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Systematic Relational Reasoning With Epistemic Graph Neural Networks
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Proposes the Epistemic GNN (EpiGNN), a parameter-efficient GNN whose node embeddings are probability distributions over primitive relations, simulating a directional approximation of algebraic closure for systematic relational reasoning, and introduces RCC-8 and Interval Algebra multi-path benchmarks.
Problem
Standard GNNs fail to systematically generalize to longer relational inference chains, and neuro-symbolic methods are poorly scalable and assume single-path reasoning that cannot handle disjunctive, multi-path constraints.
Approach
Treat node embeddings as epistemic states (distributions over primitive relations) with message passing given by learned relation-composition tensors and pooling by min or Hadamard product, so the GNN approximates directional algebraic closure; forward and backward models are combined over entities on head-tail paths.
Key results
- On CLUTRR (train k in 2-4, test 5-10 hops), EpiGNN-mul reaches 0.99 at 5 hops and 0.98 at 10 hops, on par with NCRL and R5, and above GNN and transformer baselines.
- On the new RCC-8 and IA multi-path benchmarks, EpiGNN-min is the best model while neuro-symbolic methods are largely ineffective.
- On Graphlog World 32, EpiGNN-mul achieves 0.914 accuracy, improving over the prior best of 0.841 (R5).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use EpiGNN-mul instead of the strongest reported baseline | CLUTRR · CLUTRR, 10 Hops | accuracy: 0.98$\pm$.03 -> 0.98$\pm$.02 | No clear effect |
| Use EpiGNN-mul instead of R5 | Graphlog · World 32 | accuracy: 0.841$\pm$0.03 -> 0.914$\pm$0.026 | Helped |
| Use EpiGNN-mul instead of R5 | Graphlog · World 7 | accuracy: 0.749$\pm$0.04 -> 0.611$\pm$0.026 | Hurt |
| Use EpiGNN-min for inductive KGC | Inductive KGC · FB15k-237 v1 and v2 | Hits@10: 75.12 -> 91.67; 91.21 -> 95.54 | Helped |
| Use EpiGNN-min instead of EpiGNN-mul | EpiGNN · CLUTRR | accuracy | Hurt |
| Use EpiGNN-min instead of EpiGNN-mul | EpiGNN · RCC-8 and IA | accuracy | Helped |
| Add multiple lower-dimensional facets rather than use facets=1 (ablation) | EpiGNN · CLUTRR Avg and Hard; RCC-8 Avg and Hard | accuracy: 0.94 -> 0.99; 0.85 -> 0.99; 0.92 -> 0.96; 0.68 -> 0.80 | Helped |
| Constrain embeddings to be non-negative and sum to 1 (ablation) | EpiGNN · CLUTRR Avg and RCC-8 Avg | accuracy: 0.36 -> 0.99; 0.38 -> 0.96 | Helped |
| Use bilinear composition instead of MLP+distmult composition (ablation) | EpiGNN · CLUTRR Avg and RCC-8 Avg | accuracy: 0.29 -> 0.99; 0.13 -> 0.96 | Helped |
| Add the backward model to the forward model (ablation) | EpiGNN · CLUTRR Avg and RCC-8 Avg | accuracy: 0.94 -> 0.99; 0.84 -> 0.96 | Helped |
Surprising findings
- Neuro-symbolic methods such as R5 and CTP are largely ineffective on disjunctive RCC-8 and IA benchmarks, as they cannot model disjunctive rules.
Limitations
- Statistical nature means parameters can absorb training data artefacts.
- Stronger inductive bias of neuro-symbolic methods gives them an advantage in severely data-limited settings (e.g., CLUTRR trained only on k in {2,3}).
- Directional algebraic closure is an approximation that only maintains head-to-entity relation sets and may infer less than full algebraic closure.
Experimental setup
Datasets: CLUTRR Graphlog RCC-8 benchmark (new) Interval Algebra benchmark (new) FB15k-237 inductive splits WN18RR inductive splits
Benchmarks: CLUTRR Graphlog RCC-8 Interval Algebra FB15k-237 inductive WN18RR inductive
Metrics: accuracy Hits@10
Baselines: NCRL R5 CTP GNTP Edge Transformer GAT GCN NBFNet R-GCN RNN LSTM GRU
Builds on: NBFNet algebraic closure algorithm neural theorem provers algorithmic alignment
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