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RISE: Radius of Influence based Subgraph Extraction for 3D Molecular Graph Explanation
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Proposes RISE, an explanation method for 3D molecular GNNs that learns per-atom radii of influence (directed proximity graph) to extract exact, chemically interpretable explanatory subgraphs without soft-mask relaxation.
Problem
Explaining 3D geometric GNNs on molecules is hard because cut-off radius graphs are implicitly dense and existing mask-based explainers relax binary edge masks to soft masks, producing inconsistent and chemically uninterpretable subgraphs.
Approach
Represent 3D graphs as directed proximity graphs where each node has a radius of influence; optimize these radii directly under a budget (sum of radii) with a differentiable sigmoid edge mask based on distance, avoiding discrete-to-continuous relaxation, and exploit the observation that closer messages matter more.
Key results
- On QM9 with SchNet, RISE achieves the lowest MAE in most settings, e.g., mu MAE 0.422 at 0.5 budget (79.2% edges) vs GNNExplainer 0.859 at 79.9% edges.
- On QM9 with SEGNN, RISE is best in most cells, e.g., mu MAE 0.674 at 0.6 budget (51.8% edges) vs LRI-Bernoulli 0.895 (60.0%).
- On GEOM with DimeNet at budget 0.6, RISE MAE 0.081 at 40.5% edges vs GNNExplainer 2.292 at 50.0% edges.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RISE instead of the strongest listed explainer | SchNet · QM9 μ, budget 0.3 | MAE: 1.884 -> 0.596 | Helped |
| Use RISE instead of the strongest listed explainer | SchNet · QM9 α, budget 0.5 | MAE: 2.054 -> 1.430 | Helped |
| Use RISE instead of GNNExplainer | SchNet · QM9 εHOMO, budget 0.5 | MAE: 0.154 -> 0.172 | Hurt |
| Use RISE instead of the strongest listed explainer | SEGNN · QM9 α, budget 0.6 | MAE: 15.201 -> 15.557 | Hurt |
| Use RISE instead of PGExplainer | SchNet · GEOM energy, budget 0.4 | MAE: 0.071 -> 0.098 | Hurt |
| Remove edges in progressively shorter-distance annuli rather than longer-distance annuli | SchNet on QM9 α · QM9 α, edge-removal annuli | MAE: 0.248 -> 0.253 -> 0.373 -> 0.373 -> 0.739 | Hurt |
Surprising findings
- RISE with fewer preserved edges outperforms baselines that preserve more edges, and on Ethane it recovers exactly the C-H and C-C bonds.
- Removing shorter-distance edge annuli hurts 3D GNN predictions more than removing longer-distance ones, supporting proximity-dependent message importance.
Limitations
- Evaluated only on relatively small molecules; macromolecules with long-range interactions not studied.
- Chemical interpretability is demonstrated mainly through qualitative visualizations on small molecules.
Experimental setup
Datasets: QM9 GEOM
Benchmarks: QM9 GEOM
Metrics: MAE
Baselines: GNNExplainer PGExplainer LRI-Bernoulli
Builds on: GNNExplainer PGExplainer LRI
Closest papers by meaning
- Neural P$^3$M: A Long-Range Interaction Modeling Enhancer for Geometric GNNs (NeurIPS 2024 · similarity 0.89)
- Empowering Active Learning for 3D Molecular Graphs with Geometric Graph Isomorphism (NeurIPS 2024 · similarity 0.88)
- On the Scalability of GNNs for Molecular Graphs (NeurIPS 2024 · similarity 0.87)
- MAGE: Model-Level Graph Neural Networks Explanations via Motif-based Graph Generation (ICLR 2025 · similarity 0.87)
- Neural Atoms: Propagating Long-range Interaction in Molecular Graphs through Efficient Communication Channel (ICLR 2024 · similarity 0.87)
- Lift Your Molecules: Molecular Graph Generation in Latent Euclidean Space (ICLR 2025 · similarity 0.87)
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