# Meta-Weight Graph Neural Network: Push the Limits Beyond Global Homophily

arXiv: https://arxiv.org/abs/2203.10280 · HTML: https://mlsanity.com/paper/2203.10280/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 33 references that are in the map.
- First posted on arXiv 19 Mar 2022.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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 Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [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)
- [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)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [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)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Identity-aware Graph Neural Networks](https://mlsanity.com/paper/2101.10320/) (2021)
- [AM-GCN: Adaptive Multi-channel Graph Convolutional Networks](https://mlsanity.com/paper/2007.02265/) (2020)
- [A simple yet effective baseline for non-attributed graph classification](https://mlsanity.com/paper/1811.03508/) (2018)
- [Do Diffusion Protocols Govern Cascade Growth?](https://mlsanity.com/paper/1805.07368/) (2018)

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

- [GraphGPT: Graph Instruction Tuning for Large Language Models](https://mlsanity.com/paper/2310.13023/) (2023)
- [Continual Learning on Dynamic Graphs via Parameter Isolation](https://mlsanity.com/paper/2305.13825/) (2023)
- [Homophily-oriented Heterogeneous Graph Rewiring](https://mlsanity.com/paper/2302.06299/) (2023)
- [Understanding Heterophily for Graph Neural Networks](https://mlsanity.com/paper/2401.09125/) (2024)
- [ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting](https://mlsanity.com/paper/2205.13700/) (2022)
- [MM-GNN: Mix-Moment Graph Neural Network towards Modeling Neighborhood Feature Distribution](https://mlsanity.com/paper/2208.07012/) (2022)
- [DAGPrompT: Pushing the Limits of Graph Prompting with a Distribution-aware Graph Prompt Tuning Approach](https://mlsanity.com/paper/2501.15142/) (2025)
- [Graph Neural Networks with Diverse Spectral Filtering](https://mlsanity.com/paper/2312.09041/) (2023)
- [GraphRARE: Reinforcement Learning Enhanced Graph Neural Network with Relative Entropy](https://mlsanity.com/paper/2312.09708/) (2023)
- [Heterophily-Aware Graph Attention Network](https://mlsanity.com/paper/2302.03228/) (2023)
- [ForecastGrapher: Redefining Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2405.18036/) (2024)
- [Adaptive Heterogeneous Graph Neural Networks: Bridging Heterophily and Heterogeneity](https://mlsanity.com/paper/2508.06034/) (2025)
- [Centrality-Based Node Feature Augmentation for Robust Network Alignment](https://mlsanity.com/paper/2304.12751/) (2023)
- [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) show strong expressive power on graph data mining, by aggregating information from neighbors and using the integrated representation in the downstream tasks. The same aggregation methods and parameters for each node in a graph are used to enable the GNNs to utilize the homophily relational data. However, not all graphs are homophilic, even in the same graph, the distributions may vary significantly. Using the same convolution over all nodes may lead to the ignorance of various graph patterns. Furthermore, many existing GNNs integrate node features and structure identically, which ignores the distributions of nodes and further limits the expressive power of GNNs. To solve these problems, we propose Meta Weight Graph Neural Network (MWGNN) to adaptively construct graph convolution layers for different nodes. First, we model the Node Local Distribution (NLD) from node feature, topological structure and positional identity aspects with the Meta-Weight. Then, based on the Meta-Weight, we generate the adaptive graph convolutions to perform a node-specific weighted aggregation and boost the node representations. Finally, we design extensive experiments on real-world and synthetic benchmarks to evaluate the effectiveness of MWGNN. These experiments show the excellent expressive power of MWGNN in dealing with graph data with various distributions.