# Cyber Kittens, or Some First Steps Towards Categorical Cybernetics

arXiv: https://arxiv.org/abs/2101.10483 · HTML: https://mlsanity.com/paper/2101.10483/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2021.

## Built on by (most cited first, 4 of 4)

- [Towards Compositional Interpretability for XAI](https://mlsanity.com/paper/2406.17583/) (2024)
- [Interpreting Dynamical Systems as Bayesian Reasoners](https://mlsanity.com/paper/2112.13523/) (2021)
- [Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energy](https://mlsanity.com/paper/2308.00861/) (2023)
- [Compositional Active Inference II: Polynomial Dynamics. Approximate Inference Doctrines](https://mlsanity.com/paper/2208.12173/) (2022)

## Abstract (arXiv)

We define a categorical notion of cybernetic system as a dynamical realisation of a generalized open game, along with a coherence condition. We show that this notion captures a wide class of cybernetic systems in computational neuroscience and statistical machine learning, exposes their compositional structure, and gives an abstract justification for the bidirectional structure empirically observed in cortical circuits. Our construction is built on the observation that Bayesian updates compose optically, a fact which we prove along the way, via a fibred category of state-dependent stochastic channels.