  Semantic parsing is the task of producing a structured meaning representation
for natural language utterances or questions. Recent research has pointed out
that the commonly-used sequence-to-sequence (seq2seq) semantic parsers struggle
to generalize systematically, i.e. to handle examples that require recombining
known knowledge in novel settings. In this work, we show that better systematic
generalization can be achieved by producing the meaning representation (MR)
directly as a graph and not as a sequence. To this end we propose LAGr, the
Labeling Aligned Graphs algorithm that produces semantic parses by predicting
node and edge labels for a complete multi-layer input-aligned graph. The
strongly-supervised LAGr algorithm requires aligned graphs as inputs, whereas
weakly-supervised LAGr infers alignments for originally unaligned target graphs
using an approximate MAP inference procedure. On the COGS and CFQ compositional
generalization benchmarks the strongly- and weakly- supervised LAGr algorithms
achieve significant improvements upon the baseline seq2seq parsers.
