# Heterophilous Distribution Propagation for Graph Neural Networks

arXiv: https://arxiv.org/abs/2405.20640 · HTML: https://mlsanity.com/paper/2405.20640/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 49 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 30 of 33)

- [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)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [A Comprehensive Survey on Graph Anomaly Detection with Deep Learning](https://mlsanity.com/paper/2106.07178/) (2021)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Node Similarity Preserving Graph Convolutional Networks](https://mlsanity.com/paper/2011.09643/) (2020)
- [Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns](https://mlsanity.com/paper/2106.06586/) (2021)
- [GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophily](https://mlsanity.com/paper/2110.15777/) (2021)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filter](https://mlsanity.com/paper/2104.12840/) (2021)
- [BotRGCN: Twitter Bot Detection with Relational Graph Convolutional Networks](https://mlsanity.com/paper/2106.13092/) (2021)
- [How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing](https://mlsanity.com/paper/2405.12474/) (2024)
- [Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2202.00961/) (2022)
- [Permutation Equivariant Graph Framelets for Heterophilous Graph Learning](https://mlsanity.com/paper/2306.04265/) (2023)
- [Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filtering](https://mlsanity.com/paper/2107.04755/) (2021)
- [Learning from the Dark: Boosting Graph Convolutional Neural Networks with Diverse Negative Samples](https://mlsanity.com/paper/2210.00728/) (2022)
- [Restructuring Graph for Higher Homophily via Adaptive Spectral Clustering](https://mlsanity.com/paper/2206.02386/) (2022)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have achieved remarkable success in various graph mining tasks by aggregating information from neighborhoods for representation learning. The success relies on the homophily assumption that nearby nodes exhibit similar behaviors, while it may be violated in many real-world graphs. Recently, heterophilous graph neural networks (HeterGNNs) have attracted increasing attention by modifying the neural message passing schema for heterophilous neighborhoods. However, they suffer from insufficient neighborhood partition and heterophily modeling, both of which are critical but challenging to break through. To tackle these challenges, in this paper, we propose heterophilous distribution propagation (HDP) for graph neural networks. Instead of aggregating information from all neighborhoods, HDP adaptively separates the neighbors into homophilous and heterphilous parts based on the pseudo assignments during training. The heterophilous neighborhood distribution is learned with orthogonality-oriented constraint via a trusted prototype contrastive learning paradigm. Both the homophilous and heterophilous patterns are propagated with a novel semantic-aware message passing mechanism. We conduct extensive experiments on 9 benchmark datasets with different levels of homophily. Experimental results show that our method outperforms representative baselines on heterophilous datasets.