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Maxime Meyer

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AAAI Conference 2026 Short Paper

Memorization and Expressivity in Transformers: A Learning-Theoretic Perspective

Maxime Meyer

Transformers have reshaped modern artificial intelligence, yet their theoretical foundations remain incomplete. This thesis investigates the approximation power and memory limitations of transformers. I combine tools from approximation theory and statistical learning theory to provide provable guarantees on expressivity, memorization capacity, and inherent architectural constraints. My contributions include the first rigorous proof of memory bottlenecks in prompt tuning and new results on the expressivity of transformers. The long-term goal of my doctoral research is to develop a principled theoretical framework that grounds the empirical behavior of large-scale transformer models in formal approximation-theoretic results.

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NeurIPS Conference 2025 Conference Paper

Online Learning of Pure States is as Hard as Mixed States

Maxime Meyer
Soumik Adhikary
Naixu Guo
Patrick Rebentrost

Quantum state tomography, the task of learning an unknown quantum state, is a fundamental problem in quantum information. In standard settings, the complexity of this problem depends significantly on the type of quantum state that one is trying to learn, with pure states being substantially easier to learn than general mixed states. A natural question is whether this separation holds for any quantum state learning setting. In this work, we consider the online learning framework and prove the surprising result that learning pure states in this setting is as hard as learning mixed states. More specifically, we show that both classes share almost the same sequential fat-shattering dimension, leading to identical regret scaling. We also generalize previous results on full quantum state tomography in the online setting to (i) the $\epsilon$-realizable setting and (ii) learning the density matrix only partially, using smoothed analysis.

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