Ben Grimmer

I spent a year of my PhD stuck on a 2002 problem of Schechtman. GPT 5.5-Pro helped me finish: vector balancing for zonotopes (shadows of a cube)! For any zonotope Z ⊂ ℝᵈ, v₁,...,vₙ ∈ Z, there are signs x₁,...,xₙ ∈ {-1, 1} with x₁v₁+...+xₙvₙ ∈ O(√d) Z, sharp. [1/4]

@CsabaSzepesvari @TaeHo_Y00N Excellent questions, alas with primarily open answers. Everything in our theory is limited to two norms. I'm doubtful our techniques generalize gracefully. Similarly, it's quite tricky to formulate a noncontractive family of problems where distance bounds are tractable

@prof_grimmer @TaeHo_Y00N Very cool! Love this area (and we are a potential costumer in RL). A few questions: Is the norm here 2-norm? How about other norms? Besides contractions, when can we turn the residual bound into a bound to nearest fixed point? Apologies for the naivety of these questions.

I'm excited to share some joint work done with @TaeHo_Y00N. We considered algorithm design for fixed-point problems. This area models gradient descent, minimax optimization, and more. Below I give the wild ride of this paper. Mathematically, it is gorgeous.

Discovering these results with TaeHo has been a delightful experience. I learned a lot. We drew on tools from combinatorics, spectral graph theory, performance estimation, and more. For those interested, the paper is here: arxiv.org/abs/2605.02231

Taking this duality, one may ask for methods that are self-dual. Recursively building a maximally self-dual method gives a simple fractal arc diagram and a new Fractal Self-Dual Method. This FSDM nicely balances anytimeness and robustness; see the paper for details.

My star postdoc Sarit Khirirat (sites.google.com/view/sarit-khi…) is leaving my Optimization & Machine Learning Lab (richtarik.org/i_team.html) to become an Assistant Professor in his home country (Thailand). As you can see, he is completely checked out, enjoying social media (my guess) and matcha at Zed's at KAUST. 😜😎🤟 This means I have an opening for another star postdoc! If you love mathematics, foundations, optimization and machine learning -- and have outstanding track record in highest quality research -- apply! richtarik.org/i_apply.html

"We found that resurrecting the ancient practice of logarithm tables to be useful" -- Terry Tao @ICERM

Walking with Tianjiao and Caleb：Tianjiao will join IBM Research as a Goldstine Fellow before heading to the University of Wisconsin–Madison, and Caleb will join the University of Tennessee, Knoxville as faculty. Congratulations to both!

We just put out a 180-page paper on sampling from the SK model! One big surprise we ran into: the Hessian Ascent algorithms investigated for non-convex optimization have been diffusion models in disguise the whole time! arxiv.org/abs/2605.03718 @JuspreetS @oldheneel

Fresh arxiv paper on our method and analysis: arxiv.org/abs/2604.27078

If you retract/transport vectors by projections or via Taylor approx, you can not trust the resulting subgradients give valid lower bounds. After a year of pushing, we found a bundle method form that (provably) works despite this. I'll comment a link if you want to read more.

Last year, @mateodd25 and Ian McPherson began searching for provably good nonsmooth optimization methods on manifolds. Oh boy, did I quickly learn the hard subtleties of numerical work on manifolds, especially combined with finicky subgradients.

Man, Machine, and Mathematics arXiv:2604.27052 Nonsmooth Riemannian optimization with inexact manifold primitives v... arXiv:2604.27078 Explainable Artificial Intelligence for Financial Integral Equations... arXiv:2604.27127

My lab will present two papers at ICLR 2026 in Rio de Janeiro, Brazil: "Mirror Flow Matching with Heavy-Tailed Priors for Generative Modeling on Convex Domains" and "Adaptive Gradient Descent on Riemannian Manifolds and Its Applications to Gaussian Variational Inference"