Gabriel Peyré
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gabrielpeyre.bsky.social
Gabriel Peyré
@gabrielpeyre.bsky.social
What is the set of "means" one can approximate using only arithmetic and harmonic means ? For instance the geometric mean belongs to this closure, but can one approximate any mean sandwitched between the two?
October 29, 2025 at 11:16 AM
Thought of the day: It is somewhat mysterious why Gaussians remain stable under the particle-minimizing flow (i.e. the Wasserstein gradient flow) for so many widely used energies: entropy, Fisher information, quadratic interaction potentials, functionals depending only on mean and covariance,
September 27, 2025 at 12:30 PM
Reposted by Gabriel Peyré
#Communiqué 🗞️ La médaille d'or 2025 du CNRS est décernée à Stéphane Mallat, mondialement reconnu pour ses travaux autour des mathématiques appliquées au traitement du signal et à l’intelligence artificielle. 👏

👉 cnrs.fr/fr/presse/en...

#TalentsCNRS 🏅
September 11, 2025 at 9:29 AM
To meditate while resting on the beach...
August 9, 2025 at 11:15 AM
Fun (...) fact: the only linear operators on matrices that preserves the rank are X->AXB, where A and B are invertible (with X->X^T in the square case). This was apparently first proved (?) in 1959 by Marcus and Moyls.
July 2, 2025 at 11:04 AM
Reposted by Gabriel Peyré
scPRINT is now finally on the Chan Zuckerberg Institute's Model Hub! 🎉 🧬 🌈 It is one more way you can use this cell foundation model to embed, denoise, predict cell type, get gene networks from your data from scratch, or fine-tune it on your own application / usecase: virtualcellmodels.cz...
scPRINT | v1.0 | Virtual Cells Platform
scPRINT is a cell foundation model, also called a Large Cell Model (LCM), trained on single-cell RNA sequence (scRNAseq) data from more than 50M human and mouse cells available through CZ CELLxGENE. Based on the transformer architecture, the model is fully open source and reproducible, with multiple checkpoint sizes available from 2M to 100M parameters. scPRINT demonstrated high performance for genome-wide cell-specific gene network inference when benchmarked against state-of-the-art models (e.g., scGPT, Geneformer v2, GENIE3). In addition, scPRINT has various zero-shot capabilities, including cell embedding, cell label prediction (e.g., cell type, sex, disease), and gene expression imputation, highlighting its potential as a versatile tool for single-cell analysis.
virtualcellmodels.cziscience.com
June 17, 2025 at 9:06 PM
Le prochain Data Science Colloquium à l'ENS, jeudi 12 juin, sera donné par David Louapre d'Ubisoft, "What modern AI and neuroscience can bring to non-playing characters in video games". David c'est bien sûr également le vulgarisateur scientifique de www.youtube.com/scienceetonn...
June 4, 2025 at 7:00 AM
If one of the two distributions is an isotropic Gaussian, then flow matching is equivalent to a diffusion model. This is known as Tweedie's formula. In particular, the vector field is a gradient vector, as in optimal transport. speakerdeck.com/gpeyre/compu...
May 31, 2025 at 10:16 AM
Lectures note for the course of Cyril Letrouit at Collège de France on the quantitative stability of optimal transport.
www.imo.universite-paris-saclay.fr/~cyril.letro...
www.imo.universite-paris-saclay.fr
May 25, 2025 at 9:15 AM
I have cleaned up the notebooks for my course on Optimal Transport for Machine Learners and added links to the slides and lecture notes. github.com/gpeyre/ot4ml
May 25, 2025 at 9:12 AM
I have updated my slides on the maths of AI by an optimal pairing between AI and maths researchers ... speakerdeck.com/gpeyre/the-m...
May 20, 2025 at 11:21 AM
Mon article sur les maths de l’IA est paru dans la gazette de la smf smf.emath.fr/publications...
La version en anglais est sur arxiv
arxiv.org/abs/2501.10465
May 16, 2025 at 10:35 PM
I have cleaned a bit my lecture notes on Optimal Transport for Machine Learners arxiv.org/abs/2505.06589
Optimal Transport for Machine Learners
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributi...
arxiv.org
May 13, 2025 at 5:18 AM
Reposted by Gabriel Peyré
Announcing : The 2nd International Summer School on Mathematical Aspects of Data Science
mathsdata2025.github.io
EPFL, Sept 1–5, 2025

Speakers:
Bach @bachfrancis.bsky.social
Bandeira
Mallat
Montanari
Peyré @gabrielpeyre.bsky.social

For PhD students & early-career researchers
Apply before May 15!
Mathematical Aspects of Data Science
Graduate Summer School - EPFL - Sept. 1-5, 2025
mathsdata2025.github.io
April 14, 2025 at 5:00 PM
Reposted by Gabriel Peyré
Applications are 📣OPEN📣 for #PAISS2025 THE AI summer school in #Grenoble 1-5 Sept! Speakers so far @yann-lecun.bsky.social @dimadamen.bsky.social @arthurgretton.bsky.social @gabrielpeyre.bsky.social @science4all.org A. Cristia J. Revaud M. Caron J. Carpentier M. Vladimirova ➡️ paiss.inria.fr
April 11, 2025 at 1:44 PM
The AI for Science summer school, coorganized by CNRS and U of Chicago will be in Paris, June 30th to july 4th, register asap if you want attend!
datascience.uchicago.edu/events/ai-sc...
AI+Science Summer School 2025 – DSI arrow-right-large arrow-left-smallarrow-right-large-greyarrow-right-large-yellowarrow-right-largearrow-right-long-yellowarrow-right-smallclosefacet-arrow-down...
datascience.uchicago.edu
April 1, 2025 at 4:45 PM
Futur best seller!
March 28, 2025 at 8:08 AM
Reposted by Gabriel Peyré
Characterizing finely the decay of eigenvalues of kernel matrices: many people need it, but explicit references are hard to find. This blog post reviews amazing asymptotic results from Harold Widom (1963!) and proposes new non-asymptotic bounds.
francisbach.com/spectrum-ker...
March 24, 2025 at 2:26 PM
Reposted by Gabriel Peyré
⚡️Check out our workshop tomorrow at @lpiparis.bsky.social, great speakers (@gabrielpeyre.bsky.social, @sdascoli.bsky.social, @samillingworth.com & many more) will cover Theory and Applications of Generative AI + Connexions with neuroscience 🧠
And there's food 🍰
➡️ genai-conference-website.vercel.app
February 26, 2025 at 1:57 PM
Reposted by Gabriel Peyré
@vickykalogeiton.bsky.social and @davidpicard.bsky.social updating live there slides to quote my talk just before ... next level presentation!
February 7, 2025 at 11:57 AM
Reposted by Gabriel Peyré
This is due to a beautiful and little-known covariance identity by Hoeffding (1940):

Cov(x,y) = ∫∫[F(x, y) - F(x)*F(y)] dxdy

So the difference between independence and uncorrelated-ness comes down to point-wise equality vs. a (weaker) integral equality between the CDFs.

2/2
February 1, 2025 at 2:39 AM
Reposted by Gabriel Peyré
Titouan Vayer and I are organizing a one day workshop on optimal transport and machine learning in ENS Lyon on Feb. 17. Registration is free but mandatory. The incredible keynote speakers are Laetitia Chapel, Filippo Santambrogio and @brunolevy01.bsky.social. gdr-iasis.cnrs.fr/reunions/tra...
Transport optimal et ses applications en machine learning et analyse de données - GdR IASIS
Pour les journées scientifiques organisées en 2025 : les inscriptions seront ouvertes à partir de mi-janvier et les demandes de prise en charge de missions seront traitées à partir du 27 janvier. En r...
gdr-iasis.cnrs.fr
January 17, 2025 at 5:12 PM
Reposted by Gabriel Peyré
Excited to see Sigmoid Attention accepted at ICLR 2025 !!

Make attention ~18% faster with a drop-in replacement 🚀

Code:
github.com/apple/ml-sig...

Paper
arxiv.org/abs/2409.04431
Theory, Analysis, and Best Practices for Sigmoid Self-Attention
Attention is a key part of the transformer architecture. It is a sequence-to-sequence mapping that transforms each sequence element into a weighted sum of values. The weights are typically obtained as...
arxiv.org
January 24, 2025 at 6:47 PM
Reposted by Gabriel Peyré
How do tokens evolve as they are processed by a deep Transformer?

With José A. Carrillo, @gabrielpeyre.bsky.social and @pierreablin.bsky.social, we tackle this in our new preprint: A Unified Perspective on the Dynamics of Deep Transformers arxiv.org/abs/2501.18322

ML and PDE lovers, check it out!
January 31, 2025 at 4:56 PM