Topology-induced Operators Reveal Complementary Graph Representations without Training

2026-09-08

AI Summary

本文通过传播随机特征，无需复杂模型设计和训练，利用随机游走和匿名游走诱导的隐式层次结构生成图嵌入，有效捕捉节点邻近性和结构角色。

Abstract

Graph representation learning has largely focused on designing increasingly sophisticated models to transform graph topology into vector representations, or embeddings. However, the extent to which embedding quality depends on model learning, rather than on the underlying topological transformations, remains unclear. Here, we show that informative embeddings can be derived without complicated model design and gradient-based training. Propagating random features through implicit hierarchical structures induced by random walks and anonymous walks yields embeddings that capture node proximity and structural role, respectively. These two training-free embeddings preserve complementary aspects of graph organization and perform competitively with classic and recent methods across various node-, edge-, and graph-level tasks. They often require substantially less computation, resulting in a favorable quality-efficiency trade-off. Combining the two types of embeddings further improves inference quality of some tasks compared with using either embedding type alone. Our results suggest that informative graph embeddings can arise from carefully chosen topological transformations before any learning operation is applied.

Problem

• graph representation learning
• topological transformations
• embedding quality
• model learning
• gradient-based training

Innovation

• Topology-induced Operators
• Training-free Embeddings
• Random Walks
• Anonymous Walks
• Graph Representation Learning