超双曲图形关注网络 (Hyperbolic Graph Attention Network)

Graph neural network (GNN) has shown superior performance in dealing with graphs, which has attracted considerable research attention recently. However, most of the existing GNN models are primarily designed for graphs in Euclidean spaces. Recent research has proven that the graph data exhibits non-Euclidean latent anatomy. Unfortunately, there was rarely study of GNN in non-Euclidean settings so far. To bridge this gap, in this paper, we study the GNN with attention mechanism in hyperbolic spaces at the first attempt. The research of hyperbolic GNN has some unique challenges: since the hyperbolic spaces are not vector spaces, the vector operations (e.g., vector addition, subtraction, and scalar multiplication) cannot be carried. To tackle this problem, we employ the gyrovector spaces, which provide an elegant algebraic formalism for hyperbolic geometry, to transform the features in a graph; and then we propose the hyperbolic proximity based attention mechanism to aggregate the features. Moreover, as mathematical operations in hyperbolic spaces could be more complicated than those in Euclidean spaces, we further devise a novel acceleration strategy using logarithmic and exponential mappings to improve the efficiency of our proposed model. The comprehensive experimental results on four real-world datasets demonstrate the performance of our proposed hyperbolic graph attention network model, by comparisons with other state-of-the-art baseline methods.

翻译：图表神经网络(GNN)在处理图表方面表现优异,最近引起了相当的研究关注。然而,现有的GNN模型大多主要设计于厄克里地空间的图表。最近的研究证明,图形数据显示的是非厄克里地潜潜潜潜的原子解剖。不幸的是,迄今为止在非厄科里德的设置中,很少有对GNG的研究结果。为了缩小这一差距,本文件首次尝试时,我们用超双球空间的注意机制来研究GNN,以弥补这一差距。对超双球GNN的研究有一些独特的挑战:由于超双曲GNNN的研究表明,由于超双球GNNM的研究有一些独特的挑战:由于超双波空间不是矢量空间,因此无法进行矢量操作(例如,矢量添加、减量和卡利倍增倍倍增倍增)的图形。为了解决这个问题,我们很少在非厄克里德空间的非欧科里德的设置了对GNNNNNNNNNG的研究,这为超偏偏偏偏偏偏偏偏偏的地形空间的注意机制。然后我们提议以超双球近地近的注意机制来收集这些特征的注意机制。此外,我们更进一步在超位的数学空间的数学操作模型模型模型模型的模型操作可能更加复杂化模型模型模型模型模型模型模型比EU化更复杂,利用EUCI基线空间的EUCLPLPLPL- —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— 更 —— —— —— —— 改进—— 改进- 改进—— 改进—— 改进改进改进- —— —— —— —— —— 改进改进 —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— —— 改进