Sam Power

A small note on the "Robustness of random-walk Metropolis for steep potentials", now online at arxiv.org/abs/2608.20279. The starting point is that typical analyses of MCMC methods require structural assumptions on the negative-log-density of the target which prevent it from c…

Robustness of random-walk Metropolis for steep potentials arxiv.org

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. …

Wasserstein Contraction of Coordinate Ascent Variational Inference arxiv.org

You might enjoy arxiv.org/abs/1412.4430. It has a nice duality-based derivation of the dynamic approach to optimal transport (together with some sweet reasoning for why the drift is of gradient type) which can potentially be translated into your discrete-time setting to match …

On the relation between optimal transport and Schrödinger bridges: A stochastic control viewpoint arxiv.org

A bit interesting (as many of the contributions are): proofsandprompts.com/2026/08/30/c...

Care for a little more AI? proofsandprompts.com

It's really a fascinating time for research (in maths, let's say) and kind of shocking how palpably one can feel different things changing. One could quickly understand that LLM tools really shift the floor on what sorts of calculations can now be considered "routine", as a basic example.

Meaningless grumble: I wish that the "forward process" / "reverse process" terminology for diffusion models had instead been "noising process" and "denoising process". Feels a bit related to how I find ambiguity in the use of "top-down" and "bottom-up" w.r.t. neural networks.