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New work arxiv.org/abs/2506.05500 on learning multi-index models with Alex Damian and Joan Bruna. Multi-index are of the form y= g(Ux), where U=r by d maps from d dimension to r dimension and d>>r. g is an arbitrary function. Examples of multi-index models are any neural net

The cost of the military parade on June 14th is 1/5 of the 2024 NSF spending on mathematics research.

Looking to start a probabilistic machine learning residency program at Extropic! Would very much appreciate connection to math/stats/physics PhD students/postdocs that would enjoy working on a contrarian approach to large-scale AI.

We've written a monograph on Gaussian processes and reproducing kernel methods. arxiv.org/abs/2506.17366

Generative thermodynamic computing. arxiv.org/abs/2506.15121

A spring–block phenomenological model with asymmetric friction elucidates the role of nonlinearity and randomness in the theory of feature learning for deep neural networks go.aps.org/3ZTIRwL

The beauty of math book covers from Dover Publications. 😍

Book chapter: "A Dynamical Systems Perspective on the Analysis of Neural Networks" (by Dennis Chemnitz, Maximilian Engel, Christian Kuehn, Sara-Viola Kuntz): arxiv.org/abs/2507.05164

Being a grad student is peak human existence. The end goal of all political and technological progress should be allowing everyone to be a grad student forever

Rados{\l}aw Adamczak: Concentration of measure for non-linear random matrices with applications to neural networks and non-commutative polynomials arxiv.org/abs/2507.07625 arxiv.org/pdf/2507.07625 arxiv.org/html/2507.07625

Great to see this one finally out in PNAS! Asymptotic theory of in-context learning by linear attention pnas.org/doi/10.1073/pn… Many thanks to my amazing co-authors Yue Lu, Mary Letey, Jacob Zavatone-Veth and Anindita Maiti

An excellent intro to advanced linear algebra by Teo Bancha. Goes right upto lie groups, random matrices and curved space-times. arxiv.org/abs/2506.18666

kind of crazy that literally every time I think to myself “ok, I probably don’t need to learn this right now” it ends up being fundamentally important to my research a couple years later

"From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties" (by Gennaro Auricchio, Giovanni Brigati, Paolo Giudici, Giuseppe Toscani): arxiv.org/abs/2507.11387

After studying the mathematics and computation of Sparsity for nearly 20 years, I have just realized that it is much more important than I ever realized before. It truly serves as *the* model problem to understand deep networks and even intelligence to a large extent, from a

Klartag, Lehec: Thin-shell bounds via parallel coupling arxiv.org/abs/2507.15495 arxiv.org/pdf/2507.15495 arxiv.org/html/2507.15495

Why do video models handle motion so poorly? It might be lack of motion equivariance. Very excited to introduce: Flow Equivariant RNNs (FERNNs), the first sequence models to respect symmetries over time. Paper: arxiv.org/abs/2507.14793 Blog: kempnerinstitute.harvard.edu/research/deepe… 1/🧵

Really interesting paper. Fits the theme that we should make our modeling problems harder, not easier, so that they are forced to learn more and generalize better.

Tutorial: "Building Intuition for Dynamical Mean-Field Theory: A Simple Model and the Cavity Method" (by Emmy Blumenthal): arxiv.org/abs/2507.16654

This work is super cool Shikai Qiu! Shows that careful theory (partly our recent completeP extension of muP with Blake Bordelon ☕️🧪👨‍💻 Mufan Li Nolan Dey Lorenzo Noci Joel Hestness Shane Bergsma Cengiz Pehlevan Claire Zhang) allow one to extrapolate reliably from small scale experiments