# Introduction to Predictive Coding Networks for Machine Learning

arXiv: https://arxiv.org/abs/2506.06332 · HTML: https://mlsanity.com/paper/2506.06332/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 31 May 2025.

## Builds on (most cited first, 9 of 9)

- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Deep Predictive Coding Networks for Video Prediction and Unsupervised Learning](https://mlsanity.com/paper/1605.08104/) (2016)
- [Predictive Coding Approximates Backprop along Arbitrary Computation Graphs](https://mlsanity.com/paper/2006.04182/) (2020)
- [Predictive Coding: a Theoretical and Experimental Review](https://mlsanity.com/paper/2107.12979/) (2021)
- [Hybrid Predictive Coding: Inferring, Fast and Slow](https://mlsanity.com/paper/2204.02169/) (2022)
- [A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networks](https://mlsanity.com/paper/2212.00720/) (2022)
- [A Theoretical Framework for Inference Learning](https://mlsanity.com/paper/2206.00164/) (2022)
- [Tight Stability, Convergence, and Robustness Bounds for Predictive Coding Networks](https://mlsanity.com/paper/2410.04708/) (2024)
- [Predictive Coding with Spiking Neural Networks: a Survey](https://mlsanity.com/paper/2409.05386/) (2024)

## Built on by (most cited first, 2 of 2)

- [K-Way Energy Probes for Metacognition Reduce to Softmax in Discriminative Predictive Coding Networks](https://mlsanity.com/paper/2604.11011/) (2026)
- [Topological Simplification in Predictive Coding Networks](https://mlsanity.com/paper/2608.02816/) (2026)

## Abstract (arXiv)

Predictive coding networks (PCNs) constitute a biologically inspired framework for understanding hierarchical computation in the brain, and offer an alternative to traditional feedforward neural networks in ML. This note serves as a quick, onboarding introduction to PCNs for machine learning practitioners. We cover the foundational network architecture, inference and learning update rules, and algorithmic implementation. A concrete image-classification task (CIFAR-10) is provided as a benchmark-smashing application, together with an accompanying Python notebook containing the PyTorch implementation.