mlsanityData to 7 Oct 2026

Predictive Coding: a Theoretical and Experimental Review

arXiv 2107.12979 ↗First posted 27 Jul 2021cs.AI cs.NE q-bio.NCcited by 74

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Abstract (arXiv)

Predictive coding offers a potentially unifying account of cortical function -- postulating that the core function of the brain is to minimize prediction errors with respect to a generative model of the world. The theory is closely related to the Bayesian brain framework and, over the last two decades, has gained substantial influence in the fields of theoretical and cognitive neuroscience. A large body of research has arisen based on both empirically testing improved and extended theoretical and mathematical models of predictive coding, as well as in evaluating their potential biological plausibility for implementation in the brain and the concrete neurophysiological and psychological predictions made by the theory. Despite this enduring popularity, however, no comprehensive review of predictive coding theory, and especially of recent developments in this field, exists. Here, we provide a comprehensive review both of the core mathematical structure and logic of predictive coding, thus complementing recent tutorials in the literature. We also review a wide range of classic and recent work within the framework, ranging from the neurobiologically realistic microcircuits that could implement predictive coding, to the close relationship between predictive coding and the widely-used backpropagation of error algorithm, as well as surveying the close relationships between predictive coding and modern machine learning techniques.

Key facts. Cited by 74 papers in the map (data through 7 Oct 2026). Builds on 38 of its 197 references that are in the map. First posted on arXiv 27 Jul 2021.

Builds on

38 of 197 references.

References · 38

  1. 2017Attention Is All You Needcited by 59,932
  2. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,456
  3. 2020Language Models are Few-Shot Learnerscited by 32,199
  4. 2018Representation Learning with Contrastive Predictive Codingcited by 7,662
  5. 2016WaveNet: A Generative Model for Raw Audiocited by 1,710
  6. 2016Variational Inference: A Review for Statisticianscited by 1,466
  7. 2019Mastering Atari, Go, Chess and Shogi by Planning with a Learned Modelcited by 1,327
  8. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  9. 2019Surrogate Gradient Learning in Spiking Neural Networkscited by 604
  10. 2020Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Imagescited by 261
  11. 2016Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagationcited by 251
  12. 2016Deep Predictive Coding Networks for Video Prediction and Unsupervised Learningcited by 203
26 more
  1. 2017SuperSpike: Supervised learning in multi-layer spiking neural networkscited by 178
  2. 2014Difference Target Propagationcited by 144
  3. 2018Dendritic cortical microcircuits approximate the backpropagation algorithmcited by 96
  4. 2020Predictive Coding Approximates Backprop along Arbitrary Computation Graphscited by 89
  5. 2019Deep Learning without Weight Transportcited by 87
  6. 2017The free energy principle for action and perception: A mathematical reviewcited by 66
  7. 2019Recurrence is required to capture the representational dynamics of the human visual systemcited by 58
  8. 2020Reinforcement Learning through Active Inferencecited by 47
  9. 2017Unbiased Online Recurrent Optimizationcited by 46
  10. 2018Biologically Motivated Algorithms for Propagating Local Target Representationscited by 43
  11. 2020Deep Learning and the Global Workspace Theorycited by 35
  12. 2018Deep Predictive Coding Network for Object Recognitioncited by 23
  13. 2018Generalization of Equilibrium Propagation to Vector Field Dynamicscited by 21
  14. 2020Predictive Coding, Variational Autoencoders, and Biological Connectionscited by 21
  15. 2020Going in circles is the way forward: the role of recurrence in visual inferencecited by 19
  16. 2018Deep learning with asymmetric connections and Hebbian updatescited by 16
  17. 2021Predictive Coding Can Do Exact Backpropagation on Convolutional and Recurrent Neural Networkscited by 14
  18. 2015Early Inference in Energy-Based Models Approximates Back-Propagationcited by 13
  19. 2020Relaxing the Constraints on Predictive Coding Modelscited by 12
  20. 2020Activation Relaxation: A Local Dynamical Approximation to Backpropagation in the Braincited by 11
  21. 2017Learning to represent signals spike by spikecited by 6
  22. 2020Hierarchical Predictive Coding Models in a Deep-Learning Frameworkcited by 4
  23. 2020On Kalman-Bucy filters, linear quadratic control and active inferencecited by 4
  24. 2019Making Predictive Coding Networks Generativecited by 2
  25. 2020A Bayesian perspective on classical controlcited by 1
  26. 2020Investigating the Scalability and Biological Plausibility of the Activation Relaxation Algorithmcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 10; 2023: 13; 2024: 19; 2025: 14; 2026: 14.

74 papers.

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  1. 2024Attention Heads of Large Language Models: A Surveycited by 65
  2. 2022Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation?cited by 45
  3. 2023In search of dispersed memories: Generative diffusion models are associative memory networkscited by 44
  4. 2022Learning on Arbitrary Graph Topologies via Predictive Codingcited by 33
  5. 2023Brain-inspired Computational Intelligence via Predictive Codingcited by 30
  6. 2022Backpropagation at the Infinitesimal Inference Limit of Energy-Based Models: Unifying Predictive Coding, Equilibrium Propagation, and Contrastive Hebbian Learningcited by 26
  7. 2022Hybrid Predictive Coding: Inferring, Fast and Slowcited by 25
  8. 2022A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networkscited by 21
  9. 2022A Theoretical Framework for Inference Learningcited by 17
  10. 2022Predictive Coding beyond Gaussian Distributionscited by 16
  11. 2022BayesPCN: A Continually Learnable Predictive Coding Associative Memorycited by 12
  12. 2024Only Strict Saddles in the Energy Landscape of Predictive Coding Networks?cited by 10
38 more
  1. 2025ARC-NCA: Towards Developmental Solutions to the Abstraction and Reasoning Corpuscited by 10
  2. 2024Predictive Coding Networks and Inference Learning: Tutorial and Surveycited by 7
  3. 2024Continual Learning with Neuromorphic Computing: Foundations, Methods, and Emerging Applicationscited by 7
  4. 2022Preventing Deterioration of Classification Accuracy in Predictive Coding Networkscited by 5
  5. 2022Robust Graph Representation Learning via Predictive Codingcited by 5
  6. 2023Active Sensing with Predictive Coding and Uncertainty Minimizationcited by 5
  7. 2023Extending the Forward Forward Algorithmcited by 5
  8. 2023Interpreting learning in biological neural networks as zero-order optimization methodcited by 4
  9. 2024Directed Structural Adaptation to Overcome Statistical Conflicts and Enable Continual Learningcited by 4
  10. 2024Active Inference and Human--Computer Interactioncited by 4
  11. 2024TeLU Activation Function for Fast and Stable Deep Learningcited by 4
  12. 2025ePC: Fast and Deep Predictive Coding in Digital Simulationcited by 4
  13. 2021PredProp: Bidirectional Stochastic Optimization with Precision Weighted Predictive Codingcited by 3
  14. 2023Curvature-Sensitive Predictive Coding with Approximate Laplace Monte Carlocited by 3
  15. 2024Divide-and-Conquer Predictive Coding: a structured Bayesian inference algorithmcited by 3
  16. 2024A Predictive Approach To Enhance Time-Series Forecastingcited by 3
  17. 2021Predictive coding, precision and natural gradientscited by 2
  18. 2023Learning beyond sensations: how dreams organize neuronal representationscited by 2
  19. 2023Brain-like representational straightening of natural movies in robust feedforward neural networkscited by 2
  20. 2023Meta predictive learning model of languages in neural circuitscited by 2
  21. 2024Classification and Reconstruction Processes in Deep Predictive Coding Networks: Antagonists or Allies?cited by 2
  22. 2024A spatiotemporal style transfer algorithm for dynamic visual stimulus generationcited by 2
  23. 2024pyhgf: A neural network library for predictive codingcited by 2
  24. 2025Closed-Form Feedback-Free Learning with Forward Projectioncited by 2
  25. 2025Bayesian Predictive Codingcited by 2
  26. 2025Introduction to Predictive Coding Networks for Machine Learningcited by 2
  27. 2026Accelerated Predictive Coding Networks via Direct Kolen-Pollack Feedback Alignmentcited by 2
  28. 2021Motion Illusions Generated Using Predictive Neural Networks Also Fool Humanscited by 1
  29. 2023Understanding Predictive Coding as an Adaptive Trust-Region Methodcited by 1
  30. 2023Sleep Deprivation in the Forward-Forward Algorithmcited by 1
  31. 2023Early Action Recognition with Action Prototypescited by 1
  32. 2024Language Reconstruction with Brain Predictive Coding from fMRI Datacited by 1
  33. 2024JPC: Flexible Inference for Predictive Coding Networks in JAXcited by 1
  34. 2024Active Inference for Self-Organizing Multi-LLM Systems: A Bayesian Thermodynamic Approach to Adaptationcited by 1
  35. 2025Spike-based alignment learning solves the weight transport problemcited by 1
  36. 2025An Active Inference perspective on Neurofeedback Trainingcited by 1
  37. 2025Bridging Predictive Coding and MDL: A Two-Part Code Framework for Deep Learningcited by 1
  38. 2025Modeling the Mental World for Embodied AI: A Comprehensive Reviewcited by 1

50 most cited of 74 All 74 (JSON)