# pyhgf: A neural network library for predictive coding

arXiv: https://arxiv.org/abs/2410.09206 · HTML: https://mlsanity.com/paper/2410.09206/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 66 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Deep Predictive Coding Networks for Video Prediction and Unsupervised Learning](https://mlsanity.com/paper/1605.08104/) (2016)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Acme: A Research Framework for Distributed Reinforcement Learning](https://mlsanity.com/paper/2006.00979/) (2020)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [Predictive Coding: a Theoretical and Experimental Review](https://mlsanity.com/paper/2107.12979/) (2021)
- [Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation?](https://mlsanity.com/paper/2202.09467/) (2022)
- [The Neural Coding Framework for Learning Generative Models](https://mlsanity.com/paper/2012.03405/) (2020)
- [Learning on Arbitrary Graph Topologies via Predictive Coding](https://mlsanity.com/paper/2201.13180/) (2022)
- [Benchmarking Predictive Coding Networks -- Made Simple](https://mlsanity.com/paper/2407.01163/) (2024)
- [Causal Reinforcement Learning: A Survey](https://mlsanity.com/paper/2307.01452/) (2023)
- [Predify: Augmenting deep neural networks with brain-inspired predictive coding dynamics](https://mlsanity.com/paper/2106.02749/) (2021)
- [Towards Self-Assembling Artificial Neural Networks through Neural Developmental Programs](https://mlsanity.com/paper/2307.08197/) (2023)
- [Dendritic predictive coding: A theory of cortical computation with spiking neurons](https://mlsanity.com/paper/2205.05303/) (2022)
- [Predictive Coding Networks and Inference Learning: Tutorial and Survey](https://mlsanity.com/paper/2407.04117/) (2024)
- [The generalized Hierarchical Gaussian Filter](https://mlsanity.com/paper/2305.10937/) (2023)

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

- [JPC: Flexible Inference for Predictive Coding Networks in JAX](https://mlsanity.com/paper/2412.03676/) (2024)
- [Closed-form predictive coding via hierarchical Gaussian filters](https://mlsanity.com/paper/2605.20293/) (2026)

## Abstract (arXiv)

Bayesian models of cognition have gained considerable traction in computational neuroscience and psychiatry. Their scopes are now expected to expand rapidly to artificial intelligence, providing general inference frameworks to support embodied, adaptable, and energy-efficient autonomous agents. A central theory in this domain is predictive coding, which posits that learning and behaviour are driven by hierarchical probabilistic inferences about the causes of sensory inputs. Biological realism constrains these networks to rely on simple local computations in the form of precision-weighted predictions and prediction errors. This can make this framework highly efficient, but its implementation comes with unique challenges on the software development side. Embedding such models in standard neural network libraries often becomes limiting, as these libraries' compilation and differentiation backends can force a conceptual separation between optimization algorithms and the systems being optimized. This critically departs from other biological principles such as self-monitoring, self-organisation, cellular growth and functional plasticity. In this paper, we introduce textttpyhgf: a Python package backed by JAX and Rust for creating, manipulating and sampling dynamic networks for predictive coding. We improve over other frameworks by enclosing the network components as transparent, modular and malleable variables in the message-passing steps. The resulting graphs can implement arbitrary computational complexities as beliefs propagation. But the transparency of core variables can also translate into inference processes that leverage self-organisation principles, and express structure learning, meta-learning or causal discovery as the consequence of network structural adaptation to surprising inputs. The code, tutorials and documentation are hosted at: https://github.com/ilabcode/pyhgf.