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.

翻译：双曲神经网络能够有效捕捉图数据集的内在层次结构，因而成为图神经网络的重要选择。然而，其在单层内纠缠了多个不相容的（陀螺）向量空间，导致泛化能力和可扩展性受限。本研究提出以庞加莱圆盘模型作为搜索空间，将所有近似操作均实施于圆盘上（如同将圆盘视为原点导出的切空间），从而消除了所有跨空间变换。该方法使我们能够提出双曲归一化层，并将整个双曲模型进一步简化为欧几里得模型与所提双曲归一化层的级联形式。我们将所提出的非线性双曲归一化应用于当前最先进的同质与多关系图网络。实验表明，本模型不仅继承了欧几里得网络的可解释性及各类组件的高效执行优势，同时在多个基准测试中均优于欧几里得与双曲对应模型。我们的代码已开源至 https://github.com/oom-debugger/ijcai23。