Directed Acyclic Graph Convolutional Networks

TL;DR

This paper introduces the DAG Convolutional Network (DCN), a novel GNN architecture tailored for signals on DAGs, leveraging causal filters and spectral operations to improve learning and interpretability.

Contribution

The work presents a new DAG-specific GNN architecture (DCN and PDCN) that incorporates causal graph filters and spectral convolutional operations, enhancing learning from DAG-structured data.

Findings

PDCN achieves competitive accuracy on multiple tasks.

The architectures demonstrate robustness and computational efficiency.

Permutation equivariance and expressive power are theoretically established.

Abstract

Directed acyclic graphs (DAGs) are central to science and engineering applications including causal inference, scheduling, and neural architecture search. In this work, we introduce the DAG Convolutional Network (DCN), a novel graph neural network (GNN) architecture designed specifically for convolutional learning from signals supported on DAGs. The DCN leverages causal graph filters to learn nodal representations that account for the partial ordering inherent to DAGs, a strong inductive bias does not present in conventional GNNs. Unlike prior art in machine learning over DAGs, DCN builds on formal convolutional operations that admit spectral-domain representations. We further propose the Parallel DCN (PDCN), a model that feeds input DAG signals to a parallel bank of causal graph-shift operators and processes these DAG-aware features using a shared multilayer perceptron. This way, PDCN decouples model complexity from graph size while maintaining satisfactory predictive performance. The architectures' permutation equivariance and expressive power properties are also established. Comprehensive numerical tests across several tasks, datasets, and experimental conditions demonstrate that (P)DCN compares favorably with state-of-the-art baselines in terms of accuracy, robustness, and computational efficiency. These results position (P)DCN as a viable framework for deep learning from DAG-structured data that is designed from first (graph) signal processing principles.