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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

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

The biological implausibility of backpropagation (BP) has motivated many alternative, brain-inspired algorithms that attempt to rely only on local information, such as predictive coding (PC) and equilibrium propagation. However, these…

Machine Learning · Computer Science 2025-12-01 Francesco Innocenti , El Mehdi Achour , Christopher L. Buckley

Local learning, which trains a network through layer-wise local targets and losses, has been studied as an alternative to backpropagation (BP) in neural computation. However, its algorithms often become more complex or require additional…

Machine Learning · Computer Science 2025-05-22 Satoki Ishikawa , Rio Yokota , Ryo Karakida

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

Predictive Coding (PC) is an influential account of cortical learning. Much of recent work has focused on comparing PC to Backpropagation (BP) to find whether PC offers any advantages. Small scale experiments show that PC enables learning…

Machine Learning · Computer Science 2026-05-13 Gaspard Oliviers , Elene Lominadze , Rafal Bogacz

Predictive coding (PC) is an energy-based learning algorithm that performs iterative inference over network activities before updating weights. Recent work suggests that PC can converge in fewer learning steps than backpropagation thanks to…

Machine Learning · Computer Science 2024-11-12 Francesco Innocenti , El Mehdi Achour , Ryan Singh , 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 of information processing in the brain, providing a biologically plausible alternative to backpropagation. It is motivated in terms of Bayesian inference, as hidden states and parameters are…

Energy-based learning algorithms, such as predictive coding (PC), have garnered significant attention in the machine learning community due to their theoretical properties, such as local operations and biologically plausible mechanisms for…

Machine Learning · Computer Science 2024-10-08 Ankur Mali , Tommaso Salvatori , Alexander Ororbia

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

Backpropagation has rapidly become the workhorse credit assignment algorithm for modern deep learning methods. Recently, modified forms of predictive coding (PC), an algorithm with origins in computational neuroscience, have been shown to…

Neural and Evolutionary Computing · Computer Science 2023-04-07 Umais Zahid , Qinghai Guo , Zafeirios Fountas

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

Predictive Coding (PC) offers a brain-inspired alternative to backpropagation for neural network training, described as a physical system minimizing its internal energy. However, in practice, PC is predominantly digitally simulated,…

Machine Learning · Computer Science 2026-02-03 Cédric Goemaere , Gaspard Oliviers , Rafal Bogacz , Thomas Demeester

Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…

Neurons and Cognition · Quantitative Biology 2023-03-07 Siavash Golkar , Tiberiu Tesileanu , Yanis Bahroun , Anirvan M. Sengupta , Dmitri B. Chklovskii

Recent years have witnessed a growing call for renewed emphasis on neuroscience-inspired approaches in artificial intelligence research, under the banner of NeuroAI. A prime example of this is predictive coding networks (PCNs), based on the…

Machine Learning · Computer Science 2026-03-09 Björn van Zwol , Ro Jefferson , Egon L. van den Broek

Deep learning has redefined the field of artificial intelligence (AI) thanks to the rise of artificial neural networks, which are architectures inspired by their neurological counterpart in the brain. Through the years, this dualism between…

Machine Learning · Computer Science 2023-02-21 Tommaso Salvatori , Yuhang Song , Thomas Lukasiewicz , Rafal Bogacz , Zhenghua Xu

Predictive coding (PC) is a brain-inspired local learning algorithm that has recently been suggested to provide advantages over backpropagation (BP) in biologically relevant scenarios. While theoretical work has mainly focused on showing…

Neural and Evolutionary Computing · Computer Science 2023-06-01 Francesco Innocenti , Ryan Singh , Christopher L. Buckley

Inspired by "predictive coding" - a theory in neuroscience, we develop a bi-directional and dynamic neural network with local recurrent processing, namely predictive coding network (PCN). Unlike feedforward-only convolutional neural…

Computer Vision and Pattern Recognition · Computer Science 2018-10-29 Kuan Han , Haiguang Wen , Yizhen Zhang , Di Fu , Eugenio Culurciello , Zhongming Liu

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
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