论文标题
旋转双曲线包裹的正态分布，用于分层表示学习
A Rotated Hyperbolic Wrapped Normal Distribution for Hierarchical Representation Learning
论文作者
论文摘要
我们提出了旋转的双曲线包裹正态分布（ROWN），这是双曲线包裹的正态分布（HWN）的简单而有效的改变。 HWN将概率建模的领域从欧几里得延伸到双曲线空间，在理论上，树可以用任意的低失真嵌入树。在这项工作中，我们分析了对角线HWN的几何特性，这是概率建模中分布的标准选择。分析表明，分布不适合通过其角度距离在同一层次结构级别的数据点与Poincaré磁盘模型中相同的规范表示分布。然后，我们从经验上验证了HWN的局限性，并显示鲁恩（ROWN）如何减轻各种层次数据集的局限性，包括嘈杂的合成二进制二进制树，WordNet和Atari 2600突破。该代码可在https://github.com/ml-postech/rown上找到。
We present a rotated hyperbolic wrapped normal distribution (RoWN), a simple yet effective alteration of a hyperbolic wrapped normal distribution (HWN). The HWN expands the domain of probabilistic modeling from Euclidean to hyperbolic space, where a tree can be embedded with arbitrary low distortion in theory. In this work, we analyze the geometric properties of the diagonal HWN, a standard choice of distribution in probabilistic modeling. The analysis shows that the distribution is inappropriate to represent the data points at the same hierarchy level through their angular distance with the same norm in the Poincaré disk model. We then empirically verify the presence of limitations of HWN, and show how RoWN, the proposed distribution, can alleviate the limitations on various hierarchical datasets, including noisy synthetic binary tree, WordNet, and Atari 2600 Breakout. The code is available at https://github.com/ml-postech/RoWN.
