arXiv:2605.03588v1 Announce Type: cross
Abstract: We introduce a general framework for training flow matching models on Riemannian symmetric spaces, a large class of manifolds that includes the sphere, hyperbolic space and Grassmannians. We exploit their algebraic structure to reformulate flow matching on symmetric spaces as flow matching on a subspace of the Lie algebra of their isometry group, thus linearizing the problem and greatly simplifying the handling of geodesics. As an application, we showcase our framework on the real Grassmannians $operatornameSO(n) / operatornameSO(k) times operatornameSO(n-k)$.
Crisis support teams’ technological openness and learning attitudes toward the AI based virtual patient system crisis support VR
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