# SFBKT: A Synthetically Forgetting Behavior Method for Knowledge Tracing
## 1 Introduction
According to the Ebbinghaus forgetting curve theory, students' knowledge proficiency can decline over time due to forgetting [21]. Thus, it is unreasonable to assume that a student's knowledge state will remain constant over time. Moreover, the incorporation of the forgetting factor into knowledge tracing has advanced with the development of deep learning techniques. To account for the intricate forgetting behavior, the DKT + forgetting model [22] integrates forgetting into deep knowledge tracing through the consideration of three types of side information associated with forgetting. Notably, the HawkesKT model proposes an explicit modeling of temporal cross-effects inspired by point processes, which takes into account the varying impacts of previous interactions [23]. HawkesKT is the pioneering model that incorporates the Hawkes process for the simulation of temporal cross-effects in knowledge tracing; this characteristic facilitates the more effective integration of students' forgetting behavior into the learning process. Additionally, AKT is an attention-based neural network model that utilizes distance-aware exponential decay with a global decay rate, which also integrates temporal information into the model to compute attention weights [24]. Over the past few years, there have been attempts to incorporate forgetting factors into knowledge tracing. However, the methods proposed so far have relied on either manually designed forgetting features or oversimplified process assumptions, such as fixed time intervals and global decay functions. According to temporal cross-effect theory [23] and temporal point process theory [25], every student's interaction with an exercise will significantly influence their knowledge states. Figure 1 illustrates how the impacts of different exercises on knowledge states can vary over time. Previous studies' methods have not been able to fully utilize forgotten information, resulting in a failure to capture dynamic changes in knowledge states. To address this problem, we propose a neural time series point process and a collaborative filtering-based forgetting behavior knowledge tracing model. Building on the ideas of DKT + forgetting [22], neural hawkes process [25], and collaborative filtering (CF) [26], our model considers several factors, including practice records before learning, lag time after learning, and the hidden forgetting factor in the group state. These factors are all essential to effectively capturing students' forgetting behaviorsand improving the accuracy of the model's forecasts. In particular, we modify the memory cells within the network based on the lag time after learning. This gradual alteration over time serves to mitigate the effects of mutations resulting from interactions. As a result, the training process of the model becomes more akin to the natural forgetting process of students, as opposed to abrupt and drastic changes. Specifically, we first extract three types of forgetting-related information from practice records, which are then combined with the records as joint input data. The forgetting information consists of repetition intervals, sequence intervals, and past practice times. The joint data are fed into the Continuous-Time LSTM network to generate a knowledge state that changes dynamically over time. Lastly, cosine similarity is employed to assess the similarity of the knowledge state, which is then combined with neighbor information for prediction. In summary, our main contributions are as follows:  
1. Our study proposes the Synthetically Forgetting Behavior Knowledge Tracing model, which aims to comprehensively model students' knowledge levels by incorporating pre-training forgetting information, post-training forgetting behavior, and a group forgetting state. This approach allows for a better prediction of students' performance in the next stage. 2. The Neural Hawkes Process is a seminal article in the field of time series point processes.