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Paul Thompson

Paul Thompson

@ptenigma.bsky.social

1.5K followers 1.3K following 750 posts

Neuroscientist, professor
AI guided tour - https://www.youtube.com/watch?v=fOORfzGjCTA
ENIGMA guided tour - https://www.youtube.com/watch?v=YNjP5nZsJyQ
Diffusion MRI of Brain Diseases - https://www.youtube.com/watch?v=i2jHFm0wcN0 .. more

Paul Thompson is a British-American neuroscientist, and a professor of neurology at the Imaging Genetics Center at the University of Southern California. Thompson obtained a bachelor's degree in Greek and Latin languages and mathematics from Oxford University. He also earned a master's degree in mathematics from Oxford and a PhD degree in neuroscience from University of California, Los Angeles. .. more

Neuroscience 37%

Medicine 18%

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Paul Thompson @ptenigma.bsky.social · 2d

The exponential of a velocity field is the diffeomorphism obtained by following that velocity field for unit time, and the logarithm of a diffeomorphism, when it exists (and this is cool) is the stationary velocity field whose flow produces that map, same idea as matrix exp and log.

Paul Thompson @ptenigma.bsky.social · 2d

*note we use the words exp and log for maps as it comes from the fact that diffeomorphisms form a kind of infinite-dimensional Lie group, and velocity fields are its Lie algebra.. the log is the velocity at time 0 that generates the full path at time 1.

Paul Thompson @ptenigma.bsky.social · 2d

🔥So you can now generate text and molecules in one-shot !!
[1] x.com/osclsd/statu... and arxiv.org/html/2602.12...
[2] x.com/PTenigma/sta...
[3] x.com/PTenigma/sta...
*

Paul Thompson @ptenigma.bsky.social · 2d

🔥The cool new paper [1] extends this framework to discrete data by embedding tokens in the probability simplex, allowing flows to be defined on a continuous manifold where this exact same geometric transport theory applies.

Paul Thompson @ptenigma.bsky.social · 2d

If the time-dependent flow is on the time interval [0,1], you can easily make intermediate samples by linear interpolation at times 0 < s < t < 1 and marginalise (weight these) over the data density to get the displacement of the source distribution Phi(t) given Phi(s).

Paul Thompson @ptenigma.bsky.social · 2d

If the time-dependent flow is on the time interval [0,1], you can easily make intermediate samples by linear interpolation at times 0 < s < t < 1 and marginalise (weight these) over the data density to get the displacement of the source distribution Phi(t) given Phi(s).

Paul Thompson @ptenigma.bsky.social · 2d

...between a reference distribution (usually n-dimensional Gaussian) and the target distribution you want to model (available as examples). ..🔥And flow matching builds this flow by systematically taking pairs of points in the source and target (the target is your training examples).

Paul Thompson @ptenigma.bsky.social · 2d

🔥This really ingenious paper (Categorical Flow Matching [1]) came out today.
🔥 TL;DR: generates molecules, text, images
🔥As I said yesterday [2,3], you can use generative AI to make images (or molecules) with certain properties and learn their full distribution by learning a flow ... (thread below)

Paul Thompson @ptenigma.bsky.social · 14d

Nicely organised cats

Paul Thompson @ptenigma.bsky.social · 16d

Although I never drove an Uber, they sent tax forms to the IRS saying I earned ~$30k (got another one today). I reported the identity theft to IRS/FTC/Uber (hopefully fixed it). Still curious who’s driving an Uber as me -ask them some tough neuro questions if Paul Thompson pops up in your Uber app!!

Paul Thompson @ptenigma.bsky.social · 18d

If you like modern AI with latent diffusion + flow matching, take a look at [1] well before latent diffusion, you will see how natural variation can arise naturally from statistical laws built with PDEs, continuum mechanics, + Bayesian priors that arise from these operators+their Green's functions.

Paul Thompson @ptenigma.bsky.social · 18d

This later led to metric pattern theory, a general framework to understand variation in objects, a general theory of metrics on diffeomorphisms, and procedures to construct flows that do not fold (diffeomorphisms) by integrating velocity fields.

Paul Thompson @ptenigma.bsky.social · 18d

..the deformations u(x) result from a stochastic differential equation Lu = e, where L is a self-adjoint differential operator, whose covariance can be learned from data, and may be non-stationary.

Paul Thompson @ptenigma.bsky.social · 18d

But work by Michael Miller, Ulf Grenander, and the Brown Pattern Theory school showed that natural variation in brain geometry, and function, could be modelled as a set of probabilistic transformations of a template, where ..

Paul Thompson @ptenigma.bsky.social · 18d

In the 1990s, as statistical parametric mapping was being developed, the standard way to study disease effects on the brain was to average images together.

Paul Thompson @ptenigma.bsky.social · 18d

Brilliant talk by Michael Miller at USC today. Michael has inspired countless generations of students, including me in the 1990s when his work with Ulf Grenander [1] helped new generations of mathematicians get involved with medical imaging and neuroscience.
[1] www.ams.org/journals/qam...

Paul Thompson @ptenigma.bsky.social · 19d

Brilliant to catch up with giants in neuroimaging + genetics, Anders Dale and Ole Andreassen. Thank you to Pravesh Parekh from the J Craig Venter Institute for a great talk on detecting time-dependent genomic effects on the brain, and his FEMA method to accelerate massively parallel GWAS analyses.

Paul Thompson @ptenigma.bsky.social · 20d

Hurray, many congrats !! :) 🎉

Paul Thompson @ptenigma.bsky.social · 21d

Thrilled to welcome Dr. Pauline Favre on a Fulbright Fellowship to work with us on international neuroimaging in bipolar disorder! International exchange speeds up science + medicine, opens doors to training+resources; helps everyone reach their potential

Paul Thompson @ptenigma.bsky.social · 22d

Thank you to my daughter Lauren Thompson for making this cool flyer + posting it around campus !

Paul Thompson @ptenigma.bsky.social · 26d

PUZZLE question (asking for a friend):
Does the fastest (shortest) flight from South Africa to Los Angeles go through: 1. Greenland*, 2. Brazil, 3. ask the cool bird ?
* so long as nobody is invading it

Paul Thompson @ptenigma.bsky.social · 27d

The weather got worse

Paul Thompson @ptenigma.bsky.social · 28d

This wasn't a very sensible way to get home, or edit papers for Friday's EMBC conference deadline

Paul Thompson @ptenigma.bsky.social · 28d

A world map
*yes there are no people (only mad dogs and Englishmen go out in the mid day sun)

Paul Thompson @ptenigma.bsky.social · 28d

Haha exactly :)

Paul Thompson @ptenigma.bsky.social · 28d

Today I learned you should stand still if a paraglider is approaching

Paul Thompson @ptenigma.bsky.social · Jan 18

Haha I bet the film crew decided they had to go to Switzerland :)

Paul Thompson @ptenigma.bsky.social · Jan 18

I hadn’t see these Alex and now I am going to be hooked on them!! I miss all these places but somehow only go visit for about a day at a time - more great places for the list thank you 🙏

Paul Thompson @ptenigma.bsky.social · Jan 17

Cheerio England, sad to leave