{"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/scale-invariance-of-graph-neural-networks","title":"Scale Invariance of Graph Neural Networks","arxiv_id":"2411.19392","date":"2024-11-28","proceeding":null,"authors":["Qin Jiang","Chengjia Wang","Michael Lones","Wei Pang"],"abstract":"We address two fundamental challenges in Graph Neural Networks (GNNs): (1) the lack of theoretical support for invariance learning, a critical property in image processing, and (2) the absence of a unified model capable of excelling on both homophilic and heterophilic graph datasets. To tackle these issues, we establish and prove scale invariance in graphs, extending this key property to graph learning, and validate it through experiments on real-world datasets. Leveraging directed multi-scaled graphs and an adaptive self-loop strategy, we propose ScaleNet, a unified network architecture that achieves state-of-the-art performance across four homophilic and two heterophilic benchmark datasets. Furthermore, we show that through graph transformation based on scale invariance, uniform weights can replace computationally expensive edge weights in digraph inception networks while maintaining or improving performance. For another popular GNN approach to digraphs, we demonstrate the equivalence between Hermitian Laplacian methods and GraphSAGE with incidence normalization. ScaleNet bridges the gap between homophilic and heterophilic graph learning, offering both theoretical insights into scale invariance and practical advancements in unified graph learning. Our implementation is publicly available at https://github.com/Qin87/ScaleNet/tree/Aug23.","url_abs":"https://arxiv.org/abs/2411.19392v2","url_pdf":"https://arxiv.org/pdf/2411.19392v2.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":"scale-invariance-of-graph-neural-networks","repo_url":"https://github.com/qin87/scalenet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"graph-learning","task_name":"Graph Learning"},{"task_slug":"node-classification","task_name":"Node Classification"},{"task_slug":"node-classification-on-non-homophilic","task_name":"Node Classification on Non-Homophilic (Heterophilic) Graphs"}],"methods":[{"method_slug":"1x1-convolution","method_name":"1x1 Convolution"},{"method_slug":"average-pooling","method_name":"Average Pooling"},{"method_slug":"batch-normalization","method_name":"Batch Normalization"},{"method_slug":"bottleneck-residual-block","method_name":"Bottleneck Residual Block"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"global-average-pooling","method_name":"Global Average Pooling"},{"method_slug":"graphsage","method_name":"GraphSAGE"},{"method_slug":"max-pooling","method_name":"Max Pooling"},{"method_slug":"relu","method_name":"ReLU"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"scale-aggregation-block","method_name":"Scale Aggregation Block"},{"method_slug":"scalenet","method_name":"ScaleNet"},{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/node-classification-on-citeseer-fixed-20-node","task":"Node Classification","dataset":"Citeseer: fixed 20 node per class","model":"ScaleNet","rank_in_archive_order":2,"of":2,"metrics":{"Accuracy":"68.3±1.5"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-cora-fixed-20-node-per","task":"Node Classification","dataset":"Cora: fixed 20 node per class","model":"ScaleNet","rank_in_archive_order":7,"of":9,"metrics":{"Accuracy":"82.3±1.1"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-telegram-directed-1","task":"Node Classification","dataset":"Telegram (Directed Graph label rate 60%)","model":"ScaleNet","rank_in_archive_order":1,"of":2,"metrics":{"Accuracy":"96.8±2.1"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-telegram-directed-1","task":"Node Classification","dataset":"Telegram (Directed Graph label rate 60%)","model":"1iG","rank_in_archive_order":2,"of":2,"metrics":{"Accuracy":"95.8±3.5"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-wiki-cs","task":"Node Classification","dataset":"Wiki-CS","model":"ScaleNet","rank_in_archive_order":6,"of":6,"metrics":{"Accuracy":"79.3±0.6"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-non-homophilic-11","task":"Node Classification on Non-Homophilic (Heterophilic) Graphs","dataset":"Chameleon (48%/32%/20% fixed splits)","model":"ScaleNet","rank_in_archive_order":1,"of":29,"metrics":{"1:1 Accuracy":"80.1±1.5"},"uses_additional_data":false},{"leaderboard":"/sota/node-classification-on-non-homophilic-12","task":"Node Classification on Non-Homophilic (Heterophilic) Graphs","dataset":"Squirrel (48%/32%/20% fixed splits)","model":"ScaleNet","rank_in_archive_order":1,"of":29,"metrics":{"1:1 Accuracy":"76.0±2.0"},"uses_additional_data":false}],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}