Geometric Knowledge Distillation: Topology Compression for Graph Neural Networks

We study a new paradigm of knowledge transfer that aims at encoding graph topological information into graph neural networks (GNNs) by distilling knowledge from a teacher GNN model trained on a complete graph to a student GNN model operating on a smaller or sparser graph. To this end, we revisit the connection between thermodynamics and the behavior of GNN, based on which we propose Neural Heat Kernel (NHK) to encapsulate the geometric property of the underlying manifold concerning the architecture of GNNs. A fundamental and principled solution is derived by aligning NHKs on teacher and student models, dubbed as Geometric Knowledge Distillation. We develop non-parametric and parametric instantiations and demonstrate their efficacy in various experimental settings for knowledge distillation regarding different types of privileged topological information and teacher-student schemes. * Junchi Yan is the correspondence author who is also with Shanghai AI Laboratory. 2 Geometric priors originally refer to the geometric principles naturally encoded in deep learning architectures, e.g., translational symmetry for CNNs, permutation invariance for GNNs. 36th Conference on Neural Information Processing Systems (NeurIPS 2022).