  Previous work on text generation from graph-structured data relies on
pretrained language models (PLMs) and utilizes graph linearization heuristics
rather than explicitly considering the graph structure. Efficiently encoding
the graph structure in PLMs is challenging because they were pretrained on
natural language, and modeling structured data may lead to catastrophic
forgetting of distributional knowledge. In this paper, we propose StructAdapt,
an adapter method to encode graph structure into PLMs. Contrary to prior work,
StructAdapt effectively models interactions among the nodes based on the graph
connectivity, only training graph structure-aware adapter parameters. In this
way, we avoid catastrophic forgetting while maintaining the topological
structure of the graph. We empirically show the benefits of explicitly encoding
graph structure into PLMs using adapters and achieve state-of-the-art results
on two AMR-to-text datasets, training only 5.1% of the PLM parameters.
