# SFBKT: A Synthetically Forgetting Behavior Method for Knowledge Tracing
## 2 Related Work and Motivation  
Research on knowledge tracing can be broadly classified into two phases: the development of KT models based on traditional research methods and the development of KT models based on deep learning. Traditionally, Bayesian knowledge tracing and factor analysis models have been the two primary areas of research in KT. However, in recent years, KT based on deep learning has incorporated various advanced techniques to improve its performance. Table 1 presents an overview of the principal knowledge tracing models that have been developed in the KT literature. Bayesian knowledge tracing is based on the principles of mastery learning, which assumes that students can attain mastery of a skill through practice if two conditions are met: (a) knowledge is represented as a hierarchical structure of skills, and (b) the learning experiences are structured such that students can master lower-level skills before progressing to higher-level ones [2]. The BKT approach usually employs probabilistic graphical models, such as Hidden Markov Models [8] and Bayesian Belief Network [9], to monitor how students' knowledge states evolve while they practice various skills. The BKT model posits a uniform level of prior knowledge and learning rate for all students with regard to any skill, failing to personalize model parameters for individual students. Consequently, the model may provide inaccurate estimates of learning performance, with such estimates tending to skew toward the mean. Subsequent studies have primarily focused on enhance \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Method** & **Deep Learning** \\ \hline BKT & Bayesian Knowledge Tracing & \(\times\) \\ \hline IRT & & \\ AFM & Factor Analysis Models & \(\times\) \\ PFA & & \\ KTM & & \\ \hline DKT & Sequence Modeling KT Models & \(\surd\) \\ \hline EERNN & Text-Aware KT Models & \(\surd\) \\ \hline SAKT & & \\ AKT & Attentive KT Models & \(\surd\) \\ SSAKT & & \\ RKT & & \\ \hline GKT & & \\ GIKT & Graph-Based KT Models & \(\surd\) \\ SKT & & \\ \hline DKT + Forgetting & & \\ KPT & & \\ HawkesKT & & \\ DGMN & & \\ \hline DKVMN & Memory-Augmented KT Models & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: An overview of knowledge tracing models. ing the BKT model from two key perspectives: incorporating individualized parameters for each student and modeling the interplay between various skills. [PERSON] theorem is a fundamental tool in these models that describes the relationship between two events, A and B, as follows:  
\[\text{p}(\text{A}|\text{B})=\frac{\text{p}(\text{B}|\text{A})\text{p}(\text{A}) }{\text{p}(\text{B})} \tag{1}\]  
Factor analysis models in education are based on Item Response Theory (IRT) [27], which has made significant contributions to educational measurement. IRT typically constructs a function that estimates the performance of students based on the various factors involved in their learning processes. Although the original IRT was only capable of modeling single-skill problems, subsequent research has enabled it to model problems involving multiple skills. In such cases, the relationship between skills and items is commonly expressed using a \(Q\)-matrix, where each entry \(q_{jk}\) is set to 1 if item \(j\) involves skill \(k\) and 0 otherwise. The \(Q\)-matrix is often used as an additional source of information in these models. Psychometric models can be well understood from a psychological perspective, but their ability to encode complex features is limited by simplistic parameter settings. Deep Knowledge Tracing (DKT) is an innovative knowledge tracing model that utilizes deep learning to predict learning performance. To overcome the limitations of DKT, a range of knowledge tracing models have been developed using it as a foundation. For instance, the Extended-DKT model represents an improvement over the original DKT model by incorporating both student and exercise features.