# SFBKT: A Synthetically Forgetting Behavior Method for Knowledge Tracing
## 1 Introduction  
Smart learning and education are new concepts of technology-enhanced learning [1]. In the past three decades, as intelligent education has continued to advance, numerous online education platforms have emerged as a supplement to the limitations of traditional education methodologies [2]. Online education emphasizes the importance of customized instruction that accommodates the unique abilities of individual students and recommends appropriate learning resources based on their knowledge levels. A student's knowledge level is shaped by their learning stage and cognitive capacity and constantly evolves throughout the learning process. Consequently, real-time monitoring of students' knowledge levels is indispensable for personalized online education [3]. To gain insight into students' knowledge proficiency and provide individualized guidance, knowledge tracing (KT) has garnered considerable attention from researchers. Knowledge tracing can generate models of students' knowledge states based on their past practice, analyze their interactions with online learning materials, identify patterns in their knowledge progression, and predict their future learning outcomes [4]. Specifically, knowledge tracing encompasses two primary objectives: modeling students' knowledge status and predicting their future performance. The precision of knowledge tracing is directly correlated with the relevance and efficacy of the system's provided content [5]. In contrast, a user study has shown that presenting content and questions that are excessively challenging or easy for students diminishes their engagement [6]. Therefore, it is essential to create accurate models of students' knowledge to increase their learning efficiency and satisfaction with the online education system. The notion of knowledge tracing was initially introduced by [PERSON] et al. in a technical report in 1986 to facilitate cognitive modeling and intelligent tutoring [7]. Subsequently, a variety of approaches have been devised to tackle the knowledge-tracing challenge. Initially, researchers employed Bayesian inference methods [8; 9], which often involved simplifying model assumptions (e.g., assuming only one skill) to render posterior computation more feasible. Subsequently, with the advent of classical machine learning methods, parametric factor analysis methods emerged as the dominant approach to knowledge tracing. Various factors, including those related to students, study materials, and the environment, are modeled by these methods to track students' knowledge status and make answer predictions [10; 11; 12]. Moreover, psychological research on students' learning and forgetting behavior has provided new insights into modeling students' knowledge state [13; 14]. These studies suggest that forgetting is a critical factor that affects a student's knowledge state over time. Deep learning techniques have made significant breakthroughs in recent years and have been applied extensively in various fields [15], leading to the rapid emergence of deep learning knowledge tracing models. [PERSON] et al. were the pioneers in this research direction and demonstrated the superior performance of deep learning techniques for knowledge tracing [16]. Over time, numerous knowledge tracing methods have incorporated diverse neural network architectures to enhance their efficacy by considering the unique features of the learning sequence. For instance, graph-based knowledge tracing approaches have utilized graph neural networks to model the knowledge structure in knowledge concept (KC) [17]. Attention-based knowledge tracing techniques have integrated the attention mechanism to capture dependencies among learning interactions [18]. In addition, CKT has incorporated convolutional neural networks (CNNs) to analyze the personalized phased learning patterns of students and predict their learning outcomes [19]. In real-world scenarios, forgetting is an inevitable consequence of learning [20].