# Understanding and Improving Deep Graph Neural Networks: A Probabilistic Graphical Model Perspective

arXiv: https://arxiv.org/abs/2301.10536 · HTML: https://mlsanity.com/paper/2301.10536/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 44 references that are in the map.
- First posted on arXiv 25 Jan 2023.

## Builds on (most cited first, 30 of 35)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [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)
- [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)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Graph Convolutional Networks for Text Classification](https://mlsanity.com/paper/1809.05679/) (2018)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Vision GNN: An Image is Worth Graph of Nodes](https://mlsanity.com/paper/2206.00272/) (2022)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Discriminative Embeddings of Latent Variable Models for Structured Data](https://mlsanity.com/paper/1603.05629/) (2016)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Graphite: Iterative Generative Modeling of Graphs](https://mlsanity.com/paper/1803.10459/) (2018)
- [A Unified View on Graph Neural Networks as Graph Signal Denoising](https://mlsanity.com/paper/2010.01777/) (2020)
- [How Powerful are K-hop Message Passing Graph Neural Networks](https://mlsanity.com/paper/2205.13328/) (2022)

## Abstract (arXiv)

Recently, graph-based models designed for downstream tasks have significantly advanced research on graph neural networks (GNNs). GNN baselines based on neural message-passing mechanisms such as GCN and GAT perform worse as the network deepens. Therefore, numerous GNN variants have been proposed to tackle this performance degradation problem, including many deep GNNs. However, a unified framework is still lacking to connect these existing models and interpret their effectiveness at a high level. In this work, we focus on deep GNNs and propose a novel view for understanding them. We establish a theoretical framework via inference on a probabilistic graphical model. Given the fixed point equation (FPE) derived from the variational inference on the Markov random fields, the deep GNNs, including JKNet, GCNII, DGCN, and the classical GNNs, such as GCN, GAT, and APPNP, can be regarded as different approximations of the FPE. Moreover, given this framework, more accurate approximations of FPE are brought, guiding us to design a more powerful GNN: coupling graph neural network (CoGNet). Extensive experiments are carried out on citation networks and natural language processing downstream tasks. The results demonstrate that the CoGNet outperforms the SOTA models.