不靠训练，仅用拓扑变换就能生成互补的图嵌入。
Topology-induced Operators Reveal Complementary Graph Representations without Training
- 通过随机游走和匿名游走构建隐式层次结构传播随机特征。
- 两种无训练嵌入分别捕捉节点邻近性和结构角色，性能媲美主流方法。
- 计算量小，适合对效率敏感的应用场景。
图表示学习长期依赖复杂模型将图拓扑转化为向量表示，但嵌入质量究竟多大程度源于模型学习而非拓扑转换尚不明确。本文发现，无需复杂模型设计与梯度训练，仅通过随机游走和匿名游走诱导的隐式层次结构传播随机特征，即可生成包含节点邻近性与结构角色信息的嵌入。这两种无训练嵌入保留了图组织的互补特性，在多种节点级、边级和图级任务中表现良好，且显著降低计算开销，实现更优的质量-效率平衡。二者结合在部分任务上进一步提升推理性能。结果表明，优质图嵌入可源自学习前精心设计的拓扑变换。
原文摘要 · Abstract (English)
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.
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