# Deep Graph Neural Networks via Posteriori-Sampling-based Node-Adaptive Residual Module

arXiv: https://arxiv.org/abs/2305.05368 · HTML: https://mlsanity.com/paper/2305.05368/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 34 references that are in the map.
- First posted on arXiv 9 May 2023.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [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)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [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)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Equivariant Subgraph Aggregation Networks](https://mlsanity.com/paper/2110.02910/) (2021)
- [Towards Deeper Graph Neural Networks with Differentiable Group Normalization](https://mlsanity.com/paper/2006.06972/) (2020)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [Ordered Subgraph Aggregation Networks](https://mlsanity.com/paper/2206.11168/) (2022)
- [Feature Overcorrelation in Deep Graph Neural Networks: A New Perspective](https://mlsanity.com/paper/2206.07743/) (2022)

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

- [Harnessing Feature Resonance under Arbitrary Target Alignment for Out-of-Distribution Node Detection](https://mlsanity.com/paper/2502.16076/) (2025)
- [VecFormer: Towards Efficient and Generalizable Graph Transformer with Graph Token Attention](https://mlsanity.com/paper/2602.19622/) (2026)
- [Towards a deeper GCN: Alleviate over-smoothing with iterative training and fine-tuning](https://mlsanity.com/paper/2506.17576/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs), a type of neural network that can learn from graph-structured data through neighborhood information aggregation, have shown superior performance in various downstream tasks. However, as the number of layers increases, node representations become indistinguishable, which is known as over-smoothing. To address this issue, many residual methods have emerged. In this paper, we focus on the over-smoothing issue and related residual methods. Firstly, we revisit over-smoothing from the perspective of overlapping neighborhood subgraphs, and based on this, we explain how residual methods can alleviate over-smoothing by integrating multiple orders neighborhood subgraphs to avoid the indistinguishability of the single high-order neighborhood subgraphs. Additionally, we reveal the drawbacks of previous residual methods, such as the lack of node adaptability and severe loss of high-order neighborhood subgraph information, and propose a Posterior-Sampling-based, Node-Adaptive Residual module (PSNR). We theoretically demonstrate that PSNR can alleviate the drawbacks of previous residual methods. Furthermore, extensive experiments verify the superiority of the PSNR module in fully observed node classification and missing feature scenarios. Our code is available at https://github.com/jingbo02/PSNR-GNN.