  Pre-trained language models such as BERT have become a more common choice of
natural language processing (NLP) tasks. Research in word representation shows
that isotropic embeddings can significantly improve performance on downstream
tasks. However, we measure and analyze the geometry of pre-trained BERT
embedding and find that it is far from isotropic. We find that the word vectors
are not centered around the origin, and the average cosine similarity between
two random words is much higher than zero, which indicates that the word
vectors are distributed in a narrow cone and deteriorate the representation
capacity of word embedding. We propose a simple, and yet effective method to
fix this problem: remove several dominant directions of BERT embedding with a
set of learnable weights. We train the weights on word similarity tasks and
show that processed embedding is more isotropic. Our method is evaluated on
three standardized tasks: word similarity, word analogy, and semantic textual
similarity. In all tasks, the word embedding processed by our method
consistently outperforms the original embedding (with average improvement of
13% on word analogy and 16% on semantic textual similarity) and two baseline
methods. Our method is also proven to be more robust to changes of
hyperparameter.
