I’m trying to use Category Theory to turn everything into pictures. So far, I’ve mostly been working in machine learning. By “pictures”, I really mean string diagrams. Here’s the reverse chain rule:

That comes from this paper. See my publications for more!

Research

I’m currently funded by the Ethereum Foundation to work on my project yarrow. If you’re interested in working with me, or you would like to fund my research, please reach out to me at paul AT statusfailed DOT com.

My long term goals are to understand different aspects of computation in terms of category theory, and apply this to building genuinely intelligent machine learning systems that interact with their environments.

One day, I’d like to have a computer completely defined in terms of morphisms of different categories: I imagine the “tower of abstractions” that make a modern computer as a stack of categories with functors between them; all sitting on top of the circuit morphism describing the behaviour of the CPU itself.

More immediately, I am interested in applying Category Theory (and in particular diagrammatic representations) to the following areas:

• Machine learning
• Bayesian modelling
• Compilers (specifically for array programming languages)
• Assembly language and low-level models of computing
• Circuit models

I’m currently an independent researcher working on a grant from the Ethereum Foundation. Previously, I was a Ph.D student at The University of Southampton supervised by Fabio Zanasi and Pawel Sobocinski.

Contact

Here are some places you can find me (Paul Wilson) on the internet: