  Recent works reveal that feature or label smoothing lies at the core of Graph
Neural Networks (GNNs). Concretely, they show feature smoothing combined with
simple linear regression achieves comparable performance with the carefully
designed GNNs, and a simple MLP model with label smoothing of its prediction
can outperform the vanilla GCN. Though an interesting finding, smoothing has
not been well understood, especially regarding how to control the extent of
smoothness. Intuitively, too small or too large smoothing iterations may cause
under-smoothing or over-smoothing and can lead to sub-optimal performance.
Moreover, the extent of smoothness is node-specific, depending on its degree
and local structure. To this end, we propose a novel algorithm called
node-dependent local smoothing (NDLS), which aims to control the smoothness of
every node by setting a node-specific smoothing iteration. Specifically, NDLS
computes influence scores based on the adjacency matrix and selects the
iteration number by setting a threshold on the scores. Once selected, the
iteration number can be applied to both feature smoothing and label smoothing.
Experimental results demonstrate that NDLS enjoys high accuracy --
state-of-the-art performance on node classifications tasks, flexibility -- can
be incorporated with any models, scalability and efficiency -- can support
large scale graphs with fast training.
