The authors of this paper aim to generalize knowledge state as well as describe knowledge interaction. In order to do so, they project knowledge states and skill vectors into the same vector space. Since knowledge state and skill vectors lie into the same vector space, the dot product between knowledge state vector (at time t) and skill vector (at time t+1) is taken in order to output the probability of correctness.

They limit the skill vectors to be positive orthant and have unit-length to make learning one skill independent from learning another and make logit only dependent on the direction of the related skill vector.