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We present a rotated hyperbolic wrapped normal distribution (RoWN), a simpleyet effective alteration of a hyperbolic wrapped normal distribution (HWN). TheHWN expands the domain of probabilistic modeling from Euclidean to hyperbolicspace, where a tree can be embedded with arbitrary low distortion in theory. Inthis work, we analyze the geometric properties of the diagonal HWN, a standardchoice of distribution in probabilistic modeling. The analysis shows that thedistribution is inappropriate to represent the data points at the samehierarchy level through their angular distance with the same norm in thePoincar\'e disk model. We then empirically verify the presence of limitationsof HWN, and show how RoWN, the proposed distribution, can alleviate thelimitations on various hierarchical datasets, including noisy synthetic binarytree, WordNet, and Atari 2600 Breakout. The code is available athttps://github.com/ml-postech/RoWN.

A Rotated Hyperbolic Wrapped Normal Distribution for Hierarchical Representation Learning