# Improving Graph Neural Networks with Learnable Propagation Operators

arXiv: https://arxiv.org/abs/2210.17224 · HTML: https://mlsanity.com/paper/2210.17224/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 91 references that are in the map.
- First posted on arXiv 31 Oct 2022.

## Builds on (most cited first, 30 of 69)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [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)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (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)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [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)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)

## Built on by (most cited first, 19 of 19)

- [Are GATs Out of Balance?](https://mlsanity.com/paper/2310.07235/) (2023)
- [Beyond Over-smoothing: Uncovering the Trainability Challenges in Deep Graph Neural Networks](https://mlsanity.com/paper/2408.03669/) (2024)
- [Redesigning graph filter-based GNNs to relax the homophily assumption](https://mlsanity.com/paper/2409.08676/) (2024)
- [Representation Learning on Heterophilic Graph with Directional Neighborhood Attention](https://mlsanity.com/paper/2403.01475/) (2024)
- [Graph Neural Reaction Diffusion Models](https://mlsanity.com/paper/2406.10871/) (2024)
- [Preventing Representational Rank Collapse in MPNNs by Splitting the Computational Graph](https://mlsanity.com/paper/2409.11504/) (2024)
- [Improving the Effective Receptive Field of Message-Passing Neural Networks](https://mlsanity.com/paper/2505.23185/) (2025)
- [GATE: How to Keep Out Intrusive Neighbors](https://mlsanity.com/paper/2406.00418/) (2024)
- [MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks](https://mlsanity.com/paper/2409.05100/) (2024)
- [Flexible Diffusion Scopes with Parameterized Laplacian for Heterophilic Graph Learning](https://mlsanity.com/paper/2409.09888/) (2024)
- [Quadratic Binary Optimization with Graph Neural Networks](https://mlsanity.com/paper/2404.04874/) (2024)
- [Making Classic GNNs Strong Baselines Across Varying Homophily: A Smoothness-Generalization Perspective](https://mlsanity.com/paper/2412.09805/) (2024)
- [A Signed Graph Approach to Understanding and Mitigating Oversmoothing in GNNs](https://mlsanity.com/paper/2502.11394/) (2025)
- [GTAGCN: Generalized Topology Adaptive Graph Convolutional Networks](https://mlsanity.com/paper/2403.15077/) (2024)
- [First-order PDES for Graph Neural Networks: Advection And Burgers Equation Models](https://mlsanity.com/paper/2404.03081/) (2024)
- [Personalized Layer Selection for Graph Neural Networks](https://mlsanity.com/paper/2501.14964/) (2025)
- [Simplifying Graph Convolutional Networks with Redundancy-Free Neighbors](https://mlsanity.com/paper/2504.13426/) (2025)
- [Learning from Historical Activations in Graph Neural Networks](https://mlsanity.com/paper/2601.01123/) (2026)
- [Gate the Filter, Not the Message: Node-Channel Mixtures for Pre-Propagation GNNs](https://mlsanity.com/paper/2606.01660/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are limited in their propagation operators. In many cases, these operators often contain non-negative elements only and are shared across channels, limiting the expressiveness of GNNs. Moreover, some GNNs suffer from over-smoothing, limiting their depth. On the other hand, Convolutional Neural Networks (CNNs) can learn diverse propagation filters, and phenomena like over-smoothing are typically not apparent in CNNs. In this paper, we bridge these gaps by incorporating trainable channel-wise weighting factors ω to learn and mix multiple smoothing and sharpening propagation operators at each layer. Our generic method is called ωGNN, and is easy to implement. We study two variants: ωGCN and ωGAT. For ωGCN, we theoretically analyse its behaviour and the impact of ω on the obtained node features. Our experiments confirm these findings, demonstrating and explaining how both variants do not over-smooth. Additionally, we experiment with 15 real-world datasets on node- and graph-classification tasks, where our ωGCN and ωGAT perform on par with state-of-the-art methods.