DAG Convolutional Networks

Directed acyclic graphs (DAGs) provide a natural framework for modeling directional and hierarchical relationships. We introduce the DAG Convolutional Network (DCN), a graph neural architecture specifically developed for convolutional learning on signals defined over DAGs. DCN employs causal graph filters that incorporate the inherent partial order of DAGs, introducing an inductive bias absent in conventional GNNs. Unlike existing approaches, DCN relies on formal convolutional operators that admit spectral interpretations, ensuring both theoretical grounding and efficient implementation. We further propose the Parallel DCN (PDCN), which processes shifted DAG signals through a shared multilayer perceptron, thereby decoupling parameter complexity from graph size while preserving predictive performance. Extensive evaluations confirm that (P)DCN achieves strong performance relative to state-of-the-art methods, combining accuracy, robustness, and computational efficiency within a principled signal processing framework.