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On the Expressive Power of Sparse Geometric MPNNs
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Characterizes when message-passing networks on geometric graphs generically separate graphs (E-GGNN iff connected, I-GGNN iff generically globally rigid) and proposes EGenNet, a simple provably generically maximally expressive equivariant MPNN that performs well on molecular regression.
Problem
Which sparse (non-fully-connected) graphs allow message-passing networks on geometric graphs (3D point positions) to generically separate non-isomorphic geometric graphs, and how can an equivariant MPNN be built that is provably maximally expressive for generic inputs?
Approach
Shows E-GGNN generic separation holds exactly when the underlying graph is connected (using depth d+1 and the (d+1)-power graph's generic global rigidity), I-GGNN exactly when the graph is generically globally rigid, and gives EGenNet, an EGNN-like model with multiple equivariant channels (C=2Nd+1) whose parameters are random and generically injective via the finite witness theorem.
Key results
- EGenNet achieves the best MAE on BDE (0.3170 vs 1.4503 for DimeNet++, about 78% improvement) and on Kraken L and burL, outperforming GemNet and Marcel.
- On line-graph pairs a and b, EGenNet reaches 100% separation while SchNet fails and DimeNet/SphereNet separate only pair a.
- On k-chain experiments with k=12, EGenNet is the only model that succeeds with 7 blocks, suggesting less over-squashing.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use EGenNet instead of Marcel | Chemical property prediction · Drugs IP | MAE: 0.4066 -> 0.3965 | Helped |
| Use EGenNet instead of Marcel | Chemical property prediction · Drugs EA | MAE: 0.3910 -> 0.3686 | Helped |
| Use EGenNet instead of GemNet | Chemical property prediction · Drugs χ | MAE: 0.1970 -> 0.2068 | Hurt |
| Use EGenNet instead of Marcel | Chemical property prediction · Kraken B₅ | MAE: 0.2225 -> 0.1878 | Helped |
| Use EGenNet instead of Marcel | Chemical property prediction · Kraken L | MAE: 0.3386 -> 0.1738 | Helped |
| Use EGenNet instead of Marcel | Chemical property prediction · Kraken BurB₅ | MAE: 0.1589 -> 0.1530 | Helped |
| Use EGenNet instead of Marcel | Chemical property prediction · Kraken BurL | MAE: 0.0947 -> 0.0626 | Helped |
| Use EGenNet instead of DimeNet++ | Chemical property prediction · BDE BE | MAE: 1.4503 -> 0.3170 | Helped |
| Use SchNet on the 2-power graph rather than the original graph (ablation) | SchNet · Pair a | accuracy: 50.0 { { ± 0.0}} -> 100.0 { { ± 0.0}} | Helped |
| Use SchNet on the 3-power graph rather than the original graph (ablation) | SchNet · Pair b | accuracy: 50.0 { { ± 0.0}} -> 100.0 { { ± 0.0}} | Helped |
| Use DimeNet on the 2-power graph rather than the original graph (ablation) | DimeNet · Pair b | accuracy: 50.0 { { ± 0.0}} -> 100.0 { { ± 0.0}} | Helped |
| Use EGenNet rather than SchNet on the original graph | Geometric graph pair separation · Pair a | accuracy: 50.0 { { ± 0.0}} -> 100.0 { ± 0.0} | Helped |
Surprising findings
- Invariant models with power graph preprocessing can separate pairs that plain invariant MPNNs on the original graph cannot, while DimeNet and SphereNet fail on pair b despite using angles.
- EGenNet outperforms more complex high-order equivariant models like GemNet on several molecular property tasks.
Limitations
- May struggle with symmetric or non-generic inputs where generic guarantees do not hold.
- Maximal expressivity guarantees rely on injective functions and generic inputs; practical activations only approximate this.
- Experiments are limited to medium-sized molecules and synthetic pairs.
Experimental setup
Datasets: Drugs Kraken BDE synthetic k-chain pairs synthetic line-graph pairs
Benchmarks: Drugs Kraken BDE k-chain separation line-graph pair separation
Metrics: MAE classification accuracy
Baselines: SchNet DimeNet SphereNet DimeNet++ GemNet PaiNN LEFTNet Marcel GraphGPS
Builds on: EGNN maximally expressive GNN finite witness theorem SchNet DimeNet
Closest papers by meaning
- Improving Equivariant Graph Neural Networks on Large Geometric Graphs via Virtual Nodes Learning (ICML 2024 · similarity 0.87)
- On the Generalization of Equivariant Graph Neural Networks (ICML 2024 · similarity 0.87)
- Schur Nets: exploiting local structure for equivariance in higher order graph neural networks (NeurIPS 2024 · similarity 0.87)
- On Explaining Equivariant Graph Networks via Improved Relevance Propagation (ICML 2025 · similarity 0.87)
- On the Expressive Power of Spectral Invariant Graph Neural Networks (ICML 2024 · similarity 0.87)
- On the Completeness of Invariant Geometric Deep Learning Models (ICLR 2025 · similarity 0.86)
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