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Improving Soft Unification with Knowledge Graph Embedding Methods
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Systematically integrates knowledge graph embedding (KGE) objectives and operations into Conditional Theorem Prover (CTP) via four variants, improving NTP accuracy and evaluation speed.
Problem
Neural Theorem Provers are hard to optimize due to sparse gradients from top-k soft unification, yielding poorly structured embedding spaces and slow evaluation on large KGs.
Approach
Four ways of injecting KGE methods (auxiliary loss, auxiliary score function, translation-based stepping, KGE final-step scoring) into CTP; the best variant CTP2 mixes the NTP RBF similarity with a KGE score so proof-step embeddings get structured regularization, while CTP4 replaces the final ranking step with KGE for large speedups.
Key results
- CTP2 achieves SOTA among NTP-based methods on Countries, Nations, UMLS, FB122 and CoDEx-S, reaching 0.98 Test-II MRR and 0.68 Test-ALL MRR on FB122 versus 0.63 for CTP.
- CTP4 reduces evaluation time by 942x on FB122 and 1452x on WN18RR relative to CTP, at a notable accuracy cost (0.37 vs 0.44 WN18RR MRR for CTP4 vs CTP).
- On CLUTRR, CTP2 degrades only 0.04 from 4 to 10 hops while NBFNet drops over 0.3.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add KGE score to latent proof-step scores (CTP2) | CTP · UMLS | MRR: 0.65 -> 0.85 | Helped |
| Add KGE score to latent proof-step scores (CTP2) | CTP · Nations | MRR: 0.53 -> 0.79 | Helped |
| Add KGE score to latent proof-step scores (CTP2) | CTP · WN18RR | MRR: 0.44 -> 0.51 | Helped |
| Replace top-k final ranking with KGE scoring (CTP4) | CTP · WN18RR | evaluation time reduction: 1452× | Helped |
| Add PCRA filtering to CTP3 (ablation) | CTP3 · WN18RR | MRR: 0.37 -> 0.39 | Helped |
| Add learnable entity expansion to CTP3 (ablation) | CTP3 · WN18RR | MRR: 0.37 -> 0.41 | Helped |
| Add both PCRA filtering and entity expansion to CTP3 (ablation) | CTP3 · FB122 | MRR: 0.53 -> 0.63 | Helped |
| Use ComplEx rather than RotatE as the KGE in CTP1 (ablation) | CTP1 · UMLS | MRR: 0.67 -> 0.81 | Helped |
| Increase negative samples from n = 1 to n = 32 (ablation) | CTP1 with λ = 0.8 · FB122 | MRR: 0.59 -> 0.48 | Hurt |
| Increase negative samples from n = 1 to n = 32 (ablation) | CTP2 with λ = 0.8 · FB122 | MRR: 0.65 -> 0.46 | Hurt |
| Increase negative samples from n = 1 to n = 128 (ablation) | CTP4 · FB122 | MRR: 0.32 -> 0.61 | Helped |
| Decrease λ from 0.5 to 0 for CTP1 (ablation) | CTP1 · FB122 | MRR: 0.56 -> 0.40 | Hurt |
Surprising findings
- Adding more negative samples hurt CTP2 and CTP1 at higher lambda, with CTP2 at lambda 0.8 dropping from 0.65 to 0.46 MRR when negatives rise from 1 to 32.
- CTP1 with lambda=0 (pure KGE loss) achieves 0.85 MRR on UMLS, showing KGE objectives alone can be strong on small datasets.
Limitations
- CTP2 embedding space on WN18RR lacks clear global structure compared to pure KGE training, attributed to few negatives and sparse gradients.
- CTP3 and CTP4 accuracy drops noticeably versus CTP2, especially on large datasets.
- Sparse gradient problem remains a bottleneck and is not addressed.
Experimental setup
Datasets: Kinship Nations UMLS FB122 WN18RR CoDEx-S CLUTRR
Benchmarks: Kinship Nations UMLS Countries FB122 WN18RR CoDEx-S CLUTRR
Metrics: MRR HITS@1 HITS@3 HITS@10 AUC-PR inference time per sample evaluation time per sample
Baselines: NTP GNTP CTP NeuralLP MINERVA NBFNet DRUM LERP COMPLEX DISTMULT DiffLogic
Builds on: Neural Theorem Prover Conditional Theorem Prover ComplEx PTransE
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