Graph Neural Dynamics via Learned Energy and Tangential Flows

ICLR 2026 Conference Submission18971 Authors

Keywords: Graph Neural Networks, Graph Neural Dynamics

TL;DR: TANGO learns a Lyapunov energy over node features and updates via two orthogonal flows: energy descent for stability and a learned tangential, energy-preserving flow, improving propagation, reducing oversquashing, and boosting GNNs.

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.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 18971