  Probabilistic context-free grammars (PCFGs) with neural parameterization have
been shown to be effective in unsupervised phrase-structure grammar induction.
However, due to the cubic computational complexity of PCFG representation and
parsing, previous approaches cannot scale up to a relatively large number of
(nonterminal and preterminal) symbols. In this work, we present a new
parameterization form of PCFGs based on tensor decomposition, which has at most
quadratic computational complexity in the symbol number and therefore allows us
to use a much larger number of symbols. We further use neural parameterization
for the new form to improve unsupervised parsing performance. We evaluate our
model across ten languages and empirically demonstrate the effectiveness of
using more symbols. Our code: https://github.com/sustcsonglin/TN-PCFG
