Sam Power
@spmontecarlo
Lecturer in Maths & Stats at Bristol. Interested in probabilistic + numerical computation, statistical modelling + inference. (he / him). Homepage: Seminar:
Around this claim that "canonicalisation [...] is the stage least amenable to optimisation by AI tools", I might not agree without additional context. I agree that canonicalisation of new work is likely to be more difficult, but equally, it's not the only part deserving of 'refactoring' in this way.
Lots of interesting bits and pieces cropping up in (what I've encountered of) Tao's ICM talk. I do find that this aspect of 'digestion' of mathematics is generally quite exciting to me, particularly in terms of revisiting established work. (I do understand why it's less lucrative in the short term)
A pair of notes which review and optimise a couple of fun (and by now, reasonably well-established) techniques for showing the 'contraction-on-average' property for stochastic systems, focusing on problems for which the 'obvious' metrics do not contract. (links below)
interesting stuff here: x.com/mehtaab_sawh..., and a bit funny to see the Random Walk Metropolis show up in this context. some inspiration for me to try read it properly and learn something new!
The closest I'm getting to home today (stuck at Schiphol on the journey back from Zurich!):
fiddling with the stochastic heat equation (during a talk which is partially about this)
Under these assumptions, we get a very simple proof of convergence, with a nice clean rate, and with lots of flexibility to account for e.g. local convergence, non-smoothness, and so on.
In particular, the functional-analytic approach allows one to solve problems which may not be 'literally' convex (e.g. involving log-concave measures), but which are nevertheless 'morally' convex (in terms of having the right tail behaviour, the right connectivity properties, and so on).
CAVI is a coordinate ascent method for solving this problem: fixing all components but one, find the optimal remaining factor, and then iterate. In this regard, it has a similar flavour to Gibbs sampling, the EM algorithm, and so on.
CAVI is a computational method for mean-field approximation, i.e. approximating a complicated probability measure by a product measure / approximating an arbitrary random variable with a random variable whose entries are independent of one another.
With friends at the University of Warwick (in particular, Rocco Caprio and @adriencorenflos.bsky.social), we've recently arXived some work (arxiv.org/abs/2605.30253) on a method for approximate inference known as "Coordinate Ascent Variational Inference", or "CAVI" for short. Let me explain:
A quick pass at the translation, which seems to come together pretty cleanly in the end! Anyways, I should probably just read the paper, but thought it couldn't hurt to share.
I didn't become a mathematician to have to see numbers like 20/3! (sources math.stackexchange.com/questions/82..., x.com/SSRS_cp/stat...).
Always found this type of trick very cute (I guess an instance of 'lifting?):
may have sent before, but anyhow: arun-kuchibhotla.github.io/assets/other...