Diagnosing GNN Failure Modes with Layer-Wise Probe Entropy

The paper introduces a post-hoc diagnostic for graph neural networks that freezes a trained model, fits a linear probe to each layer, and tracks probe accuracy with normalized predictive entropy. By examining layer-wise probe entropy, the authors can distinguish beneficial, neutral, and harmful smoothing effects—something existing geometric measures cannot do. The study also shows that entropy degradation patterns separate two main GNN failure modes: structural mismatch under heterophily, which appears early even in shallow models, and excessive-depth oversmoothing that emerges only as propagation depth increases.

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