# Deeper Insights into Deep Graph Convolutional Networks: Stability and Generalization

arXiv: https://arxiv.org/abs/2410.08473 · HTML: https://mlsanity.com/paper/2410.08473/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 69 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 30 of 48)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [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)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [XGNN: Towards Model-Level Explanations of Graph Neural Networks](https://mlsanity.com/paper/2006.02587/) (2020)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [Higher-Order Explanations of Graph Neural Networks via Relevant Walks](https://mlsanity.com/paper/2006.03589/) (2020)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks](https://mlsanity.com/paper/2012.07690/) (2020)
- [Stability and Generalization of Graph Convolutional Neural Networks](https://mlsanity.com/paper/1905.01004/) (2019)

## Built on by (most cited first, 6 of 6)

- [Stability and Generalization of Quantum Neural Networks](https://mlsanity.com/paper/2501.12737/) (2025)
- [Directed Acyclic Graph Convolutional Networks](https://mlsanity.com/paper/2506.12218/) (2025)
- [TypeBandit: Type-Level Context Allocation and Reweighting for Effective Attribute Completion in Heterogeneous Graph Neural Networks](https://mlsanity.com/paper/2604.27356/) (2026)
- [Rethinking Generalization in Graph Neural Networks: A Structural Complexity Perspective](https://mlsanity.com/paper/2605.13597/) (2026)
- [Difference-of-Convex Regularization for Graph Learning by Differentiable Programming](https://mlsanity.com/paper/2608.12757/) (2026)
- [When Do Language-Grounded Explanations Help? A Graph-Bottleneck for Farm Monitoring Interpretable Sheep Facial Pain](https://mlsanity.com/paper/2609.20427/) (2026)

## Abstract (arXiv)

Graph convolutional networks (GCNs) have emerged as powerful models for graph learning tasks, exhibiting promising performance in various domains. While their empirical success is evident, there is a growing need to understand their essential ability from a theoretical perspective. Existing theoretical research has primarily focused on the analysis of single-layer GCNs, while a comprehensive theoretical exploration of the stability and generalization of deep GCNs remains limited. In this paper, we bridge this gap by delving into the stability and generalization properties of deep GCNs, aiming to provide valuable insights by characterizing rigorously the associated upper bounds. Our theoretical results reveal that the stability and generalization of deep GCNs are influenced by certain key factors, such as the maximum absolute eigenvalue of the graph filter operators and the depth of the network. Our theoretical studies contribute to a deeper understanding of the stability and generalization properties of deep GCNs, potentially paving the way for developing more reliable and well-performing models.