Context Vectors Are Reflections of Word Vectors in Half the Dimensions (Extended Abstract)
Abstract
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.
Cite
Text
Assylbekov and Takhanov. "Context Vectors Are Reflections of Word Vectors in Half the Dimensions (Extended Abstract)." International Joint Conference on Artificial Intelligence, 2020. doi:10.24963/IJCAI.2020/718Markdown
[Assylbekov and Takhanov. "Context Vectors Are Reflections of Word Vectors in Half the Dimensions (Extended Abstract)." International Joint Conference on Artificial Intelligence, 2020.](https://mlanthology.org/ijcai/2020/assylbekov2020ijcai-context/) doi:10.24963/IJCAI.2020/718BibTeX
@inproceedings{assylbekov2020ijcai-context,
title = {{Context Vectors Are Reflections of Word Vectors in Half the Dimensions (Extended Abstract)}},
author = {Assylbekov, Zhenisbek and Takhanov, Rustem},
booktitle = {International Joint Conference on Artificial Intelligence},
year = {2020},
pages = {5115-5119},
doi = {10.24963/IJCAI.2020/718},
url = {https://mlanthology.org/ijcai/2020/assylbekov2020ijcai-context/}
}