# Canonical Tensor Decomposition for Knowledge Base Completion

The problem of Knowledge Base Completion can be framed as a 3rd-order binary tensor completion problem. In this light, the Canonical Tensor Decomposition (CP) (Hitchcock, 1927) seems like a natural solution; however, current implementations of CP on standard Knowledge Base Completion benchmarks are lagging behind their competitors. In this work, we attempt to understand the limits of CP for knowledge base completion. First, we motivate and test a novel regularizer, based on tensor nuclear $p$-norms. Then, we present a reformulation of the problem that makes it invariant to arbitrary choices in the inclusion of predicates or their reciprocals in the dataset. These two methods combined allow us to beat the current state of the art on several datasets with a CP decomposition, and obtain even better results using the more advanced ComplEx model.

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## Results from the Paper Edit

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Link Prediction FB15k ComplEx-N3 (reciprocal) MRR 0.86 # 2
Hits@10 0.91 # 3
Link Prediction WN18 ComplEx-N3 (reciprocal) MRR 0.95 # 8
Hits@10 0.96 # 5
Link Prediction WN18RR ComplEx-N3 (reciprocal) MRR 0.48 # 29
Hits@10 0.57 # 27
Link Prediction YAGO3-10 ComplEx-N3 (reciprocal) MRR 0.58 # 1
Hits@10 0.71 # 4