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GOAt: Explaining Graph Neural Networks via Graph Output Attribution
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Proposes GOAt, a training-free local GNN explainer that expands GNN outputs into sums of scalar product terms and attributes each term equally to its variables (edges, node features, activation patterns), evaluated on fidelity, discriminability, and stability.
Problem
Local explanations of GNNs usually rely on auxiliary trained explainer models or gradients, which yield black-boxed, hyperparameter-sensitive explanations that are often unfaithful, poorly discriminative, and inconsistent across similar samples.
Approach
Expand the GNN output analytically into a sum of scalar products over edges, node features and ReLU activation patterns, then attribute each product equally to its factors (equal-contribution lemma) and aggregate across products to get edge and node importance, with no auxiliary model training.
Key results
- GOAt achieves higher fidelity than all listed baselines across sparsity levels on GCN, with RCExplainer the strongest baseline.
- On BA-2Motifs at sparsity 0.7, GOAt's explanations exceed the original graphs' discriminability on BA-2Motifs and NCI1, and the paper reports discriminability well above baselines on a log scale.
- GOAt covers all Class 1 samples on BA-2Motifs with only three explanations, versus lower coverage for baselines in the stability study.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GOAt explanations instead of baseline explainers | pretrained GCN · GCN fidelity experiments across the evaluated datasets and sparsity levels | fidelity | Helped |
| Use GOAt explanations instead of baseline explainers | GCN · GCN discriminability experiments across datasets and sparsity levels | discriminability | Helped |
| Use GOAt explanations instead of baseline explainers | GCN · BA-2Motifs and NCI1 at sparsity=0.7 | discriminability | Helped |
| Use GOAt to extract explanations | GCN · Class 1 data samples | stability | Helped |
| Use GOAt instead of PGExplainer, SubgraphX, or RCExplainer | pretrained GNN · BA-2Motifs Class 1 | coverage: 12.8% -> 93.4% | Helped |
Surprising findings
- At sparsity 0.7, GOAt explanation embeddings have higher discriminability than the original graphs on BA-2Motifs and NCI1.
Limitations
- Theoretical equal-contribution lemmas assume a large number of nodes N; the paper argues this is not required in practice but provides no formal guarantee.
- Requires expert-designed decomposition for each GNN architecture (GCN, GraphSAGE, GIN), as acknowledged in the conclusion.
- Activation-pattern contributions are attributed approximately and equally to all relevant input features, an approximation for non-linear activations.
Experimental setup
Datasets: BA-2Motifs Mutagenicity NCI1 BA-Shapes BA-Community Tree-grid
Benchmarks: BA-2Motifs Mutagenicity NCI1
Metrics: fidelity sparsity discriminability (L2 norm of class mean embedding difference stability (top-k coverage)
Baselines: GNNExplainer PGExplainer PGM-Explainer SubgraphX CF-GNNExplainer RCExplainer RG-Explainer DEGREE
Builds on: GNNExplainer DEGREE SubgraphX
Closest papers by meaning
- GNNExplainer: Generating Explanations for Graph Neural Networks (NeurIPS 2019 · similarity 0.91)
- Towards Robust Fidelity for Evaluating Explainability of Graph Neural Networks (ICLR 2024 · similarity 0.90)
- Self-Interpretable Graph Learning with Sufficient and Necessary Explanations (AAAI 2024 · similarity 0.90)
- Generating In-Distribution Proxy Graphs for Explaining Graph Neural Networks (ICML 2024 · similarity 0.89)
- RegExplainer: Generating Explanations for Graph Neural Networks in Regression Tasks (NeurIPS 2024 · similarity 0.89)
- GraphTrail: Translating GNN Predictions into Human-Interpretable Logical Rules (NeurIPS 2024 · similarity 0.88)
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