# Context Vectors are Reflections of Word Vectors in Half the Dimensions

arXiv: https://arxiv.org/abs/1902.09859 · HTML: https://mlsanity.com/paper/1902.09859/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2019.

## Built on by (most cited first, 2 of 2)

- [Statistical Uncertainty in Word Embeddings: GloVe-V](https://mlsanity.com/paper/2406.12165/) (2024)
- [From Hyperbolic Geometry Back to Word Embeddings](https://mlsanity.com/paper/2204.12481/) (2022)

## Abstract (arXiv)

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.