Suppose we have a simplified Graph Neural Network (GNN): $\mathbf{H}^{(k)} = \mathbf{A}_{sym} \mathbf{H}^{(k-1)} \mathbf{W}^{(k)} = \mathbf{A}_{sym}^k \mathbf{X} \mathbf{W}$ If $k$ is large enough such that we reach a fixed point, then we will have $\mathbf{A}_{sym} \mathbf{H}^k = \mathbf{H}^k$. At this fixed point, all nodes will converge to be defined by the dominant eigenvector of $\mathbf{A}_{sym}$. Therefore, stacking many rounds of message passing acts as a low-pass convolutional filter, causing all node representations to become identical and uninformative. This phenomenon is known as over-smoothing.