Squashed Shifted PMI Matrix: Bridging Word Embeddings and Hyperbolic Spaces
This work provides a theoretical bridge for NLP researchers, but it is incremental as it builds on existing embedding methods without major practical improvements.
The paper tackles the problem of linking static word embeddings to hyperbolic spaces by showing that removing the sigmoid transformation in SGNS does not significantly harm quality and relates to factorizing a squashed shifted PMI matrix, which connects to hyperbolic spaces through empirical analysis of graph properties like clustering and scale-free distribution.
We show that removing sigmoid transformation in the skip-gram with negative sampling (SGNS) objective does not harm the quality of word vectors significantly and at the same time is related to factorizing a squashed shifted PMI matrix which, in turn, can be treated as a connection probabilities matrix of a random graph. Empirically, such graph is a complex network, i.e. it has strong clustering and scale-free degree distribution, and is tightly connected with hyperbolic spaces. In short, we show the connection between static word embeddings and hyperbolic spaces through the squashed shifted PMI matrix using analytical and empirical methods.