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Aggregation Dispersion: An Information-Geometric Diagnostic of Oversmoothing in Graph Neural Networks

NeurIPS 2026 · Graph learning › GNN architectures · approach: GNN generalization theory

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Proposes aggregation dispersion, an information-geometric diagnostic that measures oversmoothing in GNNs via the spread of per-node walk distributions across depth.

Problem

Oversmoothing in message-passing GNNs: stacking many layers makes all node representations converge, harming performance; existing measures lack a geometric account of this collapse.

Approach

At each depth k, each node v gets a walk distribution p_v^(k) over all nodes induced by the propagation operator; oversmoothing is framed as these distributions becoming indistinguishable, and a dispersion measure on them serves as an information-geometric diagnostic.

Experimental setup

Builds on: message passing neural networks

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