论文标题
欧几里得和双曲线图神经网络的统一框架
A Unification Framework for Euclidean and Hyperbolic Graph Neural Networks
论文作者
论文摘要
双曲神经网络可以有效地捕获图形数据集的固有层次结构，从而是GNN的强大选择。但是，它们纠缠了一层中的多个不一致（Gyro-）向量空间，这使它们在概括和可扩展性方面受到限制。在这项工作中，我们将Poincare磁盘模型作为我们的搜索空间提出，并在磁盘上应用所有近似值（好像磁盘是从原点得出的切线空间），从而摆脱了所有空间间变换。这种方法使我们能够提出双曲线归一化层，并进一步简化了用双曲线归一化层级联的欧几里得模型的整个双曲线模型。我们将提出的非线性双曲线归一化应用于当前的最新同质和多关系图网络。我们证明，我们的模型不仅利用欧几里得网络的功能，例如解释性和有效执行各种模型组件，而且在各种基准上都优于欧几里得和双曲线对应物。我们的代码可在https://github.com/oom-debugger/ijcai23上公开提供。
Hyperbolic neural networks can effectively capture the inherent hierarchy of graph datasets, and consequently a powerful choice of GNNs. However, they entangle multiple incongruent (gyro-)vector spaces within a layer, which makes them limited in terms of generalization and scalability. In this work, we propose the Poincare disk model as our search space, and apply all approximations on the disk (as if the disk is a tangent space derived from the origin), thus getting rid of all inter-space transformations. Such an approach enables us to propose a hyperbolic normalization layer and to further simplify the entire hyperbolic model to a Euclidean model cascaded with our hyperbolic normalization layer. We applied our proposed nonlinear hyperbolic normalization to the current state-of-the-art homogeneous and multi-relational graph networks. We demonstrate that our model not only leverages the power of Euclidean networks such as interpretability and efficient execution of various model components, but also outperforms both Euclidean and hyperbolic counterparts on various benchmarks. Our code is made publicly available at https://github.com/oom-debugger/ijcai23.
