论文标题
图中的双曲表示形式是否相等？
Are Hyperbolic Representations in Graphs Created Equal?
论文作者
论文摘要
最近，人们对在非欧盟几何形状中的图神经网络的应用越来越兴趣。但是，非欧国人表示对图形学习任务总是有用的吗？对于诸如节点分类和链接预测等不同问题，我们计算双曲线嵌入，并得出结论，对于需要全局预测一致性的任务，使用非欧洲裔嵌入可能很有用，而对于其他任务，欧几里得模型是优越的。为此，我们首先修复了与优化过程相关的现有模型的问题。当前的双曲模型以临时方式处理起源的梯度，这效率低下，可能导致数值不稳定性。我们在零曲率情况下解决了Kappa-Stereographic模型的不稳定性，并评估将图形嵌入到几个图表表示任务中的歧管中的方法。
Recently there was an increasing interest in applications of graph neural networks in non-Euclidean geometry; however, are non-Euclidean representations always useful for graph learning tasks? For different problems such as node classification and link prediction we compute hyperbolic embeddings and conclude that for tasks that require global prediction consistency it might be useful to use non-Euclidean embeddings, while for other tasks Euclidean models are superior. To do so we first fix an issue of the existing models associated with the optimization process at zero curvature. Current hyperbolic models deal with gradients at the origin in ad-hoc manner, which is inefficient and can lead to numerical instabilities. We solve the instabilities of kappa-Stereographic model at zero curvature cases and evaluate the approach of embedding graphs into the manifold in several graph representation learning tasks.
