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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 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

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

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

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

Integrated photonic neural networks (PNNs) have demonstrated significant potential to complement the digital electronic counterparts [1-3]. Nevertheless, robust and repeatable performance of scalable integrated PNNs is directly tied to the…

Optics · Physics 2025-06-18 Farshid Ashtiani , Mohamad Hossein Idjadi , Kwangwoong Kim

We present the first theoretical framework that connects predictive coding (PC), a biologically inspired local learning rule, with the minimum description length (MDL) principle in deep networks. We prove that layerwise PC performs…

Machine Learning · Computer Science 2025-07-17 Benjamin Prada , Shion Matsumoto , Abdul Malik Zekri , Ankur Mali

How the brain performs credit assignment is a fundamental unsolved problem in neuroscience. Many `biologically plausible' algorithms have been proposed, which compute gradients that approximate those computed by backpropagation (BP), and…

Machine Learning · Computer Science 2022-08-05 Beren Millidge , Yuhang Song , Tommaso Salvatori , Thomas Lukasiewicz , Rafal Bogacz

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

Predictive coding networks are neural models that perform inference through an iterative energy minimization process, whose operations are local in space and time. While effective in shallow architectures, they suffer significant…

Machine Learning · Computer Science 2025-10-13 Chang Qi , Matteo Forasassi , Thomas Lukasiewicz , Tommaso Salvatori

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 the remarkable success of the end-to-end paradigm in deep learning, it often suffers from slow convergence and heavy reliance on large-scale datasets, which fundamentally limits its efficiency and applicability in data-scarce…

Computer Vision and Pattern Recognition · Computer Science 2025-10-20 Feifei Zhang , Zhenhong Jia , Sensen Song , Fei Shi , Dayong Ren

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 Networks (PCNs) aim to learn a generative model of the world. Given observations, this generative model can then be inverted to infer the causes of those observations. However, when training PCNs, a noticeable pathology is…

Artificial Intelligence · Computer Science 2022-09-02 Paul F Kinghorn , Beren Millidge , Christopher L Buckley

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

Probabilistic circuits (PCs) are a tractable representation of probability distributions allowing for exact and efficient computation of likelihoods and marginals. There has been significant recent progress on improving the scale and…

Machine Learning · Computer Science 2022-11-24 Meihua Dang , Anji Liu , Guy Van den Broeck

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 biologically inspired algorithm for training neural networks that relies only on local updates, allowing parallel learning across layers. However, practical implementations face two key limitations: error signals…

Machine Learning · Computer Science 2026-03-10 Davide Casnici , Martin Lefebvre , Justin Dauwels , Charlotte Frenkel

Predictive coding is an influential theory of cortical function which posits that the principal computation the brain performs, which underlies both perception and learning, is the minimization of prediction errors. While motivated by…

Neurons and Cognition · Quantitative Biology 2020-10-13 Beren Millidge , Alexander Tschantz , Anil Seth , Christopher L Buckley

Spiking Neural Networks (SNNs), regarded as the third generation of neural networks, emulate the brain's information processing with unparalleled biological plausibility compared to traditional neural networks. However, their non-linear,…

Neural and Evolutionary Computing · Computer Science 2026-02-10 Haidong Wang , Xiaogang Xiong , Mengting Lan , Yinghao Chu , Zixuan Jiang , KC Santosh , Shimin Wang , Renxin Zhong