论文标题
部分可观测时空混沌系统的无模型预测
Generalized energy and gradient flow via graph framelets
论文作者
论文摘要
在这项工作中，我们通过能量梯度流的角度对基于帧的图形神经网络提供了理论上的理解。通过将基于帧的模型视为某些能量的离散梯度流，我们表明它可以通过不同频率组件的单独重量矩阵诱导低频和高频为主导的动力学。这证实了其在同质和异性图上的良好经验表现。然后，我们通过帧分解提出了广义能量，并显示其梯度流导致了新型的图神经网络，其中包括许多现有模型作为特殊情况。然后，我们解释了提出的模型通常如何导致更灵活的动力学，从而有可能增强图神经网络的表示能力。
In this work, we provide a theoretical understanding of the framelet-based graph neural networks through the perspective of energy gradient flow. By viewing the framelet-based models as discretized gradient flows of some energy, we show it can induce both low-frequency and high-frequency-dominated dynamics, via the separate weight matrices for different frequency components. This substantiates its good empirical performance on both homophilic and heterophilic graphs. We then propose a generalized energy via framelet decomposition and show its gradient flow leads to a novel graph neural network, which includes many existing models as special cases. We then explain how the proposed model generally leads to more flexible dynamics, thus potentially enhancing the representation power of graph neural networks.
