Zipfian Whitening

TL;DR

This paper demonstrates that applying Zipfian-weighted PCA whitening to word embeddings, which accounts for the non-uniform distribution of word frequencies, significantly enhances NLP task performance.

Contribution

It introduces a simple yet effective method of Zipfian-weighted whitening for word embeddings and provides a theoretical framework linking it to exponential family distributions and natural language processing models.

Findings

Zipfian-weighted whitening improves task performance.

Theoretical link between word frequency distribution and embedding properties.

Existing NLP methods encode empirical word frequency in embeddings.

Abstract

The word embedding space in neural models is skewed, and correcting this can improve task performance. We point out that most approaches for modeling, correcting, and measuring the symmetry of an embedding space implicitly assume that the word frequencies are uniform; in reality, word frequencies follow a highly non-uniform distribution, known as Zipf's law. Surprisingly, simply performing PCA whitening weighted by the empirical word frequency that follows Zipf's law significantly improves task performance, surpassing established baselines. From a theoretical perspective, both our approach and existing methods can be clearly categorized: word representations are distributed according to an exponential family with either uniform or Zipfian base measures. By adopting the latter approach, we can naturally emphasize informative low-frequency words in terms of their vector norm, which becomes evident from the information-geometric perspective, and in terms of the loss functions for imbalanced classification. Additionally, our theory corroborates that popular natural language processing methods, such as skip-gram negative sampling, WhiteningBERT, and headless language models, work well just because their word embeddings encode the empirical word frequency into the underlying probabilistic model.