Canonical Tensor Decomposition for Knowledge Base Completion

TL;DR

This paper explores the use of Canonical Tensor Decomposition (CP) for knowledge base completion, introducing novel regularization and reformulation techniques that improve performance over existing methods and surpass state-of-the-art results.

Contribution

It presents a new regularizer based on tensor nuclear p-norms and a reformulation making CP invariant to dataset predicate choices, enhancing knowledge base completion performance.

Findings

CP with new regularizer outperforms previous tensor methods

Reformulation improves invariance and results

Achieves state-of-the-art on several datasets

Abstract

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.