Weshowthat GDC isclosely related to spectral-based models and thus combines the strengths ofboth spatial (message passing) and spectral methods.

We also report the accuracy of the base and smooth classifier (binary attr.).

Graph convolution is the core of most Graph Neural Networks (GNNs) and usually approximated by message passing between direct (one-hop) neighbors. In this work, we remove the restriction of using only the direct neighbors by introducing a powerful, yet spatially localized graph convolution: Graph diffusion convolution (GDC). GDC leverages generalized graph diffusion, examples of which are the heat kernel and personalized PageRank. It alleviates the problem of noisy and often arbitrarily defined edges in real graphs. We show that GDC is closely related to spectral-based models and thus combines the strengths of both spatial (message passing) and spectral methods. We demonstrate that replacing message passing with graph diffusion convolution consistently leads to significant performance improvements across a wide range of models on both supervised and unsupervised tasks and a variety of datasets. Furthermore, GDC is not limited to GNNs but can trivially be combined with any graph-based model or algorithm (e.g.

Notably, message passing based GNNs, e.g., graph convolutional networks, leverage Furthermore, we break the conventional assumption that all GNN layers and feature channels (dimensions) should use the same neighborhood size for propagation. Now at Meta AI and work done when at Microsoft.

This paper introduces graph diffusion convolution (GDC), a pre-processing pipeline for graphs useful in node classification experiments on homophilic network datasets (e.g., citation networks). The preprocessing pipeline consists of two steps: 1) replacing the original adjacency matrix with a diffusion matrix (obtained as a polynomial function of the original adjacency matrix), and 2) sparsification by, e.g., thresholding the values on the edges. When using the newly obtained adjacency matrix in typical graph learning frameworks, results on node classification improve in many cases. The paper is extremely well written and scores very high in terms of clarity and quality of exposition. Related work is covered in great detail.

Graph convolution is the core of most Graph Neural Networks (GNNs) and usually approximated by message passing between direct (one-hop) neighbors. In this work, we remove the restriction of using only the direct neighbors by introducing a powerful, yet spatially localized graph convolution: Graph diffusion convolution (GDC). GDC leverages generalized graph diffusion, examples of which are the heat kernel and personalized PageRank. It alleviates the problem of noisy and often arbitrarily defined edges in real graphs. We show that GDC is closely related to spectral-based models and thus combines the strengths of both spatial (message passing) and spectral methods. We demonstrate that replacing message passing with graph diffusion convolution consistently leads to significant performance improvements across a wide range of models on both supervised and unsupervised tasks and a variety of datasets.