# NodeMixup: Tackling Under-Reaching for Graph Neural Networks

arXiv: https://arxiv.org/abs/2312.13032 · HTML: https://mlsanity.com/paper/2312.13032/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 40 references that are in the map.
- First posted on arXiv 20 Dec 2023.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [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)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [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)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learning](https://mlsanity.com/paper/2101.06329/) (2021)
- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
- [Topology-Imbalance Learning for Semi-Supervised Node Classification](https://mlsanity.com/paper/2110.04099/) (2021)
- [GraphMixup: Improving Class-Imbalanced Node Classification on Graphs by Self-supervised Context Prediction](https://mlsanity.com/paper/2106.11133/) (2021)
- [Position-aware Structure Learning for Graph Topology-imbalance by Relieving Under-reaching and Over-squashing](https://mlsanity.com/paper/2208.08302/) (2022)
- [Graph Transplant: Node Saliency-Guided Graph Mixup with Local Structure Preservation](https://mlsanity.com/paper/2111.05639/) (2021)
- [GraphMAD: Graph Mixup for Data Augmentation using Data-Driven Convex Clustering](https://mlsanity.com/paper/2210.15721/) (2022)
- [Metric Based Few-Shot Graph Classification](https://mlsanity.com/paper/2206.03695/) (2022)

## Built on by (most cited first, 12 of 12)

- [Unified Spatial-Temporal Edge-Enhanced Graph Networks for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2502.02504/) (2025)
- [AdaGMLP: AdaBoosting GNN-to-MLP Knowledge Distillation](https://mlsanity.com/paper/2405.14307/) (2024)
- [IntraMix: Intra-Class Mixup Generation for Accurate Labels and Neighbors](https://mlsanity.com/paper/2405.00957/) (2024)
- [Discrepancy-Aware Graph Mask Auto-Encoder](https://mlsanity.com/paper/2506.19343/) (2025)
- [On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL condition](https://mlsanity.com/paper/2507.08861/) (2025)
- [Backward Oversmoothing: why is it hard to train deep Graph Neural Networks?](https://mlsanity.com/paper/2505.16736/) (2025)
- [ProGMLP: A Progressive Framework for GNN-to-MLP Knowledge Distillation with Efficient Trade-offs](https://mlsanity.com/paper/2507.19031/) (2025)
- [VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks](https://mlsanity.com/paper/2510.01022/) (2025)
- [Traceable Latent Variable Discovery Based on Multi-Agent Collaboration](https://mlsanity.com/paper/2602.14456/) (2026)
- [MDGMIX: Boundary-Aware Subgraph Mixing for Multi-Domain Graph Pre-Training](https://mlsanity.com/paper/2605.25771/) (2026)
- [Dual-perspective Cross Contrastive Learning in Graph Transformers](https://mlsanity.com/paper/2406.00403/) (2024)
- [Conf-GNNRec: Quantifying and Calibrating the Prediction Confidence for GNN-based Recommendation Methods](https://mlsanity.com/paper/2505.16466/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have become mainstream methods for solving the semi-supervised node classification problem. However, due to the uneven location distribution of labeled nodes in the graph, labeled nodes are only accessible to a small portion of unlabeled nodes, leading to the under-reaching issue. In this study, we firstly reveal under-reaching by conducting an empirical investigation on various well-known graphs. Then, we demonstrate that under-reaching results in unsatisfactory distribution alignment between labeled and unlabeled nodes through systematic experimental analysis, significantly degrading GNNs' performance. To tackle under-reaching for GNNs, we propose an architecture-agnostic method dubbed NodeMixup. The fundamental idea is to (1) increase the reachability of labeled nodes by labeled-unlabeled pairs mixup, (2) leverage graph structures via fusing the neighbor connections of intra-class node pairs to improve performance gains of mixup, and (3) use neighbor label distribution similarity incorporating node degrees to determine sampling weights for node mixup. Extensive experiments demonstrate the efficacy of NodeMixup in assisting GNNs in handling under-reaching. The source code is available at urlhttps://github.com/WeigangLu/NodeMixup.