Geodesic Semantic Search:

Geodesic Semantic Search: Cartographic Navigation of Citation Graphs with Learned Local Riemannian Maps

arXiv:2602.23665v5 Announce Type: replace Abstract: We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search. Unlike standard embedding-based retrieval that relies on fixed Euclidean distances, \gss{} learns a low-rank metric tensor $\mL_i \in \R^{d \times r}$ at each node, inducing a local positive semi-definite metric $\mG_i = \mL_i \mL_i^\top + \eps \mI$.