# Directed Acyclic Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2506.12218 · HTML: https://mlsanity.com/paper/2506.12218/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 56 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [A Survey of Machine Learning for Big Code and Naturalness](https://mlsanity.com/paper/1709.06182/) (2017)
- [Graph HyperNetworks for Neural Architecture Search](https://mlsanity.com/paper/1810.05749/) (2018)
- [D-VAE: A Variational Autoencoder for Directed Acyclic Graphs](https://mlsanity.com/paper/1904.11088/) (2019)
- [Graph Neural Networks: Architectures, Stability and Transferability](https://mlsanity.com/paper/2008.01767/) (2020)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [Directed Acyclic Graph Neural Networks](https://mlsanity.com/paper/2101.07965/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning](https://mlsanity.com/paper/2502.10818/) (2025)
- [Graph Signal Processing: History, Development, Impact, and Outlook](https://mlsanity.com/paper/2303.12211/) (2023)
- [Signal Processing on Directed Graphs](https://mlsanity.com/paper/2008.00586/) (2020)
- [Transformers over Directed Acyclic Graphs](https://mlsanity.com/paper/2210.13148/) (2022)
- [Untrained Graph Neural Networks for Denoising](https://mlsanity.com/paper/2109.11700/) (2021)
- [CoLiDE: Concomitant Linear DAG Estimation](https://mlsanity.com/paper/2310.02895/) (2023)
- [Causal Fourier Analysis on Directed Acyclic Graphs and Posets](https://mlsanity.com/paper/2209.07970/) (2022)
- [Beyond Over-smoothing: Uncovering the Trainability Challenges in Deep Graph Neural Networks](https://mlsanity.com/paper/2408.03669/) (2024)
- [Discrete Signal Processing on Meet/Join Lattices](https://mlsanity.com/paper/2012.04358/) (2020)
- [Redesigning graph filter-based GNNs to relax the homophily assumption](https://mlsanity.com/paper/2409.08676/) (2024)
- [Multiscale Causal Structure Learning](https://mlsanity.com/paper/2207.07908/) (2022)

## Built on by (most cited first, 1 of 1)

- [Exploiting Non-Negativity in DAG Structure Learning](https://mlsanity.com/paper/2605.19947/) (2026)

## Abstract (arXiv)

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.