## 1 Introduction  
Knowledge tracing (KT) is an innovative technique that has revolutionized the field of educational technology [1, 2]. By leveraging data from learners' interactions with educational materials, knowledge tracing algorithms can accurately measure and predict their knowledge and skills over time. This approach enables educators and educational platforms to provide personalized and adaptive learning experiences for students, where the instruction is tailored to their individual needs and abilities. Through the analysis of patterns in learner responses, knowledge tracing algorithms can determine their current knowledge state, identify areas of strength and weakness, and make targeted recommendations for instruction. This personalized approach to learning not only enhances engagement and motivation but also leads to improved academic performance [3, 4, 5, 6]. Inspired by the success of deep learning, recent studies on knowledge tracing have applied deep learning techniques. Deep knowledge tracing (DKT) [7] leverages recurrent neural networks (RNNs) [8] or long short-term memory neural networks (LSTMs) [9] to capture the temporal dependencies in learners' interactions. It takes into account the sequence of learners' responses along with additional factors such as the time spent on each task to predict their future performance accurately, and it has also demonstrated great potential for solving the knowledge tracing problem. Several studies [10, 11, 12, 13, 14] have been conducted on transformer architecture, and researchers have explored the incorporation of attention mechanisms into knowledge tracing models. These approaches address a drawback of the DKT model, which treats all questions within a sequence as equally important. While the specific attention mechanisms may differ, they share a common goal: to learn the attention weights for questions within a sequence of interactions. By doing so, these models aim to capture the relative importance of each question in predicting the likelihood of correctly answering the next question. To better capture the dynamics of student knowledge and address the challenge of data sparsity in knowledge tracing tasks, existing transformer approaches essentially integrate two models based on prior knowledge: temporal decay attention and Rasch-model-based embedding. Temporal decay attention: Psychological studies have shown that the consideration of forgetting is crucial for accurately estimating a student's knowledge state. This is because a student's mastery of knowledge tends to decline exponentially over time since their last practice with related questions [15]. Therefore, the standard attention function in a transformer is replaced by an attention function with a fixed-range temporal decay model [13; 16]. Rasch-model-based embedding: In knowledge tracing tasks, the number of questions is often much larger than the number of knowledge concepts. To avoid data sparsity, and instead of directly embedding each question, an embedding representation that considers a parameter controlling the deviation of a question from the knowledge concept it involves is proposed by following the Rasch model [13; 17; 18]. Although the two models mentioned above can accurately characterize certain features of the learning process, we argue that there is still room for improvement in both of these models. First, because learners have different forgetting rates for various knowledge concepts, a fixed-range temporal decay attention model may not adequately accommodate these differences. Second, the Rasch model fixes the variation in the questions as a linear combination of two embedding vectors related to the knowledge concept covering them. Although it reduces the number of parameters, it also weakens the representative power of the model. Therefore, we propose an enhanced deep knowledge tracing model that operates via multiband attention and quantized question embedding.