In the world of sphere packing, there’s been debate about whether order or a dash of chaos will give the best results. A recent proof marks a win for order. www.quantamagazine.org/new-sphere-p...

"A simpler nested sampling identity" Interesting blogpost on nested sampling & SMC by Nicolas Chopin statisfaction-blog.github.io/posts/04-06-...

Here's how the gradient flow for minimizing KL(pi, target) looks under the Fisher-Rao metric. I thought some probability mass would be disappearing on the left and appearing on the right (i.e. teleportation), like a geodesic under the same metric, but I was very wrong... What's the right intuition?

Once you have tried symplectic integrators, you never go back.

The full (?) program of talks etc. for BayesComp seems to be online now (bayescomp2025.sg#programme), and looks pretty exciting - I will need to set aside some time to carve out my own schedule!

<proud advisor> Hot off the arXiv! 🦬 "Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation" 🌍 Appa is our novel 1.5B-parameter probabilistic weather model that unifies reanalysis, filtering, and forecasting in a single framework. A thread 🧵

These sparse Gaussian Processes have been around longer than some grad students, but still fun to code! (and today was my first time coding one...)

Today, re-reading a classic.. the 1953 paper that started it all

Cute way to upper bound the connective constant of Z^d. For some length L, enumerate {w_1, w_2, ... , w_N} the Self-Avoiding-Walks of size L. An upper bound is given by the largest eigenvalue of the NxN matrix where M_{i,j}=1 iff there is a SAW of size (L+1) that starts with w_i and ends with w_j.

Approximating N(L), the number of Self-Avoiding-Walks in Z^2 of length L, is an assignment in my Simulation course this year. The connective constant is: C = \lim N(L)^1/L ~ 2.638.. Still open-problem to this day: is it true that 1/C equals the zero of the polynomial P(x)=581*x^4 + 7*x^2 - 13 😱

Sequential Monte Carlo (aka. Particle Socialism?): "why send one explorer when you can send a whole army of clueless one"

Next week is the MCMC chapter of my simulation course. Asked chatgpt to come up with a funny drawing:

I already advertised for this document when I posted it on arXiv, and later when it was published. This week, with the agreement of the publisher, I uploaded the published version on arXiv. Less typos, more references and additional sections including PAC-Bayes Bernstein. arxiv.org/abs/2110.11216

Are you at AAAI in Philadelphia and interested about #tensor-factorizations or #circuits or even both? Then join us today at our tutorial: "From tensor factorizations to circuits (and back!)" Details and materials here april-tools.github.io/aaai25-tf-pc... Time 4:15pm - 6:00pm, Room 117

New video! Terence Tao on how we measure the cosmos: youtu.be/YdOXS_9_P4U

A recording of my talk from this afternoon: youtu.be/jSeXZ6IjKn8?...

Proof smbc-comics.com/comic/proof-3

I'm really looking forward to the CRiSM 2.0 Conference warwick.ac.uk/fac/sci/stat... from 21st-23rd May. We've been lucky enough to get a really nice list of speakers; registrations open now if anyone is in the market for some interesting talks in May.

Don't forget #AABI, the Symposium on Advances in Approximate Bayesian Inference is coming to Singapore!! Co-located #ICLR2025 Workshop Track: February 7, AoE Proceedings Track: February 7, AoE Fast Track: February 18 / March 14, AoE approximateinference.org/call/ #ML #Bayes #GenAI

Tonight, on the taxi ride home, the 72-year-old driver, super friendly and insightful, spent ~10 minutes sharing his first impressions when using DeepSeek, comparing its pros and cons with ChatGPT, and even diving into the potential geopolitical implications 😅

When implementing parallel tempering, it's fashionable to alternate even and odd index temperature swap to try to maximise the inter-temperature movements. But when the temperatures are appropriately tuned, this very new paper by Roberts & Rosenthal shows that the gains are quite modest!

Asked to the students of my "statistical simulation" class: In Buffon's experiment where a needle of length L falls on parallel strips (unit width), the needle crosses 2L/π strips on average. To maximize the accuracy of the resulting estimate of π, how should one choose the length of the needle?

It’s finally out — and I got to blurb it!

Very neat result by Pozza & Zanella: multi-proposal MCMC schemes are basically not worth it! And with GPUs, the gains are at most modest... arxiv.org/abs/2410.23174

Slides for a general introduction to the use of Optimal Transport methods in learning, with an emphasis on diffusion models, flow matching, training 2 layers neural networks and deep transformers. speakerdeck.com/gpeyre/optim...

Villani on the contributions of Joseph Fourier: www.youtube.com/watch?v=Ue-r...

😍😍😍 lmbp.uca.fr/stflour/

🙂

A perfectly trained diffusion/flow model will just memorize the training data, so why isn't it the case in practice? Super interesting work 👇👇

I've been thinking about in-context learning for nearly 3 years. While there is still plenty I don't fully understand, five papers have--to a very large extent--shaped my perspective on it, and I believe everyone should read them.

Some of you might enjoy my lectures on "asymptotics and perturbation methods". youtube.com/playlist?lis... These are ingenious methods for approximating the solutions to integrals and differential equations by exploiting the presence of a small or large parameter in the problem.

Eight years ago, I worked on mathematical modeling of gene regulation. Always, thought why the relevant literature and lessons from this field are not present in popular science. Well, now here it is. A moving piece by @philipcball.bsky.social #biology #gene #emergence nautil.us/how-life-rea...

My book is (at last) out, just in time for Christmas! A blog post to celebrate and present it: francisbach.com/my-book-is-o...

Gauss-Lucas theorem states that the roots of the derivative of a polynomial with complex coefficients always lie within the convex hull of the original polynomial's roots.

A funny result is that any square matrix M can be expressed as the product of two symmetric matrices: M=UV. Maybe surprisingly (?), it seems like just doing a super basic gradient descent on ||M-UV||^2 almost always give such a decomposition...

One #postdoc position is still available at the National University of Singapore (NUS) to work on sampling, high-dimensional data-assimilation, and diffusion/flow models. Applications are open until the end of January. Details: alexxthiery.github.io/jobs/2024_di...

Langevin Monte Carlo (LMC). Just tried to generate a video to visualize the process 😀

Today something crazy happened. POT has reached 1000 citations (total) 🤩🚀. Very proud to be part of a scientific community that acknowledges open source research software. Please continue to use, cite and contribute to POT ! Small🧵below for those interested pythonot.github.io

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!

Fantastic #neurips keynote by Arnaud Doucet! Really like this slide tracing back many of the modern flow-matching / stochastic interpolants ideas to a 1986 result by probabilist Istvan Gyongy describing how to "Markovianize" a diffusion process (eg. having coefficients depending on all the past)

Every Author as First Author, problem solved!

Did you know that randomized Nyström approximation of A is equivalent to running the randomized SVD on A⁰ᐧ⁵? This and other surprising facts on this week's blog post on the "Gram correspondence" www.ethanepperly.com/index.php/20...

copilot, simulate a "Brownian bee" process for me 😛 arxiv.org/abs/2006.06486

A bit ashamed to admit that I've never really read about conformal inference; luckily, we had a very nice seminar talk about it today, so the occasion to code the most basic version of (split) conformal inference. Ten lines of code later, it kinda works & I want to learn more! recommended readings?

Morley's theorem (1899) states that the intersections of the adjacent angle trisectors of any triangle defines an equilateral triangle. https://www.cut-the-knot.org/triangle/Morley/

An artist was hired to write a few equations on the wall of our new building... The calligraphy is a bit special, but I approve of the choice of equation! #mcmc

I'm thinking of asking my stats students next year to come up with at least 10 reasons why this statement is probably misleading 🙂 "participants who consumed ≥5 servings/week of any chocolate showed a 10% lower relative risk of Type 2 diabete"

new laptop arrived and first time I've got a GPU on my MacBook, should I expect #Jax + M4 GPU to just work?

finally over the past weekend, i read <the Atomic Human> by @lawrennd.bsky.social . i couldn't have enjoyed it more, and this will be my go-to recommendation for people who want to know more about AI, its place in history and its consequences and implications. kyunghyuncho.me/the-atomic-h...

Anne Gagneux, Ségolène Martin, @quentinbertrand.bsky.social Remi Emonet and I wrote a tutorial blog post on flow matching: dl.heeere.com/conditional-... with lots of illustrations and intuition! We got this idea after their cool work on improving Plug and Play with FM: arxiv.org/abs/2410.02423