A Proof for Theorem 1 Suppose (M,µ) is the base manifold of dimension n with respect to graph G and GNN model f

Lebesgue integrable by thinking of nodes embedded on the manifold, i.e., g 2 L We justify parametric GKD from a variational inference perspective. By definition in Section 4.2 we have a forward GNN model Correspondingly in Eqn. 7, the left equation is a general GNN layer (corresponding to discretized Further considering different discretization schemes (e.g., implicit scheme, multi-step schemes) yields different variants of GRAND [ All experiments are conducted on NVIDIA V100 with 16 GB memory. We train the model by Adam optimizer. For the main results reported in Tab. 1 and 2, we choose the backbone We choose three benchmark citation network datasets, i.e., Cora, Citeseer and Pubmed, and a large-scale network dataset OGB-Arxivfor node classification. For parameter tuning, we adopt grid search method to search for hyper-parameters on validation set.