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Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo fractional derivative to leverage the non-local properties of fractional calculus. This approach enables the capture of long-term dependencies in feature updates, moving beyond the Markovian update mechanisms in conventional integer-order models and offering enhanced capabilities in graph representation learning. We offer an interpretation of the node feature updating process in FROND from a non-Markovian random walk perspective when the feature updating is particularly governed by a diffusion process. We demonstrate analytically that oversmoothing can be mitigated in this setting. Experimentally, we validate the FROND framework by comparing the fractional adaptations of various established integer-order continuous GNNs, demonstrating their consistently improved performance and underscoring the framework's potential as an effective extension to enhance traditional continuous GNNs. The code is available at \\url{https://github.com/zknus/ICLR2024-FROND}.","url_abs":"https://arxiv.org/abs/2404.17099v1","url_pdf":"https://arxiv.org/pdf/2404.17099v1.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":"unleashing-the-potential-of-fractional","repo_url":"https://github.com/zknus/iclr2024-frond","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"unleashing-the-potential-of-fractional","repo_url":"https://github.com/zknus/torchfde","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"graph-neural-network","task_name":"Graph Neural Network"},{"task_slug":"graph-representation-learning","task_name":"Graph Representation Learning"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"},{"method_slug":"graph-neural-network","method_name":"Graph Neural Network"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2404.17099","atlas_url":"https://app.syntology.ai/?focus=2404.17099","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2404.17099"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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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