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Geodesic Semantic Search: Cartographic Navigation of Citation Graphs with Learned Local Riemannian Maps
- 为每个论文节点学习局部黎曼度量，让相似性计算更符合学术脉络。
- 在16.9万篇arXiv论文上，召回率比基线高23%。
- 适合需要精准定位学术脉络的研究者，尤其擅长跨领域检索。
我们提出地缘语义搜索（Geodesic Semantic Search, GSS），一种在引用图上学习节点特定黎曼度量的检索系统，实现几何感知的语义搜索。与依赖固定欧氏距离的嵌入检索不同，GSS在每个节点学习一个低秩度量张量 $\mL_i \in \R^{d \times r}$，生成局部半正定度量 $\mG_i = \mL_i \mL_i^\top + \eps \mI$，确保度量有效性且模型可训练。检索通过多源Dijkstra算法基于学习的测地距离进行，随后使用最大边际相关性重排序和路径一致性过滤。在包含16.9万篇arXiv论文的引用预测基准上，GSS相较SPECTER+FAISS基线实现23%的相对召回率提升。我们提供了桥接恢复保证，刻画了测地检索在何种情况下优于直接相似性；给出了训练损失与检索质量间的边界分离结果；并分析了低秩度量参数化的表达能力。通过层次化的粗到精搜索结合k-means池化，计算成本降低4倍，同时保持97%的检索质量。
原文摘要 · Abstract (English)
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 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 $4\times$ while maintaining 97\% retrieval quality.
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