{"id":39104,"date":"2026-08-21T15:30:15","date_gmt":"2026-08-21T15:30:15","guid":{"rendered":"https:\/\/lamarr-institute.org\/publication\/learning-generalized-hessian-on-graphs-for-continuous-graph-learning\/"},"modified":"2026-11-13T10:59:32","modified_gmt":"2026-11-13T10:59:32","slug":"learning-generalized-hessian-on-graphs-for-continuous-graph-learning","status":"publish","type":"publication","link":"https:\/\/lamarr-institute.org\/de\/publication\/learning-generalized-hessian-on-graphs-for-continuous-graph-learning\/","title":{"rendered":"Learning Generalized Hessian on\u00a0Graphs for\u00a0Continuous Graph Learning"},"content":{"rendered":"<p>In this work, we propose HbInOut (Hessian-based Influx Outflux), a continuous graph neural network for graph learning and graph ensemble (snapshot) learning. HbInOut models diffusion on graphs by incorporating flow-based priors in its forward-pass construction and includes directionality through learnable influx and outflux operators. We analyze key theoretical properties of the HbInOut diffusion and empirically demonstrate that HbInOut mitigates oversmoothing. Across a diverse set of graph datasets, HbInOut achieves strong performance and exceeds state-of-the-art baselines, with particularly clear gains on directed and flow-structured datasets. For example, HbInOut attains up to 4\\% gain in test accuracy on a graph learning task, and reduces 5.5 times test MSE on a synthetic graph ensemble task.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this work, we propose HbInOut (Hessian-based Influx Outflux), a continuous graph neural network for graph learning and graph ensemble (snapshot) learning. HbInOut models diffusion on graphs by incorporating flow-based priors in its forward-pass construction and includes directionality through learnable influx and outflux operators. We analyze key theoretical properties of the HbInOut diffusion and empirically demonstrate that HbInOut mitigates oversmoothing. Across a diverse set of graph datasets, HbInOut achieves strong [&hellip;]<\/p>\n","protected":false},"author":14,"featured_media":0,"template":"","meta":{"_acf_changed":false,"footnotes":""},"publication-type":[32],"publication-year":[1680],"class_list":["post-39104","publication","type-publication","status-publish","hentry","publication-type-inproceedings","publication-year-1680"],"acf":[],"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/39104","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication"}],"about":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/types\/publication"}],"author":[{"embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":1,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/39104\/revisions"}],"predecessor-version":[{"id":43803,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/39104\/revisions\/43803"}],"wp:attachment":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/media?parent=39104"}],"wp:term":[{"taxonomy":"publication-type","embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication-type?post=39104"},{"taxonomy":"publication-year","embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication-year?post=39104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}