HHC-GS: Hyperbolic Hierarchical Context for Compact Multi-Scale Gaussian Splatting

3D Gaussian Splatting (3DGS) enables high-quality rendering with explicit scene representations, but incurs substantial storage costs in large-scale scenes. Existing multiscale methods reduce rendering overhead by selectively activating anchors at different levels of detail, while retaining independently stored high-dimensional features for individual anchors. To reduce this redundancy, we propose HHC-GS, a compact multiscale Gaussian mapping method based on hyperbolic hierarchical context. HHC-GS uses hyperbolic relations to modulate ancestor-conditioned feature prediction, allowing each non-root anchor to store only low-dimensional structural variables and a bounded residual. For local map loading, feature-generation dependencies are restricted to ancestor paths, and dependency closure ensures consistent feature generation between local subsets and the complete map. We further jointly optimize multiple hierarchy prefixes with frozen-teacher supervision to improve reconstruction under different representation budgets while preserving full-map quality. Experiments on MatrixCity, BungeeNeRF, and UrbanScene3D show that HHC-GS maintains competitive reconstruction quality across representation budgets while substantially reducing storage. Compared with Octree-GS, HHC-GS achieves comparable or better reconstruction quality while reducing model size by more than 85% on all three datasets.