Iolo Jones

thanks so much!!

We apply these tools for geodesic distances, data topology, PDES, vector field flows, curvature, Morse theory...

Take a look at arxiv.org/abs/2602.06006

Our method generalises easily to all the operators in geometry, e.g. the divergence and the vorticity (2-form) of vector fields:

Calculus / geometry are used everywhere in theory, but are hard to apply directly to data in practice. Diffusion geometry lets you compute them on arbitrary data manifolds.

e.g. finding the gradient vector field of a function:

I'm so happy to finally share this work - Computing Diffusion Geometry

We present a simple, data-driven method for the *whole* toolkit of Riemannian geometry, PDEs, and vector calculus!

It's epoch 50. Do you know whether your LLM is grokking?

It's epoch 50. Do you know whether your LLM is grokking?

In our #NeurIPS2025 paper "Less is More: Local Intrinsic Dimensions of Contextual Language Models," we study how the local intrinsic dimension (LID) of embeddings changes during training and fine-tuning.

#research

🧵1/n

Pretty humbled to win one of the poster prizes at the joint BMC/BAMC conference this week for my work with @nina-otter.bsky.social and Renata Turkeš on persistent homology transforms!

Check out our paper here if you haven’t already arxiv.org/pdf/2412.18452

Iolo Jones (02/26/25): New methods in diffusion geometry YouTube video by Applied Algebraic Topology Network

also contains a rant about why manifolds don't exist
www.youtube.com/watch?v=rbBEs0E4XSY

Thanks a lot to AATRN for having me yesterday!

See below for my talk about diffusion geometry, including new stuff like geodesics, PDEs e.g. wave equation, and circular coordinates

A picture of a fantasy-style map of Vienna, a photo of Annabelle and a series of geoart sketches

I’m SO excited and grateful to be one of the artists in residence at @eurogeosciences.bsky.social this year! Looking forward to lots of discussions about #geoart 🌋🦖

You can read more about it here t.co/hNC8fnU13N and introduce yourself to Liliane, another artist in residence!

Is there another way??

That’s amazing where is it?

Very pleased to announce that our package for Multiscale Spatial Analysis - MuSpAn - has landed!

The preprint is on biorxiv now, but you can find a lot more details at www.muspan.co.uk, including documentation, worked tutorials (an ever-expanding list), install guides, and how to get the code!