用能量梯度与切向流动构建图神经网络新动态，缓解特征挤压问题。
TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows
- 通过可学习的能量函数引导节点特征演化，保证收敛稳定。
- 引入消息传递学习的切向分量，实现能量不变下的灵活特征更新。
- 适用于多种图神经网络架构，尤其在平坦区域表现更优。
我们提出TANGO——一种受动力系统启发的图表示学习框架，通过可学习的能量景观及其下降动力学来调控节点特征演化。核心在于对节点嵌入定义可学习的李雅普诺夫函数，其梯度构成能量降低方向，确保收敛与稳定性。为增强灵活性并保留能量动力学优势，我们引入一种新颖的切向分量，通过消息传递学习，使特征在保持能量值不变的情况下演化。这种能量梯度下降与切向演化的正交分解，形成灵活的图动态形式，支持在平坦或病态能量区域的有效信号传播，常见于图学习任务中。该方法缓解了过度压缩问题，且兼容不同图神经网络主干。实证表明，TANGO在多样化的节点与图分类及回归基准上表现强劲，验证了联合学习的能量函数与切向流对图神经网络的有效性。
原文摘要 · Abstract (English)
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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