U ∈ R d×nu and R ∈ R d×nr are then used to construct a word-word similarity matrix M 1 ∈ R nu×nr and a sequence-sequence similarity matrix M 2 ∈ R nu×nr which are two input channels of a convolutional neural network (CNN).
the CNN distills important matching information from the matrices and encodes the information into a matching vector v. ∀i, j, the M 1 models the matching between u and r on a word level.