For linear GNNs, the oversmoothing rate is exactly the second eigenvalue magnitude of the neighbor-averaging matrix, and residual connections provably push that rate toward 1 for many weight distributions.
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Residual connections provably mitigate oversmoothing in graph neural networks
For linear GNNs, the oversmoothing rate is exactly the second eigenvalue magnitude of the neighbor-averaging matrix, and residual connections provably push that rate toward 1 for many weight distributions.