Improved large-scale graph learning through ridge spectral sparsification

arXiv cs.LG / 4/23/2026

📰 NewsDeveloper Stack & InfrastructureIdeas & Deep AnalysisModels & Research

共有:

Key Points

The paper studies distributed, streaming graph learning over the graph Laplacian, where edges arrive in real time and quickly approximating a distributed representation of the Laplacian is difficult.
It introduces GSQUEAK, a new algorithm that sparsifies the Laplacian by maintaining only a small subset of effective resistances.
The method is designed to work in a single pass over edges while supporting distributed processing across multiple workers.
The authors provide strong spectral approximation guarantees, showing that the produced sparsifiers preserve key spectral properties of the original Laplacian.
Overall, GSQUEAK targets efficient large-scale graph learning by combining ridge spectral sparsification ideas with distributed streaming constraints.

Abstract

Graph-based techniques and spectral graph theory have enriched the field of machine learning with a variety of critical advances. A central object in the analysis is the graph Laplacian L, which encodes the structure of the graph. We consider the problem of learning over this Laplacian in a distributed streaming setting, where new edges of the graph are observed in real time by a network of workers. In this setting, it is hard to learn quickly or approximately while keeping a distributed representation of L. To address this challenge, we present a novel algorithm, GSQUEAK, which efficiently sparsifies the Laplacian by maintaining a small subset of effective resistances. We show that our algorithm produces sparsifiers with strong spectral approximation guarantees, all while processing edges in a single pass and in a distributed fashion.