Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation?
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Abstract (arXiv)
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 parallelize at scale and is unlike how learning works in the brain. Neuroscience-inspired learning algorithms, however, such as predictive coding, which utilize local learning, have the potential to overcome these limitations and advance beyond current deep learning technologies. While predictive coding originated in theoretical neuroscience as a model of information processing in the cortex, recent work has developed the idea into a general-purpose algorithm able to train neural networks using only local computations. In this survey, we review works that have contributed to this perspective and demonstrate the close theoretical connections between predictive coding and backpropagation, as well as works that highlight the multiple advantages of using predictive coding models over backpropagation-trained neural networks. Specifically, we show the substantially greater flexibility of predictive coding networks against equivalent deep neural networks, which can function as classifiers, generators, and associative memories simultaneously, and can be defined on arbitrary graph topologies. Finally, we review direct benchmarks of predictive coding networks on machine learning classification tasks, as well as its close connections to control theory and applications in robotics.
Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). Builds on 24 of its 75 references that are in the map. First posted on arXiv 18 Feb 2022.
Builds on
24 of 75 references.
References · 24
- 2017Attention Is All You Needcited by 59,932
- 2015Deep Residual Learning for Image Recognitioncited by 51,809
- 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
- 2020Scaling Laws for Neural Language Modelscited by 6,411
- 2018Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Reviewcited by 466
- 2020Hopfield Networks is All You Needcited by 461
- 2016Deep Predictive Coding Networks for Video Prediction and Unsupervised Learningcited by 203
- 2020Predictive Coding Approximates Backprop along Arbitrary Computation Graphscited by 89
- 2021Predictive Coding: a Theoretical and Experimental Reviewcited by 74
- 2017The free energy principle for action and perception: A mathematical reviewcited by 66
- 2021Active Inference in Robotics and Artificial Agents: Survey and Challengescited by 52
- 2019Overparameterized Neural Networks Implement Associative Memorycited by 45
12 more
- 2020The Neural Coding Framework for Learning Generative Modelscited by 44
- 2018Biologically Motivated Algorithms for Propagating Local Target Representationscited by 43
- 2020On the Relationship Between Active Inference and Control as Inferencecited by 42
- 2021Associative Memories via Predictive Codingcited by 42
- 2022Learning on Arbitrary Graph Topologies via Predictive Codingcited by 33
- 2018Deep Predictive Coding Network with Local Recurrent Processing for Object Recognitioncited by 25
- 2019End-to-End Pixel-Based Deep Active Inference for Body Perception and Actioncited by 24
- 2018Adaptive robot body learning and estimation through predictive codingcited by 13
- 2020Relaxing the Constraints on Predictive Coding Modelscited by 12
- 2019A Novel Adaptive Controller for Robot Manipulators based on Active Inferencecited by 11
- 2021Habitual and Reflective Control in Hierarchical Predictive Codingcited by 3
- 2021A Brain Inspired Learning Algorithm for the Perception of a Quadrotor in Windcited by 2
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Citing papers per year: 2022: 5; 2023: 13; 2024: 10; 2025: 11; 2026: 6.
45 papers.
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- 2023Consciousness in Artificial Intelligence: Insights from the Science of Consciousnesscited by 99
- 2023Neither hype nor gloom do DNNs justicecited by 40
- 2023Brain-inspired Computational Intelligence via Predictive Codingcited by 30
- 2022Backpropagation at the Infinitesimal Inference Limit of Energy-Based Models: Unifying Predictive Coding, Equilibrium Propagation, and Contrastive Hebbian Learningcited by 26
- 2022Hybrid Predictive Coding: Inferring, Fast and Slowcited by 25
- 2022A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networkscited by 21
- 2022A Theoretical Framework for Inference and Learning in Predictive Coding Networkscited by 16
- 2022Predictive Coding beyond Gaussian Distributionscited by 16
- 2024Only Strict Saddles in the Energy Landscape of Predictive Coding Networks?cited by 10
- 2023Predictive Coding as a Neuromorphic Alternative to Backpropagation: A Critical Evaluationcited by 8
- 2024Predictive Coding Networks and Inference Learning: Tutorial and Surveycited by 7
- 2023Block-local learning with probabilistic latent representationscited by 6
33 more
- 2025Backpropagation-free Spiking Neural Networks with the Forward-Forward Algorithmcited by 5
- 2024Improving deep learning with prior knowledge and cognitive models: A survey on enhancing explainability, adversarial robustness and zero-shot learningcited by 4
- 2025ePC: Fast and Deep Predictive Coding in Digital Simulationcited by 4
- 2023The Compositional Structure of Bayesian Inferencecited by 3
- 2024Tight Stability, Convergence, and Robustness Bounds for Predictive Coding Networkscited by 3
- 2025Deep Active Inference Agents for Delayed and Long-Horizon Environmentscited by 3
- 2023Meta predictive learning model of languages in neural circuitscited by 2
- 2024pyhgf: A neural network library for predictive codingcited by 2
- 2025Bayesian Predictive Codingcited by 2
- 2025Self-orthogonalizing attractor neural networks emerging from the free energy principlecited by 2
- 2026Accelerated Predictive Coding Networks via Direct Kolen-Pollack Feedback Alignmentcited by 2
- 2023Beyond the limitations of any imaginable mechanism: large language models and psycholinguisticscited by 1
- 2023Understanding Predictive Coding as an Adaptive Trust-Region Methodcited by 1
- 2023Deep Predictive Coding with Bi-directional Propagation for Classification and Reconstructioncited by 1
- 2023Advancing Perception in Artificial Intelligence through Principles of Cognitive Sciencecited by 1
- 2024Report on Candidate Computational Indicators for Conscious Valenced Experiencecited by 1
- 2024Active Inference Meeting Energy-Efficient Control of Parallel and Identical Machinescited by 1
- 2024JPC: Flexible Inference for Predictive Coding Networks in JAXcited by 1
- 2025Predictive Learning in Energy-based Models with Attractor Structurescited by 1
- 2025Bridging Predictive Coding and MDL: A Two-Part Code Framework for Deep Learningcited by 1
- 2023Gibbs Sampling the Posterior of Neural Networkscited by 0
- 2023Fixing the problems of deep neural networks will require better training data and learning algorithmscited by 0
- 2024Deep hybrid models: infer and plan in a dynamic worldcited by 0
- 2024Provable Accuracy Bounds for Hybrid Dynamical Optimization and Samplingcited by 0
- 2025DMPCN: Dynamic Modulated Predictive Coding Network with Hybrid Feedback Representationscited by 0
- 2025Local Pairwise Distance Matching for Backpropagation-Free Reinforcement Learningcited by 0
- 2025Predictive Coding-based Deep Neural Network Fine-tuning for Computationally Efficient Domain Adaptationcited by 0
- 2025Structural Plasticity as Active Inference: A Biologically-Inspired Architecture for Homeostatic Controlcited by 0
- 2026GRAFNet: Multiscale Retinal Processing via Guided Cortical Attention Feedback for Enhancing Medical Image Polyp Segmentationcited by 0
- 2026Vision Hopfield Memory Networks for Image Recognitioncited by 0
- 2026Affinity Is Not Enough: Recovering the Free Energy Principle in Mixture-of-Expertscited by 0
- 2026Recursive Gaussian Processes and the Bayesian Braincited by 0
- 2026Single State Update Predictive Coding training for Time Series Forecasting and Anomaly Detectioncited by 0
- 2026Single State Update Predictive Coding training for Time Series Forecasting and Anomaly Detection25 Aug 2026
- 2026Recursive Gaussian Processes and the Bayesian Brain1 Aug 2026
- 2026Affinity Is Not Enough: Recovering the Free Energy Principle in Mixture-of-Experts1 May 2026
- 2026Vision Hopfield Memory Networks for Image Recognition26 Mar 2026
- 2026Accelerated Predictive Coding Networks via Direct Kolen-Pollack Feedback Alignment17 Feb 2026
- 2026GRAFNet: Multiscale Retinal Processing via Guided Cortical Attention Feedback for Enhancing Medical Image Polyp Segmentation15 Feb 2026
- 2025Structural Plasticity as Active Inference: A Biologically-Inspired Architecture for Homeostatic Control4 Nov 2025
- 2025Predictive Coding-based Deep Neural Network Fine-tuning for Computationally Efficient Domain Adaptation24 Sep 2025
- 2025Local Pairwise Distance Matching for Backpropagation-Free Reinforcement Learning15 Jul 2025
- 2025Self-orthogonalizing attractor neural networks emerging from the free energy principle28 May 2025
- 2025ePC: Fast and Deep Predictive Coding in Digital Simulation26 May 2025
- 2025Deep Active Inference Agents for Delayed and Long-Horizon Environments26 May 2025
33 more
- 2025Bridging Predictive Coding and MDL: A Two-Part Code Framework for Deep Learning20 May 2025
- 2025DMPCN: Dynamic Modulated Predictive Coding Network with Hybrid Feedback Representations20 Apr 2025
- 2025Bayesian Predictive Coding31 Mar 2025
- 2025Backpropagation-free Spiking Neural Networks with the Forward-Forward Algorithm19 Feb 2025
- 2025Predictive Learning in Energy-based Models with Attractor Structures23 Jan 2025
- 2024JPC: Flexible Inference for Predictive Coding Networks in JAX4 Dec 2024
- 2024pyhgf: A neural network library for predictive coding11 Oct 2024
- 2024Provable Accuracy Bounds for Hybrid Dynamical Optimization and Sampling8 Oct 2024
- 2024Tight Stability, Convergence, and Robustness Bounds for Predictive Coding Networks7 Oct 2024
- 2024Only Strict Saddles in the Energy Landscape of Predictive Coding Networks?21 Aug 2024
- 2024Predictive Coding Networks and Inference Learning: Tutorial and Survey4 Jul 2024
- 2024Active Inference Meeting Energy-Efficient Control of Parallel and Identical Machines13 Jun 2024
- 2024Report on Candidate Computational Indicators for Conscious Valenced Experience25 Apr 2024
- 2024Improving deep learning with prior knowledge and cognitive models: A survey on enhancing explainability, adversarial robustness and zero-shot learning11 Mar 2024
- 2024Deep hybrid models: infer and plan in a dynamic world1 Feb 2024
- 2023Neither hype nor gloom do DNNs justice8 Dec 2023
- 2023Advancing Perception in Artificial Intelligence through Principles of Cognitive Science13 Oct 2023
- 2023Fixing the problems of deep neural networks will require better training data and learning algorithms26 Sep 2023
- 2023Meta predictive learning model of languages in neural circuits8 Sep 2023
- 2023Consciousness in Artificial Intelligence: Insights from the Science of Consciousness17 Aug 2023
- 2023Brain-inspired Computational Intelligence via Predictive Coding15 Aug 2023
- 2023Gibbs Sampling the Posterior of Neural Networks5 Jun 2023
- 2023Deep Predictive Coding with Bi-directional Propagation for Classification and Reconstruction29 May 2023
- 2023Understanding Predictive Coding as an Adaptive Trust-Region Method29 May 2023
- 2023Block-local learning with probabilistic latent representations24 May 2023
- 2023The Compositional Structure of Bayesian Inference10 May 2023
- 2023Predictive Coding as a Neuromorphic Alternative to Backpropagation: A Critical Evaluation5 Apr 2023
- 2023Beyond the limitations of any imaginable mechanism: large language models and psycholinguistics28 Feb 2023
- 2022A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networks16 Nov 2022
- 2022Predictive Coding beyond Gaussian Distributions7 Nov 2022
- 2022A Theoretical Framework for Inference and Learning in Predictive Coding Networks21 Jul 2022
- 2022Backpropagation at the Infinitesimal Inference Limit of Energy-Based Models: Unifying Predictive Coding, Equilibrium Propagation, and Contrastive Hebbian Learning31 May 2022
- 2022Hybrid Predictive Coding: Inferring, Fast and Slow5 Apr 2022
- 2026Vision Hopfield Memory Networks for Image Recognitioncited by 0
- 2026Vision Hopfield Memory Networks for Image Recognition26 Mar 2026
- 2023Consciousness in Artificial Intelligence: Insights from the Science of Consciousnesscited by 99
- 2023Neither hype nor gloom do DNNs justicecited by 40
- 2023Brain-inspired Computational Intelligence via Predictive Codingcited by 30
- 2022Backpropagation at the Infinitesimal Inference Limit of Energy-Based Models: Unifying Predictive Coding, Equilibrium Propagation, and Contrastive Hebbian Learningcited by 26
- 2022Hybrid Predictive Coding: Inferring, Fast and Slowcited by 25
- 2022A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networkscited by 21
- 2022Predictive Coding beyond Gaussian Distributionscited by 16
- 2024Only Strict Saddles in the Energy Landscape of Predictive Coding Networks?cited by 10
- 2023Predictive Coding as a Neuromorphic Alternative to Backpropagation: A Critical Evaluationcited by 8
- 2024Predictive Coding Networks and Inference Learning: Tutorial and Surveycited by 7
- 2023Block-local learning with probabilistic latent representationscited by 6
- 2025Backpropagation-free Spiking Neural Networks with the Forward-Forward Algorithmcited by 5
12 most cited of 41 All 41 (JSON)
- 2026Single State Update Predictive Coding training for Time Series Forecasting and Anomaly Detection25 Aug 2026
- 2026Recursive Gaussian Processes and the Bayesian Brain1 Aug 2026
- 2026Accelerated Predictive Coding Networks via Direct Kolen-Pollack Feedback Alignment17 Feb 2026
- 2026GRAFNet: Multiscale Retinal Processing via Guided Cortical Attention Feedback for Enhancing Medical Image Polyp Segmentation15 Feb 2026
- 2025Structural Plasticity as Active Inference: A Biologically-Inspired Architecture for Homeostatic Control4 Nov 2025
- 2025Predictive Coding-based Deep Neural Network Fine-tuning for Computationally Efficient Domain Adaptation24 Sep 2025
- 2025Local Pairwise Distance Matching for Backpropagation-Free Reinforcement Learning15 Jul 2025
- 2025Self-orthogonalizing attractor neural networks emerging from the free energy principle28 May 2025
- 2025ePC: Fast and Deep Predictive Coding in Digital Simulation26 May 2025
- 2025Bridging Predictive Coding and MDL: A Two-Part Code Framework for Deep Learning20 May 2025
- 2025DMPCN: Dynamic Modulated Predictive Coding Network with Hybrid Feedback Representations20 Apr 2025
- 2025Bayesian Predictive Coding31 Mar 2025
12 newest of 41 All 41 (JSON)