arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2202.13060cs.LGstat.ML
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图注意力回顾

Graph Attention Retrospective

David R. Cheriton School of Computer Science, University of Waterloo(滑铁卢大学大卫·R·切里顿计算机科学学院);Department of Applied Mathematics, University of Waterloo(滑铁卢大学应用数学系)

Kimon Fountoulakis, Amit Levi, Shenghao Yang, Aseem Baranwal, Aukosh Jagannath

AI总结:

本文从理论上研究了图注意力网络在上下文随机块模型节点分类中的行为,证明了其在“简单”机制下能实现完美分类且对结构噪声具有鲁棒性,而在“困难”机制下则存在局限性。

摘要:

基于图的学习是机器学习中快速发展的一个子领域,应用于社交网络、引文网络和生物信息学。最受欢迎的模型之一是图注意力网络。它的引入是为了允许节点以非均匀的方式聚合来自邻居节点特征的信息,这与不区分节点邻居的简单图卷积形成对比。在本文中,我们从理论上研究了图注意力网络的行为。我们针对上下文随机块模型的节点分类问题,证明了关于图注意力机制性能的多个结果。在这里,节点特征从高斯混合模型中获得,边从随机块模型中获得。我们表明,在“简单”机制下,即高斯分布均值之间的距离足够大时,图注意力能够区分类间边和类内边。因此,它保留了重要边的权重,并显著降低了不重要边的权重。因此,我们表明这意味着完美的节点分类。在“困难”机制下,我们表明每种注意力机制都无法区分类内边和类间边。此外,我们表明,即使类内边可以与类间边分离,图注意力卷积也无法(几乎)完美地对节点进行分类。除了完美的节点分类之外,我们还提供了关于图注意力对图中结构噪声鲁棒性的正面结果。特别是,我们的鲁棒性结果表明,图注意力可以严格优于简单图卷积和节点特征的最佳线性分类器。我们在合成和真实世界数据上评估了我们的理论结果。

英文摘要:

Graph-based learning is a rapidly growing sub-field of machine learning with applications in social networks, citation networks, and bioinformatics. One of the most popular models is graph attention networks. They were introduced to allow a node to aggregate information from features of neighbor nodes in a non-uniform way, in contrast to simple graph convolution which does not distinguish the neighbors of a node. In this paper, we theoretically study the behaviour of graph attention networks. We prove multiple results on the performance of the graph attention mechanism for the problem of node classification for a contextual stochastic block model. Here, the node features are obtained from a mixture of Gaussians and the edges from a stochastic block model. We show that in an "easy" regime, where the distance between the means of the Gaussians is large enough, graph attention is able to distinguish inter-class from intra-class edges. Thus it maintains the weights of important edges and significantly reduces the weights of unimportant edges. Consequently, we show that this implies perfect node classification. In the "hard" regime, we show that every attention mechanism fails to distinguish intra-class from inter-class edges. In addition, we show that graph attention convolution cannot (almost) perfectly classify the nodes even if intra-class edges could be separated from inter-class edges. Beyond perfect node classification, we provide a positive result on graph attention's robustness against structural noise in the graph. In particular, our robustness result implies that graph attention can be strictly better than both the simple graph convolution and the best linear classifier of node features. We evaluate our theoretical results on synthetic and real-world data.

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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