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Sound Logical Explanations for Mean Aggregation Graph Neural Networks
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Shows which monotonic ALCQ-style rules can be sound for mean-aggregation GNNs with non-negative weights (MAGNNs), gives an explanation procedure, and tests rule extraction on KG completion and LUBM node classification.
Problem
Mean-aggregation GNNs are widely used but lack logical explainability and expressivity results, unlike sum and max GNNs; it is unclear which sound logical rules can explain their predictions.
Approach
Restrict mean-GNNs to non-negative weights (MAGNNs) so they are monotonic under dataset extension; characterise the ELUQ monotonic rules that can be sound, reduce them to a finite set of simple rules checkable on a small base dataset, and build explanatory FOL-fragment rules for any prediction.
Key results
- Non-negative mean-GNNs match or beat standard ones on WN-hier, WN-sym, FB237v1, WN18RRv1 and NELLv1 (e.g. NELLv1 accuracy 75.2 standard vs 93.4 non-negative), but drop on LUBM (97.1 to 91.5) and WN-hier_nmhier.
- Sound monotonic rules were found on LUBM, WN-hier, WN-hier_nmhier and FB237v1, with almost none on WN-sym, WN18RRv1 and NELLv1.
- Sound rules exposed nonsensical learned behaviour, e.g. the empty-body rule top subsumed by Publication on LUBM and 29 empty-body sound rules on average on FB237v1.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Restrict mean-GNN weights to non-negative values | Mean-GNN · LUBM test | F1: 97.1 \pm 0.0 -> 91.9 \pm 0.0 | Hurt |
| Restrict mean-GNN weights to non-negative values | Mean-GNN · WN-hier test | F1: 99.5 \pm 0.0 -> 99.8 \pm 0.0 | Helped |
| Restrict mean-GNN weights to non-negative values | Mean-GNN · WN-sym test | F1: 99.4 \pm 0.0 -> 100 \pm 0.0 | Helped |
| Restrict mean-GNN weights to non-negative values | Mean-GNN · WN-hier_nmhier test | F1: 86.5 \pm 0.0 -> 67.2 \pm 0.0 | Hurt |
| Restrict mean-GNN weights to non-negative values | Mean-GNN · FB237v1 test | F1: 55.7 \pm 0.0 -> 69.7 \pm 0.0 | Helped |
| Restrict mean-GNN weights to non-negative values | Mean-GNN · WN18RRv1 test | F1: 93.4 \pm 0.0 -> 95.3 \pm 0.0 | Helped |
| Restrict mean-GNN weights to non-negative values | Mean-GNN · NELLv1 test | F1: 65.7 \pm 0.2 -> 93.8 \pm 0.0 | Helped |
Surprising findings
- Almost no sound monotonic rules are obtained on WN-sym, despite the dataset being populated by monotonic rules.
- Sound rules with empty bodies (e.g. top subsumed by Publication) are learned by the trained models, which are nonsensical.
Limitations
- Number of candidate rules grows exponentially in the number of predicates, making search intractable (e.g. FB237v1).
- Unknown whether ELUQ is a maximal monotonic fragment of ALCQ.
- Only the <= threshold classifier is analysed; using < gives different theoretical results.
Experimental setup
Datasets: WN18RRv1 FB237v1 NELLv1 LUBM LogInfer-WN-hier LogInfer-WN-sym LogInfer-WN-hier_nmhier
Benchmarks: WN18RRv1 FB237v1 NELLv1 LUBM LogInfer-WN-hier LogInfer-WN-sym LogInfer-WN-hier_nmhier
Metrics: accuracy precision recall F1
Baselines: Standard (unrestricted) mean-GNN max-GNN sum-GNN
Builds on: Tena Cucala et al. sound rules for non-negative GNNs R-GCN ALCQ LogInfer
Closest papers by meaning
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- Recurrent Graph Neural Networks and Their Connections to Bisimulation and Logic (AAAI 2024 · similarity 0.88)
- Self-Interpretable Graph Learning with Sufficient and Necessary Explanations (AAAI 2024 · similarity 0.88)
- Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective (ICML 2025 · similarity 0.88)
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