{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-equivalence-of-graph-convolution-and","title":"On the Equivalence of Graph Convolution and Mixup","arxiv_id":"2310.00183","date":"2023-09-29","proceeding":null,"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"],"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.","url_abs":"https://arxiv.org/abs/2310.00183v2","url_pdf":"https://arxiv.org/pdf/2310.00183v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"on-the-equivalence-of-graph-convolution-and","repo_url":"https://github.com/ahxt/graphconv_is_mixup","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"data-augmentation","task_name":"Data Augmentation"},{"task_slug":"graph-neural-network","task_name":"Graph Neural Network"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"graph-neural-network","method_name":"Graph Neural Network"},{"method_slug":"mixup","method_name":"Mixup"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}