Authors

Gabriel Peyré

Publications 2

Preprint Open access

Global Exponential Convergence of Two-Layer Linear Network Training

Stephen Y Zhang, Gabriel Peyré · 2026

We prove global exponential (linear) convergence with an explicit rate in the rich scaling for wide two-layer linear networks trained with smooth Polyak-Lojasiewicz predictor losses. Gradient flow in the factors closes exactly in terms of a finite-dimensional Bures flow of the neuron law covariance, in which the predic …

Preprint Open access

Universality and Generalization of Causal Transformers Across Context Lengths

Takashi Furuya, Maarten V. de Hoop, Gabriel Peyré · 2026

Long contexts are central to modern transformer systems, but most expressivity results choose a different network for each fixed sequence length. We study whether one masked transformer can approximate causal token-to-token maps uniformly over sequences of arbitrary length sampling a fixed normalized horizon. To relate …

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