3 accepted papers
We study flow-matching transformers when data lie on a low-dimensional manifold. Our key insight is a flow decomposition that splits motion along the manifold from motion off the manifold. The scheme works for first- and higher-order flow matching and ties model complexity to the intrinsic manifold …
Biological neural systems often represent information on low-dimensional manifolds that reflect the topology of their encoded variables. This suggests that neural activity can be naturally organized in geometrically meaningful ways, as seen in rodent head direction cells forming circular manifolds.…
We investigate the statistical and computational limits of latent **Di**ffusion **T**ransformers (**DiTs**) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs score function, as well as the distribution reco…