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

arXiv:2602.23665v3 Announce Type: replace-cross 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 imes r} at each node, inducing a local positive semi-definite metric mG_i = mL_i mL_i^op + 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 arXiv papers, GSS achieves 23% relative improvement in Recall@20 over SPECTER+FAISS baselines. We provide a Bridge Recovery Guarantee characterizing when geodesic retrieval qualitatively outperforms direct similarity, a margin separation result connecting training loss to retrieval quality, and characterize the expressiveness of low-rank metric parameterization. Our hierarchical coarse-to-fine search with k-means pooling reduces computational cost by 4imes while maintaining 97% retrieval quality.

Bayesian Ego-graph Inference for Networked Multi-Agent Reinforcement Learning

Source: arXiv cs.LG | 2026-04-21

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