Reproduce “Isotropy, Clusters, and Classifiers” on OpenResearch

About this paper

Timothee Mickus, Stig-Arne Grönroos, Joseph Attieh

This research formalizes and empirically validates the inherent conflict between strict isotropy in embedding spaces and the formation of distinct clusters, which are essential for effective linear classification. It demonstrates that optimizing for classification tasks consistently leads to more anisotropic and clustered latent representations.

Key insights

• Strict isotropy in embedding spaces is mathematically incompatible with the formation of distinct data clusters, which require minimizing intra-cluster and maximizing inter-cluster distances.
• Optimizing for linear classification objectives inherently drives embedding spaces towards clustered and, consequently, anisotropic configurations.
• The utility of isotropic embeddings is fundamentally task-dependent: they are counterproductive for tasks requiring clear categorical separation but potentially beneficial for tasks focused on fine-grained similarity.

Summary by alphaXiv.