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 appears from the earliest layers even in shallow models, and excessive-depth oversmoothing, which emerges only as propagation depth increases.
These results establish probe-entropy trajectories as a tool for analyzing information flow in GNNs and motivate future work on adaptive depth selection and early-exit mechanisms.