Research map / Graph learning / GNN architectures
Not too little, not too much: a theoretical analysis of graph (over)smoothing
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply one round of mean-aggregation smoothing before ridge regression | Linear ridge regression on projected Gaussian latent features · Synthetic Gaussian regression | test MSE | Helped |
| Apply one round of mean-aggregation smoothing before ridge regression | Linear ridge regression on projected Gaussian latent features · Synthetic Gaussian regression with signal aligned to a high-variance direction | test MSE | Helped |
| Apply smoothing when the regression signal is aligned with a low-variance direction | Linear ridge regression on projected Gaussian latent features · Synthetic heterophilic regression | test MSE | Hurt |
| Apply one round of mean-aggregation smoothing before ridge regression | Linear ridge regression on projected Gaussian latent features · Synthetic regression with equal covariance eigenvalues | test MSE | No clear effect |
| Apply one round of mean-aggregation smoothing before ridge regression | Linear ridge regression on projected Gaussian latent features · Two-class Gaussian classification | test MSE | Helped |
| Continue smoothing toward the infinite-layer limit rather than stopping at a beneficial finite depth | Mean-aggregation linear GNN · Connected graphs | test risk | Hurt |
| Increase smoothing depth in the two-Gaussian classification setting | Mean-aggregation linear GNN · Two-class Gaussian classification | test MSE | Mixed |
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