  We investigate adaptive layer-wise graph convolution in deep GCN models. We
propose AdaGPR to learn generalized Pageranks at each layer of a GCNII network
to induce adaptive convolution. We show that the generalization bound for
AdaGPR is bounded by a polynomial of the eigenvalue spectrum of the normalized
adjacency matrix in the order of the number of generalized Pagerank
coefficients. By analysing the generalization bounds we show that oversmoothing
depends on both the convolutions by the higher orders of the normalized
adjacency matrix and the depth of the model. We performed evaluations on
node-classification using benchmark real data and show that AdaGPR provides
improved accuracies compared to existing graph convolution networks while
demonstrating robustness against oversmoothing. Further, we demonstrate that
analysis of coefficients of layer-wise generalized Pageranks allows us to
qualitatively understand convolution at each layer enabling model
interpretations.
