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Static word embedding is still useful, particularly for context-unavailabletasks, because in the case of no context available, pre-trained language modelsoften perform worse than static word embeddings. Although dimension is a keyfactor determining the quality of static word embeddings, automatic dimensionselection is rarely discussed. In this paper, we investigate the impact of wordfrequency on the dimension selection, and empirically find that word frequencyis so vital that it needs to be taken into account during dimension selection.Based on such an empirical finding, this paper proposes a dimension selectionmethod that uses a metric (Mixed Product Distance, MPD) to select a properdimension for word embedding algorithms without training any word embedding.Through applying a post-processing function to oracle matrices, the MPD-basedmethod can de-emphasize the impact of word frequency. Experiments on bothcontext-unavailable and context-available tasks demonstrate the betterefficiency-performance trade-off of our MPD-based dimension selection methodover baselines.

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