Cyber Kittens, or Some First Steps Towards Categorical Cybernetics

TL;DR

This paper introduces a categorical framework for cybernetic systems, unifying concepts from neuroscience and machine learning, and explains their compositional structure and bidirectional interactions.

Contribution

It defines a new categorical notion of cybernetic systems as dynamical realizations of open games with coherence, linking them to neural and machine learning models.

Findings

Categorical cybernetic systems encompass neural and machine learning models.

Bayesian updates compose optically within this framework.

The approach provides an abstract justification for bidirectional cortical circuits.

Abstract

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.