Here we use two different ways to perform the comparison, depending on whether the entailment vectors are learned using the standard neural network model or the set-theoretic model.
if the standard neural network model is used to learn the entailment vectors, we simply concatenate all the vectors to perform comparison as follows: if the entailment vectors are learned using the set-theoretic model, because of the special properties of the entailment vectors as explained in Section 2.1, we perform comparison as follows: where ⊙ is element-wise multiplication of two vectors.