For learner $i$ at time step $t$ , we denote the combination of the question that they answered, the concept this question covers, and their graded response as a tuple, ($q_t^i, c_t^i, r_t^i$), where $q_t^i \in N^+$ is the question index, $c_t^i \in N^+$ is the concept index, and $r_t^i$ ∈ {0, 1} is the response.

Given a learner's past history up to time $t − 1$ as $\{(q_1, c_1, r_1), . . . , (q_{t−1}, c_{t−1}, r_{t−1})\}$, the paper aims to predict their response $r_t$ to question $q_t$ on concept $c_t$ at the current time step, $t$.

The paper uses real-valued embedding vectors $x_t ∈ R^D$ and $y_t ∈ R^D$ to represent each question and each question-response pair $(q_t , r_t )$, respectively. $x_t$ characterizes information about questions, and $y_t$ characterizes the knowledge learners acquire by responding to questions, with two separate embeddings for correct and incorrect responses, respectively.