Frequency-aware Dimension Selection for Static Word Embedding by Mixed Product Distance

Abstract: Static word embedding is still useful, particularly for context-unavailable tasks, because in the case of no context available, pre-trained LLMs often perform worse than static word embeddings. Although dimension is a key factor determining the quality of static word embeddings, automatic dimension selection is rarely discussed. In this paper, we investigate the impact of word frequency on the dimension selection, and empirically find that word frequency is so vital that it needs to be taken into account during dimension selection. Based on such an empirical finding, this paper proposes a dimension selection method that uses a metric (Mixed Product Distance, MPD) to select a proper dimension for word embedding algorithms without training any word embedding. Through applying a post-processing function to oracle matrices, the MPD-based method can de-emphasize the impact of word frequency. Experiments on both context-unavailable and context-available tasks demonstrate the better efficiency-performance trade-off of our MPD-based dimension selection method over baselines.