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On Explaining Equivariant Graph Networks via Improved Relevance Propagation
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Proposes EquiGX, a Deep Taylor / LRP-based relevance propagation method that explains spherical equivariant GNNs (TFN-style) by decomposing tensor-product message passing into hidden, distance and direction relevance.
Problem
Explaining equivariant graph neural networks on 3D geometric graphs, where existing XAI methods either are designed for 2D graphs or fail to handle positional/geometric features and tensor-product message passing.
Approach
Extends layer-wise relevance propagation to spherical equivariant GNNs by applying Deep Taylor decomposition to tensor-product messages, splitting each message's relevance equally across hidden features, edge distance and edge direction, and adding norm-based nonlinearity and linear-layer LRP-epsilon rules.
Key results
- EquiGX reaches 84.31 AUROC on Shapes vs 82.83 for the next best (PG-Explainer) and 83.57 AUROC on Spiral Noise vs 79.69 for GNN-Explainer.
- On ActsTrack EquiGX achieves 76.96 AUROC and 60.47 AP, the best among all compared methods (GNN-Explainer 65.18 AUROC).
- On BioLiP, EquiGX gives the best fidelity-sparsity trade-off curve in Figure 5, though no numeric table is reported.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use EquiGX instead of PG-Explainer | TFN explanations · Shapes | AUROC: 82.83 ± 11.7 -> 84.31 ± 8.89 | Helped |
| Use EquiGX instead of PG-Explainer | TFN explanations · Shapes | AP: 90.86 ± 5.66 -> 91.00 ± 5.32 | Helped |
| Use EquiGX instead of GNN-Explainer | TFN explanations · Spiral Noise | AUROC: 79.69 ± 2.30 -> 83.57 ± 10.07 | Helped |
| Use EquiGX instead of GNN-Explainer | TFN explanations · Spiral Noise | AP: 82.37 ± 1.90 -> 86.82 ± 8.30 | Helped |
| Use EquiGX instead of GNN-Explainer | TFN explanations · SCOP | AUROC: 77.26 ± 0.19 -> 81.51 ± 4.61 | Helped |
| Use EquiGX instead of PG-Explainer | TFN explanations · SCOP | AP: 72.63 ± 0.13 -> 82.69 ± 3.49 | Helped |
| Use EquiGX instead of GNN-Explainer | TFN explanations · ActsTrack | AUROC: 65.18 ± 0.59 -> 76.96 ± 1.69 | Helped |
| Use EquiGX instead of Grad-CAM | TFN explanations · ActsTrack | AP: 44.95 ± 1.40 -> 60.47 ± 1.71 | Helped |
Surprising findings
- The TFN model shows low fidelity (around 0.02) when binding-site nodes are masked on BioLiP, suggesting it does not rely on the binding site for predictions.
Limitations
- Extension to invariant, scalarization-based and spherical-scalarization models (e.g., EquiformerV2, MACE, HEGNN) is left open and requires new LRP rules for attention and inner-product operations.
- Relevance split equally across three components (hidden, distance, direction) is an assumption borrowed from prior work rather than derived.
- Experiments evaluate only a TFN backbone and a small set of datasets.
Experimental setup
Datasets: Shapes Spiral Noise SCOP BioLiP ActsTrack
Benchmarks: Shapes Spiral Noise SCOP ActsTrack BioLiP
Metrics: AUROC AP Fidelity Sparsity
Baselines: Grad Grad-CAM GNN-Explainer LRI-Bern LRI-Gaussian PG-Explainer
Builds on: Layer-wise Relevance Propagation Deep Taylor Decomposition TFN LRP-epsilon
Closest papers by meaning
- Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks? (NeurIPS 2024 · similarity 0.90)
- Universally Invariant Learning in Equivariant GNNs (NeurIPS 2025 · similarity 0.89)
- On the Generalization of Equivariant Graph Neural Networks (ICML 2024 · similarity 0.89)
- Improving Equivariant Graph Neural Networks on Large Geometric Graphs via Virtual Nodes Learning (ICML 2024 · similarity 0.88)
- EiG-Search: Generating Edge-Induced Subgraphs for GNN Explanation in Linear Time (ICML 2024 · similarity 0.88)
- E(n) Equivariant Topological Neural Networks (ICLR 2025 · similarity 0.87)
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