{"paper":{"title":"Geodesic Semantic Search: Cartographic Navigation of Citation Graphs with Learned Local Riemannian Maps","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Learning node-specific Riemannian metrics on citation graphs turns direct similarity search into geodesic navigation that improves recall.","cross_cats":["cs.LG","cs.SI"],"primary_cat":"cs.IR","authors_text":"Brandon Yee, Kundana Kommini, Lucas Wang","submitted_at":"2026-02-27T04:17:41Z","abstract_excerpt":"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"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"On citation prediction benchmarks with 169K arXiv papers, GSS achieves 23% relative improvement in Recall@20 over SPECTER+FAISS baselines.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the learned local Riemannian metrics meaningfully capture semantic relationships in the citation graph rather than merely fitting training patterns.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"GSS learns per-node low-rank Riemannian metrics on citation graphs and retrieves via geodesic distances, yielding 23% higher Recall@20 than SPECTER+FAISS on 169K arXiv papers.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Learning node-specific Riemannian metrics on citation graphs turns direct similarity search into geodesic navigation that improves recall.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"78e649727e028ab9e697045600bdde60eefef7bbab4d2eae358752f0c4007eb0"},"source":{"id":"2602.23665","kind":"arxiv","version":5},"verdict":{"id":"3f9ee4e5-78ce-4b45-99ed-e516bca13b11","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T19:18:33.912220Z","strongest_claim":"On citation prediction benchmarks with 169K arXiv papers, GSS achieves 23% relative improvement in Recall@20 over SPECTER+FAISS baselines.","one_line_summary":"GSS learns per-node low-rank Riemannian metrics on citation graphs and retrieves via geodesic distances, yielding 23% higher Recall@20 than SPECTER+FAISS on 169K arXiv papers.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the learned local Riemannian metrics meaningfully capture semantic relationships in the citation graph rather than merely fitting training patterns.","pith_extraction_headline":"Learning node-specific Riemannian metrics on citation graphs turns direct similarity search into geodesic navigation that improves recall."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.23665/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}