Comparing E uclidean and Hyperbolic Embeddings on the W ord N et Nouns Hypernymy Graph (2021)

Abstract: 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.

## experimental setup we use the source code released by the authors to carry out all experiments in this study, reusing the data processing, model training, and evaluation pipelines. dataset. following nickel and kiela (2017), we embed the wordnet noun hierarchy (fellbaum, 1998, wordnet-nouns) in both euclidean and hyperbolic space. though the original study also published results on additional datasets, we restrict our focus to wordnet-nouns, which exhibited a considerable gap in performance between embeddings. ## conclusion in our reproduction of the experiments in however, part of nickel and kiela (2017)'s impact came from the astounding gains from hyperbolic embeddings over euclidean across a wide range of embedding widths. subsequent application of poincaré embeddings often report mixed results when using non-euclidean vs. euclidean embeddings in downstream tasks (dhingra et al., 2018; lópez et al., 2019). we hope that this reproduction will serve as a valuable reference for others who are just beginning to explore hyperbolic embeddings. we use the poincare-embeddings implementation https://github. com/facebookresearch/ poincare-embeddings at commit 4c7316b14dce3b89e6a2d0c7994d418dffb42c94.