Graph Contrastive Learning with Low-Rank Regularization and Low-Rank Attention for Noisy Node Classification

Yancheng Wang, Ping Li, Yingzhen Yang
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:7200-7228, 2026.

Abstract

Graph Neural Networks (GNNs) have shown strong performance in learning node representations and node classification, but their effectiveness can be substantially degraded by noise in real-world graph data. To address this challenge, we introduce a robust and innovative node representation learning method named Graph Contrastive Learning with Low-Rank Regularization, or GCL-LRR, which follows a two-stage transductive learning framework for node classification. In the first stage, the GCL-LRR encoder is trained via prototypical contrastive learning with a low-rank regularization objective, and in the second stage, the learned representations are used by a linear transductive classifier to predict labels for unlabeled nodes. Our GCL-LRR is inspired by the Low Frequency Property (LFP) of the graph data and its labels, and it is also theoretically motivated by our sharp generalization bound for transductive learning. Our theoretical result is among the first to theoretically demonstrate the advantage of low-rank regularization in transductive learning, which is also supported by strong empirical results. To further enhance the performance of GCL-LRR, we present an improved model named GCL-LR-Attention, which incorporates a novel LR-Attention layer into GCL-LRR. GCL-LR-Attention reduces the kernel complexity of GCL-LRR and contributes to a tighter generalization bound, leading to improved performance. Extensive evaluations on standard benchmark datasets evidence the effectiveness and robustness of both GCL-LRR and GCL-LR-Attention. The code of GCL-LRR and GCL-LR-Attention is available at https://github.com/Statistical-Deep-Learning/GCL-LR-Attention.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-wang26h, title = {Graph Contrastive Learning with Low-Rank Regularization and Low-Rank Attention for Noisy Node Classification}, author = {Wang, Yancheng and Li, Ping and Yang, Yingzhen}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {7200--7228}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/wang26h/wang26h.pdf}, url = {https://proceedings.mlr.press/v337/wang26h.html}, abstract = {Graph Neural Networks (GNNs) have shown strong performance in learning node representations and node classification, but their effectiveness can be substantially degraded by noise in real-world graph data. To address this challenge, we introduce a robust and innovative node representation learning method named Graph Contrastive Learning with Low-Rank Regularization, or GCL-LRR, which follows a two-stage transductive learning framework for node classification. In the first stage, the GCL-LRR encoder is trained via prototypical contrastive learning with a low-rank regularization objective, and in the second stage, the learned representations are used by a linear transductive classifier to predict labels for unlabeled nodes. Our GCL-LRR is inspired by the Low Frequency Property (LFP) of the graph data and its labels, and it is also theoretically motivated by our sharp generalization bound for transductive learning. Our theoretical result is among the first to theoretically demonstrate the advantage of low-rank regularization in transductive learning, which is also supported by strong empirical results. To further enhance the performance of GCL-LRR, we present an improved model named GCL-LR-Attention, which incorporates a novel LR-Attention layer into GCL-LRR. GCL-LR-Attention reduces the kernel complexity of GCL-LRR and contributes to a tighter generalization bound, leading to improved performance. Extensive evaluations on standard benchmark datasets evidence the effectiveness and robustness of both GCL-LRR and GCL-LR-Attention. The code of GCL-LRR and GCL-LR-Attention is available at https://github.com/Statistical-Deep-Learning/GCL-LR-Attention.} }
Endnote
%0 Conference Paper %T Graph Contrastive Learning with Low-Rank Regularization and Low-Rank Attention for Noisy Node Classification %A Yancheng Wang %A Ping Li %A Yingzhen Yang %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-wang26h %I PMLR %P 7200--7228 %U https://proceedings.mlr.press/v337/wang26h.html %V 337 %X Graph Neural Networks (GNNs) have shown strong performance in learning node representations and node classification, but their effectiveness can be substantially degraded by noise in real-world graph data. To address this challenge, we introduce a robust and innovative node representation learning method named Graph Contrastive Learning with Low-Rank Regularization, or GCL-LRR, which follows a two-stage transductive learning framework for node classification. In the first stage, the GCL-LRR encoder is trained via prototypical contrastive learning with a low-rank regularization objective, and in the second stage, the learned representations are used by a linear transductive classifier to predict labels for unlabeled nodes. Our GCL-LRR is inspired by the Low Frequency Property (LFP) of the graph data and its labels, and it is also theoretically motivated by our sharp generalization bound for transductive learning. Our theoretical result is among the first to theoretically demonstrate the advantage of low-rank regularization in transductive learning, which is also supported by strong empirical results. To further enhance the performance of GCL-LRR, we present an improved model named GCL-LR-Attention, which incorporates a novel LR-Attention layer into GCL-LRR. GCL-LR-Attention reduces the kernel complexity of GCL-LRR and contributes to a tighter generalization bound, leading to improved performance. Extensive evaluations on standard benchmark datasets evidence the effectiveness and robustness of both GCL-LRR and GCL-LR-Attention. The code of GCL-LRR and GCL-LR-Attention is available at https://github.com/Statistical-Deep-Learning/GCL-LR-Attention.
APA
Wang, Y., Li, P. & Yang, Y.. (2026). Graph Contrastive Learning with Low-Rank Regularization and Low-Rank Attention for Noisy Node Classification. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:7200-7228 Available from https://proceedings.mlr.press/v337/wang26h.html.

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