Graph Neural Dynamics via Learned Energy and Tangential Flows

Moshe Eliasof, Eldad Haber, Carola-Bibiane Schönlieb
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:27891-27917, 2026.

Abstract

We introduce TANGO, a dynamical-systems-inspired framework for graph representation learning that governs node feature evolution through a learned energy landscape and its associated descent dynamics. At the core of our approach is a learnable Lyapunov function over node embeddings, whose gradient defines an energy non-increasing direction that guarantees stability. To enhance flexibility while preserving the benefits of energy-based dynamics, we incorporate a novel tangential component, learned via message passing, that evolves features while maintaining the energy value. This decomposition into orthogonal flows of energy gradient descent and tangential evolution yields a flexible form of graph dynamics, and enables effective signal propagation even in flat or ill-conditioned energy regions, that often appear in graph learning. Our method is designed to help alleviate oversquashing, and is compatible with different graph neural network backbones. Empirically, TANGO achieves strong performance across a diverse set of node and graph classification and regression benchmarks, demonstrating the effectiveness of jointly learned energy functions and tangential flows for graph neural networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-eliasof26a, title = {Graph Neural Dynamics via Learned Energy and Tangential Flows}, author = {Eliasof, Moshe and Haber, Eldad and Sch\"{o}nlieb, Carola-Bibiane}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {27891--27917}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/eliasof26a/eliasof26a.pdf}, url = {https://proceedings.mlr.press/v306/eliasof26a.html}, abstract = {We introduce TANGO, a dynamical-systems-inspired framework for graph representation learning that governs node feature evolution through a learned energy landscape and its associated descent dynamics. At the core of our approach is a learnable Lyapunov function over node embeddings, whose gradient defines an energy non-increasing direction that guarantees stability. To enhance flexibility while preserving the benefits of energy-based dynamics, we incorporate a novel tangential component, learned via message passing, that evolves features while maintaining the energy value. This decomposition into orthogonal flows of energy gradient descent and tangential evolution yields a flexible form of graph dynamics, and enables effective signal propagation even in flat or ill-conditioned energy regions, that often appear in graph learning. Our method is designed to help alleviate oversquashing, and is compatible with different graph neural network backbones. Empirically, TANGO achieves strong performance across a diverse set of node and graph classification and regression benchmarks, demonstrating the effectiveness of jointly learned energy functions and tangential flows for graph neural networks.} }
Endnote
%0 Conference Paper %T Graph Neural Dynamics via Learned Energy and Tangential Flows %A Moshe Eliasof %A Eldad Haber %A Carola-Bibiane Schönlieb %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-eliasof26a %I PMLR %P 27891--27917 %U https://proceedings.mlr.press/v306/eliasof26a.html %V 306 %X We introduce TANGO, a dynamical-systems-inspired framework for graph representation learning that governs node feature evolution through a learned energy landscape and its associated descent dynamics. At the core of our approach is a learnable Lyapunov function over node embeddings, whose gradient defines an energy non-increasing direction that guarantees stability. To enhance flexibility while preserving the benefits of energy-based dynamics, we incorporate a novel tangential component, learned via message passing, that evolves features while maintaining the energy value. This decomposition into orthogonal flows of energy gradient descent and tangential evolution yields a flexible form of graph dynamics, and enables effective signal propagation even in flat or ill-conditioned energy regions, that often appear in graph learning. Our method is designed to help alleviate oversquashing, and is compatible with different graph neural network backbones. Empirically, TANGO achieves strong performance across a diverse set of node and graph classification and regression benchmarks, demonstrating the effectiveness of jointly learned energy functions and tangential flows for graph neural networks.
APA
Eliasof, M., Haber, E. & Schönlieb, C.. (2026). Graph Neural Dynamics via Learned Energy and Tangential Flows. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:27891-27917 Available from https://proceedings.mlr.press/v306/eliasof26a.html.

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