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Knowledge Graph Completion by Intermediate Variables Regularization
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Derives a general block-term form unifying tensor-decomposition KGC models (CP, ComplEx, SimplE, ANALOGY, QuatE, TuckER) and proposes intermediate variables regularization (IVR) that upper-bounds the overlapped trace norm of the predicted tensor.
Problem
Tensor decomposition-based knowledge graph completion models overfit severely, and existing regularizers (squared Frobenius, N3, DURA) only penalize embedding norms, are tied to CP decomposition, and perform suboptimally.
Approach
Penalize the norms of intermediate variables arising from all ways of computing the predicted tensor (embeddings, pairwise products like W×1H×2R, and Kronecker products), and prove the resulting regularizer upper-bounds the overlapped trace norm of the predicted tensor, applicable to most TDB models.
Key results
- TuckER-IVR reaches MRR 0.501 on WN18RR vs 0.446 for TuckER and 0.449 for TuckER-F2.
- ComplEx-IVR reaches MRR 0.494 on WN18RR vs 0.491 for ComplEx-N3 and 0.484 for ComplEx-DURA; on FB15k-237 IVR is comparable to DURA (0.370 vs 0.372).
- On Kinship, TuckER-IVR lowers the overlapped trace norm L(X) from 30,786 (TuckER) to 11,037.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add IVR regularization to CP | CP · WN18RR, FB15k-237, YAGO3-10 | MRR: 0.438 -> 0.478; 0.332 -> 0.365; 0.567 -> 0.579 | Helped |
| Add IVR regularization to ComplEx | ComplEx · WN18RR, FB15k-237, YAGO3-10 | MRR: 0.464 -> 0.494; 0.348 -> 0.370; 0.574 -> 0.586 | Helped |
| Add IVR regularization to SimplE | SimplE · WN18RR, FB15k-237, YAGO3-10 | MRR: 0.443 -> 0.470; 0.337 -> 0.357; 0.565 -> 0.578 | Helped |
| Add IVR regularization to ANALOGY | ANALOGY · WN18RR, FB15k-237, YAGO3-10 | MRR: 0.458 -> 0.482; 0.348 -> 0.367; 0.573 -> 0.582 | Helped |
| Add IVR regularization to QuatE | QuatE · WN18RR, FB15k-237, YAGO3-10 | MRR: 0.460 -> 0.493; 0.349 -> 0.369; 0.566 -> 0.582 | Helped |
| Add IVR regularization to TuckER | TuckER · WN18RR, FB15k-237, YAGO3-10 | MRR: 0.446 -> 0.501; 0.321 -> 0.368; 0.551 -> 0.581 | Helped |
| Replace CP-DURA with CP-IVR | CP · WN18RR, FB15k-237, YAGO3-10 | MRR: 0.471 -> 0.478; 0.364 -> 0.365; 0.577 -> 0.579 | Mixed |
| Replace ComplEx-DURA with ComplEx-IVR | ComplEx · WN18RR, FB15k-237, YAGO3-10 | MRR: 0.484 -> 0.494; 0.372 -> 0.370; 0.585 -> 0.586 | Mixed |
| Use only IVR upper bound 1 instead of full IVR (ablation) | TuckER · WN18RR, FB15k-237, YAGO3-10 | MRR: 0.501 -> 0.497; 0.368 -> 0.366; 0.581 -> 0.576 | Hurt |
| Use only IVR upper bound 2 instead of full IVR (ablation) | TuckER · WN18RR, FB15k-237, YAGO3-10 | MRR: 0.501 -> 0.459; 0.368 -> 0.336; 0.581 -> 0.568 | Hurt |
| Combine IVR upper bounds 1 and 2 rather than using either alone (ablation) | TuckER · Kinship | overlapped trace norm: 17,003 -> 11,037; 18,330 -> 11,037 | Helped |
Surprising findings
- Using only one regularization coefficient (IVR-1) performs comparably to the full IVR with four coefficients.
- The paper reports that the bound from Proposition 2 is not always tight, yet combining it with the tight bound gives better performance.
Limitations
- Exact overlapped trace norm is impractical to compute on large KGs, so the bound-verification experiment is limited to the small Kinship dataset.
- Regularizer is limited to tensor decomposition-based models and not applied to translation-based or neural KGC models.
- The bound from the second proposition is not always tight, so the combined regularizer is only heuristically justified.
Experimental setup
Datasets: WN18RR FB15k-237 YAGO3-10 Kinship
Benchmarks: WN18RR FB15k-237 YAGO3-10 Kinship
Metrics: filtered MRR Hits@1 Hits@10 overlapped trace norm L(X)
Baselines: CP-F2 CP-N3 CP-DURA ComplEx-F2 ComplEx-N3 ComplEx-DURA SimplE-F2 ANALOGY-F2 QuatE-F2 TuckER-F2
Builds on: N3 regularization DURA TuckER ComplEx overlapped trace norm
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