Departure from Regularity: Degree Heterogeneity and Eigengap as the Structural Drivers of ASE-LSE Latent Subspace Disagreement
Authors: Minh Triet Pham, Ian Gallagher
Summary
arXiv:2605. 22346v1 Announce Type: new Abstract: Two of the most widely used methods for analysing graph data, Adjacency Spectral Embedding and Laplacian Spectral Embedding, often produce different results when applied to the same network.
Relevance
Read next because Departure from Regularity: Degree Heterogeneity and Eigengap as the Structural Drivers of ASE-LSE Latent Subspace Disagreement overlaps with clean result "LoRA persona trained on alone emits at 23.5% when a co-trained partner learns ..., vs 0% control on Qwen2.5-7B-Instruct (MODERATE confidence)", clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)". Matching terms: strong, under, control. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.22346v1 Announce Type: new Abstract: Two of the most widely used methods for analysing graph data, Adjacency Spectral Embedding and Laplacian Spectral Embedding, often produce different results when applied to the same network. Yet the structural reasons behind this disagreement remain incompletely understood. This paper provides a structural account. We show that regularity is a sufficient condition for perfect agreement: when every node has the same number of connections, the two methods produce identical latent subspaces. Any departure from this regularity introduces disagreement, and we prove an explicit bound whose two terms suggest the structural ingredients controlling it: degree heterogeneity, which pushes the methods apart, and community structure strength, which pulls them back together. We validate both drivers empirically across thousands of simulated networks, confirming that heterogeneity drives disagreement up, community strength suppresses it, and their ratio provides a strong predictor of when the two embeddings can be treated as interchangeable and when they cannot.