# Graph Neural Networks with convolutional ARMA filters

arXiv: https://arxiv.org/abs/1901.01343 · HTML: https://mlsanity.com/paper/1901.01343/

## Key facts

- Cited by 185 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2019.

## Built on by (most cited first, 30 of 185)

- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Sign and Basis Invariant Networks for Spectral Graph Representation Learning](https://mlsanity.com/paper/2202.13013/) (2022)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [GraphWorld: Fake Graphs Bring Real Insights for GNNs](https://mlsanity.com/paper/2203.00112/) (2022)
- [Transferability of Graph Neural Networks: an Extended Graphon Approach](https://mlsanity.com/paper/2109.10096/) (2021)
- [VQ-GNN: A Universal Framework to Scale up Graph Neural Networks using Vector Quantization](https://mlsanity.com/paper/2110.14363/) (2021)
- [Graph Neural Networks with Learnable and Optimal Polynomial Bases](https://mlsanity.com/paper/2302.12432/) (2023)
- [Unlearning Graph Classifiers with Limited Data Resources](https://mlsanity.com/paper/2211.03216/) (2022)
- [Parallel and Distributed Graph Neural Networks: An In-Depth Concurrency Analysis](https://mlsanity.com/paper/2205.09702/) (2022)
- [Dynamic Scenario Representation Learning for Motion Forecasting with Heterogeneous Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/2303.04364/) (2023)
- [PC-Conv: Unifying Homophily and Heterophily with Two-fold Filtering](https://mlsanity.com/paper/2312.14438/) (2023)
- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [Learning Conjoint Attentions for Graph Neural Nets](https://mlsanity.com/paper/2102.03147/) (2021)
- [High-Level Synthesis Performance Prediction using GNNs: Benchmarking, Modeling, and Advancing](https://mlsanity.com/paper/2201.06848/) (2022)
- [EvenNet: Ignoring Odd-Hop Neighbors Improves Robustness of Graph Neural Networks](https://mlsanity.com/paper/2205.13892/) (2022)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [NAS-Bench-Graph: Benchmarking Graph Neural Architecture Search](https://mlsanity.com/paper/2206.09166/) (2022)
- [Power Flow Balancing with Decentralized Graph Neural Networks](https://mlsanity.com/paper/2111.02169/) (2021)
- [Learning Connectivity with Graph Convolutional Networks for Skeleton-based Action Recognition](https://mlsanity.com/paper/2112.03328/) (2021)
- [HoloNets: Spectral Convolutions do extend to Directed Graphs](https://mlsanity.com/paper/2310.02232/) (2023)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspective](https://mlsanity.com/paper/2207.11311/) (2022)
- [Beyond Low-Pass Filters: Adaptive Feature Propagation on Graphs](https://mlsanity.com/paper/2103.14187/) (2021)
- [Distill n' Explain: explaining graph neural networks using simple surrogates](https://mlsanity.com/paper/2303.10139/) (2023)
- [RoSGAS: Adaptive Social Bot Detection with Reinforced Self-Supervised GNN Architecture Search](https://mlsanity.com/paper/2206.06757/) (2022)
- [TIDE: Time Derivative Diffusion for Deep Learning on Graphs](https://mlsanity.com/paper/2212.02483/) (2022)
- [Node-oriented Spectral Filtering for Graph Neural Networks](https://mlsanity.com/paper/2212.03654/) (2022)
- [Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approach](https://mlsanity.com/paper/2406.03464/) (2024)

## Abstract (arXiv)

Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more robust to noise, and better captures the global graph structure. We propose a graph neural network implementation of the ARMA filter with a recursive and distributed formulation, obtaining a convolutional layer that is efficient to train, localized in the node space, and can be transferred to new graphs at test time. We perform a spectral analysis to study the filtering effect of the proposed ARMA layer and report experiments on four downstream tasks: semi-supervised node classification, graph signal classification, graph classification, and graph regression. Results show that the proposed ARMA layer brings significant improvements over graph neural networks based on polynomial filters.