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 …

This book is an invitation to discover advanced topics in category theory through concrete,
real-world examples. It aims to give a tour: a gentle, quick introduction to guide later …

String diagrams are a powerful and intuitive graphical syntax, originating in theoretical
physics and later formalised in the context of symmetric monoidal categories. In recent …

Graphical linear algebra is a diagrammatic language allowing to reason compositionally
about different types of linear computing devices. In this paper, we extend this formalism with …

We introduce the resource calculus, a string diagrammatic language for concurrent systems.
Significantly, it uses the same syntax and operational semantics as the signal flow calculus …

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 …

This document is an elementary introduction to string diagrams. It takes a computer science
perspective: rather than using category theory as a starting point, we build on intuitions from …

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 …

Polygraphs are a higher-dimensional generalization of the notion of directed graph. Based
on those as unifying concept, this monograph on polygraphs revisits the theory of rewriting …