HPoolGCL: Augmentation-Free Cross-Granularity Graph Contrastive Learning With Hierarchical Pooling

Abstract

Graph contrastive learning (GCL) has emerged as a dominant paradigm for self-supervised representation learning for attributed graph data. However, existing GCL methods heavily rely on empirical graph data augmentation, which may distort intrinsic graph semantics and produce poor generalisation without carefully chosen or designed augmentation techniques. Furthermore, most GCL approaches focus on same-granularity contrastive learning (e.g., node vs. node), neglecting the hierarchical and multigranular properties inherent in real-world networks, leading to suboptimal performance. To address these limitations, we propose HPoolGCL, a cross-granularity GCL framework compatible with various hierarchical graph pooling methods to capture multigranularity information. Our framework eliminates the need for handcrafted augmentations, explicit negative sampling and complex multiencoder architectures by applying two novel loss functions in hierarchical graph pooling. The theoretical analysis is provided to explain the effectiveness of unified MGC and HiCR losses from three perspectives, namely, the information maximisation principle, the redundancy reduction principle and the information bottleneck principle. The experimental results demonstrate that HPoolGCL achieves state-of-the-art performance across multiple downstream tasks on five benchmarks. Our codes are available at https://github.com/Heycen/HPoolGCL.

Keywords

data mining / deep learning / machine learning / neural network / unsupervised learning

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grants 62366008 and 61966005).

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data that support the findings of this study are publicly available. All the datasets can be accessed at https://github.com/pyg-team/pytorch_geometric.

References

[1] L. Jing and Y. Tian, “Self-Supervised Visual Feature Learning With Deep Neural Networks: A Survey,” IEEE Transactions on Pattern Analysis and Machine Intelligence 43, no. 11 (November 2021): 4037-4058, https://doi.org/10.1109/tpami.2020.2992393.

[2] K. He, H. Fan, Y. Wu, S. Xie, and R. Girshick, “Momentum Contrast for Unsupervised Visual Representation Learning,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (2020), 9729-9738.

[3] T. Chen, S. Kornblith, M. Norouzi, and G. Hinton, “A Simple Framework for Contrastive Learning of Visual Representations,” in Proceedings of the 37th International Conference on Machine Learning (2020), 1597-1607.

[4] J.-B. Grill, F. Strub, F. Altché, et al., Bootstrap Your Own Latent-a New Approach to Self-Supervised Learning,” Advances in Neural Information Processing Systems 33 (2020): 21271-21284, https://proceedings.neurips.cc/paper_files/paper/2020/file/f3ada80d5c4ee70142b17b8192b2958e-Paper.pdf.

[5] J. Devlin, M.-W. Chang, K. Lee, and K. Toutanova, “Bert: Pre-Training of Deep Bidirectional Transformers for Language Understanding,” in Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (2019), 4171-4186.

[6] Z. Yang, Z. Dai, Y. Yang, J. Carbonell, R. R. Salakhutdinov, and Q. V. Le, “Xlnet: Generalized Autoregressive Pretraining for Language Understanding,” in Advances in Neural Information Processing Systems, Vol. 32 (2019).

[7] J. Gui, T. Chen, J. Zhang, et al. , “A Survey on Self-Supervised Learning: Algorithms, Applications, and Future Trends,” IEEE Transactions on Pattern Analysis and Machine Intelligence 46, no. 12 (December 2024): 9052-9071, https://doi.org/10.1109/tpami.2024.3415112.

[8] Y. Li, P. Hu, Z. Liu, D. Peng, J. T. Zhou, and X. Peng, “Contrastive Clustering,” Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 10 (2021): 8547-8555, https://doi.org/10.1609/aaai.v35i10.17037.

[9] Y. Li, M. Yang, D. Peng, T. Li, J. Huang, and X. Peng, “Twin Contrastive Learning for Online Clustering,” International Journal of Computer Vision 130, no. 9 (2022): 2205-2221, https://doi.org/10.1007/s11263-022-01639-z.

[10] Y. Zhu, Y. Xu, F. Yu, Q. Liu, S. Wu, and L. Wang, “Deep Graph Contrastive Representation Learning,” Preprint arXiv:2006.04131, (2020).

[11] C. Mavromatis and G. Karypis, “Graph Infoclust: Maximizing Coarse-Grain Mutual Information in Graphs,” in Advances in Knowledge Discovery and Data Mining: 25Th Pacific-Asia Conference, PAKDD 2021, Virtual Event, May 11-14, 2021, Proceedings, Part, Vol. I (2021), 541-553, https://doi.org/10.1007/978-3-030-75762-5_43.

[12] Y. Zhu, Y. Xu, F. Yu, Q. Liu, S. Wu, and L. Wang, “Graph Contrastive Learning With Adaptive Augmentation,” in Proceedings of the Web Conference 2021 (2021), 2069-2080.

[13] J. Xia, L. Wu, J. Chen, B. Hu, and S. Z. Li, “Simgrace: A Simple Framework for Graph Contrastive Learning Without Data Augmentation,” in Proceedings of the ACM Web Conference 2022 (2022), 1070-1079.

[14] P. Veličković, W. Fedus, W. L. Hamilton, P. Liò, Y. Bengio, and R. D. Hjelm, “Deep Graph Infomax,” in International Conference on Learning Representations (2018).

[15] K. Hassani and A. H. Khasahmadi, “Contrastive multi-view Representation Learning on Graphs,” in Proceedings of the 37th International Conference on Machine Learning (2020), 4116-4126.

[16] Y. Zhang, Y. Chen, Z. Song, and I. King, “Contrastive Cross-Scale Graph Knowledge Synergy,” in Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (2023), 3422-3433.

[17] Y. You, T. Chen, Y. Sui, T. Chen, Z. Wang, and Y. Shen, “Graph Contrastive Learning With Augmentations,” in Advances in Neural Information Processing Systems, Vol. 33 (2020), 5812-5823.

[18] T. Zhao, W. Jin, Y. Liu, et al., Graph Data Augmentation for Graph Machine Learning: A Survey,” Preprint arXiv:2202.08871 (2022).

[19] N. Lee, J. Lee, and C. Park, “Augmentation-Free Self-Supervised Learning on Graphs,” in Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 36, no. 7 (2022), 7372-7380, https://doi.org/10.1609/aaai.v36i7.20700.

[20] H. Li, J. Cao, J. Zhu, Q. Luo, S. He, and X. Wang, “Augmentation-Free Graph Contrastive Learning of Invariant-Discriminative Representations,” IEEE Transactions on Neural Networks and Learning Systems 35, no. 8 (August 2024): 11157-11167, https://doi.org/10.1109/tnnls.2023.3248871.

[21] H. Zhao, X. Yang, K. Wei, C. Deng, and D. Tao, “Unsupervised Graph Transformer With Augmentation-Free Contrastive Learning,” IEEE Transactions on Knowledge and Data Engineering 36, no. 11 (November 2024): 7296-7307, https://doi.org/10.1109/tkde.2024.3386984.

[22] Z.-F. Zhou, D. Huang, and C.-D. Wang, “Pyramid Contrastive Learning for Clustering,” Neural Networks 185 (2025): 107217, https://doi.org/10.1016/j.neunet.2025.107217.

[23] D. Huang, X. Deng, D.-H. Chen, et al., Deep Clustering With Hybrid-Grained Contrastive and Discriminative Learning,” IEEE Transactions on Circuits and Systems for Video Technology 34, no. 10 (2024): 9472-9483, https://doi.org/10.1109/tcsvt.2024.3399596.

[24] S. Thakoor, C. Tallec, M. G. Azar, R. Munos, P. Veličković, and M. Valko, “Bootstrapped Representation Learning on Graphs,” in ICLR 2021 Workshop on Geometrical and Topological Representation Learning (2021).

[25] W. Sun, J. Li, L. Chen, B. Wu, Y. Bian, and Z. Zheng, “Rethinking and Simplifying Bootstrapped Graph Latents,” in Proceedings of the 17th ACM International Conference on Web Search and Data Mining (2024), 665-673.

[26] H. Zhang, Q. Wu, J. Yan, D. Wipf, and P. S. Yu, “From Canonical Correlation Analysis to Self-Supervised Graph Neural Networks,” Advances in Neural Information Processing Systems 34 (2021): 76-89, https://proceedings.neurips.cc/paper/2021/file/00ac8ed3b4327bdd4ebbebcb2ba10a00-Paper.pdf.

[27] B. Han, Y. Wei, Q. Wang, and S. Wan, “Colm2s: Contrastive Self-Supervised Learning on Attributed Multiplex Graph Network With Multi-Scale Information,” CAAI Transactions on Intelligence Technology 8, no. 4 (2023): 1464-1479, https://doi.org/10.1049/cit2.12168.

[28] J. Wang, W. Li, C. Hou, et al., Hcl: Improving Graph Representation With Hierarchical Contrastive Learning,” in International Semantic Web Conference (Springer, 2022), 108-124.

[29] R. Yang, Y. Yang, F. Zhou, and Q. Sun, “Directional Diffusion Models for Graph Representation Learning,” Advances in Neural Information Processing Systems 36 (2023): 32720-32731, https://proceedings.neurips.cc/paper_files/paper/2023/file/6751ee6546b31ceb7d4ee12276b9f4d9-Paper-Conference.pdf.

[30] J. Zhu, L. He, C. Gao, et al., SDMG: Smoothing Your Diffusion Models for Powerful Graph Representation Learning,” in Forty-Second International Conference on Machine Learning (2025): [Online], https://openreview.net/forum?id=lNyaQIJ5Z7.

[31] Y. You, T. Chen, Y. Shen, and Z. Wang, “Graph Contrastive Learning Automated,” in Proceedings of the 38th International Conference on Machine Learning (2021), 12121-12132.

[32] X. Cai, C. Huang, L. Xia, and X. Ren, “Lightgcl: Simple Yet Effective Graph Contrastive Learning for Recommendation,” in The Eleventh International Conference on Learning Representations (2022).

[33] C. Xu, T. Wang, M. Chen, J. Chen, and Z. Pan, “Class-Aware Graph Siamese Representation Learning,” Neurocomputing 620 (2025): 129209, https://doi.org/10.1016/j.neucom.2024.129209.

[34] O. Vinyals, S. Bengio, and M. Kudlur, “Order Matters: Sequence to Sequence for Sets,” in 4th International Conference on Learning Representations, ICLR 2016, San Juan, Puerto Rico, May 2-4, 2016, Conference Track Proceedings, ed., Y. Bengio and Y. LeCun (2016) [Online], http://arxiv.org/abs/1511.06391.

[35] M. Zhang, Z. Cui, M. Neumann, and Y. Chen, “An end-to-end Deep Learning Architecture for Graph Classification,” in Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 32, no. 1 (2018), https://doi.org/10.1609/aaai.v32i1.11782.

[36] Z. Ying, J. You, C. Morris, X. Ren, W. Hamilton, and J. Leskovec, “Hierarchical Graph Representation Learning With Differentiable Pooling,” Advances in Neural Information Processing Systems 31 (2018), https://proceedings.neurips.cc/paper_files/paper/2018/file/e77dbaf6759253c7c6d0efc5690369c7-Paper.pdf.

[37] F. M. Bianchi, D. Grattarola, and C. Alippi, “Spectral Clustering With Graph Neural Networks for Graph Pooling,” in International Conference on Machine Learning (PMLR, 2020), 874-883.

[38] A. H. Khasahmadi, K. Hassani, P. Moradi, L. Lee, and Q. Morris, “Memory-Based Graph Networks,” in International Conference on Learning Representations, https://openreview.net/pdf?id=r1laNeBYPB.

[39] H. Gao and S. Ji, “Graph u-Nets,” in International Conference on Machine Learning (PMLR, 2019), 2083-2092.

[40] J. Lee, I. Lee, and J. Kang, “Self-Attention Graph Pooling,” in International Conference on Machine Learning (pmlr, 2019), 3734-3743.

[41] Z. Zhang, J. Bu, M. Ester, et al., Hierarchical Graph Pooling With Structure Learning,” Preprint arXiv:1911.05954 (2019).

[42] Z. Zhang, J. Bu, M. Ester, et al., Hierarchical Multi-View Graph Pooling With Structure Learning,” IEEE Transactions on Knowledge and Data Engineering 35, no. 1 (2021): 545-559, https://doi.org/10.1109/TKDE.2021.3090664.

[43] Z. Zhong, C.-T. Li, and J. Pang, “Multi-Grained Semantics-Aware Graph Neural Networks,” IEEE Transactions on Knowledge and Data Engineering 35, no. 7 (2022): 7251-7262, https://doi.org/10.1109/tkde.2022.3195004.

[44] M. Li, S. Chen, Y. Zhang, and I. Tsang, “Graph Cross Networks With Vertex Infomax Pooling,” Advances in Neural Information Processing Systems 33 (2020): 14093-14105, https://proceedings.neurips.cc/paper_files/paper/2020/file/a26398dca6f47b49876cbaffbc9954f9-Paper.pdf.

[45] Y. Pang, Y. Zhao, and D. Li, “Graph Pooling via Coarsened Graph Infomax,” in Proceedings of the 44th International ACM SIGIR Conference on Research and Development in Information Retrieval (2021), 2177-2181.

[46] X. Chen and K. He, “Exploring Simple Siamese Representation Learning,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (2021), 15750-15758.

[47] T. N. Kipf and M. Welling, “Semi-Supervised Classification With Graph Convolutional Networks,” in 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings (OpenReview.net, 2017): [Online], https://openreview.net/forum?id=SJU4ayYgl.

[48] W. Hamilton, Z. Ying, and J. Leskovec, “Inductive Representation Learning on Large Graphs,” Advances in Neural Information Processing Systems 30 (2017), https://proceedings.neurips.cc/paper/2017/file/5dd9db5e033da9c6fb5ba83c7a7ebea9-Paper.pdf.

[49] P. Velickovic, G. Cucurull, A. Casanova, A. Romero, P. Liò, and Y. Bengio, “Graph Attention Networks,” in 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30-May 3, 2018, Conference Track Proceedings (OpenReview.net, 2018): [Online], https://openreview.net/forum?id=rJXMpikCZ.

[50] A. V. D. Oord, Y. Li, and O. Vinyals, “Representation Learning With Contrastive Predictive Coding,” Preprint arXiv:1807.03748 (2018).

[51] Z. Su, Z. Hu, and Y. Li, “Hierarchical Graph Representation Learning With Local Capsule Pooling,” in Proceedings of the 3rd ACM International Conference on Multimedia in Asia (2021), 1-7, https://doi.org/10.1145/3469877.3495645.

[52] J. Zbontar, L. Jing, I. Misra, Y. LeCun, and S. Deny, “Barlow Twins: Self-Supervised Learning via Redundancy Reduction,” in Proceedings of the 38th International Conference on Machine Learning (2021), https://proceedings.mlr.press/v139/zbontar21a/zbontar21a.pdf.

[53] H. B. Barlow, “Possible Principles Underlying the Transformation of Sensory Messages,” Sensory communication 1, no. 1 (1961): 217-233, https://doi.org/10.7551/mitpress/9780262518420.003.0013.

[54] N. Tishby, F. C. Pereira, and W. Bialek, “The Information Bottleneck Method,” preprint, arXiv:physics/0004057, April 24, 2000, https://doi.org/10.48550/arXiv.physics/0004057.

[55] J. Zhu, C. Gao, Z. Yin, X. Li, and J. Kurths, “Propagation Structure-Aware Graph Transformer for Robust and Interpretable Fake News Detection,” in Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (2024), 4652-4663.

[56] P. Mernyei and C. Cangea, “Wiki-Cs: A Wikipedia-Based Benchmark for Graph Neural Networks,” Preprint arXiv:2007.02901 (2020).

[57] J. McAuley, C. Targett, Q. Shi, and A. Van Den Hengel, “Image-Based Recommendations on Styles and Substitutes,” in Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval (2015), 43-52.

[58] A. Sinha, Z. Shen, Y. Song, et al., An Overview of Microsoft Academic Service (Mas) and Applications,” in Proceedings of the 24th International Conference on World Wide Web (2015), 243-246.

[59] O. Shchur, M. Mumme, A. Bojchevski, and S. Günnemann, “Pitfalls of Graph Neural Network Evaluation,” Preprint arXiv:1811.05868 (2018).

[60] B. Perozzi, R. Al-Rfou, and S. Skiena, “Deepwalk: Online Learning of Social Representations,” in Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2014), 701-710.

[61] A. Grover and J. Leskovec, “node2vec: Scalable Feature Learning for Networks,” in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2016), 855-864.

[62] Y. Liu, T. He, T. Zheng, and J. Zhao, “Negative-Free Self-Supervised Gaussian Embedding of Graphs,” Neural Networks 181 (2025): 106846, https://doi.org/10.1016/j.neunet.2024.106846.

[63] J. Miao, F. Cao, M. Li, B. Yang, and H. Ye, “Triplet Teaching Graph Contrastive Networks With Self-Evolving Adaptive Augmentation,” Pattern Recognition 142 (2023): 109687, https://doi.org/10.1016/j.patcog.2023.109687.

[64] W. Bu, X. Cao, Y. Zheng, and S. Pan, “Improving Augmentation Consistency for Graph Contrastive Learning,” Pattern Recognition 148 (2024): 110182, https://doi.org/10.1016/j.patcog.2023.110182.

[65] Z. Wu, Y. Xiong, S. X. Yu, and D. Lin, “Unsupervised Feature Learning via Non-Parametric Instance Discrimination,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2018), 3733-3742.