From Moments to Models: Graphon-Mixture Learning for Mixup and Contrastive Learning

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Abstract:Real-world graph datasets often arise from mixtures of populations, where graphs are generated by multiple distinct underlying distributions. In this work, we propose a unified framework that explicitly models graph data as a mixture of probabilistic graph generative models represented by graphons. To characterize and estimate these graphons, we leverage graph moments (motif densities) to cluster graphs generated from the same underlying model. We establish a novel theoretical guarantee, deriving a tighter bound showing that graphs sampled from structurally similar graphons exhibit similar motif densities with high probability. This result enables principled estimation of graphon mixture components. We show how incorporating estimated graphon mixture components enhances two widely used downstream paradigms: graph data augmentation via mixup and graph contrastive learning. By conditioning these methods on the underlying generative models, we develop graphon-mixture-aware mixup (GMAM) and model-aware graph contrastive learning (MGCL). Extensive experiments on both simulated and real-world datasets demonstrate strong empirical performance. In supervised learning, GMAM outperforms existing augmentation strategies, achieving new state-of-the-art accuracy on 6 out of 7 datasets. In unsupervised learning, MGCL performs competitively across seven benchmark datasets and achieves the lowest average rank overall.

Subjects:

Machine Learning (cs.LG); Machine Learning (stat.ML)

Cite as: arXiv:2510.03690 [cs.LG]

(or arXiv:2510.03690v3 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2510.03690

arXiv-issued DOI via DataCite

Submission history

From: Ali Azizpour [view email] [v1] Sat, 4 Oct 2025 06:03:04 UTC (9,627 KB) [v2] Thu, 9 Oct 2025 17:55:28 UTC (9,627 KB) [v3] Tue, 31 Mar 2026 16:42:15 UTC (4,951 KB)