Whether embedding spaces use all their dimensions equally, i.e., whether they are isotropic, has been a recent subject of discussion. Evidence has been accrued both for and against enforcing isotropy in embedding spaces. In the present paper, we stress that isotropy imposes requirements on the embedding space that are not compatible with the presence of clusters -- which also negatively impacts linear classification objectives. We demonstrate this fact empirically and use it to shed light on previous results from the literature.

翻译：嵌入空间是否均匀利用所有维度（即是否具有各向同性）是近期讨论的焦点。已有证据分别支持或反对在嵌入空间中强制实现各向同性。本文强调，各向同性对嵌入空间施加的要求与聚类的存在不兼容——这也会对线性分类目标产生负面影响。我们通过实验验证了这一事实，并据此对文献中的先前结果进行了阐释。