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SPAC: Sparse Partitioning and Adaptive Core Tensor Pruning Model for Knowledge Graph Completion
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Proposes SPAC, a tensor decomposition model for knowledge graph completion that uses a block-diagonal sparse core tensor (main Tucker-style cores plus auxiliary CP-style cores), a gating mechanism for inter-group interaction, and adaptive core pruning during training.
Problem
Knowledge graph completion with tensor decomposition models faces a trade-off: overly sparse core tensors (DistMult, ComplEx) limit interactions between embedding dimensions, while dense Tucker core tensors overfit and are costly.
Approach
Partition the diagonal sparse core tensor into dense main cores for fine-grained interactions and 1x1x1 auxiliary cores for sparse general interactions, add a batch-normalized linear gating layer to couple groups, and dynamically prune low-importance/low-diversity dimensions during training, replacing them with auxiliary cores.
Key results
- On FB15k-237, SPAC reaches Hits@1 of 0.280, 0.4% above ComplEx-DURA and 0.6% above MEIM.
- On WN18RR, SPAC reaches Hits@10 of 0.591, 1.8% above ComplEx-DURA and 1.4% above MEIM.
- On YAGO3-10, SPAC slightly outperforms MEIM (MRR 0.586 vs 0.585) with fewer core-tensor parameters than Tucker.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SPAC instead of MEIM | Tensor decomposition models · FB15k-237 | Hits@1: 0.274 -> 0.280 | Helped |
| Use SPAC instead of MEIM | Tensor decomposition models · WN18RR | Hits@10: 0.577 -> 0.591 | Helped |
| Use SPAC instead of MEIM | Tensor decomposition models · YAGO3-10 | Hits@10: 0.716 -> 0.720 | Helped |
| Add the intermediate-output gating mechanism (ablation) | SPAC · FB15k-237 | Hits@1 | Helped |
| Add adaptive pruning during training (ablation) | SPAC · FB15k-237 | Hits@1 | Helped |
| Add auxiliary cores to the main cores (ablation) | SPAC · FB15k-237 | Hits@1 | Helped |
| Use sparse auxiliary interactions alongside dense main-core interactions (ablation) | SPAC · FB15k-237 and WN18RR | Hits@1 | Mixed |
| Add gating to DistMult, ComplEx, Tucker, and MEIM | DistMult, ComplEx, Tucker, and MEIM · FB15k-237 and WN18RR | Hits@1 | Helped |
| Apply the pruning strategy | Tucker and MEIM · FB15k-237 | Hits@1 | No clear effect |
Surprising findings
- Dense-rate tau of 0.8 or 0.9 sometimes outperforms tau = 1.0 (fully dense main cores), suggesting sparse auxiliary interactions help.
Limitations
- Gains over the strongest baselines (MEIM, ComplEx-DURA) are small, often under 1 point.
- Adaptive pruning adds hyperparameters (alpha, c_min, buffer size N, update period T) whose sensitivity is not thoroughly studied.
Experimental setup
Datasets: FB15k-237 WN18RR YAGO3-10
Benchmarks: FB15k-237 WN18RR YAGO3-10
Metrics: Hits@1 Hits@3 Hits@10 MRR
Baselines: TransE DistMult ComplEx-DURA ComplEx-N3 TuckER MEIM MEI NePTuNe RotatE ConvE CompGCN KG-BERT
Builds on: Tucker decomposition MEIM DistMult ComplEx NePTuNe
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