Graph Neural Networks as Gradient Flows. (arXiv:2206.10991v1 [cs.LG])

Dynamical systems minimizing an energy are ubiquitous in geometry and
physics. We propose a gradient flow framework for GNNs where the equations
follow the direction of steepest descent of a learnable energy. This approach
allows to explain the GNN evolution from a multi-particle perspective as
learning attractive and repulsive forces in feature space via the positive and
negative eigenvalues of a symmetric "channel-mixing" matrix. We perform
spectral analysis of the solutions and conclude that gradient flow graph
convolutional models can …

arxiv gradient graph graph neural networks lg networks neural networks