Optimal Transport Augmentation Preserves Node Degree Information in Graph Contrastive Learning

A research study published in Knowledge and Information Systems describes a novel framework, named OTGCL, designed to mitigate degree distortion in graph contrastive learning. In graph contrastive learning, models learn representations from augmented graph views, but standard perturbations applied to graph topology can alter critical degree information at the individual node level. Authors Tao Xie, Cheng Liu, Zhuopeng Xu, Jun Tan, Jinglin Li, and Ning Gui characterized this topological distortion through marginal structural distributions, which correspond to the normalized row and column sums of a weighted adjacency matrix.

To protect node-level degree structure during the graph augmentation process, OTGCL introduces Diverse Optimal Transport Augmentation, or DOTA. This component constructs alternative topological views by formulating local optimal transport problems under explicit constraints designed to preserve each node’s incoming and outgoing weighted degrees. To ensure that the augmented views remain diverse while simultaneously restricting the computational dimensions of the optimal transport problem, the framework applies random subgraph sampling.

Alongside DOTA, the OTGCL system incorporates Marginal Structure-based Sampling, or MSS, to refine how models select contrastive training examples. Instead of choosing negative samples indiscriminately, MSS utilizes node degree information to select within-view negative pairs. By integrating degree-informed sampling with structure-preserving optimal transport, the combined framework aims to maintain fidelity to the underlying network architecture throughout the contrastive learning pipeline.

The investigators evaluated OTGCL across eight benchmark graph datasets to assess its predictive capabilities on common network analysis tasks. Empirical testing revealed clear gains in degree prediction, alongside competitive performance in both node classification and link prediction. The experimental results further demonstrated that incorporating DOTA provided consistent, measurable benefits across all of the tested graph contrastive learning backbone architectures.

Detailed structural measurements verified that weighted-marginal preservation was achieved to numerical precision, while also quantifying changes occurring in binary degrees and higher-order network properties. Accompanying cost and sampling studies revealed that computational responses depend on the characteristics of the specific graph and the target task. Additionally, the authors established that local optimal transport successfully supports representation learning on larger graphs. Together with these computational measurements, the studies characterize both the predictive performance and computational costs associated with weighted-marginal-preserving graph augmentation.

Subject of Research: Graph contrastive learning and optimal transport augmentation

Article Title: Structural invariant augmentation for graph contrastive learning based on optimal transport

Article References: Xie, T., Liu, C., Xu, Z., Tan, J., Li, J., & Gui, N. (2026). Structural invariant augmentation for graph contrastive learning based on optimal transport. Knowledge and Information Systems, 68(1), Article 308. https://doi.org/10.1007/s10115-026-02915-x

Image Credits: AI Generated

DOI: 10.1007/s10115-026-02915-x

Keywords: graph contrastive learning, optimal transport, data augmentation, marginal structural distributions, node classification, link prediction, degree prediction, graph representation learning, Structural, invariant, augmentation, graph