Comment by pleshkov

The polynomial lift in this post originally came out of an unsuccessful experiment with hyperbolic embeddings. The idea was to embed corpora into a hyperbolic ball (anisotropic embeddings have a tree-like structure that hyperbolic space could exploit). The lift was a tool to go from hyperbolic latent back to Euclidean for retrieval. Hyperbolic part didn't work; the lift evaluated standalone kept showing real signal, and that became this post.