Cybernetic systems self-adapt through the observations they make of the 'environment' which interacts with them. In games, this dynamics brings players to play equilibria. In machine learning, it makes models learn from a dataset and RL agent adapt to an environment. In control theory, it keeps systems in a viable state.
Category theory can put the mathematical treatment of these systems on strong and flexible foundations. We can then use string diagrams to describe systems compositionally, categorical logic to impose guarantees on their behaviour, and functional programming to produce efficient and effable programs to analyse them.
My main research focus is develop structural primitives for cybernetics, working in the groove of categorical systems theory. A concrete goal is characterizing good regulators abstractly, and develop a modern, model-free internal model principle.
Reading list
- The series of posts on open cybernetics on this blog
- Towards Foundations of Categorical Cybernetics by me, Bruno Gavranovic, Jules Hedges, Eigil Fjeldgren Rischel
- From categorical systems theory to categorical cybernetics, by me
- Mathematical Foundations for a Compositional Account of the Bayesian Brain, by Toby St Clere Smithe
- A Bayesian Interpretation of the Internal Model Principle, by Manuel Baltieri, Martin Biehl, Nathaniel Virgo, and me
