# Semantic Level of Detail for Knowledge Graphs: Discovering Abstraction Boundaries via Spectral Heat Diffusion

Source: [Semantic Level of Detail for Knowledge Graphs: Discovering Abstraction Boundaries via Spectral Heat Diffusion](<https://www.sota2.com/research/paper/69b0f6f12d603e6de3e45c21>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-05T05:00:04.460Z

Authors: Edward Izgorodin

Published: 2026-03-09T21:54:08.000Z

## Abstract

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 $\\gamma$), 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 ($\\tau = 0.79$), 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Hierarchical Ancestor Retrieval on WordNet noun hierarchy (100 stratified leaf nodes)](<https://www.sota2.com/research/sota/hierarchical-ancestor-retrieval-on-wordnet-noun-hierarchy-100-stratified-leaf-nodes.md>): Hierarchical Ancestor Retrieval; WordNet noun hierarchy (100 stratified leaf nodes); Kendall's τ: 0.79.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2603.08965>)

[PDF](<https://arxiv.org/pdf/2603.08965.pdf>)