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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 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

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 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 (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

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

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 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

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) replaces global backpropagation with local optimization over weights and activations. We show that linear PC networks admit a natural formulation as cellular sheaves: the sheaf coboundary maps activations to edge-wise…

Machine Learning · Computer Science 2025-11-17 Jeffrey Seely

Hierarchical Bayesian models of perception and learning feature prominently in contemporary cognitive neuroscience where, for example, they inform computational concepts of mental disorders. This includes predictive coding and hierarchical…

Neural and Evolutionary Computing · Computer Science 2025-12-04 Lilian Aline Weber , Peter Thestrup Waade , Nicolas Legrand , Anna Hedvig Møller , Klaas Enno Stephan , Christoph Mathys

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

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

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

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

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) networks are a biologically interesting class of neural networks. Their layered hierarchy mimics the reciprocal connectivity pattern observed in the mammalian cortex, and they can be trained using local learning rules…

Neural and Evolutionary Computing · Computer Science 2019-10-29 Jeff Orchard , Wei Sun

Despite extensive progress on image generation, common deep generative model architectures are not easily applied to lossless compression. For example, VAEs suffer from a compression cost overhead due to their latent variables. This…

Machine Learning · Computer Science 2022-03-17 Anji Liu , Stephan Mandt , Guy Van den Broeck

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

Based on the predictive coding theory in neuroscience, we designed a bi-directional and recurrent neural net, namely deep predictive coding networks (PCN). It has feedforward, feedback, and recurrent connections. Feedback connections from a…

Computer Vision and Pattern Recognition · Computer Science 2018-07-31 Haiguang Wen , Kuan Han , Junxing Shi , Yizhen Zhang , Eugenio Culurciello , Zhongming Liu
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