  In NLP, a large volume of tasks involve pairwise comparison between two
sequences (e.g. sentence similarity and paraphrase identification).
Predominantly, two formulations are used for sentence-pair tasks: bi-encoders
and cross-encoders. Bi-encoders produce fixed-dimensional sentence
representations and are computationally efficient, however, they usually
underperform cross-encoders. Cross-encoders can leverage their attention heads
to exploit inter-sentence interactions for better performance but they require
task fine-tuning and are computationally more expensive. In this paper, we
present a completely unsupervised sentence representation model termed as
Trans-Encoder that combines the two learning paradigms into an iterative joint
framework to simultaneously learn enhanced bi- and cross-encoders.
Specifically, on top of a pre-trained Language Model (PLM), we start with
converting it to an unsupervised bi-encoder, and then alternate between the bi-
and cross-encoder task formulations. In each alternation, one task formulation
will produce pseudo-labels which are used as learning signals for the other
task formulation. We then propose an extension to conduct such
self-distillation approach on multiple PLMs in parallel and use the average of
their pseudo-labels for mutual-distillation. Trans-Encoder creates, to the best
of our knowledge, the first completely unsupervised cross-encoder and also a
state-of-the-art unsupervised bi-encoder for sentence similarity. Both the
bi-encoder and cross-encoder formulations of Trans-Encoder outperform recently
proposed state-of-the-art unsupervised sentence encoders such as Mirror-BERT
and SimCSE by up to 5% on the sentence similarity benchmarks.
