As an experiment, I tried to use automated tools to formalize (in as "mindless" a fashion as possible) a one-page human written proof into Lean. You can watch the results here: www.youtube.com/watch?v=cyyR...

Scientists, in their purest form, are interested only in truth, capable of self-criticism along with respectful but fierce disagreement with peers, and willing to sacrifice comfort in pursuit of these values

So you can see why, in being so opposite of the people now in power, they become the enemy.

Slicing Unbalanced Optimal Transport

Clément Bonet, Kimia Nadjahi, Thibault Sejourne, Kilian FATRAS, Nicolas Courty

Action editor: Benjamin Guedj

https://openreview.net/forum?id=AjJTg5M0r8

#transport #outliers #optimal

I wrote a blog post on how quaternions can be used to derive the equations of spherical geometry, as well as the sunrise equation relating the time of sunrise or sunset to one's latitude and the declination of the Sun. terrytao.wordpress.com/2024/12/19/q...

Great talk by Luigi Ambrosio at the International Congress of Mathematicians (ICM) 2018: youtu.be/JCHNQWhcSLs?...
Quote:
“The relevance of the identifications of concepts stated in Eulerian terms with those stated in Lagrangian terms is not sufficiently recognized when everything is smooth.”

Hellinger and Wasserstein are the two main geodesic distances on probability distributions. While both minimize the same energy, they differ in their interpolation methods: Hellinger focuses on density, whereas Wasserstein emphasizes position displacements.

Convex functions are differentiable (Hans Rademacher, 1919) and twice differentiable (Alexandre Alexandrov, 1939) almost everywhere. en.wikipedia.org/wiki/Alexand...

Exciting news! 🚀 The Learning Meaningful Representations of Life ( #LMRL 🌟) workshop is returning at #ICLR2025! 🎉

On 27th / 28th April 2025 in Singapore 🇸🇬, this popular event returns with a fresh organizing team 👇 & bold new ideas 🧠 to explore bridging AI & life sciences 🧬

After watching this beautiful keynote by @arnauddoucet.bsky.social , I *had* to give these Schrodinger bridges a try! Very interesting to be able to "straighten" a basic flow-matching approach. Super cool work by @vdebortoli.bsky.social & co-author!

Optimal transport computes an interpolation between two distributions using an optimal coupling. Flow matching, on the other hand, uses a simpler “independent” coupling, which is the product of the marginals.

It is well known that symmetric matrices can be diagonalized on R. A lesser known, more general, result is that if A and B are symmetric d x d matrices and A is positive definite, then AB is diagonalizable.