# Learning to Drop: Robust Graph Neural Network via Topological Denoising

arXiv: https://arxiv.org/abs/2011.07057 · HTML: https://mlsanity.com/paper/2011.07057/

## Key facts

- Cited by 127 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2020.

## Built on by (most cited first, 30 of 127)

- [NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification](https://mlsanity.com/paper/2306.08385/) (2023)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [A Comprehensive Survey on Trustworthy Graph Neural Networks: Privacy, Robustness, Fairness, and Explainability](https://mlsanity.com/paper/2204.08570/) (2022)
- [Mining Latent Structures for Multimedia Recommendation](https://mlsanity.com/paper/2104.09036/) (2021)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [A Survey on Graph Structure Learning: Progress and Opportunities](https://mlsanity.com/paper/2103.03036/) (2021)
- [Learning from Counterfactual Links for Link Prediction](https://mlsanity.com/paper/2106.02172/) (2021)
- [Graph Data Augmentation for Graph Machine Learning: A Survey](https://mlsanity.com/paper/2202.08871/) (2022)
- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [GSLB: The Graph Structure Learning Benchmark](https://mlsanity.com/paper/2310.05174/) (2023)
- [Does Graph Distillation See Like Vision Dataset Counterpart?](https://mlsanity.com/paper/2310.09192/) (2023)
- [A Comprehensive Survey on Data Augmentation](https://mlsanity.com/paper/2405.09591/) (2024)
- [Are Defenses for Graph Neural Networks Robust?](https://mlsanity.com/paper/2301.13694/) (2023)
- [Contrastive Meta Learning with Behavior Multiplicity for Recommendation](https://mlsanity.com/paper/2202.08523/) (2022)
- [SE-GSL: A General and Effective Graph Structure Learning Framework through Structural Entropy Optimization](https://mlsanity.com/paper/2303.09778/) (2023)
- [Reliable Representations Make A Stronger Defender: Unsupervised Structure Refinement for Robust GNN](https://mlsanity.com/paper/2207.00012/) (2022)
- [Graph Machine Learning in the Era of Large Language Models (LLMs)](https://mlsanity.com/paper/2404.14928/) (2024)
- [T2-GNN: Graph Neural Networks for Graphs with Incomplete Features and Structure via Teacher-Student Distillation](https://mlsanity.com/paper/2212.12738/) (2022)
- [OpenGSL: A Comprehensive Benchmark for Graph Structure Learning](https://mlsanity.com/paper/2306.10280/) (2023)
- [DropMessage: Unifying Random Dropping for Graph Neural Networks](https://mlsanity.com/paper/2204.10037/) (2022)
- [Modeling Multivariate Biosignals With Graph Neural Networks and Structured State Space Models](https://mlsanity.com/paper/2211.11176/) (2022)
- [Disentangled Contrastive Collaborative Filtering](https://mlsanity.com/paper/2305.02759/) (2023)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Noise-robust Graph Learning by Estimating and Leveraging Pairwise Interactions](https://mlsanity.com/paper/2106.07451/) (2021)
- [Graph Sanitation with Application to Node Classification](https://mlsanity.com/paper/2105.09384/) (2021)
- [Training Robust Graph Neural Networks with Topology Adaptive Edge Dropping](https://mlsanity.com/paper/2106.02892/) (2021)
- [A Survey of Trustworthy Graph Learning: Reliability, Explainability, and Privacy Protection](https://mlsanity.com/paper/2205.10014/) (2022)
- [Concept-Aware Denoising Graph Neural Network for Micro-Video Recommendation](https://mlsanity.com/paper/2109.13527/) (2021)
- [Latent Structure Mining with Contrastive Modality Fusion for Multimedia Recommendation](https://mlsanity.com/paper/2111.00678/) (2021)
- [Structure-Preserving Graph Representation Learning](https://mlsanity.com/paper/2209.00793/) (2022)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have shown to be powerful tools for graph analytics. The key idea is to recursively propagate and aggregate information along edges of the given graph. Despite their success, however, the existing GNNs are usually sensitive to the quality of the input graph. Real-world graphs are often noisy and contain task-irrelevant edges, which may lead to suboptimal generalization performance in the learned GNN models. In this paper, we propose PTDNet, a parameterized topological denoising network, to improve the robustness and generalization performance of GNNs by learning to drop task-irrelevant edges. PTDNet prunes task-irrelevant edges by penalizing the number of edges in the sparsified graph with parameterized networks. To take into consideration of the topology of the entire graph, the nuclear norm regularization is applied to impose the low-rank constraint on the resulting sparsified graph for better generalization. PTDNet can be used as a key component in GNN models to improve their performances on various tasks, such as node classification and link prediction. Experimental studies on both synthetic and benchmark datasets show that PTDNet can improve the performance of GNNs significantly and the performance gain becomes larger for more noisy datasets.