Pre-trained language models have been shown to encode linguistic structures like parse trees in their embeddings while being trained unsupervised. Some doubts have been raised whether the models are doing parsing or only some computation weakly correlated with it. Concretely: (a) Is it possible to explicitly describe transformers with realistic embedding dimensions, number of heads, etc. that are capable of doing parsing — or even approximate parsing? (b) Why do pre-trained models capture parsing structure? This paper takes a step toward answering these questions in the context of generative modeling with PCFGs. We show that masked language models like BERT or RoBERTa of moderate sizes can approximately execute the Inside-Outside algorithm for the English PCFG (Marcus et al., 1993). We also show that the Inside-Outside algorithm is optimal for masked language modeling loss on the PCFG-generated data. We conduct probing experiments on models pre-trained on PCFG-generated data to show that this not only allows recovery of approximate parse tree, but also recovers marginal span probabilities computed by the Inside-Outside algorithm, which suggests an implicit bias of masked language modeling towards this algorithm.

We present an unsupervised method to generate Word2Sense word embeddings that are interpretable — each dimension of the embedding space corresponds to a fine-grained sense, and the non-negative value of the embedding along the j-th dimension represents the relevance of the j-th sense to the word. The underlying LDA-based generative model can be extended to refine the representation of a polysemous word in a short context, allowing us to use the embedings in contextual tasks. On computational NLP tasks, Word2Sense embeddings compare well with other word embeddings generated by unsupervised methods. Across tasks such as word similarity, entailment, sense induction, and contextual interpretation, Word2Sense is competitive with the state-of-the-art method for that task. Word2Sense embeddings are at least as sparse and fast to compute as prior art.