Diagnosing GNN Failure Modes with Layer-Wise Probe Entropy

Graph neural networks (GNNs) are typically evaluated only at their final layer, obscuring how task-relevant information evolves during message passing. We introduce a post-hoc diagnostic that freezes a trained GNN, fits an independent linear probe to each layer, and tracks probe accuracy alongside normalized predictive entropy. Across real and synthetic graph settings, layer-wise probe entropy distinguishes beneficial, neutral, and harmful smoothing, a capability not demonstrated by existing geometric measures. Moreover, by comparing shallow and deep models, we show that the onset of entropy degradation separates the two main GNN failure modes: structural mismatch under heterophily, which...

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