  Syntactic structures used to play a vital role in natural language processing
(NLP), but since the deep learning revolution, NLP has been gradually dominated
by neural models that do not consider syntactic structures in their design. One
vastly successful class of neural models is transformers. When used as an
encoder, a transformer produces contextual representation of words in the input
sentence. In this work, we propose a new model of contextual word
representation, not from a neural perspective, but from a purely syntactic and
probabilistic perspective. Specifically, we design a conditional random field
that models discrete latent representations of all words in a sentence as well
as dependency arcs between them; and we use mean field variational inference
for approximate inference. Strikingly, we find that the computation graph of
our model resembles transformers, with correspondences between dependencies and
self-attention and between distributions over latent representations and
contextual embeddings of words. Experiments show that our model performs
competitively to transformers on small to medium sized datasets. We hope that
our work could help bridge the gap between traditional syntactic and
probabilistic approaches and cutting-edge neural approaches to NLP, and inspire
more linguistically-principled neural approaches in the future.
