Beyond Trained Models: Compiling GNNs for a Sound Explainer Benchmark

Explainers for Graph Neural Networks (GNNs) are commonly evaluated by their plausibility, i.e., how well their explanations recover a predefined ground truth, such as a motif planted in the data. This protocol implicitly assumes that a GNN trained on such data relies on the intended motif. Although prior work has questioned this assumption, plausibility remains widespread. First, we show that the assumption is violated on several widely used benchmarks, where, e.g., degree statistics alone suffice to solve the task. Then, we remove this confounder by replacing training with compilation. We achieve this by introducing mathsfGracr, the first compiler translating graded modal logic formulas into GNN weights, yielding models that replicate the behaviour of the corresponding formulas. Since the behaviour of the model is now known by construction, we can define its ground truth explanation formally and compute it exactly. Building on this, we introduce mathsfGracrmathsfBench, a benchmark of compiled GNNs for the evaluation of explainers against this exact ground truth. Experiments on eleven explainers across six tasks show its effectiveness for fine-grained diagnostic evaluation: notably, we discover that most explainers are not robust to indirect influences or alternative implementations of the same formula. These results position mathsfGracrmathsfBench as a novel, rigorous evaluation setting for graph post-hoc explainability.