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arXiv 2408.09266cs.LG
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使用 GNN 进行图分类:优化、表示与归纳偏置

Graph Classification with GNNs: Optimisation, Representation and Inductive Bias

IIT Madras(印度马德拉斯理工学院)

P. Krishna Kumar a, Harish G. Ramaswamy

AI总结:

本文指出 GNN 等价性研究忽略了优化问题,通过理论与实验证明了图分类中消息传递层在不同全局池化下寻找判别性子图或节点的隐式归纳偏置,并展示了其在注意力架构中融入领域知识的应用。

摘要:

关于 GNN 表示能力的理论研究主要集中在理解 GNN 的等价性上,使用 WL 测试来检测图同构。在本文中,我们论证了这种等价性忽略了伴随的优化问题,并且未能提供 GNN 学习过程的全局视角。我们通过示例和实验说明了表示与优化之间的这些差距。在图分类任务的背景下,我们还探索了 GNN 中是否存在隐式归纳偏置(例如,全连接网络倾向于在其输入空间中学习低频函数)。我们进一步从理论上证明,图中的消息传递层倾向于搜索判别性子图,或分散在图中的判别性节点集合,具体取决于所使用的不同全局池化层。我们通过对真实世界和合成数据集的实验,从经验上验证了这种偏置。最后,我们展示了我们的工作如何有助于通过基于注意力的架构融入领域知识,并能表明它们区分连贯子图的能力。

英文摘要:

Theoretical studies on the representation power of GNNs have been centered around understanding the equivalence of GNNs, using WL-Tests for detecting graph isomorphism. In this paper, we argue that such equivalence ignores the accompanying optimization issues and does not provide a holistic view of the GNN learning process. We illustrate these gaps between representation and optimization with examples and experiments. We also explore the existence of an implicit inductive bias (e.g. fully connected networks prefer to learn low frequency functions in their input space) in GNNs, in the context of graph classification tasks. We further prove theoretically that the message-passing layers in the graph, have a tendency to search for either discriminative subgraphs, or a collection of discriminative nodes dispersed across the graph, depending on the different global pooling layers used. We empirically verify this bias through experiments over real-world and synthetic datasets. Finally, we show how our work can help in incorporating domain knowledge via attention based architectures, and can evince their capability to discriminate coherent subgraphs.

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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