  Transformer models bring propelling advances in various NLP tasks, thus
inducing lots of interpretability research on the learned representations of
the models. However, we raise a fundamental question regarding the reliability
of the representations. Specifically, we investigate whether transformers learn
essentially isomorphic representation spaces, or those that are sensitive to
the random seeds in their pretraining process. In this work, we formulate the
Bijection Hypothesis, which suggests the use of bijective methods to align
different models' representation spaces. We propose a model based on invertible
neural networks, BERT-INN, to learn the bijection more effectively than other
existing bijective methods such as the canonical correlation analysis (CCA). We
show the advantage of BERT-INN both theoretically and through extensive
experiments, and apply it to align the reproduced BERT embeddings to draw
insights that are meaningful to the interpretability research. Our code is at
https://github.com/twinkle0331/BERT-similarity.
