Context Vectors Are Reflections of Word Vectors in Half the Dimensions (Extended Abstract)
Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
Journal track. Pages 5115-5119. https://doi.org/10.24963/ijcai.2020/718
This paper takes a step towards the 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 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.
Natural Language Processing: Embeddings
Machine Learning: Probabilistic Machine Learning
Machine Learning: Tensor and Matrix Methods
Machine Learning: Unsupervised Learning