# SCR: Training Graph Neural Networks with Consistency Regularization

arXiv: https://arxiv.org/abs/2112.04319 · HTML: https://mlsanity.com/paper/2112.04319/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 51 references that are in the map.
- First posted on arXiv 8 Dec 2021.

## Builds on (most cited first, 30 of 36)

- [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)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Unsupervised Data Augmentation for Consistency Training](https://mlsanity.com/paper/1904.12848/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results](https://mlsanity.com/paper/1703.01780/) (2017)
- [Regularization With Stochastic Transformations and Perturbations for Deep Semi-Supervised Learning](https://mlsanity.com/paper/1606.04586/) (2016)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Learning with Pseudo-Ensembles](https://mlsanity.com/paper/1412.4864/) (2014)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [R-Drop: Regularized Dropout for Neural Networks](https://mlsanity.com/paper/2106.14448/) (2021)
- [Adaptive Sampling Towards Fast Graph Representation Learning](https://mlsanity.com/paper/1809.05343/) (2018)
- [Node Feature Extraction by Self-Supervised Multi-scale Neighborhood Prediction](https://mlsanity.com/paper/2111.00064/) (2021)
- [Multi-Stage Self-Supervised Learning for Graph Convolutional Networks on Graphs with Few Labels](https://mlsanity.com/paper/1902.11038/) (2019)

## Built on by (most cited first, 10 of 10)

- [UniGraph: Learning a Unified Cross-Domain Foundation Model for Text-Attributed Graphs](https://mlsanity.com/paper/2402.13630/) (2024)
- [UniGraph2: Learning a Unified Embedding Space to Bind Multimodal Graphs](https://mlsanity.com/paper/2502.00806/) (2025)
- [Evaluating the Paperclip Maximizer: Are RL-Based Language Models More Likely to Pursue Instrumental Goals?](https://mlsanity.com/paper/2502.12206/) (2025)
- [LazyGNN: Large-Scale Graph Neural Networks via Lazy Propagation](https://mlsanity.com/paper/2302.01503/) (2023)
- [Efficient Heterogeneous Graph Learning via Random Projection](https://mlsanity.com/paper/2310.14481/) (2023)
- [Generalizing Graph Transformers Across Diverse Graphs and Tasks via Pre-training](https://mlsanity.com/paper/2407.03953/) (2024)
- [Graph-based Knowledge Distillation: A survey and experimental evaluation](https://mlsanity.com/paper/2302.14643/) (2023)
- [Integrating Structural and Semantic Signals in Text-Attributed Graphs with BiGTex](https://mlsanity.com/paper/2504.12474/) (2025)
- [Variational Graph Auto-Encoder Based Inductive Learning Method for Semi-Supervised Classification](https://mlsanity.com/paper/2403.17500/) (2024)
- [Optimal Transport-Guided Adversarial Attacks on Graph Neural Network-Based Bot Detection](https://mlsanity.com/paper/2602.00318/) (2026)

## Abstract (arXiv)

We present the SCR framework for enhancing the training of graph neural networks (GNNs) with consistency regularization. Regularization is a set of strategies used in Machine Learning to reduce overfitting and improve the generalization ability. However, it is unclear how to best design the generalization strategies in GNNs, as it works in a semi-supervised setting for graph data. The major challenge lies in how to efficiently balance the trade-off between the error from the labeled data and that from the unlabeled data. SCR is a simple yet general framework in which we introduce two strategies of consistency regularization to address the challenge above. One is to minimize the disagreements among the perturbed predictions by different versions of a GNN model. The other is to leverage the Mean Teacher paradigm to estimate a consistency loss between teacher and student models instead of the disagreement of the predictions. We conducted experiments on three large-scale node classification datasets in the Open Graph Benchmark (OGB). Experimental results demonstrate that the proposed SCR framework is a general one that can enhance various GNNs to achieve better performance. Finally, SCR has been the top-1 entry on all three OGB leaderboards as of this submission.