  We introduce Latent Vector Grammars (LVeGs), a new framework that extends
latent variable grammars such that each nonterminal symbol is associated with a
continuous vector space representing the set of (infinitely many) subtypes of
the nonterminal. We show that previous models such as latent variable grammars
and compositional vector grammars can be interpreted as special cases of LVeGs.
We then present Gaussian Mixture LVeGs (GM-LVeGs), a new special case of LVeGs
that uses Gaussian mixtures to formulate the weights of production rules over
subtypes of nonterminals. A major advantage of using Gaussian mixtures is that
the partition function and the expectations of subtype rules can be computed
using an extension of the inside-outside algorithm, which enables efficient
inference and learning. We apply GM-LVeGs to part-of-speech tagging and
constituency parsing and show that GM-LVeGs can achieve competitive accuracies.
Our code is available at https://github.com/zhaoyanpeng/lveg.
