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There is an increasing convergence between biologically plausible computational models of inference and learning with local update rules and the global gradient-based optimization of neural network models employed in machine learning. One…

Machine Learning · Computer Science 2021-11-16 Andre Ofner , Raihan Kabir Ratul , Suhita Ghosh , Sebastian Stober

We propose proximal backpropagation (ProxProp) as a novel algorithm that takes implicit instead of explicit gradient steps to update the network parameters during neural network training. Our algorithm is motivated by the step size…

Machine Learning · Computer Science 2018-02-21 Thomas Frerix , Thomas Möllenhoff , Michael Moeller , Daniel Cremers

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

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

Backpropagation of error (backprop) is a powerful algorithm for training machine learning architectures through end-to-end differentiation. However, backprop is often criticised for lacking biological plausibility. Recently, it has been…

Machine Learning · Computer Science 2020-10-07 Beren Millidge , Alexander Tschantz , Christopher L. Buckley

Predictive coding networks are neural models that perform inference through an iterative energy minimization process, whose operations are local in space and time. While effective in shallow architectures, they suffer significant…

Machine Learning · Computer Science 2025-10-13 Chang Qi , Matteo Forasassi , Thomas Lukasiewicz , Tommaso Salvatori

Predictive Coding Networks (PCNs) aim to learn a generative model of the world. Given observations, this generative model can then be inverted to infer the causes of those observations. However, when training PCNs, a noticeable pathology is…

Artificial Intelligence · Computer Science 2022-09-02 Paul F Kinghorn , Beren Millidge , Christopher L Buckley

Predictive coding networks (PCNs) are an influential model for information processing in the brain. They have appealing theoretical interpretations and offer a single mechanism that accounts for diverse perceptual phenomena of the brain. On…

Machine Learning · Computer Science 2021-03-08 Tommaso Salvatori , Yuhang Song , Thomas Lukasiewicz , Rafal Bogacz , Zhenghua Xu

Predictive coding (PC) is an influential theory in computational neuroscience, which argues that the cortex forms unsupervised world models by implementing a hierarchical process of prediction error minimization. PC networks (PCNs) are…

Neural and Evolutionary Computing · Computer Science 2022-08-05 Beren Millidge , Yuhang Song , Tommaso Salvatori , Thomas Lukasiewicz , Rafal Bogacz

Deep neural networks are powerful parametric models that can be trained efficiently using the backpropagation algorithm. Stochastic neural networks combine the power of large parametric functions with that of graphical models, which makes…

Machine Learning · Computer Science 2016-02-26 Shixiang Gu , Sergey Levine , Ilya Sutskever , Andriy Mnih

Predictive coding (PC) is a general theory of cortical function. The local, gradient-based learning rules found in one kind of PC model have recently been shown to closely approximate backpropagation. This finding suggests that this…

Neural and Evolutionary Computing · Computer Science 2021-12-09 Nick Alonso , Emre Neftci

In this paper, we introduce weight prediction into the AdamW optimizer to boost its convergence when training the deep neural network (DNN) models. In particular, ahead of each mini-batch training, we predict the future weights according to…

Machine Learning · Computer Science 2023-08-09 Lei Guan

We present a novel optimization-based decoding algorithm for LDPC codes that is suitable for hardware architectures specialized to feed-forward neural networks. The algorithm is based on the projected gradient descent algorithm with a…

Information Theory · Computer Science 2019-01-16 Tadashi Wadayama , Satoshi Takabe

Pruning neural networks at initialization would enable us to find sparse models that retain the accuracy of the original network while consuming fewer computational resources for training and inference. However, current methods are…

This paper presents a new learning algorithm, termed Deep Bi-directional Predictive Coding (DBPC) that allows developing networks to simultaneously perform classification and reconstruction tasks using the same weights. Predictive Coding…

Machine Learning · Computer Science 2023-05-31 Senhui Qiu , Saugat Bhattacharyya , Damien Coyle , Shirin Dora

This paper is dedicated to an efficient compression of weights and optimizer states (called checkpoints) obtained at different stages during a neural network training process. First, we propose a prediction-based compression approach, where…

Machine Learning · Computer Science 2025-06-16 Yuriy Kim , Evgeny Belyaev

Training deep neural networks is challenging. To accelerate training and enhance performance, we propose PadamP, a novel optimization algorithm. PadamP is derived by applying the adaptive estimation of the p-th power of the second-order…

Optimization and Control · Mathematics 2025-03-14 Yongqi Li , Xiaowei Zhang

In this paper, we propose a general deep learning training framework XGrad which introduces weight prediction into the popular gradient-based optimizers to boost their convergence and generalization when training the deep neural network…

Machine Learning · Computer Science 2024-04-09 Lei Guan , Dongsheng Li , Yanqi Shi , Jian Meng

Stochastic gradient descent with backpropagation is the workhorse of artificial neural networks. It has long been recognized that backpropagation fails to be a biologically plausible algorithm. Fundamentally, it is a non-local procedure --…

Machine Learning · Statistics 2021-12-24 Ganlin Song , Ruitu Xu , John Lafferty

A large amount of recent research has the far-reaching goal of finding training methods for deep neural networks that can serve as alternatives to backpropagation (BP). A prominent example is predictive coding (PC), which is a…

Machine Learning · Computer Science 2022-11-08 Luca Pinchetti , Tommaso Salvatori , Yordan Yordanov , Beren Millidge , Yuhang Song , Thomas Lukasiewicz
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