On the Equivalence of Graph Convolution and Mixup

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) Homophily Relabel - assigning the target node's label to all its neighbors, and 2) 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.