Rob Cornish

@ruminaik There's a growing community interested in categorical approaches to probability as an alternative to measure theory. It's natural to ask how far these approaches can go. This paper shows that with the right setup, they can encompass substantive topics in modern MCMC.

@ruminaik Thanks for your comment. Building on arXiv:2012.14881, which gave sufficient conditions, we also give necessary conditions for reversibility and skew-reversibility of a general MH-type sampler. That said, our motivation is broader than these specific technical results:

A categorical account of the Metropolis-Hastings algorithm arxiv.org/abs/2601.22911 Joint work with Andi Wang. We give algebraic (i.e. measure theory-free) necessary and sufficient conditions for an abstract Metropolis-Hastings-type sampler to be reversible wrt a given target.🧵

With this additional structure, we can formulate an abstract version of an involutive-style MH kernel and give conditions under which it is reversible. When instantiated in terms of measure theory, we recover the results of Andrieu et al. (arxiv.org/pdf/2012.14881).

We also study CD categories enriched over commutative monoids. This provides an expressive setting for reasoning about: * Substochastic kernels * Probability values * Finiteness and sigma-finiteness * (Pointwise) absolute continuity * Singular measures * Lebesgue decompositions

I still have positions available for a January 2026 intake - get in touch ASAP! Later intakes are also possible (please get in touch to discuss). For more information, and details on how to apply, please see: jrmcornish.github.io/recruitment.ht…

We develop methodology with precise guarantees under minimal assumptions, with large-scale safety-critical applications in mind. We also develop better tools for describing and reasoning about AI systems, using category theory, programming languages theory, and proof assistants.

I'm looking for talented and ambitious PhD students to join me at Nanyang Technological University Singapore to work on safe and robust AI systems! Full scholarships covering tuition and a stipend are available, and are open to local and international students alike.

We finally have the strong law of large numbers in Markov categories. arxiv.org/abs/2503.21576

@leoeleoleo1 Much more

part of the fun of this project was being able to find a practical application of category theory (more to come?)

You can also find an extended abstract of my longer Markov categories paper here: arxiv.org/abs/2412.09469

If this is of interest to you, here is a recent talk that @PaoloPMath and I gave for a class at MIT: youtube.com/watch?v=ozN4zL…

A meta-point of this paper is that category theory has utility for reasoning about current problems of interest in mainstream machine learning. The theory is predictive, not just descriptive. 🧵(1/6)

Awesome work by @leoeleoleo1 @kiaashour and led by excellent and inspiring @rob_cornish !

@DavidCorfield8 @PaoloPMath @mattecapu I wasn't sure what this was adding, so I removed it in a later version. Would indeed be keen to discuss!

@DavidCorfield8 @PaoloPMath @mattecapu This is interesting. At one stage I described the bijection (12) as an equivalence of categories between the full image of R and the co-Kleisli category of the comonad ER. (Remark 5.1 of arxiv.org/abs/2406.11814… )

This is such an outstanding paper, incredible stuff 🤯