提出可连续缩放的知识图谱抽象边界发现方法，无需人工调参。
Semantic Level of Detail for Knowledge Graphs: Discovering Abstraction Boundaries via Spectral Heat Diffusion
- 基于庞加莱球嵌入的kNN图与热核扩散定义连续缩放操作
- 在合成数据上边界检测准确，宏观聚类精度达1.00，中观达0.89
- 适用于真实知识图谱，自动发现语义层次结构，无需调参
图结构知识系统（如知识图谱、GraphRAG流程）将信息组织为分层社区，但缺乏连续分辨率控制的理论机制：抽象层级间的质性边界在哪里？代理应如何导航？现有方法依赖手动调参的离散社区检测（如Leiden γ），无法实现连续缩放且无形式保证。本文提出语义层级细节（SLoD）框架，通过图拉普拉斯矩阵上的热核扩散定义连续缩放算子，其kNN结构由庞加莱球嵌入诱导。证明了树极限下的层级一致性（精确树+ Sarkar 嵌入），逼近误差有界；在噪声层次结构上表现一致的边界检测行为；图拉普拉斯谱间隙引发涌现尺度边界——表示发生质变的尺度，可无需人工调参检测。在合成层次结构（HSBM，1024节点）上，边界扫描检测尺度下的谱聚类恢复预设层级，宏观ARI在高信噪比下饱和至1.00（50次种子中位数），中观ARI达0.89[0.86, 0.92]（r=200）。在完整WordNet名词层次（82K同义词集）上，使用100个分层叶节点查询，检测边界与真实分类深度相关性τ=0.79，展示真实知识图谱中无需调参的有意义抽象层级发现。复合权重、MAD阈值及kNN参数规则（k = max(10, min(floor(sqrt(N)), 50))）在HSBM与WordNet间保持不变；其在隐含或定性不同层次结构图上的表现仍待探索。
原文摘要 · Abstract (English)
Graph-structured knowledge systems -- from knowledge graphs to GraphRAG pipelines -- organize information into hierarchical communities, yet lack a principled mechanism for continuous resolution control: where do the qualitative boundaries between abstraction levels lie, and how should an agent navigate them? Current approaches rely on discrete community detection with manually tuned resolution parameters (e.g., Leiden $γ$), offering no continuous zoom and no formal guarantees. We introduce Semantic Level of Detail (SLoD), a framework that addresses both problems by defining a continuous zoom operator via heat kernel diffusion on a graph Laplacian whose kNN structure is induced by a Poincare-ball embedding. We prove hierarchical coherence in the tree limit (exact tree with Sarkar embedding), with bounded approximation error, and demonstrate consistent boundary-detection behaviour on noisy hierarchies; spectral gaps in the graph Laplacian then induce emergent scale boundaries -- scales where the representation undergoes qualitative transitions -- detectable without manual resolution tuning. On synthetic hierarchies (HSBM, 1024 nodes), spectral clustering at the BoundaryScan-detected scale recovers planted levels, with macro ARI saturating at 1.00 in the high-SNR regime (50-seed median) and meso ARI reaching 0.89 [0.86, 0.92] at r=200. On the full WordNet noun hierarchy (82K synsets), using 100 stratified leaf queries, detected boundaries align with true taxonomic depth ($τ= 0.79$), demonstrating meaningful abstraction-level discovery in real-world knowledge graphs without resolution-parameter tuning. The composite weights, MAD threshold, and kNN-parameter rule ($k = \max(10, \min(\lfloor\sqrt{N}\rfloor, 50))$) use defaults that transferred unchanged between HSBM and WordNet; their behaviour on graphs with implicit or qualitatively different hierarchical structure is open.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。