TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows

Moshe Eliasof, Eldad Haber, Carola-Bibiane Schönlieb

Keywords: Graph Neural Networks, Graph Lyapunov Dynamics, Graph Tangential Flows

TL;DR: We propose TANGO, a Lyapunov-inspired GNN framework that jointly learns a task-specific energy function and a tangential flow to enable stable and expressive graph feature dynamics for downstream tasks.

Abstract: We introduce TANGO, a dynamical-systems framework for graph representation learning that steers node features via a learned energy landscape. At its core is a learnable Lyapunov function whose gradient defines an energy-decreasing direction, guaranteeing stability and convergence. To preserve flexibility, we add a learned tangential message-passing component that evolves features along energy level sets. This orthogonal decomposition—gradient descent plus tangential evolution—enables effective signal propagation even in flat or ill-conditioned regions common in graph learning, mitigates oversquashing, and remains compatible with diverse GNN backbones. Empirically, TANGO achieves strong performance across node and graph classification and regression benchmarks, validating jointly learned energy functions and tangential flows.

Submission Type: Extended abstract (max 4 main pages).

Submission Number: 68