  Linearized Graph Neural Networks (GNNs) have attracted great attention in
recent years for graph representation learning. Compared with nonlinear Graph
Neural Network (GNN) models, linearized GNNs are much more time-efficient and
can achieve comparable performances on typical downstream tasks such as node
classification. Although some linearized GNN variants are purposely crafted to
mitigate ``over-smoothing", empirical studies demonstrate that they still
somehow suffer from this issue. In this paper, we instead relate over-smoothing
with the vanishing gradient phenomenon and craft a gradient-free training
framework to achieve more efficient and effective linearized GNNs which can
significantly overcome over-smoothing and enhance the generalization of the
model. The experimental results demonstrate that our methods achieve better and
more stable performances on node classification tasks with varying depths and
cost much less training time.
