# Graph Mixup with Soft Alignments

arXiv: https://arxiv.org/abs/2306.06788 · HTML: https://mlsanity.com/paper/2306.06788/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 58 references that are in the map.
- First posted on arXiv 11 Jun 2023.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Graph Contrastive Learning Automated](https://mlsanity.com/paper/2106.07594/) (2021)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2006.06830/) (2020)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [Deep Graph Matching Consensus](https://mlsanity.com/paper/2001.09621/) (2020)
- [Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching](https://mlsanity.com/paper/1911.11308/) (2019)
- [Towards Domain-Agnostic Contrastive Learning](https://mlsanity.com/paper/2011.04419/) (2020)
- [REGAL: Representation Learning-based Graph Alignment](https://mlsanity.com/paper/1802.06257/) (2018)
- [Graph Transplant: Node Saliency-Guided Graph Mixup with Local Structure Preservation](https://mlsanity.com/paper/2111.05639/) (2021)
- [Boundary thickness and robustness in learning models](https://mlsanity.com/paper/2007.05086/) (2020)
- [Model-Agnostic Augmentation for Accurate Graph Classification](https://mlsanity.com/paper/2202.10107/) (2022)

## Built on by (most cited first, 15 of 15)

- [A Comprehensive Survey on Data Augmentation](https://mlsanity.com/paper/2405.09591/) (2024)
- [Pairwise Alignment Improves Graph Domain Adaptation](https://mlsanity.com/paper/2403.01092/) (2024)
- [Improved Generalization of Weight Space Networks via Augmentations](https://mlsanity.com/paper/2402.04081/) (2024)
- [Graph Out-of-Distribution Generalization with Controllable Data Augmentation](https://mlsanity.com/paper/2308.08344/) (2023)
- [Cross-Domain Graph Data Scaling: A Showcase with Diffusion Models](https://mlsanity.com/paper/2406.01899/) (2024)
- [DropEdge not Foolproof: Effective Augmentation Method for Signed Graph Neural Networks](https://mlsanity.com/paper/2409.19620/) (2024)
- [Marginal Nodes Matter: Towards Structure Fairness in Graphs](https://mlsanity.com/paper/2310.14527/) (2023)
- [Data Augmentations in Deep Weight Spaces](https://mlsanity.com/paper/2311.08851/) (2023)
- [Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2401.09953/) (2024)
- [Graph Neural Network Generalization with Gaussian Mixture Model Based Augmentation](https://mlsanity.com/paper/2411.08638/) (2024)
- [AugWard: Augmentation-Aware Representation Learning for Accurate Graph Classification](https://mlsanity.com/paper/2503.21105/) (2025)
- [Gradient Rewiring for Editable Graph Neural Network Training](https://mlsanity.com/paper/2410.15556/) (2024)
- [VS-Graph: Scalable and Efficient Graph Classification Using Hyperdimensional Computing](https://mlsanity.com/paper/2512.03394/) (2025)
- [Tackling Diverse Minorities in Imbalanced Classification](https://mlsanity.com/paper/2308.14838/) (2023)
- [From Moments to Models: Graphon-Mixture Learning for Mixup and Contrastive Learning](https://mlsanity.com/paper/2510.03690/) (2025)

## Abstract (arXiv)

We study graph data augmentation by mixup, which has been used successfully on images. A key operation of mixup is to compute a convex combination of a pair of inputs. This operation is straightforward for grid-like data, such as images, but challenging for graph data. The key difficulty lies in the fact that different graphs typically have different numbers of nodes, and thus there lacks a node-level correspondence between graphs. In this work, we propose S-Mixup, a simple yet effective mixup method for graph classification by soft alignments. Specifically, given a pair of graphs, we explicitly obtain node-level correspondence via computing a soft assignment matrix to match the nodes between two graphs. Based on the soft assignments, we transform the adjacency and node feature matrices of one graph, so that the transformed graph is aligned with the other graph. In this way, any pair of graphs can be mixed directly to generate an augmented graph. We conduct systematic experiments to show that S-Mixup can improve the performance and generalization of graph neural networks (GNNs) on various graph classification tasks. In addition, we show that S-Mixup can increase the robustness of GNNs against noisy labels.