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 …

Artificial intelligence (AI) is currently based largely on black-box machine learning models
which lack interpretability. The field of eXplainable AI (XAI) strives to address this major …

We introduce diagrammatic differentiation for tensor calculus by generalising the dual
number construction from rigs to monoidal categories. Applying this to ZX diagrams, we …

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 …

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 …

This thesis introduces quantum natural language processing (QNLP) models based on a
simple yet powerful analogy between computational linguistics and quantum mechanics …

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of
new evidence. If the process is believed to have a complex compositional structure, we may …

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 study the two dual quantum information effects to manipulate the amount of information
in quantum computation: hiding and allocation. The resulting type-and-effect system is fully …

We study semantic models of probabilistic programming languages over graphs, and
establish a connection to graphons from graph theory and combinatorics. We show that …