  The Directed Acyclic Transformer is a fast non-autoregressive (NAR) model
that performs well in Neural Machine Translation. Two issues prevent its
application to general Natural Language Generation (NLG) tasks: frequent
Out-Of-Vocabulary (OOV) errors and the inability to faithfully generate entity
names. We introduce Control-DAG, a constrained decoding algorithm for our
Directed Acyclic T5 (DA-T5) model which offers lexical, vocabulary and length
control. We show that Control-DAG significantly enhances DA-T5 on the Schema
Guided Dialogue and the DART datasets, establishing strong NAR results for
Task-Oriented Dialogue and Data-to-Text NLG.
