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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

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

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…

Artificial intelligence (AI) is rapidly becoming one of the key technologies of this century. The majority of results in AI thus far have been achieved using deep neural networks trained with a learning algorithm called error…

Artificial Intelligence · Computer Science 2025-10-30 Tommaso Salvatori , Ankur Mali , Christopher L. Buckley , Thomas Lukasiewicz , Rajesh P. N. Rao , Karl Friston , Alexander Ororbia

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

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) 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 (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

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) offers a local and biologically grounded alternative to backpropagation in the training of artificial neural networks, yet to date, it remains slower, and performance degrades sharply as network depth increases. We…

Machine Learning · Computer Science 2026-05-21 Aleksandrs Baskakovs , Sylvain Estebe , Kenneth Enevoldsen , Kristoffer Nielbo , Chris Mathys , Nicolas Legrand

Artificial neural networks are often interpreted as abstract models of biological neuronal networks, but they are typically trained using the biologically unrealistic backpropagation algorithm and its variants. Predictive coding has been…

Neurons and Cognition · Quantitative Biology 2024-04-25 Robert Rosenbaum

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

Training with backpropagation (BP) in standard deep learning consists of two main steps: a forward pass that maps a data point to its prediction, and a backward pass that propagates the error of this prediction back through the network.…

Machine Learning · Computer Science 2022-10-13 Tommaso Salvatori , Luca Pinchetti , Beren Millidge , Yuhang Song , Tianyi Bao , Rafal Bogacz , Thomas Lukasiewicz

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 (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 a biologically-inspired learning framework characterised by local, parallelisable operations, properties that enable energy-efficient implementation on neuromorphic hardware. Despite this, extending PC effectively…

Machine Learning · Computer Science 2026-02-23 Tom Potter , Oliver Rhodes

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

Robotic systems operating at the edge require efficient online learning algorithms that can continuously adapt to changing environments while processing streaming sensory data. Traditional backpropagation, while effective, conflicts with…

Machine Learning · Computer Science 2025-10-31 Darius Masoum Zadeh-Jousdani , Elvin Hajizada , Eyke Hüllermeier

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
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