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.
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