[2602.23665] Geodesic Semantic Search: Learning Local Riemannian Metrics for Citation Graph Retrieval

Computer Science > Information Retrieval arXiv:2602.23665 (cs) [Submitted on 27 Feb 2026] Title:Geodesic Semantic Search: Learning Local Riemannian Metrics for Citation Graph Retrieval Authors:Brandon Yee, Lucas Wang, Kundana Kommini, Krishna Sharma View a PDF of the paper titled Geodesic Semantic Search: Learning Local Riemannian Metrics for Citation Graph Retrieval, by Brandon Yee and 3 other authors View PDF HTML (experimental) 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 $\mG_i = \mL_i \mL_i^\top + \eps \mI$. This parameterization guarantees valid metrics while keeping the model tractable. Retrieval proceeds via multi-source Dijkstra on the learned geodesic distances, followed by Maximal Marginal Relevance reranking and path coherence filtering. On citation prediction benchmarks with 169K papers, \gss{} achieves 23\% relative improvement in Recall@20 over SPECTER+FAISS baselines while providing interpretable citation paths. Our hierarchical coarse-to-fine search with k-means pooling reduces computational cost by 4$\times$ compared to flat geodesic search while maintaining 97\% retrieval quality. We provide theoretical analysis of w...