Directed Acyclic Graph Convolutional Networks

2025-06-13

AI Summary

Modeling directed acyclic graphs (DAGs) faces a fundamental trade-off among preserving partial-order structure, expressive power, and computational scalability. Method: We propose the DAG Convolutional Network (DCN) and its parallel variant, PDCN. DCN introduces spectral-domain causal graph filters—grounded in graph signal processing—by defining convolution via a causal graph shift operator that respects DAG topology. PDCN decouples model complexity from graph size through parallel feature extraction and shared MLP-based fusion, while strictly preserving permutation equivariance. Contribution/Results: Extensive experiments demonstrate that DCN and PDCN achieve state-of-the-art performance across diverse DAG-structured tasks—including causal inference, task scheduling, and neural architecture search—outperforming existing methods in accuracy, robustness, and computational efficiency.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Develops DAG Convolutional Network for learning from DAG-structured data
• Introduces causal graph filters to handle DAG partial ordering
• Proposes Parallel DCN to decouple complexity from graph size

Innovation

• DAG Convolutional Network for graph learning
• Causal graph filters for nodal representations
• Parallel DCN decouples complexity from size