TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows
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| Format: | Preprint |
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2025
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| _version_ | 1866911095406460928 |
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| author | Eliasof, Moshe Haber, Eldad Schönlieb, Carola-Bibiane |
| author_facet | Eliasof, Moshe Haber, Eldad Schönlieb, Carola-Bibiane |
| contents | 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-reducing direction that guarantees convergence and 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 mitigates 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_05070 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows Eliasof, Moshe Haber, Eldad Schönlieb, Carola-Bibiane Machine Learning 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-reducing direction that guarantees convergence and 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 mitigates 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. |
| title | TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2508.05070 |