Representing Hyperbolic Space Accurately using Multi-Component Floats
Representing Hyperbolic Space Accurately using Multi-Component Floats
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发表时间：
2021
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通讯作者：
Tao Yu-
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作者：
Tao Yu-
双曲空间对于嵌入具有层次结构的数据特别有用；然而，用普通浮点数表示双曲空间，由于其不可避免的数值误差，极大地影响了性能。简单地提高浮点数的精度并不能解决问题，而且在gpu等不支持双精度以上浮点数的硬件上模拟浮点数会带来很高的计算成本。在本文中，我们提出了一个简单、可行且易于理解的解决方案，用于双曲空间上的数值精确学习。为此，我们提出了一种新的方法，在poincar<s:1>上半空间模型中使用多分量浮点数（MCF）来表示双曲空间。理论和实验表明，我们的模型具有较小的数值误差，并且在跨各种数据集嵌入任务时，由多分量浮点表示的模型获得了更多的容量，并且在gpu上运行速度比以前的工作快得多。
Hyperbolic space is particularly useful for embedding data with hierarchical structure; however, representing hyperbolic space with ordinary floating-point numbers greatly affects the performance due to its ineluctable numerical errors. Simply increasing the precision of floats fails to solve the problem and incurs a high computation cost for simulating greater-than-double-precision floats on hardware such as GPUs, which does not support them. In this paper, we propose a simple, feasible-on-GPUs, and easy-to-understand solution for numerically accurate learning on hyperbolic space. We do this with a new approach to represent hyperbolic space using multi-component floating-point (MCF) in the Poincaré upper-half space model. Theoretically and experimentally we show our model has small numerical error, and on embedding tasks across various datasets, models represented by multi-component floating-points gain more capacity and run significantly faster on GPUs than prior work.