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Human judgments of word similarity have been a popular method of evaluatingthe quality of word embedding. But it fails to measure the geometry propertiessuch as asymmetry. For example, it is more natural to say "Ellipses are likeCircles" than "Circles are like Ellipses". Such asymmetry has been observedfrom a psychoanalysis test called word evocation experiment, where one word isused to recall another. Although useful, such experimental data have beensignificantly understudied for measuring embedding quality. In this paper, weuse three well-known evocation datasets to gain insights into asymmetryencoding of embedding. We study both static embedding as well as contextualembedding, such as BERT. Evaluating asymmetry for BERT is generally hard due tothe dynamic nature of embedding. Thus, we probe BERT's conditionalprobabilities (as a language model) using a large number of Wikipedia contextsto derive a theoretically justifiable Bayesian asymmetry score. The resultshows that contextual embedding shows randomness than static embedding onsimilarity judgments while performing well on asymmetry judgment, which alignswith its strong performance on "extrinsic evaluations" such as textclassification. The asymmetry judgment and the Bayesian approach provides a newperspective to evaluate contextual embedding on intrinsic evaluation, and itscomparison to similarity evaluation concludes our work with a discussion on thecurrent state and the future of representation learning.

Circles are like Ellipses, or Ellipses are like Circles? Measuring the  Degree of Asymmetry of Static and Contextual Embeddings and the Implications  to Representation Learning