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KGCRR: An Effective Metric-Driven Knowledge Graph Completion Framework by Designing a Novel Upper Bound Function with Adaptive Approximation to Reciprocal Rank
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Proposes CRR, a log-transformed sigmoid-based upper bound on reciprocal rank with a pressure parameter ρ, used as a plug-and-play loss for knowledge graph embedding models on FB15k-237 and WN18RR.
Problem
Knowledge graph completion is typically trained with margin-based or log-likelihood losses that are misaligned with the reciprocal rank (RR/MRR) evaluation metric, while directly optimizing RR suffers from gradient vanishing.
Approach
CRR is a nonlinear (log) transformation of a rank-based surrogate built on a shifted sigmoid with pressure parameter ρ; increasing ρ makes the surrogate a closer approximation to RR, and the loss is a plug-and-play replacement for existing KGE objectives.
Key results
- CRR loss improves MRR over margin-based loss by an average of 26.49% on FB15k-237 and 7.51% on WN18RR, and over log-likelihood loss by 32.31% and 9.93% respectively.
- Removing the log transformation (w/o T) lowers CRR performance across models, e.g., TransE on WN18RR drops from 0.241 to 0.207 MRR.
- Across the two datasets and seven KGE models, the paper reports an average 19.06% MRR improvement from CRR.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace margin-based loss with CRR loss | KGE methods on FB15k-237 · FB15k-237 | MRR: 26.49% | Helped |
| Replace Log-Likelihood loss with CRR loss | KGE methods on FB15k-237 · FB15k-237 | MRR: 32.31% | Helped |
| Replace margin-based loss with CRR loss | KGE methods on WN18RR · WN18RR | MRR: 7.51% | Helped |
| Replace Log-Likelihood loss with CRR loss | KGE methods on WN18RR · WN18RR | MRR: 9.93% | Helped |
| Add the transformation function T (log function) to CRR (ablation) | CompoundE on FB15k-237 · FB15k-237 | MRR: 0.414 -> 0.428 | Helped |
| Add the transformation function T (log function) to CRR (ablation) | CompoundE on WN18RR · WN18RR | MRR: 0.468 -> 0.484 | Helped |
| Increase pressure parameter ρ from 0.0 toward an effective value (ablation) | CRR on FB15k-237 and WN18RR · FB15k-237 and WN18RR | MRR | Mixed |
Surprising findings
- The best loss depends on dataset and model: ComplEx with log-likelihood loss outperforms margin-based loss on WN18RR but not on FB15k-237.
- Increasing the pressure parameter ρ beyond an optimum degrades performance, likely due to gradient vanishing similar to direct RR loss.
Limitations
- Gains are larger on FB15k-237 than on WN18RR, possibly because of fewer candidate entities per query.
- Only the log function was tested as the transformation; other transformations were left for future work.
- Evaluated only on two standard datasets with shallow KGE models and pressure/temperature hyperparameters tuned by grid search.
Experimental setup
Datasets: FB15k-237 WN18RR
Benchmarks: FB15k-237 WN18RR
Metrics: MRR Hits@1 Hits@10
Baselines: margin-based loss log-likelihood loss rank loss RR loss PairRE CompoundE
Builds on: Smooth-AP Smooth-AUC OpenKE
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