# Rethinking Graph Regularization for Graph Neural Networks

arXiv: https://arxiv.org/abs/2009.02027 · HTML: https://mlsanity.com/paper/2009.02027/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2020.

## Built on by (most cited first, 30 of 36)

- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [Deep Graph Clustering via Dual Correlation Reduction](https://mlsanity.com/paper/2112.14772/) (2021)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [Understanding and Improving Graph Injection Attack by Promoting Unnoticeability](https://mlsanity.com/paper/2202.08057/) (2022)
- [Rethinking Graph Auto-Encoder Models for Attributed Graph Clustering](https://mlsanity.com/paper/2107.08562/) (2021)
- [Train Your Own GNN Teacher: Graph-Aware Distillation on Textual Graphs](https://mlsanity.com/paper/2304.10668/) (2023)
- [Graph Anomaly Detection in Time Series: A Survey](https://mlsanity.com/paper/2302.00058/) (2023)
- [Improved Dual Correlation Reduction Network](https://mlsanity.com/paper/2202.12533/) (2022)
- [Learning Topology-Specific Experts for Molecular Property Prediction](https://mlsanity.com/paper/2302.13693/) (2023)
- [Convergent Graph Solvers](https://mlsanity.com/paper/2106.01680/) (2021)
- [Joint Graph Rewiring and Feature Denoising via Spectral Resonance](https://mlsanity.com/paper/2408.07191/) (2024)
- [Leveraging Label Non-Uniformity for Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2305.00139/) (2023)
- [Are GATs Out of Balance?](https://mlsanity.com/paper/2310.07235/) (2023)
- [Finding Heterophilic Neighbors via Confidence-based Subgraph Matching for Semi-supervised Node Classification](https://mlsanity.com/paper/2302.09755/) (2023)
- [Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling](https://mlsanity.com/paper/2409.02135/) (2024)
- [Calibrating and Improving Graph Contrastive Learning](https://mlsanity.com/paper/2101.11525/) (2021)
- [GATE: How to Keep Out Intrusive Neighbors](https://mlsanity.com/paper/2406.00418/) (2024)
- [ERGNN: Spectral Graph Neural Network With Explicitly-Optimized Rational Graph Filters](https://mlsanity.com/paper/2412.19106/) (2024)
- [Improving Your Graph Neural Networks: A High-Frequency Booster](https://mlsanity.com/paper/2210.08251/) (2022)
- [Global-Local Graph Neural Networks for Node-Classification](https://mlsanity.com/paper/2406.10863/) (2024)
- [LEReg: Empower Graph Neural Networks with Local Energy Regularization](https://mlsanity.com/paper/2203.10565/) (2022)
- [Towards Understanding Graph Neural Networks: An Algorithm Unrolling Perspective](https://mlsanity.com/paper/2206.04471/) (2022)
- [Improving Signed Propagation for Graph Neural Networks in Multi-Class Environments](https://mlsanity.com/paper/2301.08918/) (2023)
- [OrthoReg: Improving Graph-regularized MLPs via Orthogonality Regularization](https://mlsanity.com/paper/2302.00109/) (2023)
- [Decoupling and Damping: Structurally-Regularized Gradient Matching for Multimodal Graph Condensation](https://mlsanity.com/paper/2511.20222/) (2025)
- [Deep Manifold Learning with Graph Mining](https://mlsanity.com/paper/2207.08377/) (2022)
- [Every Node Counts: Improving the Training of Graph Neural Networks on Node Classification](https://mlsanity.com/paper/2211.16631/) (2022)
- [Distributional Signals for Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2304.03507/) (2023)
- [Self-attention Dual Embedding for Graphs with Heterophily](https://mlsanity.com/paper/2305.18385/) (2023)
- [Customizing Graph Neural Networks using Path Reweighting](https://mlsanity.com/paper/2106.10866/) (2021)

## Abstract (arXiv)

The graph Laplacian regularization term is usually used in semi-supervised representation learning to provide graph structure information for a model f(X). However, with the recent popularity of graph neural networks (GNNs), directly encoding graph structure A into a model, i.e., f(A, X), has become the more common approach. While we show that graph Laplacian regularization brings little-to-no benefit to existing GNNs, and propose a simple but non-trivial variant of graph Laplacian regularization, called Propagation-regularization (P-reg), to boost the performance of existing GNN models. We provide formal analyses to show that P-reg not only infuses extra information (that is not captured by the traditional graph Laplacian regularization) into GNNs, but also has the capacity equivalent to an infinite-depth graph convolutional network. We demonstrate that P-reg can effectively boost the performance of existing GNN models on both node-level and graph-level tasks across many different datasets.