  Phrase-based statistical machine translation (SMT) systems have previously
been used for the task of grammatical error correction (GEC) to achieve
state-of-the-art accuracy. The superiority of SMT systems comes from their
ability to learn text transformations from erroneous to corrected text, without
explicitly modeling error types. However, phrase-based SMT systems suffer from
limitations of discrete word representation, linear mapping, and lack of global
context. In this paper, we address these limitations by using two different yet
complementary neural network models, namely a neural network global lexicon
model and a neural network joint model. These neural networks can generalize
better by using continuous space representation of words and learn non-linear
mappings. Moreover, they can leverage contextual information from the source
sentence more effectively. By adding these two components, we achieve
statistically significant improvement in accuracy for grammatical error
correction over a state-of-the-art GEC system.
