algorithm offers a…

Computer Vision and Pattern Recognition · Computer Science 2026-05-26 Jie-En Yao , Hong-En Chen , C. -C. Jay Kuo

The back-propagation algorithm has long been the de-facto standard in optimizing weights and biases in neural networks, particularly in cutting-edge deep learning models. Its widespread adoption in fields like natural language processing,…

Computer Vision and Pattern Recognition · Computer Science 2023-07-04 Sidike Paheding , Abel A. Reyes-Angulo

Neural stochastic differential equation model with a Brownian motion term can capture epistemic uncertainty of deep neural network from the perspective of a dynamical system. The goal of this paper is to improve the convergence rate of the…

Numerical Analysis · Mathematics 2025-09-09 Daili Sheng , Minghui Song , Xiang Peng , Xuanqi Dong
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