{"ID":2885033,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.05070","arxiv_id":"2508.05070","title":"TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows","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-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.","short_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-r...","url_abs":"https://arxiv.org/abs/2508.05070","url_pdf":"https://arxiv.org/pdf/2508.05070v1","authors":"[\"Moshe Eliasof\",\"Eldad Haber\",\"Carola-Bibiane Schönlieb\"]","published":"2025-08-07T06:44:01Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Graph Neural Network\"]","has_code":false}