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.

中文翻译：

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比较 WordNet 名词 Hypernymy Graph 上的欧几里得嵌入和双曲嵌入

Nickel 和 Kiela (2017) 提出了一种在 Poincare 球中嵌入树节点的新方法，并表明这些双曲线嵌入在将节点嵌入大型分层结构图中（如 WordNet 名词上位树）时，比欧几里德嵌入更有效。在低维情况下尤其如此（Nickel 和 Kiela，2017，表 1）。在这项工作中，我们试图重现他们关于嵌入和重建 WordNet 名词上位图的实验。与他们报告的相反，我们发现欧几里得嵌入至少能够和 Poincare 嵌入一样表示这棵树，当允许至少 50 维时。我们注意到，鉴于双曲线嵌入在极低维设置中的出色表现，这并没有削弱他们工作的重要性。然而，