TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows

• URL: http://arxiv.org/abs/2508.05070v1
• Date: Thu, 07 Aug 2025 06:44:01 GMT
• Title: TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows
• Authors: Moshe Eliasof, Eldad Haber, Carola-Bibiane Schönlieb,
• Abstract summary: We introduce TANGO -- a dynamical systems inspired framework for graph representation learning.<n>At the core of our approach is a learnable Lyapunov function over node embeddings.<n>We incorporate a novel tangential component, learned via message passing, that evolves features while maintaining the energy value.
• Score: 17.546965223021786
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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