HB

Convex analysis meets model checking🧐 Probabilistic model checking can be seen as set inclusion test between a safe region and the achievability set to failure states in MDP. Using convex analysis, we propose a computationally efficient query. arxiv.org/abs/2610.17541

We are excited to have following papers at #NeurIPS2026! I'm proud of all of them, but in particular, it's fantastic to have the first collaboration with my first PhD student @XianliangLi910 on momentum analysis of Muon. Come to see his work 👉 nitter.gq/XianliangLi910/status/…

My latest work: GD's max-margin bias is well-known, but its conv rate is very slow. Still we can observe decent convergence in practice (see fig). I have been thinking it for a while and figured out early weak alignment is possible (with a clean proof!) arxiv.org/abs/2608.04382

To all convex analysis freaks: here's new perspective of flow matching🔭 The denoising operator from the corrupted to the target data is indeed a proximal operator of the Brenier potential (fig 1)! This viewpoint leads to Lyapunov analysis: FM identifies target support (fig 2).

🚨Muon can smash anisotropy of inputs! Our new work investigates learning dynamics of phase retrieval (f(x)=xᵀMx) on the spiked covariance (I+λvvᵀ), for which spectral GD (≒muon) is less affected by the spike direction v than standard GD. arxiv.org/pdf/2601.22652

This is a lovely method because it only needs literally a few lines of codes to make it work (see this!). The code is already made public here: github.com/levelfour/Brenier… And I've been excited to finally collaborate with my longtime friend Yutong, and his smart student Amir!

Delighted to have our "Brenier isotonic regression" accepted at #AISTATS2026! We extend isotonic regression to *multiclass* setup based on Brenier optimal transport, which can be used for multiclass calibration, improving the calibration map nicely over binning etc.

Folks, here's our latest work on convolutional Fenchel-Young losses! We show convex smooth losses can have a linear surrogate regret bound on discrete losses (e.g. 01 loss, Prec@k), and it's relies on inf-conv, which is the most beautiful proof I saw ever. arxiv.org/abs/2505.09432

「『事実』の交差点」がナカニシヤ出版から 3/31 に発売されます。出版記念シンポジウム（3/8@京大吉田キャンパス）の参加登録はまだ受け付けています。ぜひ！ シンポジウム詳細: nitter.gq/HakubiProject/status/1… 参加登録: docs.google.com/forms/d/e/1F… 書籍詳細: nakanishiya.co.jp/book/b1013…

Officially I moved to the Institute of Statistical Mathematics as an associate professor. This was not possible without the supports of my collaborators. I would like to thank all of them and further develop ML theory (+ more!) in the new environment.

🧗‍♂️Why GD converges beyond [step size]<2/[smoothness]? We investigate loss functions and identify their *separation margin* is an important factor. Surprisingly Renyi 2-entropy yields super fast rate T=Ω(ε^{-1/3})! (collab w/ @shinsaku_sakaue @YukiTakeza) arxiv.org/abs/2502.04889