  Graph-structured data ubiquitously appears in science and engineering. Graph
neural networks (GNNs) are designed to exploit the relational inductive bias
exhibited in graphs; they have been shown to outperform other forms of neural
networks in scenarios where structure information supplements node features.
The most common GNN architecture aggregates information from neighborhoods
based on message passing. Its generality has made it broadly applicable. In
this paper, we focus on a special, yet widely used, type of graphs -- DAGs --
and inject a stronger inductive bias -- partial ordering -- into the neural
network design. We propose the \emph{directed acyclic graph neural network},
DAGNN, an architecture that processes information according to the flow defined
by the partial order. DAGNN can be considered a framework that entails earlier
works as special cases (e.g., models for trees and models updating node
representations recurrently), but we identify several crucial components that
prior architectures lack. We perform comprehensive experiments, including
ablation studies, on representative DAG datasets (i.e., source code, neural
architectures, and probabilistic graphical models) and demonstrate the
superiority of DAGNN over simpler DAG architectures as well as general graph
architectures.
