To avoid adding another inner loop to our algorithm, we turn to a simple but fast approximation method based on the following single-matrix cost.
for each relation r, we consider the induced cost L H r,i where only a single projection matrix i is used for the head entity: is the corresponding energy function, and the subscript in P r and N r denotes the subsets with relation r. Intuitively, L H r,i measures, given the current tail attention vector α α α T r , if only one project matrix could be chosen for the head entity, how implausible D i would be.