# Boosting Graph Neural Networks by Injecting Pooling in Message Passing

arXiv: https://arxiv.org/abs/2202.04768 · HTML: https://mlsanity.com/paper/2202.04768/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 8 Feb 2022.

## Builds on (most cited first, 29 of 29)

- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [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)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Learning Multiagent Communication with Backpropagation](https://mlsanity.com/paper/1605.07736/) (2016)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [Towards Deeper Graph Neural Networks with Differentiable Group Normalization](https://mlsanity.com/paper/2006.06972/) (2020)
- [Towards Sparse Hierarchical Graph Classifiers](https://mlsanity.com/paper/1811.01287/) (2018)
- [Memory-Based Graph Networks](https://mlsanity.com/paper/2002.09518/) (2020)
- [Spectral Clustering with Graph Neural Networks for Graph Pooling](https://mlsanity.com/paper/1907.00481/) (2019)
- [When Work Matters: Transforming Classical Network Structures to Graph CNN](https://mlsanity.com/paper/1807.02653/) (2018)
- [Embedding Bilateral Filter in Least Squares for Efficient Edge-preserving Image Smoothing](https://mlsanity.com/paper/1812.07122/) (2018)

## Abstract (arXiv)

There has been tremendous success in the field of graph neural networks (GNNs) as a result of the development of the message-passing (MP) layer, which updates the representation of a node by combining it with its neighbors to address variable-size and unordered graphs. Despite the fruitful progress of MP GNNs, their performance can suffer from over-smoothing, when node representations become too similar and even indistinguishable from one another. Furthermore, it has been reported that intrinsic graph structures are smoothed out as the GNN layer increases. Inspired by the edge-preserving bilateral filters used in image processing, we propose a new, adaptable, and powerful MP framework to prevent over-smoothing. Our bilateral-MP estimates a pairwise modular gradient by utilizing the class information of nodes, and further preserves the global graph structure by using the gradient when the aggregating function is applied. Our proposed scheme can be generalized to all ordinary MP GNNs. Experiments on five medium-size benchmark datasets using four state-of-the-art MP GNNs indicate that the bilateral-MP improves performance by alleviating over-smoothing. By inspecting quantitative measurements, we additionally validate the effectiveness of the proposed mechanism in preventing the over-smoothing issue.