  Graph encoders in AMR-to-text generation models often rely on neighborhood
convolutions or global vertex attention. While these approaches apply to
general graphs, AMRs may be amenable to encoders that target their tree-like
structure. By clustering edges into a hierarchy, a tree decomposition
summarizes graph structure. Our model encodes a derivation forest of tree
decompositions and extracts an expected tree. From tree node embeddings, it
builds graph edge features used in vertex attention of the graph encoder.
Encoding TD forests instead of shortest-pairwise paths in a self-attentive
baseline raises BLEU by 0.7 and chrF++ by 0.3. The forest encoder also
surpasses a convolutional baseline for molecular property prediction by 1.92%
ROC-AUC.
