# Calibrated Q-Matrix-Enhanced Deep Knowledge Tracing with Relational Attention Mechanism
###### Abstract
The Q-matrix is proven to have implicit semantic information and is directly helpful in tracking students' knowledge proficiency. Figure 1: A depiction of the KT task for a student on mathematical exercises. The knowledge tracing process estimates the number of skills students mastered. A student can choose some exercises (e.g., e\({}_{1}\), e\({}_{2}\), e\({}_{3}\), e\({}_{4}\)) containing different knowledge points from problem sets for practicing and leave his/her response logs. Now, the student wants to answer the exercise e\({}_{1}\). In order to track the knowledge state evolution of students, a sequential modeling method called the deep knowledge tracing (DKT) model has been designed based on the idea of deep learning (e.g., [8]). The relation between KCs incorporated in the design of the DKT model has been proven to be significant. For example, the dynamic Bayesian network model is applied to model the pre-requisite relationship between KCs [9]. However, the relationship between these KCs is often treated as a priori inputs, which require a great deal of labor. Therefore, some models are created to automatically estimate the relationship between exercises. For example, Reference [10] utilized the question text of exercises to simulate the relationship of semantically comparable exercises. However, those knowledge tracing models do not take into consideration the time elapsed between exercises. Knowledge tracing's temporal variables were discussed in [11; 12]. Those techniques primarily focus on the time since the last interactions with the same KC or previous interactions. However, as mentioned, previous interactions and student behaviors are both engaged in the preceding interactions' different effects on the knowledge tracing task. These techniques do not consider previous interactions and student behaviors. The Q-matrix is used for the modeling of learning resources applied in many models (e.g., [5; 13]). The Q-matrix is designed as a binary matrix, which only reflects the relationship between knowledge points and exercises. However, the binary Q-matrix ignores the relationship between knowledge points, such as the hierarchical levels of knowledge points. For example, in the knowledge graph, the rational number is the parent node of the fraction. However, when marking the Q-matrix, those two knowledge points are simply marked as \"1\" when an exercise contains both knowledge points: the rational number and the fraction. In this paper, a novel relational attention knowledge tracing (RAKT) model and its extension model, the calibrated Q-matrix relational attention knowledge tracing model (QRAKT), are proposed. In the RAKT model, two types of self-attention mechanisms are applied for the KT task, the positional attention layer and the relational attention layer. Specifically, the positional attention layer is used to replace traditional absolute position encoding in the attention mechanism with a positional attention layer. The outputs of the positional attention layer are used as the inputs of the relational attention layer. The relational attention layer incorporates text information with relation modeling, including relation modeling exercises, forgetting behavior modeling, and student behavior modeling. These two types of attention mechanisms retain the adaptability and clarity of the traditional attention mechanism; see the works of [14]. When considering the student behaviors and the guessing factor and slipping factor, the RAKT model can more efficiently track the students' knowledge state. Therefore, the online educational system, which applies the RAKT model, can provide personalized exercises for students based on each student's behaviors. In the end, the extension of the RAKT model, QRAKT, was designed based on a calibrated Q-matrix, which not only indicates the relationship between exercises and KCs, but also presents the relationship between KCs in the same exercise.