Comparing Euclidean and Hyperbolic Embeddings on the WordNet Nouns Hypernymy Graph

TL;DR

This paper reevaluates the effectiveness of Euclidean versus hyperbolic embeddings for the WordNet nouns hypernymy graph, finding Euclidean embeddings perform comparably at higher dimensions, challenging prior claims of hyperbolic superiority.

Contribution

The study provides an updated, more accurate comparison between Euclidean and hyperbolic embeddings, especially at higher dimensions, correcting previous overestimations of hyperbolic methods.

Findings

Euclidean embeddings perform as well as hyperbolic embeddings at 50+ dimensions

Hyperbolic embeddings excel in low-dimensional settings

Reproduction of prior results shows different conclusions at higher dimensions

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.