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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

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 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

Neuroscience and Artificial Intelligence (AI) have progressed in tandem, each contributing to our understanding of the brain, and inspiring recent developments in biologically-plausible neural networks (NNs) and learning rules. Predictive…

Neural and Evolutionary Computing · Computer Science 2024-06-24 Ehsan Ganjidoost , Mallory Snow , Jeff Orchard

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 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…

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

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

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

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

Random backpropagation (RBP) is a variant of the backpropagation algorithm for training neural networks, where the transpose of the forward matrices are replaced by fixed random matrices in the calculation of the weight updates. It is…

Machine Learning · Computer Science 2017-12-25 Pierre Baldi , Peter Sadowski , Zhiqin Lu

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

Binary Neural Networks (BNNs), which constrain both weights and activations to binary values, offer substantial reductions in computational complexity, memory footprint, and energy consumption. These advantages make them particularly well…

Machine Learning · Computer Science 2026-02-18 Luca Colombo , Fabrizio Pittorino , Daniele Zambon , Carlo Baldassi , Manuel Roveri , Cesare Alippi

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

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

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

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

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

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

We present PredProp, a method for optimization of weights and states in predictive coding networks (PCNs) based on the precision of propagated errors and neural activity. PredProp jointly addresses inference and learning via stochastic…

Machine Learning · Computer Science 2023-05-08 André Ofner , Sebastian Stober
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