Scoring functions are cores

Every model in this family scores a triple as a multilinear form in three embeddings, e_s, w_r and e_o. The core decides which coordinates may meet.

• DistMult — superdiagonal core, one entity table (“tied”): φ = Σₖ e_s,k · w_r,k · e_o,k, unchanged when s and o swap.
• CP, untied — separate subject and object tables: asymmetric.
• ComplEx — superdiagonal over complex embeddings; the complex conjugate on the object breaks the symmetry.
• RESCAL — a full matrix M_r per relation: Tucker-2.
• TuckER — a dense core shared by every relation. At d_e = d_r = 200 it holds 8,000,000 numbers, paid once for the whole graph.

TuckER’s paper shows RESCAL, DistMult, ComplEx and SimplE are all special cases of TuckER. The modelling choice is which constraint to pay for.