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Colloquium

Provable Self-Improvement via Coherence

Speaker: Mehryar Mohri (NYU) Professor of Computer Science and Mathematics Courant Institute of Mathematical Sciences New York University Wednesday, October 28, 2026 12:00PM - 1:00PM Lunch 11:30am-12:00pm Talk 12:00pm-1:00pm Location: Yale Institute for Foundations of Data Science & Webcast, 219 Prospect Street, 13th Floor, New Haven, CT 06511 and via Webcast: https://yale.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=80ffc32e-88ea-461a-94ac-b4ec014a5e7a

Abstract: Self-improvement, in which a model is trained on its own outputs, is now a standard ingredient of post-training for large language models: self-consistency, self-refine, self-rewarding models, and RLAIF all rely on it. Yet these methods have the model judge itself, and none comes with a guarantee that the update cannot make things worse.

This talk asks: with no new labels, what information can a model exploit to provably improve?

We propose *coherence*. Coherence is a convex constraint satisfied by the ideal model, and, crucially, one the model can check on itself using an ability (recognizing equivalence) that is far easier than the task itself. We show that the Bregman projection of a baseline model onto the coherent set improves the loss against every coherent ground truth by at least the distance moved, that this guarantee is maximin optimal, and that it degrades gracefully under approximately coherent truths, finite samples, and soft constraints.

Across several divergences, orbit averaging is the unique universal improver and no universal improver exists otherwise. Conversely, every mechanism with a provable guarantee is a Bregman projection onto an induced coherence set, a structure that is rigid across generators. Finally, Fenchel duality turns answer-level coherence into a two-player game whose updates are GRPO steps, yielding label-free accuracy gains on TriviaQA and GSM8K.

Joint work with Jon Schneider and Yifan Wu.

Speaker Bio: Mehryar Mohri is a Distinguished Scientist at Google Research, where he leads the ML Theory team, and a Professor at the Courant Institute of Mathematical Sciences, New York University, where he has been on the faculty since 2004. Before joining NYU and Google, he spent a decade at AT&T Bell Labs and AT&T Labs–Research, in the later years as a Research Department Head and then as a Technology Leader, and he taught at the Ecole Polytechnique and the University of Paris 7. He studied at the Ecole Polytechnique and the Ecole Normale Superieure (Ulm) and received his Ph.D. in computer science from the University of Paris 7.

A theoretical computer scientist and mathematician, he works on machine learning theory and algorithms, including statistical learning theory, optimization, reinforcement learning, online learning and games, and decision making under uncertainty. His recent research addresses the foundations of large language models: post-training and alignment, self-improvement, and sequence models that combine Transformers with weighted automata. He is the lead author of “Foundations of Machine Learning” (MIT Press), a reference and textbook widely used in graduate courses and research around the world.

His learning algorithms have been used in a variety of impactful applications at Google. His theory and algorithms for weighted automata and transducers have been the core technology behind Google’s Voice Search and Gboard and are used in many deployed systems across the industry. He is also a key contributor to the core algorithms of open-source libraries such as OpenFst. His research has received numerous best paper awards, most recently at EC 2025. He is President of the Association for Algorithmic Learning Theory and an action editor of the Journal of Machine Learning Research, and he has served as program co-chair of COLT and ALT.

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