Complex Embeddings for Simple Link Prediction

20 Jun 2016  ·  Théo Trouillon, Johannes Welbl, Sebastian Riedel, Éric Gaussier, Guillaume Bouchard ·

In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.

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Results from the Paper


Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Link Prediction FB122 ComplEx HITS@3 67.3 # 4
Hits@5 69.5 # 4
Hits@10 71.9 # 4
MRR 64.1 # 4
Link Prediction FB15k-237 ComplEx Hits@10 0.428 # 61
Link Property Prediction ogbl-biokg ComplEx Test MRR 0.8095 ± 0.0007 # 13
Validation MRR 0.8105 ± 0.0001 # 13
Number of params 187648000 # 6
Ext. data No # 1
Link Property Prediction ogbl-wikikg2 ComplEx (50dim) Validation MRR 0.3534 ± 0.0052 # 26
Test MRR 0.3804 ± 0.0022 # 26
Number of params 250113900 # 12
Ext. data No # 1
Link Property Prediction ogbl-wikikg2 ComplEx (250dim) Validation MRR 0.3759 ± 0.0016 # 25
Test MRR 0.4027 ± 0.0027 # 25
Number of params 1250569500 # 26
Ext. data No # 1
Link Prediction WN18 ComplEx MRR 0.941 # 20
Hits@10 0.947 # 26
Hits@3 0.936 # 20
Hits@1 0.936 # 16

Results from Other Papers


Task Dataset Model Metric Name Metric Value Rank Source Paper Compare
Link Prediction UMLS ComplEx Hits@10 0.967 # 9
MR 2.59 # 9
Link Prediction WN18RR ComplEx MRR 0.440 # 58
Hits@10 0.510 # 65
Hits@1 0.410 # 49

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