Geodesic Semantic Search: Cartographic Navigation of Citation Graphs with Learned Local Riemannian Maps
arXiv:2602.23665v5 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 $\mL_i \in \R^{d \times r}$ 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 Dijks
The continuous advancements in graph neural networks and the increasing complexity of semantic search demands more sophisticated retrieval mechanisms beyond fixed Euclidean distances.
This development represents a significant step towards more accurate and context-aware information retrieval, directly impacting the efficacy of AI agents and knowledge management systems.
Semantic search will move beyond simple embedding similarity to incorporate the underlying geometric structure of knowledge graphs, leading to more nuanced and relevant results.
- · AI Agent developers
- · Knowledge graph platform providers
- · Enterprise search solutions
- · Researchers in information retrieval
- · Legacy embedding-based search engines
Citation graphs and other large-scale knowledge bases become more navigable and their insights more accessible.
Improved semantic search capabilities accelerate research and development cycles across various scientific and technical domains.
Enhanced AI agents powered by geometry-aware retrieval could autonomously answer complex queries and execute sophisticated tasks with higher accuracy.
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Read at arXiv cs.LG