mlsanityData to 14 Oct 2026

Learning on Arbitrary Graph Topologies via Predictive Coding

arXiv 2201.13180 ↗First posted 31 Jan 2022cs.LGcited by 33

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Abstract (arXiv)

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. This process is highly effective when the goal is to minimize a specific objective function. However, it does not allow training on networks with cyclic or backward connections. This is an obstacle to reaching brain-like capabilities, as the highly complex heterarchical structure of the neural connections in the neocortex are potentially fundamental for its effectiveness. In this paper, we show how predictive coding (PC), a theory of information processing in the cortex, can be used to perform inference and learning on arbitrary graph topologies. We experimentally show how this formulation, called PC graphs, can be used to flexibly perform different tasks with the same network by simply stimulating specific neurons, and investigate how the topology of the graph influences the final performance. We conclude by comparing against simple baselines trained~with~BP.

Key facts. Cited by 33 papers in the map (data through 14 Oct 2026). Builds on 16 of its 64 references that are in the map. First posted on arXiv 31 Jan 2022.

Builds on

16 of 64 references.

References · 16

  1. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  2. 2016Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagationcited by 259
  3. 2016Dense Associative Memory for Pattern Recognitioncited by 236
  4. 2016Deep Predictive Coding Networks for Video Prediction and Unsupervised Learningcited by 204
  5. 2021Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systemscited by 128
  6. 2018Dendritic cortical microcircuits approximate the backpropagation algorithmcited by 97
  7. 2020Predictive Coding Approximates Backprop along Arbitrary Computation Graphscited by 90
  8. 2021Predictive Coding: a Theoretical and Experimental Reviewcited by 77
  9. 2020Training End-to-End Analog Neural Networks with Equilibrium Propagationcited by 63
  10. 2020The Neural Coding Framework for Learning Generative Modelscited by 44
  11. 2021Associative Memories via Predictive Codingcited by 44
  12. 2017Artificial Intelligence and Statisticscited by 43
4 more
  1. 2018Biologically Motivated Algorithms for Propagating Local Target Representationscited by 43
  2. 2018Generalization of Equilibrium Propagation to Vector Field Dynamicscited by 23
  3. 2021Reverse Differentiation via Predictive Codingcited by 23
  4. 2020Relaxing the Constraints on Predictive Coding Modelscited by 12

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 8; 2023: 5; 2024: 7; 2025: 5; 2026: 8.

33 papers.

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  1. 2022Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation?cited by 45
  2. 2023Brain-inspired Computational Intelligence via Predictive Codingcited by 30
  3. 2024Benchmarking Predictive Coding Networks -- Made Simplecited by 30
  4. 2022Backpropagation at the Infinitesimal Inference Limit of Energy-Based Models: Unifying Predictive Coding, Equilibrium Propagation, and Contrastive Hebbian Learningcited by 26
  5. 2022A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networkscited by 22
  6. 2022A Theoretical Framework for Inference Learningcited by 17
  7. 2022A Theoretical Framework for Inference and Learning in Predictive Coding Networkscited by 17
  8. 2022Predictive Coding beyond Gaussian Distributionscited by 16
  9. 2023Sequential Memory with Temporal Predictive Codingcited by 16
  10. 2024Predictive Coding Networks and Inference Learning: Tutorial and Surveycited by 7
  11. 2023Block-local learning with probabilistic latent representationscited by 6
  12. 2023Predictive Coding beyond Correlationscited by 6
21 more
  1. 2024A Review of Neuroscience-Inspired Machine Learningcited by 6
  2. 2022Preventing Deterioration of Classification Accuracy in Predictive Coding Networkscited by 5
  3. 2022Robust Graph Representation Learning via Predictive Codingcited by 5
  4. 2025Bidirectional predictive codingcited by 5
  5. 2024Divide-and-Conquer Predictive Coding: a structured Bayesian inference algorithmcited by 3
  6. 2026Faster Predictive Coding Networks via Better Initializationcited by 3
  7. 2024pyhgf: A neural network library for predictive codingcited by 2
  8. 2025Toward Practical Equilibrium Propagation: Brain-inspired Recurrent Neural Network with Feedback Regulation and Residual Connectionscited by 2
  9. 2023Deep Predictive Coding with Bi-directional Propagation for Classification and Reconstructioncited by 1
  10. 2025Bridging Predictive Coding and MDL: A Two-Part Code Framework for Deep Learningcited by 1
  11. 2026Predictive Coding Graphs are a Superset of Feedforward Neural Networkscited by 1
  12. 2026Closed-form predictive coding via hierarchical Gaussian filterscited by 1
  13. 2026Augmented Lagrangian Predictive Codingcited by 1
  14. 2024Nature-Inspired Local Propagationcited by 0
  15. 2024Predictive Attractor Modelscited by 0
  16. 2025Meta-Representational Predictive Coding: Neuroscience-Informed Self-Supervised Learningcited by 0
  17. 2025DMPCN: Dynamic Modulated Predictive Coding Network with Hybrid Feedback Representationscited by 0
  18. 2026Learning Long-Range Dependencies with Temporal Predictive Codingcited by 0
  19. 2026Spiking Graph Predictive Coding for Reliable OOD Generalizationcited by 0
  20. 2026Bio-inspired Learning and Decision-Making with Probabilistic In-Memory Computing Hardware: Part 1cited by 0
  21. 2026Analog-Friendly Predictive Coding without Activation Derivativescited by 0