# GRAIN: Multi-Granular and Implicit Information Aggregation Graph Neural Network for Heterophilous Graphs

arXiv: https://arxiv.org/abs/2504.06649 · HTML: https://mlsanity.com/paper/2504.06649/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 9 Apr 2025.

## Builds on (most cited first, 20 of 20)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [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)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [AM-GCN: Adaptive Multi-channel Graph Convolutional Networks](https://mlsanity.com/paper/2007.02265/) (2020)
- [Non-Local Graph Neural Networks](https://mlsanity.com/paper/2005.14612/) (2020)
- [GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophily](https://mlsanity.com/paper/2110.15777/) (2021)
- [Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?](https://mlsanity.com/paper/2109.05641/) (2021)
- [Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothing](https://mlsanity.com/paper/2302.01524/) (2023)
- [Graph Neural Networks Inspired by Classical Iterative Algorithms](https://mlsanity.com/paper/2103.06064/) (2021)
- [No prejudice! Fair Federated Graph Neural Networks for Personalized Recommendation](https://mlsanity.com/paper/2312.10080/) (2023)

## Built on by (most cited first, 3 of 3)

- [HeterSEED: Semantics-Structure Decoupling for Heterogeneous Graph Learning under Heterophily](https://mlsanity.com/paper/2605.04594/) (2026)
- [HP-JEPA: Hierarchical Partitioning for Multi-Resolution Graph Joint-Embedding Predictive Learning](https://mlsanity.com/paper/2608.00491/) (2026)
- [VLM-based automatic multi-granularity graph representation of building layouts for design informatics](https://mlsanity.com/paper/2608.24886/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have shown significant success in learning graph representations. However, recent studies reveal that GNNs often fail to outperform simple MLPs on heterophilous graph tasks, where connected nodes may differ in features or labels, challenging the homophily assumption. Existing methods addressing this issue often overlook the importance of information granularity and rarely consider implicit relationships between distant nodes. To overcome these limitations, we propose the Granular and Implicit Graph Network (GRAIN), a novel GNN model specifically designed for heterophilous graphs. GRAIN enhances node embeddings by aggregating multi-view information at various granularity levels and incorporating implicit data from distant, non-neighboring nodes. This approach effectively integrates local and global information, resulting in smoother, more accurate node representations. We also introduce an adaptive graph information aggregator that efficiently combines multi-granularity and implicit data, significantly improving node representation quality, as shown by experiments on 13 datasets covering varying homophily and heterophily. GRAIN consistently outperforms 12 state-of-the-art models, excelling on both homophilous and heterophilous graphs.