# The Heterophilic Snowflake Hypothesis: Training and Empowering GNNs for Heterophilic Graphs

arXiv: https://arxiv.org/abs/2406.12539 · HTML: https://mlsanity.com/paper/2406.12539/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 75 references that are in the map.
- First posted on arXiv 18 Jun 2024.

## Builds on (most cited first, 30 of 55)

- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [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)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (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)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Session-based Recommendation with Graph Neural Networks](https://mlsanity.com/paper/1811.00855/) (2018)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)

## Built on by (most cited first, 6 of 6)

- [Rethinking Fair Graph Neural Networks from Re-balancing](https://mlsanity.com/paper/2407.11624/) (2024)
- [Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modeling](https://mlsanity.com/paper/2505.18728/) (2025)
- [Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophily](https://mlsanity.com/paper/2511.06608/) (2025)
- [TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows](https://mlsanity.com/paper/2508.05070/) (2025)
- [LAMP: Learnable Meta-Path Guided Adversarial Contrastive Learning for Heterogeneous Graphs](https://mlsanity.com/paper/2409.06323/) (2024)
- [Fast Track to Winning Tickets: Repowering One-Shot Pruning for Graph Neural Networks](https://mlsanity.com/paper/2412.07605/) (2024)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have become pivotal tools for a range of graph-based learning tasks. Notably, most current GNN architectures operate under the assumption of homophily, whether explicitly or implicitly. While this underlying assumption is frequently adopted, it is not universally applicable, which can result in potential shortcomings in learning effectiveness. In this paper, for the first time, we transfer the prevailing concept of ``one node one receptive field" to the heterophilic graph. By constructing a proxy label predictor, we enable each node to possess a latent prediction distribution, which assists connected nodes in determining whether they should aggregate their associated neighbors. Ultimately, every node can have its own unique aggregation hop and pattern, much like each snowflake is unique and possesses its own characteristics. Based on observations, we innovatively introduce the Heterophily Snowflake Hypothesis and provide an effective solution to guide and facilitate research on heterophilic graphs and beyond. We conduct comprehensive experiments including (1) main results on 10 graphs with varying heterophily ratios across 10 backbones; (2) scalability on various deep GNN backbones (SGC, JKNet, etc.) across various large number of layers (2,4,6,8,16,32 layers); (3) comparison with conventional snowflake hypothesis; (4) efficiency comparison with existing graph pruning algorithms. Our observations show that our framework acts as a versatile operator for diverse tasks. It can be integrated into various GNN frameworks, boosting performance in-depth and offering an explainable approach to choosing the optimal network depth. The source code is available at urlhttps://github.com/bingreeky/HeteroSnoH.