# Noise-robust Graph Learning by Estimating and Leveraging Pairwise Interactions

arXiv: https://arxiv.org/abs/2106.07451 · HTML: https://mlsanity.com/paper/2106.07451/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 155 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 30 of 67)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [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)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Exploring the Limits of Weakly Supervised Pretraining](https://mlsanity.com/paper/1805.00932/) (2018)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Training Deep Neural Networks on Noisy Labels with Bootstrapping](https://mlsanity.com/paper/1412.6596/) (2014)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)

## Built on by (most cited first, 21 of 21)

- [ARGS: Alignment as Reward-Guided Search](https://mlsanity.com/paper/2402.01694/) (2024)
- [Process Reward Model with Q-Value Rankings](https://mlsanity.com/paper/2410.11287/) (2024)
- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [Graph Anomaly Detection in Time Series: A Survey](https://mlsanity.com/paper/2302.00058/) (2023)
- [NoisyGL: A Comprehensive Benchmark for Graph Neural Networks under Label Noise](https://mlsanity.com/paper/2406.04299/) (2024)
- [ERASE: Error-Resilient Representation Learning on Graphs for Label Noise Tolerance](https://mlsanity.com/paper/2312.08852/) (2023)
- [On the Learnability of Out-of-distribution Detection](https://mlsanity.com/paper/2404.04865/) (2024)
- [Mitigating Label Noise on Graph via Topological Sample Selection](https://mlsanity.com/paper/2403.01942/) (2024)
- [Delving into Instance-Dependent Label Noise in Graph Data: A Comprehensive Study and Benchmark](https://mlsanity.com/paper/2506.12468/) (2025)
- [DeGLIF for Label Noise Robust Node Classification using GNNs](https://mlsanity.com/paper/2506.00244/) (2025)
- [Identifying and Correcting Label Noise for Robust GNNs via Influence Contradiction](https://mlsanity.com/paper/2601.17469/) (2026)
- [Balanced Edge Pruning for Graph Anomaly Detection with Noisy Labels](https://mlsanity.com/paper/2407.05934/) (2024)
- [Energy Guided smoothness to improve Robustness in Graph Classification](https://mlsanity.com/paper/2412.08419/) (2024)
- [Training Robust Graph Neural Networks by Modeling Noise Dependencies](https://mlsanity.com/paper/2502.19670/) (2025)
- [Weak Supervision for Real World Graphs](https://mlsanity.com/paper/2506.02451/) (2025)
- [EDN: A Novel Edge-Dependent Noise Model for Graph Data](https://mlsanity.com/paper/2506.11368/) (2025)
- [When LLM Agents Meet Graph Optimization: An Automated Data Quality Improvement Approach](https://mlsanity.com/paper/2510.08952/) (2025)
- [DREAM: Dual-Standard Semantic Homogeneity with Dynamic Optimization for Graph Learning with Label Noise](https://mlsanity.com/paper/2601.17449/) (2026)
- [OpenRTAG: A Comprehensive Benchmark for Robust Text-Attributed Graph Learning under Data Quality Degradation](https://mlsanity.com/paper/2607.19108/) (2026)
- [Towards Trustworthy Hypergraph Neural Networks under Label Noise](https://mlsanity.com/paper/2608.04377/) (2026)
- [Particle Competition and Cooperation for Robust Graph Convolutional Network Learning Under Label Noise](https://mlsanity.com/paper/2609.22053/) (2026)

## Abstract (arXiv)

Teaching Graph Neural Networks (GNNs) to accurately classify nodes under severely noisy labels is an important problem in real-world graph learning applications, but is currently underexplored. Although pairwise training methods have demonstrated promise in supervised metric learning and unsupervised contrastive learning, they remain less studied on noisy graphs, where the structural pairwise interactions (PI) between nodes are abundant and thus might benefit label noise learning rather than the pointwise methods. This paper bridges the gap by proposing a pairwise framework for noisy node classification on graphs, which relies on the PI as a primary learning proxy in addition to the pointwise learning from the noisy node class labels. Our proposed framework PI-GNN contributes two novel components: (1) a confidence-aware PI estimation model that adaptively estimates the PI labels, which are defined as whether the two nodes share the same node labels, and (2) a decoupled training approach that leverages the estimated PI labels to regularize a node classification model for robust node classification. Extensive experiments on different datasets and GNN architectures demonstrate the effectiveness of PI-GNN, yielding a promising improvement over the state-of-the-art methods. Code is publicly available at https://github.com/TianBian95/pi-gnn.