Geometric Knowledge Distillation: Topology Compression for Graph Neural Networks
This addresses the challenge of compressing graph topology for GNNs, which is incremental as it builds on existing knowledge distillation methods.
The paper tackles the problem of transferring graph topological information from a teacher GNN to a student GNN by proposing Geometric Knowledge Distillation, which aligns Neural Heat Kernels to encode geometric properties, and demonstrates its efficacy in various experimental settings.
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- 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.