La recherche

This collective introduction presents the historical, institutional, and mathematical context of the forty-year correspondence between Gösta Mittag-Leffler and Vito Volterra. It traces their relationship, the development of Acta Mathematica, Volterra’s international career, the emergence of functional analysis, and the effects of the First World War.

Drifting models offer a promising route to faster generative AI: they perform gradual transport during training, while generating new samples in a single step. This paper asks whether the underlying drifting process can converge rapidly to a target distribution under ideal conditions, before finite-data or optimization effects are introduced. We show that its convergence rate depends critically on how it handles spatial scale. With a single fixed resolution, fine-scale features of the target can become nearly invisible, leading to extremely slow convergence. We introduce a multihead approach that combines scale-normalized information across a continuum of resolutions. We prove that this multihead approach restores exponential convergence near standard reference distributions. These results identify fixed resolution as a key bottleneck and provide a simple route to faster one-step generative models.