TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows
This work addresses graph neural network challenges like oversquashing and signal propagation, offering a novel dynamical systems approach for graph learning tasks.
The authors tackled the problem of graph representation learning by introducing TANGO, a framework that uses learned energy landscapes and tangential flows to govern node feature evolution, achieving strong performance on node and graph classification and regression benchmarks.
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.