We propose a categorical semantics of gradient-based machine learning algorithms in terms
of lenses, parametric maps, and reverse derivative categories. This foundation provides a …

We propose a categorical framework for processes which interact bidirectionally with both
an environment and a'controller'. Examples include open learners, in which the controller is …

We spell out the paradigm of exact conditioning as an intuitive and powerful way of
conditioning on observations in probabilistic programs. This is contrasted with likelihood …

We define a probabilistic programming language for Gaussian random variables with a first-
class exact conditioning construct. We give operational, denotational and equational …

Probability theory and statistics are fundamental disciplines in a data-driven world. Synthetic
probability theory is a general, axiomatic formalism to describe their underlying structures …

We universally characterize the produoidal category of monoidal lenses over a monoidal
category. In the same way that each category induces a cofree promonoidal category of …

We introduce the normal produoidal category of monoidal contexts over an arbitrary
monoidal category. In the same sense that a monoidal morphism represents a process, a …

We compare two possible ways of defining a category of 1-combs, the first intensionally as
coend optics and the second extensionally as a quotient by the operational behaviour of 1 …

Morphisms in a monoidal category are usually interpreted as processes, and graphically
depicted as square boxes. In practice, we are faced with the problem of interpreting what …

This dissertation reports some first steps towards a compositional account of active inference
and the Bayesian brain. Specifically, we use the tools of contemporary applied category …