  Neural models for NLP typically use large numbers of parameters to reach
state-of-the-art performance, which can lead to excessive memory usage and
increased runtime. We present a structure learning method for learning sparse,
parameter-efficient NLP models. Our method applies group lasso to rational RNNs
(Peng et al., 2018), a family of models that is closely connected to weighted
finite-state automata (WFSAs). We take advantage of rational RNNs' natural
grouping of the weights, so the group lasso penalty directly removes WFSA
states, substantially reducing the number of parameters in the model. Our
experiments on a number of sentiment analysis datasets, using both GloVe and
BERT embeddings, show that our approach learns neural structures which have
fewer parameters without sacrificing performance relative to parameter-rich
baselines. Our method also highlights the interpretable properties of rational
RNNs. We show that sparsifying such models makes them easier to visualize, and
we present models that rely exclusively on as few as three WFSAs after pruning
more than 90% of the weights. We publicly release our code.
