  QDMR is a meaning representation for complex questions, which decomposes
questions into a sequence of atomic steps. While state-of-the-art QDMR parsers
use the common sequence-to-sequence (seq2seq) approach, a QDMR structure
fundamentally describes labeled relations between spans in the input question,
and thus dependency-based approaches seem appropriate for this task. In this
work, we present a QDMR parser that is based on dependency graphs (DGs), where
nodes in the graph are words and edges describe logical relations that
correspond to the different computation steps. We propose (a) a
non-autoregressive graph parser, where all graph edges are computed
simultaneously, and (b) a seq2seq parser that uses gold graph as auxiliary
supervision. We find that a graph parser leads to a moderate reduction in
performance (0.47 to 0.44), but to a 16x speed-up in inference time due to the
non-autoregressive nature of the parser, and to improved sample complexity
compared to a seq2seq model. Second, a seq2seq model trained with auxiliary
graph supervision has better generalization to new domains compared to a
seq2seq model, and also performs better on questions with long sequences of
computation steps.
