arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2410.08473cs.LGcs.AIstat.ML
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深入理解深度图卷积网络:稳定性与泛化性

Deeper Insights into Deep Graph Convolutional Networks: Stability and Generalization

Department of Mathematics, College of Mathematics and Informatics, South China Agricultural University, Guangzhou, China(数学系,数学与信息学学院,华南农业大学,广州,中国);Zhejiang Key Laboratory of Intelligent Education Technology and Application, Zhejiang Normal University, Jinhua, China(智能教育技术与应用浙江省重点实验室,浙江师范大学,金华,中国);Department of Mathematics, City University of Hong Kong, Hong Kong, China(数学系,香港城市大学,香港,中国)

Guangrui Yang, Ming Li, Han Feng, Xiaosheng Zhuang

AI总结:

针对深度图卷积网络理论分析不足的问题,本文严格刻画其稳定性与泛化性上界,揭示图滤波器最大绝对特征值和网络深度的关键影响。

摘要:

图卷积网络(GCN)已成为图学习任务的强大模型,在多个领域展现出良好性能。尽管其实证成功显而易见,但从理论角度理解其本质能力的需求日益增长。现有理论研究主要集中于单层 GCN 的分析,而对深度 GCN 的稳定性和泛化性进行全面理论探索仍然有限。本文通过深入研究深度 GCN 的稳定性和泛化性来弥合这一差距,旨在通过严格刻画相关上界提供有价值的见解。理论结果表明,深度 GCN 的稳定性和泛化性受到某些关键因素的影响,例如图滤波器算子的最大绝对特征值和网络深度。本文的理论研究有助于更深入地理解深度 GCN 的稳定性和泛化性,或为开发更可靠、性能更优的模型铺平道路。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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