  Nickel and Kiela (2017) present a new method for embedding tree nodes in the
Poincare ball, and suggest that these hyperbolic embeddings are far more
effective than Euclidean embeddings at embedding nodes in large, hierarchically
structured graphs like the WordNet nouns hypernymy tree. This is especially
true in low dimensions (Nickel and Kiela, 2017, Table 1). In this work, we seek
to reproduce their experiments on embedding and reconstructing the WordNet
nouns hypernymy graph. Counter to what they report, we find that Euclidean
embeddings are able to represent this tree at least as well as Poincare
embeddings, when allowed at least 50 dimensions. We note that this does not
diminish the significance of their work given the impressive performance of
hyperbolic embeddings in very low-dimensional settings. However, given the wide
influence of their work, our aim here is to present an updated and more
accurate comparison between the Euclidean and hyperbolic embeddings.
