On the Downstream Performance of Compressed Word Embeddings

TL;DR

This paper introduces the eigenspace overlap score as a new measure for evaluating compressed word embeddings, linking it to downstream task performance and demonstrating its effectiveness in selecting high-quality embeddings efficiently.

Contribution

It proposes the eigenspace overlap score, relates it to downstream performance through generalization bounds, and shows its practical utility in embedding selection and compression analysis.

Findings

Eigenspace overlap score correlates with downstream task performance.

Lower bounds for the score are derived for uniform quantization.

Using the score improves embedding selection accuracy by up to 2x.

Abstract

Compressing word embeddings is important for deploying NLP models in memory-constrained settings. However, understanding what makes compressed embeddings perform well on downstream tasks is challenging---existing measures of compression quality often fail to distinguish between embeddings that perform well and those that do not. We thus propose the eigenspace overlap score as a new measure. We relate the eigenspace overlap score to downstream performance by developing generalization bounds for the compressed embeddings in terms of this score, in the context of linear and logistic regression. We then show that we can lower bound the eigenspace overlap score for a simple uniform quantization compression method, helping to explain the strong empirical performance of this method. Finally, we show that by using the eigenspace overlap score as a selection criterion between embeddings drawn from a representative set we compressed, we can efficiently identify the better performing embedding with up to $2\times$ lower selection error rates than the next best measure of compression quality, and avoid the cost of training a model for each task of interest.