Over-smoothing in GNNs

The problem, from first principles

Over-smoothing is a phenomenon where node representations become indistinguishable after many GNN layers. Nodes converge to the same representation regardless of their local structure.

From theory to code

Implement:

detect_over_smoothing(features, adj, num_layers)

Measures over-smoothing by computing feature divergence after each layer.

Constraints

• features shape: (num_nodes, feature_dim).
• adj shape: (num_nodes, num_nodes).
• num_layers: number of GNN layers to simulate.
• Return: divergence scores per layer.