Simple Hardware-Efficient PCFGs with Independent Left and Right Productions

Abstract

Scaling dense PCFGs to thousands of nonterminals via low-rank parameterizations of the rule probability tensor has been shown to be beneficial for unsupervised parsing. However, PCFGs scaled this way still perform poorly as a language model, and even underperform similarly-sized HMMs. This work introduces $\emph{SimplePCFG}$, a simple PCFG formalism with independent left and right productions. Despite imposing a stronger independence assumption than the low-rank approach, we find that this formalism scales more effectively both as a language model and as an unsupervised parser. We further introduce $\emph{FlashInside}$, a hardware IO-aware implementation of the inside algorithm for efficiently scaling simple PCFGs. Through extensive experiments on multiple grammar induction benchmarks, we validate the effectiveness of simple PCFGs over low-rank baselines.