# Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filtering

arXiv: https://arxiv.org/abs/2107.04755 · HTML: https://mlsanity.com/paper/2107.04755/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 58 references that are in the map.
- First posted on arXiv 10 Jul 2021.

## Builds on (most cited first, 30 of 43)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)

## Built on by (most cited first, 14 of 14)

- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Finding the Missing-half: Graph Complementary Learning for Homophily-prone and Heterophily-prone Graphs](https://mlsanity.com/paper/2306.07608/) (2023)
- [TraverseNet: Unifying Space and Time in Message Passing for Traffic Forecasting](https://mlsanity.com/paper/2109.02474/) (2021)
- [From Unsupervised to Few-shot Graph Anomaly Detection: A Multi-scale Contrastive Learning Approach](https://mlsanity.com/paper/2202.05525/) (2022)
- [Spatial Heterophily Aware Graph Neural Networks](https://mlsanity.com/paper/2306.12139/) (2023)
- [Homophily-Related: Adaptive Hybrid Graph Filter for Multi-View Graph Clustering](https://mlsanity.com/paper/2401.02682/) (2024)
- [Learning Optimal Graph Filters for Clustering of Attributed Graphs](https://mlsanity.com/paper/2211.04634/) (2022)
- [Heterophilous Distribution Propagation for Graph Neural Networks](https://mlsanity.com/paper/2405.20640/) (2024)
- [Learning from Heterophilic Graphs: A Spectral Theory Perspective on the Impact of Self-Loops and Parallel Edges](https://mlsanity.com/paper/2509.13139/) (2025)
- [Multi-Head Spectral-Adaptive Graph Anomaly Detection](https://mlsanity.com/paper/2512.22291/) (2025)
- [SIEFormer: Spectral-Interpretable and -Enhanced Transformer for Generalized Category Discovery](https://mlsanity.com/paper/2602.13067/) (2026)
- [Graph Signal Processing Meets Mamba2: Adaptive Filter Bank via Delta Modulation](https://mlsanity.com/paper/2603.22333/) (2026)
- [Convex--Concave Quadratic Spectral Filtering for Graph Neural Networks](https://mlsanity.com/paper/2606.24956/) (2026)

## Abstract (arXiv)

Graph convolutional networks are becoming indispensable for deep learning from graph-structured data. Most of the existing graph convolutional networks share two big shortcomings. First, they are essentially low-pass filters, thus the potentially useful middle and high frequency band of graph signals are ignored. Second, the bandwidth of existing graph convolutional filters is fixed. Parameters of a graph convolutional filter only transform the graph inputs without changing the curvature of a graph convolutional filter function. In reality, we are uncertain about whether we should retain or cut off the frequency at a certain point unless we have expert domain knowledge. In this paper, we propose Automatic Graph Convolutional Networks (AutoGCN) to capture the full spectrum of graph signals and automatically update the bandwidth of graph convolutional filters. While it is based on graph spectral theory, our AutoGCN is also localized in space and has a spatial form. Experimental results show that AutoGCN achieves significant improvement over baseline methods which only work as low-pass filters.