{
  "id": "2310.00183",
  "version": "v1",
  "published": "2023-09-29T23:09:54.000Z",
  "updated": "2023-09-29T23:09:54.000Z",
  "title": "On the Equivalence of Graph Convolution and Mixup",
  "authors": [
    "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"
  ],
  "categories": [
    "cs.LG",
    "cs.AI"
  ],
  "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 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-29T23:09:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equivalence",
      "multiple samples",
      "data augmentation technique",
      "graph neural network",
      "conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}