  Pre-trained seq2seq models excel at graph semantic parsing with rich
annotated data, but generalize worse to out-of-distribution (OOD) and long-tail
examples. In comparison, symbolic parsers under-perform on population-level
metrics, but exhibit unique strength in OOD and tail generalization. In this
work, we study compositionality-aware approach to neural-symbolic inference
informed by model confidence, performing fine-grained neural-symbolic reasoning
at subgraph level (i.e., nodes and edges) and precisely targeting subgraph
components with high uncertainty in the neural parser. As a result, the method
combines the distinct strength of the neural and symbolic approaches in
capturing different aspects of the graph prediction, leading to well-rounded
generalization performance both across domains and in the tail. We empirically
investigate the approach in the English Resource Grammar (ERG) parsing problem
on a diverse suite of standard in-domain and seven OOD corpora. Our approach
leads to 35.26% and 35.60% error reduction in aggregated Smatch score over
neural and symbolic approaches respectively, and 14% absolute accuracy gain in
key tail linguistic categories over the neural model, outperforming prior
state-of-art methods that do not account for compositionality or uncertainty.
