Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this study, we generalize the fundamental components of neural networks in a single hyperbolic geometry model, namely, the Poincar\'e ball model. This novel methodology constructs a multinomial logistic regression, fully-connected layers, convolutional layers, and attention mechanisms under a unified mathematical interpretation, without increasing the parameters. Experiments show the superior parameter efficiency of our methods compared to conventional hyperbolic components, and stability and outperformance over their Euclidean counterparts.
翻译:超曲空间由于数量成倍增长,有能力嵌入树结构而不造成扭曲,这些空间最近被用于机器学习,以更好地捕捉数据的等级性质。在本研究中,我们将神经网络的基本组成部分归纳为单一的双曲几何模型,即Poincar\'e球模型。这种新颖方法在不增加参数的情况下,在统一的数学解释下构建了多音级后勤回归、完全相连的层层、交替层和关注机制。 实验显示,我们的方法比传统的超双曲元组件具有更高的参数效率,并且比欧洲对等系统具有稳定性和超效性能。