# Transfer Learning on Edge Connecting Probability Estimation under Graphon Model

arXiv: https://arxiv.org/abs/2510.05527 · HTML: https://mlsanity.com/paper/2510.05527/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 67 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Builds on (most cited first, 30 of 32)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [Graph Optimal Transport for Cross-Domain Alignment](https://mlsanity.com/paper/2006.14744/) (2020)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Sliced Gromov-Wasserstein](https://mlsanity.com/paper/1905.10124/) (2019)
- [Graph Few-shot Learning via Knowledge Transfer](https://mlsanity.com/paper/1910.03053/) (2019)
- [Does Graph Distillation See Like Vision Dataset Counterpart?](https://mlsanity.com/paper/2310.09192/) (2023)
- [Stochastic blockmodel approximation of a graphon: Theory and consistent estimation](https://mlsanity.com/paper/1311.1731/) (2013)
- [OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphs](https://mlsanity.com/paper/2205.15117/) (2022)
- [A Consistent Histogram Estimator for Exchangeable Graph Models](https://mlsanity.com/paper/1402.1888/) (2014)
- [Learning Graphons via Structured Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2012.05644/) (2020)
- [Estimating network edge probabilities by neighborhood smoothing](https://mlsanity.com/paper/1509.08588/) (2015)
- [Rates of Convergence of Spectral Methods for Graphon Estimation](https://mlsanity.com/paper/1709.03183/) (2017)
- [GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomics](https://mlsanity.com/paper/2310.09254/) (2023)
- [Network cross-validation by edge sampling](https://mlsanity.com/paper/1612.04717/) (2016)
- [Gromov-Wasserstein Factorization Models for Graph Clustering](https://mlsanity.com/paper/1911.08530/) (2019)
- [Bayesian Models of Graphs, Arrays and Other Exchangeable Random Structures](https://mlsanity.com/paper/1312.7857/) (2013)
- [Implicit Graphon Neural Representation](https://mlsanity.com/paper/2211.03329/) (2022)
- [Supervised Community Detection with Line Graph Neural Networks](https://mlsanity.com/paper/1705.08415/) (2017)
- [Robust and computationally feasible community detection in the presence of arbitrary outlier nodes](https://mlsanity.com/paper/1404.6000/) (2014)
- [Wasserstein-based Graph Alignment](https://mlsanity.com/paper/2003.06048/) (2020)
- [On a linear fused Gromov-Wasserstein distance for graph structured data](https://mlsanity.com/paper/2203.04711/) (2022)
- [Scalable Implicit Graphon Learning](https://mlsanity.com/paper/2410.17464/) (2024)
- [Outlier-Robust Gromov-Wasserstein for Graph Data](https://mlsanity.com/paper/2302.04610/) (2023)
- [The Gromov-Wasserstein distance between spheres](https://mlsanity.com/paper/2306.10586/) (2023)
- [Graphon Estimation from Partially Observed Network Data](https://mlsanity.com/paper/1906.00494/) (2019)

## Built on by (most cited first, 1 of 1)

- [SPR: Toward a Graph Foundation Model for Transferable Graph Cognition via Spectral Patterns and Relational Geometry](https://mlsanity.com/paper/2606.03315/) (2026)

## Abstract (arXiv)

Graphon models provide a flexible nonparametric framework for estimating latent connectivity probabilities in networks, enabling a range of downstream applications such as link prediction and data augmentation. However, accurate graphon estimation typically requires a large graph, whereas in practice, one often only observes a small-sized network. One approach to addressing this issue is to adopt a transfer learning framework, which aims to improve estimation in a small target graph by leveraging structural information from a larger, related source graph. In this paper, we propose a novel method, namely GTRANS, a transfer learning framework that integrates neighborhood smoothing and Gromov-Wasserstein optimal transport to align and transfer structural patterns between graphs. To prevent negative transfer, GTRANS includes an adaptive debiasing mechanism that identifies and corrects for target-specific deviations via residual smoothing. We provide theoretical guarantees on the stability of the estimated alignment matrix and demonstrate the effectiveness of GTRANS in improving the accuracy of target graph estimation through extensive synthetic and real data experiments. These improvements translate directly to enhanced performance in downstream applications, such as the graph classification task and the link prediction task.