Cyber Kittens, or Some First Steps Towards Categorical Cybernetics
This work provides a foundational framework for understanding cybernetic systems, which is incremental in applying categorical methods to computational neuroscience and machine learning.
The paper tackles the problem of formalizing cybernetic systems by defining a categorical notion as a dynamical realization of generalized open games, showing it captures systems in computational neuroscience and machine learning and justifies bidirectional cortical circuit structures. The result includes proving that Bayesian updates compose optically via a fibred category of state-dependent stochastic channels.
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.