Scene Adaptation as Radial Transport in Hyperbolic Space

Top-leading solutions for scene adaptation typically build on pseudo-label self-training with cross-domain mixing. Though demonstrating steady gains in mean IoU, they remain less reliable on small and rare categories: we observe that self-training improves large categories such as truck and sky while degrading bicycle and rider. In this paper, we reveal the underlying nature of this phenomenon: these approaches regulate how far features move but overlook their direction, and thus fall short in balancing domain alignment against label preservation. To this end, we introduce RadDA, which formulates scene adaptation as radial transport in hyperbolic space. Drawing inspiration from the observation that, in a low-dimensional Poincaré ball, the class of a pixel is encoded in its angle, rare categories occupy the narrowest sectors, and the domain shift is only partially radial, RadDA measures this trade-off by the angular action $\epsilon$ of the transport. Specifically, RadDA: i) couples source and target pixels via class-aware optimal transport, ii) learns a Riemannian flow under an explicit penalty on $\epsilon$, and iii) gates out paths that turn beyond a pixel's angular margin. Since $\epsilon$ bounds both label corruption and the $O(\epsilon /K)$ integration error, one integration step suffices and inference is unchanged. Extensive experiments with a frozen DINOv2 encoder demonstrate that RadDA improves tail-class mIoU on GTA→Cityscapes by 8.0 over the source-only head and 7.0 over self-training at higher mean IoU.