解析深度图卷积网络的稳定性与泛化能力，揭示关键影响因素。
Deeper Insights into Deep Graph Convolutional Networks: Stability and Generalization
- 从理论角度分析深层图卷积网络的稳定性和泛化性。
- 发现最大特征值和网络深度显著影响模型性能。
- 为设计更可靠图学习模型提供理论依据，适合研究者参考。
图卷积网络（GCNs）在图学习任务中表现出色，但其深层结构的理论理解仍不充分。现有研究多集中于单层GCN，对深层GCN的稳定性与泛化性缺乏系统分析。本文首次深入研究深层GCN的稳定性与泛化能力，通过严格推导上界，揭示其受图滤波算子最大绝对特征值及网络深度的影响。理论结果为理解深层GCN的本质特性提供了新视角，有助于开发更稳定、性能更优的图神经网络模型。
原文摘要 · Abstract (English)
Graph convolutional networks (GCNs) have emerged as powerful models for graph learning tasks, exhibiting promising performance in various domains. While their empirical success is evident, there is a growing need to understand their essential ability from a theoretical perspective. Existing theoretical research has primarily focused on the analysis of single-layer GCNs, while a comprehensive theoretical exploration of the stability and generalization of deep GCNs remains limited. In this paper, we bridge this gap by delving into the stability and generalization properties of deep GCNs, aiming to provide valuable insights by characterizing rigorously the associated upper bounds. Our theoretical results reveal that the stability and generalization of deep GCNs are influenced by certain key factors, such as the maximum absolute eigenvalue of the graph filter operators and the depth of the network. Our theoretical studies contribute to a deeper understanding of the stability and generalization properties of deep GCNs, potentially paving the way for developing more reliable and well-performing models.
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