It is widely accepted that fine-tuning pre-trained language models usually brings about performance improvements in downstream tasks. However, there are limited studies on the reasons behind this effectiveness, particularly from the viewpoint of structural changes in the embedding space. Trying to fill this gap, in this paper, we analyze the extent to which the isotropy of the embedding space changes after fine-tuning. We demonstrate that, even though isotropy is a desirable geometrical property, fine-tuning does not necessarily result in isotropy enhancements. Moreover, local structures in pre-trained contextual word representations (CWRs), such as those encoding token types or frequency, undergo a massive change during fine-tuning. Our experiments show dramatic growth in the number of elongated directions in the embedding space, which, in contrast to pre-trained CWRs, carry the essential linguistic knowledge in the fine-tuned embedding space, making existing isotropy enhancement methods ineffective.

The representation degeneration problem in Contextual Word Representations (CWRs) hurts the expressiveness of the embedding space by forming an anisotropic cone where even unrelated words have excessively positive correlations. Existing techniques for tackling this issue require a learning process to re-train models with additional objectives and mostly employ a global assessment to study isotropy. Our quantitative analysis over isotropy shows that a local assessment could be more accurate due to the clustered structure of CWRs. Based on this observation, we propose a local cluster-based method to address the degeneration issue in contextual embedding spaces. We show that in clusters including punctuations and stop words, local dominant directions encode structural information, removing which can improve CWRs performance on semantic tasks. Moreover, we find that tense information in verb representations dominates sense semantics. We show that removing dominant directions of verb representations can transform the space to better suit semantic applications. Our experiments demonstrate that the proposed cluster-based method can mitigate the degeneration problem on multiple tasks.