  Abstract Meaning Representations (AMR) are a broad-coverage semantic
formalism which represents sentence meaning as a directed acyclic graph. To
train most AMR parsers, one needs to segment the graph into subgraphs and align
each such subgraph to a word in a sentence; this is normally done at
preprocessing, relying on hand-crafted rules. In contrast, we treat both
alignment and segmentation as latent variables in our model and induce them as
part of end-to-end training.
  As marginalizing over the structured latent variables is infeasible, we use
the variational autoencoding framework.
  To ensure end-to-end differentiable optimization, we introduce a
differentiable relaxation of the segmentation and alignment problems. We
observe that inducing segmentation yields substantial gains over using a
`greedy' segmentation heuristic. The performance of our method also approaches
that of a model that relies on the segmentation rules of
\citet{lyu-titov-2018-amr}, which were hand-crafted to handle individual AMR
constructions.
