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Related papers: Reverse Differentiation via Predictive Coding

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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

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

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 (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

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 (BP), the standard learning algorithm for artificial neural networks, is often considered biologically implausible. In contrast, the standard learning algorithm for predictive coding (PC) models in neuroscience, known as the…

Neural and Evolutionary Computing · Computer Science 2023-05-24 Nick Alonso , Jeff Krichmar , Emre Neftci

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

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

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

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

By and large, Backpropagation (BP) is regarded as one of the most important neural computation algorithms at the basis of the progress in machine learning, including the recent advances in deep learning. However, its computational structure…

Artificial Intelligence · Computer Science 2018-08-22 Alessandro Betti , Marco Gori , Giuseppe Marra

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…

The backpropagation of error algorithm (BP) is impossible to implement in a real brain. The recent success of deep networks in machine learning and AI, however, has inspired proposals for understanding how the brain might learn across…

Machine Learning · Computer Science 2018-11-21 Sergey Bartunov , Adam Santoro , Blake A. Richards , Luke Marris , Geoffrey E. Hinton , Timothy Lillicrap

Backpropagation is a cornerstone algorithm in training neural networks for supervised learning, which uses a gradient descent method to update network weights by minimizing the discrepancy between actual and desired outputs. Despite its…

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

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

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

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

The backpropagation (BP) algorithm is often thought to be biologically implausible in the brain. One of the main reasons is that BP requires symmetric weight matrices in the feedforward and feedback pathways. To address this "weight…

Machine Learning · Computer Science 2018-12-24 Will Xiao , Honglin Chen , Qianli Liao , Tomaso Poggio
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