Graph Neural Dynamics via Learned Energy and Tangential Flows

Moshe Eliasof, Eldad Haber, Carola-Bibiane Schönlieb

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 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.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 18971