Context Vectors are Reflections of Word Vectors in Half the Dimensions
This provides a theoretical foundation for embedding models, which is incremental but clarifies a key aspect for NLP researchers.
The paper tackles the theoretical relationship between word and context embeddings in models like word2vec, showing that under probabilistic assumptions, context vectors are reflections of word vectors in about half the dimensions, leading to a method for tying weights in the SGNS model.
This paper takes a step towards theoretical analysis of the relationship between word embeddings and context embeddings in models such as word2vec. We start from basic probabilistic assumptions on the nature of word vectors, context vectors, and text generation. These assumptions are well supported either empirically or theoretically by the existing literature. Next, we show that under these assumptions the widely-used word-word PMI matrix is approximately a random symmetric Gaussian ensemble. This, in turn, implies that context vectors are reflections of word vectors in approximately half the dimensions. As a direct application of our result, we suggest a theoretically grounded way of tying weights in the SGNS model.