{"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/re-think-and-re-design-graph-neural-networks","title":"Re-Think and Re-Design Graph Neural Networks in Spaces of Continuous Graph Diffusion Functionals","arxiv_id":"2307.00222","date":"2023-07-01","proceeding":"NeurIPS 2023 11","authors":[],"abstract":"Graph neural networks (GNNs) are widely used in domains like social networks and biological systems. However, the locality assumption of GNNs, which limits information exchange to neighboring nodes, hampers their ability to capture long-range dependencies and global patterns in graphs. To address this, we propose a new inductive bias based on variational analysis, drawing inspiration from the Brachistochrone problem. Our framework establishes a mapping between discrete GNN models and continuous diffusion functionals. This enables the design of application-specific objective functions in the continuous domain and the construction of discrete deep models with mathematical guarantees. To tackle over-smoothing in GNNs, we analyze the existing layer-by-layer graph embedding models and identify that they are equivalent to l2-norm integral functionals of graph gradients, which cause over-smoothing. Similar to edge-preserving filters in image denoising, we introduce total variation (TV) to align the graph diffusion pattern with global community topologies. Additionally, we devise a selective mechanism to address the trade-off between model depth and over-smoothing, which can be easily integrated into existing GNNs. Furthermore, we propose a novel generative adversarial network (GAN) that predicts spreading flows in graphs through a neural transport equation. To mitigate vanishing flows, we customize the objective function to minimize transportation within each community while maximizing inter-community flows. Our GNN models achieve state-of-the-art (SOTA) performance on popular graph learning benchmarks such as Cora, Citeseer, and Pubmed.","url_abs":"https://arxiv.org/abs/2307.00222v1","url_pdf":"https://arxiv.org/pdf/2307.00222v1.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":"re-think-and-re-design-graph-neural-networks","repo_url":"https://github.com/Dandy5721/GNN-PDE-COV","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":null,"task_name":"Generative Adversarial Network"},{"task_slug":"graph-embedding","task_name":"Graph Embedding"},{"task_slug":"graph-learning","task_name":"Graph Learning"},{"task_slug":"image-denoising","task_name":"Image Denoising"},{"task_slug":"inductive-bias","task_name":"Inductive Bias"},{"task_slug":"node-classification","task_name":"Node Classification"}],"methods":[{"method_slug":"align","method_name":"ALIGN"},{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/node-classification-on-cora-with-public-split","task":"Node Classification","dataset":"Cora with Public Split: fixed 20 nodes per class","model":"GCN-TV","rank_in_archive_order":2,"of":36,"metrics":{"Accuracy":"86.3%"},"uses_additional_data":false}],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2307.00222","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2307.00222"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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