The proposed embedding form can be seen as a generalization over the input-label embeddings with a bilinear form, because its degenerate form is equivalent to the bilinear form of Equation (5).
this can be simply derived if we set one of the two nonlinear projection functions in the second line of Equation (9) to be the identity function (e.g., g out (•) = I), set all biases to zero, and make the σ(.)