SLoD: Continuous Zoom for Knowledge Graphs via Spectral Heat Diffusion
Researchers introduce Semantic Level of Detail (SLoD), a framework enabling continuous resolution control in hierarchical graph-structured knowledge systems like knowledge graphs and GraphRAG pipelines. SLoD defines a continuous zoom operator using heat kernel diffusion on a graph Laplacian, with kNN structure induced by a Poincaré-ball embedding. The framework proves hierarchical coherence in the tree limit with bounded approximation error and demonstrates consistent boundary-detection on noisy hierarchies. This addresses the lack of principled mechanisms for continuous resolution control in current discrete community detection approaches (e.g., Leiden γ). The work is published on arXiv under identifier 2603.08965.
Key facts
- SLoD uses heat kernel diffusion on a graph Laplacian for continuous zoom.
- kNN structure is induced by a Poincaré-ball embedding.
- Proves hierarchical coherence in the tree limit with Sarkar embedding.
- Bounded approximation error is established.
- Demonstrates consistent boundary-detection on noisy hierarchies.
- Addresses limitations of discrete community detection like Leiden γ.
- Published on arXiv as 2603.08965.
- Framework applies to knowledge graphs and GraphRAG pipelines.
Entities
Institutions
- arXiv