On the Equivalence of Graph Convolution and Mixup
Xiaotian Han Hanqing Zeng Yu Chen Shaoliang Nie Jingzhou Liu Kanika Narang Zahra Shakeri Karthik Abinav Sankararaman Song Jiang Madian Khabsa Qifan Wang Xia Hu
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
these two approaches. Our investigation reveals that, under two mild
conditions, graph convolution can be viewed as a specialized form of Mixup that
is applied during both the training and testing phases. The two conditions 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 (GCN) and simplified graph convolution (SGC) can be
expressed as a form of Mixup. We also empirically verify the equivalence by
training an MLP using the two conditions to achieve comparable performance.