  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
Poincar\'e 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.
