# Beyond Low-Pass Filters: Adaptive Feature Propagation on Graphs

arXiv: https://arxiv.org/abs/2103.14187 · HTML: https://mlsanity.com/paper/2103.14187/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 47 references that are in the map.
- First posted on arXiv 26 Mar 2021.

## Builds on (most cited first, 30 of 32)

- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec](https://mlsanity.com/paper/1710.02971/) (2017)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Adaptive Sampling Towards Fast Graph Representation Learning](https://mlsanity.com/paper/1809.05343/) (2018)
- [Scaling Graph Neural Networks with Approximate PageRank](https://mlsanity.com/paper/2007.01570/) (2020)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [PTE: Predictive Text Embedding through Large-scale Heterogeneous Text Networks](https://mlsanity.com/paper/1508.00200/) (2015)
- [Non-Local Graph Neural Networks](https://mlsanity.com/paper/2005.14612/) (2020)
- [Flow Smoothing and Denoising: Graph Signal Processing in the Edge-Space](https://mlsanity.com/paper/1808.02111/) (2018)

## Built on by (most cited first, 18 of 18)

- [How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implications](https://mlsanity.com/paper/2106.07767/) (2021)
- [Homophily-oriented Heterogeneous Graph Rewiring](https://mlsanity.com/paper/2302.06299/) (2023)
- [Augmentation-Free Graph Contrastive Learning with Performance Guarantee](https://mlsanity.com/paper/2204.04874/) (2022)
- [Single-Pass Contrastive Learning Can Work for Both Homophilic and Heterophilic Graph](https://mlsanity.com/paper/2211.10890/) (2022)
- [GraphGLOW: Universal and Generalizable Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2306.11264/) (2023)
- [Robust Graph Structure Learning under Heterophily](https://mlsanity.com/paper/2403.03659/) (2024)
- [Restructuring Graph for Higher Homophily via Adaptive Spectral Clustering](https://mlsanity.com/paper/2206.02386/) (2022)
- [Towards Expressive Spectral-Temporal Graph Neural Networks for Time Series Forecasting](https://mlsanity.com/paper/2305.06587/) (2023)
- [Shape-aware Graph Spectral Learning](https://mlsanity.com/paper/2310.10064/) (2023)
- [Homophily-Related: Adaptive Hybrid Graph Filter for Multi-View Graph Clustering](https://mlsanity.com/paper/2401.02682/) (2024)
- [Improving Your Graph Neural Networks: A High-Frequency Booster](https://mlsanity.com/paper/2210.08251/) (2022)
- [Spectral-Aware Augmentation for Enhanced Graph Representation Learning](https://mlsanity.com/paper/2310.13845/) (2023)
- [Framelet Message Passing](https://mlsanity.com/paper/2302.14806/) (2023)
- [GPatcher: A Simple and Adaptive MLP Model for Alleviating Graph Heterophily](https://mlsanity.com/paper/2306.14340/) (2023)
- [Simplified PCNet with Robustness](https://mlsanity.com/paper/2403.03676/) (2024)
- [HeroFilter: Adaptive Spectral Graph Filter for Varying Heterophilic Relations](https://mlsanity.com/paper/2510.10864/) (2025)
- [Divergent Paths: Separating Homophilic and Heterophilic Learning for Enhanced Graph-level Representations](https://mlsanity.com/paper/2504.05344/) (2025)
- [Graph as a feature: improving node classification with non-neural graph-aware logistic regression](https://mlsanity.com/paper/2411.12330/) (2024)

## Abstract (arXiv)

Graph neural networks (GNNs) have been extensively studied for prediction tasks on graphs. As pointed out by recent studies, most GNNs assume local homophily, i.e., strong similarities in local neighborhoods. This assumption however limits the generalizability power of GNNs. To address this limitation, we propose a flexible GNN model, which is capable of handling any graphs without being restricted by their underlying homophily. At its core, this model adopts a node attention mechanism based on multiple learnable spectral filters; therefore, the aggregation scheme is learned adaptively for each graph in the spectral domain. We evaluated the proposed model on node classification tasks over eight benchmark datasets. The proposed model is shown to generalize well to both homophilic and heterophilic graphs. Further, it outperforms all state-of-the-art baselines on heterophilic graphs and performs comparably with them on homophilic graphs.