# NodeReg: Mitigating the Imbalance and Distribution Shift Effects in Semi-Supervised Node Classification via Norm Consistency

arXiv: https://arxiv.org/abs/2503.03211 · HTML: https://mlsanity.com/paper/2503.03211/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 48 references that are in the map.
- First posted on arXiv 5 Mar 2025.

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

- [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)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Return of Frustratingly Easy Domain Adaptation](https://mlsanity.com/paper/1511.05547/) (2015)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)
- [Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path](https://mlsanity.com/paper/2106.02073/) (2021)
- [GraphSMOTE: Imbalanced Node Classification on Graphs with Graph Neural Networks](https://mlsanity.com/paper/2103.08826/) (2021)
- [Knowledge Graph Convolutional Networks for Recommender Systems](https://mlsanity.com/paper/1904.12575/) (2019)
- [Extended Unconstrained Features Model for Exploring Deep Neural Collapse](https://mlsanity.com/paper/2202.08087/) (2022)
- [Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Data](https://mlsanity.com/paper/2108.01099/) (2021)
- [Are All Losses Created Equal: A Neural Collapse Perspective](https://mlsanity.com/paper/2210.02192/) (2022)
- [NRGNN: Learning a Label Noise-Resistant Graph Neural Network on Sparsely and Noisily Labeled Graphs](https://mlsanity.com/paper/2106.04714/) (2021)
- [Topology-Imbalance Learning for Semi-Supervised Node Classification](https://mlsanity.com/paper/2110.04099/) (2021)
- [Twitch Gamers: a Dataset for Evaluating Proximity Preserving and Structural Role-based Node Embeddings](https://mlsanity.com/paper/2101.03091/) (2021)
- [Learning to Extrapolate Knowledge: Transductive Few-shot Out-of-Graph Link Prediction](https://mlsanity.com/paper/2006.06648/) (2020)
- [Estimating Node Importance in Knowledge Graphs Using Graph Neural Networks](https://mlsanity.com/paper/1905.08865/) (2019)
- [Graph Out-of-Distribution Generalization via Causal Intervention](https://mlsanity.com/paper/2402.11494/) (2024)
- [Rethinking Semi-Supervised Imbalanced Node Classification from Bias-Variance Decomposition](https://mlsanity.com/paper/2310.18765/) (2023)
- [Quantifying the Optimization and Generalization Advantages of Graph Neural Networks Over Multilayer Perceptrons](https://mlsanity.com/paper/2306.13926/) (2023)
- [Resurrecting Label Propagation for Graphs with Heterophily and Label Noise](https://mlsanity.com/paper/2310.16560/) (2023)

## Built on by (most cited first, 1 of 1)

- [Learning Robust Heterogeneous Graph Representations via Contrastive-Reconstruction under Sparse Semantics](https://mlsanity.com/paper/2506.06682/) (2025)

## Abstract (arXiv)

Aggregating information from neighboring nodes benefits graph neural networks (GNNs) in semi-supervised node classification tasks. Nevertheless, this mechanism also renders nodes susceptible to the influence of their neighbors. For instance, this will occur when the neighboring nodes are imbalanced or the neighboring nodes contain noise, which can even affect the GNN's ability to generalize out of distribution. We find that ensuring the consistency of the norm for node representations can significantly reduce the impact of these two issues on GNNs. To this end, we propose a regularized optimization method called NodeReg that enforces the consistency of node representation norms. This method is simple but effective and satisfies Lipschitz continuity, thus facilitating stable optimization and significantly improving semi-supervised node classification performance under the above two scenarios. To illustrate, in the imbalance scenario, when training a GCN with an imbalance ratio of 0.1, NodeReg outperforms the most competitive baselines by 1.4%-25.9% in F1 score across five public datasets. Similarly, in the distribution shift scenario, NodeReg outperforms the most competitive baseline by 1.4%-3.1% in accuracy.