Aaron Roth

How many samples do you need from an unknown distribution in order to train a model with multicalibration error at most epsilon? Answer: 1/epsilon^3 samples is both necessary and sufficient.

AI has now solved a major open problem -- one of the best known Erdos problems called the unit distance problem, one of Erdos's favourite questions and one that many mathematicians had tried. openai.com/index/model-di…

@vishalcseiitg The paper is real only the date is wrong

@Aaroth I know stoica but she works on a different topic.

A clearly hallucinated citation! NeurIPS 2026 decisions aren't out yet. But wait --- the hallucination is also present in the bibtex entries from openreview openreview.net/forum?id=fAjbY… and Google Scholar scholar.googleusercontent.com/scholar.bib?q=…

@Pooyahat Yep

@Aaroth It seems it's just the year that is off?

I just learned about this closely related concurrent paper by Liu, Luo, and Ratliff that went up on arxiv yesterday: arxiv.org/abs/2605.11490 --- it also looks very interesting, check it out!

The paper is here: arxiv.org/abs/2605.09273 --- this is joint work with Zhiming Huang, Jamie Morgenstern, and Claire Jie Zhang.

Recently we showed that the minimax optimal rate for multicalibration is T^{2/3}. But that doesn't mean you have to do that badly on all instances. We give an algorithm that can adapt to easy instances and get better rates while still being minimax optimal in the worst case.

@roydanroy So the more group functions you include, the more permissive the measure is because you've got a larger basis in which to represent the mapping from features to labels.

@roydanroy But if there are groups, moving around a lot is fine so long as the moves are predictable from the contexts in a way that can be detected by the group functions.

I'm giving this talk at the MIT CS theory seminar tomorrow. Stop by if you are around!

What if I want my coding agent to mention goblins? (If you don't know the context for this, I suspect it will become viral soon enough)

@thegautamkamath @eatcs_secretary Woo, congrats and well deserved!

I am honoured (and still a bit stunned) to receive the 2026 Presburger Award from @eatcs_secretary. This recognizes 1 or 2 young scientists for outstanding contributions in theoretical CS This honour is shared w my collaborators, students, institutions, & research community 1/7

We updated our paper --- and solved the open problem highlighted in the old version. Now our lower bound construction has only polylog(1/eps) many groups instead of poly(1/eps) many groups. The construction is also simplified.

--There is a phase change. If the group family |G| is of constant size, Theta(1/eps^2) samples are necessary and sufficient. But when |G| > polylog(1/eps), Omega(1/eps^3) samples are necessary and remain sufficient for any |G| = poly(1/eps). - The upper bounds are randomized.

Some interesting things: - Multicalibration requires substantially more samples than marginal calibration. - Unlike marginal calibration, multicalibration is just as hard to obtain in the batch setting as the online setting.

How many samples do you need from an unknown distribution in order to train a model with multicalibration error at most epsilon? Answer: 1/epsilon^3 samples is both necessary and sufficient.

April is #AIMonthAtPenn! On 4/24, @WarrenCntrPenn faculty affiliate @Aaroth will give the George H. Heilmeier Faculty Award Lecture in Amy Gutmann Hall. More information and registration here: ai.upenn.edu/heilmeier-awar…