  There has been tremendous success in the field of graph neural networks
(GNNs) as a result of the development of the message-passing (MP) layer, which
updates the representation of a node by combining it with its neighbors to
address variable-size and unordered graphs. Despite the fruitful progress of MP
GNNs, their performance can suffer from over-smoothing, when node
representations become too similar and even indistinguishable from one another.
Furthermore, it has been reported that intrinsic graph structures are smoothed
out as the GNN layer increases. Inspired by the edge-preserving bilateral
filters used in image processing, we propose a new, adaptable, and powerful MP
framework to prevent over-smoothing. Our bilateral-MP estimates a pairwise
modular gradient by utilizing the class information of nodes, and further
preserves the global graph structure by using the gradient when the aggregating
function is applied. Our proposed scheme can be generalized to all ordinary MP
GNNs. Experiments on five medium-size benchmark datasets using four
state-of-the-art MP GNNs indicate that the bilateral-MP improves performance by
alleviating over-smoothing. By inspecting quantitative measurements, we
additionally validate the effectiveness of the proposed mechanism in preventing
the over-smoothing issue.
