On the Equivalence of Graph Convolution and Mixup
Abstract: This paper investigates the relationship between graph convolution and Mixup techniques. Graph convolution in a graph neural network involves aggregating features from neighboring samples to learn representative features for a specific node or sample. On the other hand, Mixup is a data augmentation technique that generates new examples by averaging features and one-hot labels from multiple samples. One commonality between these techniques is their utilization of information from multiple samples to derive feature representation. This study aims to explore whether a connection exists between the two. Our investigation reveals that, under two mild modifications, graph convolution can be viewed as a specialized form of Mixup that is applied during both the training and testing phases. The two modifications are 1) \textit{Homophily Relabel} - assigning the target node's label to all its neighbors, and 2) \textit{Test-Time Mixup} - Mixup the feature during the test time. We establish this equivalence mathematically by demonstrating that graph convolution networks and simplified graph convolution can be expressed as a form of Mixup. We also empirically verify the equivalence by training an MLP using the two modifications to achieve comparable performance.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: We extend our gratitude to the reviewers and Action Editor for their insightful feedback and suggestions. In the camera-ready version, we have integrated all revisions discussed during the rebuttal phase and expanded our analysis of Mixup's linearity. These additions offer a more comprehensive view of our research.
Once again, we value your thorough review of our paper and appreciate your time and expertise devoted to improving our work
Assigned Action Editor: ~Alessandro_Sperduti1
Submission Number: 2708
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