A two-state co-evolutionary method for predicting students' future performance in knowledge tracing process

Abstract

The present invention discloses a two-state co-evolution prediction method for student performance in a knowledge tracking process, which is characterized in that a dynamic routing method is used to extract knowledge commonality from original knowledge points, and simultaneously update and maintain the knowledge state at the knowledge point level and the knowledge state at the knowledge commonality level, and predict the student's future learning performance. The method introduces important correlation information between exercises and knowledge points, and uses the criterion of maximizing mutual information to learn the representation of all exercises and knowledge points. The learned representation can provide richer information for the representation of exercises and knowledge points. Compared with the prior art, the present invention takes into account the characteristics of the knowledge points themselves that students are exposed to and the correlation between the knowledge points, solves the problem of single representation of knowledge states, and can help teachers track students' knowledge mastery in an instant and convenient manner, thereby adjusting teaching plans and teaching content, thereby improving teaching quality.

Description

Technical Field

[0001] The present invention relates to the field of human intelligence education and data mining technology, and in particular to a method for tracking changes in students' knowledge states during their learning process and predicting their future performance through dual-state co-evolution. Background Art

[0002] Online education has gradually become popular in recent years and has achieved great development. Knowledge tracking plays an extremely important role in online education. It aims to instantly grasp the changes in students' knowledge status so that the education system can use this information to provide students with more personalized learning plans. Specifically, knowledge tracking analyzes a large number of students' historical question sequences, models students' learning status, and predicts students' future answering performance, thereby reflecting students' current learning level.

[0003] Previously, there have been quite a lot of works on the technology of knowledge tracking, and good results have been achieved. A large number of works use various methods to characterize the learning status of students. For example, Bayesian Knowledge Tracking (BKT) uses a binary variable to indicate whether the student has mastered a certain knowledge point, or Deep Knowledge Tracking (DKT) uses a recurrent neural network (RNN) to model the student's learning process from the student's historical answer records, and uses the hidden state in the RNN to characterize the student's state. Many subsequent works also use a framework similar to the DKT model. Generally speaking, it is necessary to track the student's state for individual knowledge points in a differentiated manner, which can provide stronger interpretability for our knowledge tracking process, and at the same time, it allows us to make full use of the correlation information between exercises and knowledge points. In summary, although there have been a lot of explorations in the knowledge tracking task, there is still a need to explore more effectively in expressing the student's knowledge state.

[0004] The problem with the existing technology is that a single hidden state cannot specifically monitor students' mastery of a specific knowledge point; on the other hand, modeling the knowledge state for a specific knowledge point alone tends to ignore the correlation between knowledge points. Due to the sparse nature of the question sequence data, a specific knowledge point may not be practiced by students for a long time, and the results of the questions related to the knowledge point cannot affect the state of the knowledge point, making the final prediction effect of the algorithm worse. Although some work has improved this problem by constructing a knowledge point association graph, it has not achieved a very significant effect due to the lack of explicit relationships between knowledge points. Summary of the invention

[0005] The content of the present invention is to provide a two-state co-evolution method for predicting students' future performance in the knowledge tracking process in response to the deficiencies of the existing technology. The method adopts a dynamic routing method to extract knowledge commonalities from the original knowledge points, and simultaneously updates and maintains the knowledge state at the knowledge point level and the knowledge state at the knowledge commonality level, so as to predict students' future learning performance. The representation of all exercises and knowledge points is learned using the criterion of maximizing mutual information. The learned representation can provide richer information for the representation of exercises and knowledge points, so as to introduce important correlation information between exercises and knowledge points, and help improve the effect of the entire algorithm. It not only takes into account the characteristics of the knowledge points themselves that students are exposed to and the correlation between knowledge points, but also better solves the problem of single representation of knowledge states. It provides a new knowledge state representation and evolution method for online education to improve the performance of knowledge tracking models in student performance prediction, and can help teachers track students' knowledge mastery instantly and conveniently, so as to adjust teaching plans and teaching content, thereby improving teaching quality.

[0006] The purpose of the present invention is achieved as follows: a method for predicting students' future performance by dual-state co-evolution for knowledge tracking process, which is characterized in that the method includes a pre-training module for representing exercises and knowledge points, a knowledge commonality extraction, and a set of modules for updating knowledge states and using states to predict students' performance. The method uses a dynamic routing method to extract knowledge commonalities from original knowledge points, and simultaneously updates and maintains knowledge states at the knowledge point level and knowledge states at the knowledge commonality level, so as to predict students' future learning performance, and specifically includes the following steps:

[0007] Step a: First, assume that in the knowledge tracking task there is an exercise set ε containing M exercises and a knowledge point set containing N knowledge points. And an exercise-knowledge point association matrix Q. If exercise i contains knowledge point j, then Q ij =1.

[0008] Step b: Use a pre-training method based on the mutual information maximization criterion to obtain feature representations that introduce information about the association between exercises and knowledge points. In this process, based on the inclusion relationship between exercises and knowledge points, positive and negative examples of knowledge points for specific exercises are obtained, and then effective feature representations are learned by optimizing the InfoNCE loss calculated from their representations.

[0009] Step c: Next, extract the knowledge commonality representation from the pre-trained knowledge point feature representation. The present invention uses multiple vectors to represent the knowledge commonality, which is used to model the student knowledge state at the knowledge commonality level. In order to obtain these knowledge commonality vectors, a knowledge commonality extractor is designed, which uses the dynamic routing method in the capsule network, which can be regarded as a special clustering method, and finally uses the clustering result as the knowledge commonality. This process is carried out in an iterative form, and the specific implementation process is as follows:

[0010] c-1: First, use the preset mapping matrix W j Each knowledge point c i Mapped to the contribution factor u to the jth knowledge commonality i|j ;

[0011] c-2: At the rth iteration, calculate the weighted sum of all contribution factors to obtain the candidate knowledge commonality vector Then divide it by its own modulus for normalization to obtain the commonality vector of this iteration

[0012] c-3: Weights of weighted calculation Dynamically updated at the end of each iteration for the next iteration. At the beginning of the first iteration, all weights are initialized to the same value, and then in each iteration, the weights accumulate the current knowledge commonality vector and the contribution factor u of knowledge commonality i|j The degree of consistency (calculated as );

[0013] c-4: After multiple iterations, the knowledge commonality extractor can obtain multiple knowledge commonality vectors v j , stack them up to form the knowledge commonality matrix V.

[0014] Step d: After obtaining the knowledge commonality matrix, the evolution tracking module of the student's knowledge status is carried out. The whole module is divided into two parts: using the current student's knowledge status to predict the student's next performance, and updating the student's knowledge status (knowledge point level and knowledge commonality level) according to the student's current performance. The specific steps are as follows:

[0015] d-1: Initialize the knowledge point state matrix H t and knowledge commonality state matrix G t ;

[0016] d-2: Prediction part: At the current time step t, assuming that the question the student has to do is e t , first use e t The feature representation Calculate the weight coefficient with the knowledge commonality matrix V (indicates the correlation between the question and the i-th knowledge commonality), using this coefficient and G t Perform weighted sum calculation to obtain the knowledge commonality state r relative to the question t At the same time, suppose that the knowledge point c contained in the question is in H t The corresponding part is The combination of the two is sent into a single-layer neural network to obtain the student’s prediction y for the current question performance. t ;

[0017] d-3: State update part: At the current time step t, assuming that the student's answer is x t =(e t , r t ), where r t Indicates the correctness of the result. For the knowledge point state matrix H t , using a gated recurrent unit (GRU) to update. For the knowledge commonality state matrix G t , we need to discard invalid information in the historical state and introduce the latest information, so we calculate an erasure vector z t and increase vector a t , then combine the previously calculated weight coefficient For G t The corresponding parts will be updated.

[0018] Step e: Execute the above prediction and update parts at each time step, and finally calculate the loss function based on the predicted results and the actual results. By minimizing the loss function, update the parameters in the entire method and complete the entire method.

[0019] Compared with the prior art, the present invention has the significant feature of improving the prediction effect. It takes into account the characteristics of the knowledge points themselves that students are exposed to and the correlation between the knowledge points. It will not ignore the correlation between the knowledge points, enhances the explicit relationship between the knowledge points, and better solves the problem of single representation of knowledge state. It provides a new knowledge state representation and evolution method for online education to improve the performance of knowledge tracking models in predicting student performance. It can help teachers track students' knowledge mastery instantly and conveniently, so as to adjust teaching plans and teaching content, thereby improving teaching quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A diagram for visual representation of the knowledge tracing task;

[0021] Figure 2 It is the relationship diagram between exercises and knowledge points;

[0022] Figure 3This is the extraction diagram of the knowledge commonality extraction module;

[0023] Figure 4 Schematic diagram of the prediction and state update of the two-state evolution module. DETAILED DESCRIPTION

[0024] The present invention includes a pre-training module for representing exercises and knowledge points, a knowledge commonality extraction module, and a two-state evolution tracking module to update the knowledge state and use the state to predict student performance. The method improves the performance of the knowledge tracking model in predicting student performance by designing a new knowledge state representation and evolution method. This new method can introduce important correlation information between exercises and knowledge points, extract knowledge commonalities from the original knowledge points using a dynamic routing method, and simultaneously update and maintain the knowledge state at the knowledge point level and the knowledge state at the knowledge commonality level, thereby predicting students' future learning performance. In addition, in order to introduce important correlation information between exercises and knowledge points, the method uses the criterion of maximizing mutual information to learn the representations of all exercises and knowledge points. The learned representations can provide richer information for the representation of exercises and knowledge points, helping to improve the effectiveness of the entire algorithm.

[0025] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0026] 1. Pre-training module for exercises and knowledge point representation

[0027] See also Figure 1 , based on the representation pre-training of maximizing mutual information, for each exercise, the knowledge points it contains provide more information about the exercise. At the same time, for a knowledge point, all exercises associated with it can summarize the characteristics of this knowledge point. Therefore, the present invention strengthens the representation of exercises and knowledge points by modeling the relationship between exercises and knowledge points.

[0028] See also Figure 2 , e in the figure 1 、e 2 、e 3 and e 4 Node representation exercises, c 1 、c 2 、c 3 and c 4 Nodes represent knowledge points. There is a many-to-many relationship between exercises and knowledge points. Shaded arrows indicate that the corresponding exercises and knowledge points will appear as positive examples in the representation pre-training task, and hollow arrows indicate that they will appear as negative examples. Given an exercise i, the set of knowledge points it contains is C i ={j|Q ij =1}, let e i represents the embedding of exercise i, c jRepresents the embedding of knowledge point j. Maximize exercises and knowledge

[0029] The mutual information represented by the point can be converted into the minimization loss function of the following formula (1):

[0030]

[0031] Where: c k represents the feature representation of any knowledge point in the knowledge point set; f is set in the present invention to be the dot product with a sigmoid activation function expressed by the following formula (2):

[0032] f(e i , c j )=σ(e i ·c j ) (2);

[0033] The loss function of the above single exercise can be easily extended to the entire exercise set ε. By minimizing the loss, the feature representation of exercises and knowledge points can be learned.

[0034] 2. Knowledge Commonality Extraction Module

[0035] The present invention assumes that there are certain knowledge commonalities between different knowledge points, and uses multiple vectors to represent these knowledge commonalities. In order to obtain these knowledge commonality vectors, the knowledge point representations are specially clustered with the help of the dynamic routing method in the capsule network.

[0036] See also Figure 3 ,The basic process of special clustering of knowledge point representations using the dynamic routing method in capsule networks is as follows:

[0037] 1) Given the original knowledge point embedding c i , calculate the mapping of each knowledge point on the knowledge commonality according to the following formula (3):

[0038] u i|j =W j c i (3);

[0039] Where: W j is the mapping matrix, which transforms the knowledge point c i Converted to the contribution factor u of the j-th knowledge commonality i|j .

[0040] 2) In the rth iteration, the candidate knowledge commonality vector The weighted sum of all knowledge points after mapping is calculated by the following formula (4):

[0041]

[0042] 3) Divide the candidate knowledge commonality vector by its own modulus After normalization, the result of this iteration is obtained as shown in the following formula (5):

[0043]

[0044] in, is the coupling coefficient and is calculated by the following formula (6):

[0045]

[0046] It is initialized to 0 before the first round of iteration, and the current knowledge commonality vector is accumulated after each round of iteration. and the contribution factor u of knowledge commonality i|j The consistency score is calculated by the following formula (7):

[0047]

[0048] 4) After multiple rounds of iterations, the final v j Stacked into the knowledge commonality matrix V.

[0049] 3. Two-state evolution tracking module

[0050] See also Figure 4 At time t, it is assumed that students have two knowledge states, namely, the knowledge state H specific to a knowledge point and t , and the state of knowledge commonality G t The update process of the two parts of the state is as follows Figure 4 Shown in the lower part.

[0051] a) Student performance prediction part

[0052] This part will predict the results of the questions that students are going to practice. The process is as follows Figure 4 The input exercise feature is represented by e t The dot product operation will be performed with the knowledge commonality matrix to obtain the importance of the question on all knowledge commonality vectors, and a set of weight coefficients expressed by the following formula (8) will be obtained through a softmax unit:

[0053]

[0054] Where: V i represents the i-th row of the knowledge commonality matrix. Using this set of weights, we can t The common knowledge state related to the question is expressed by the following formula (9):

[0055]

[0056] Hypothesis Exercise e t Contains n knowledge points, then the student answers e t The probability of is expressed by the following equations (10) and (11):

[0057]

[0058]

[0059] in: Indicates H t The state corresponding to the knowledge point c; Represents vector concatenation operation; W p and W s is the weight matrix in the neural network; b p and b s is the bias term.

[0060] b) Status update part

[0061] At time step t, the student’s actual test result (e t , r t )’s feature representation x t It is expressed by the following formula (12):

[0062]

[0063] Among them: 1 = (1, 1, ..., 1), which means a vector of all 1s, and 0 is similar.

[0064] For the knowledge point state Ht, the gated recurrent unit (GRU) of the following formula (13) is used to update:

[0065]

[0066] For the common state, the module uses the write process to update it. In order to forget some historical information and introduce new information, the erase vector z t and increase vector a t Calculate using the following formulas (14) to (15):

[0067] z t =Sigmoid(W z x t +b z ) (14)

[0068] a t =5ogmoid(W a x t +b a ) (15)

[0069] Where: W z and W a is the weight matrix; b z and b a is the bias term.

[0070] The new common state matrix G t+1 It is calculated by the following formulas (16) to (17):

[0071]

[0072]

[0073] 3. Training Phase

[0074] Based on the predicted probability of the student answering the exercise correctly at the current time step, all trainable parameters will be updated by minimizing the binary cross entropy function as follows (18):

[0075]

[0076] Compared with the knowledge tracking method represented by a single knowledge state, the present invention has greatly improved the prediction of student performance, and the experimental results on multiple public data sets have verified the superiority of the present invention. It can be applied to online teaching systems to help teachers track students' knowledge mastery in real time and conveniently, so as to adjust teaching plans and teaching content, thereby improving teaching quality.

[0077] The above is only a further explanation of the present invention and is not intended to limit this patent. Any equivalent implementation of the present invention should be included in the scope of the claims of this patent.

Claims

1. A two-state co-evolutionary method for predicting student performance in the knowledge tracking process. Features Using the dynamic routing method, we extract knowledge commonalities from the original knowledge points, update and maintain the knowledge state at the knowledge point level and the knowledge state at the knowledge commonality level, and predict the students' future learning performance. The specific steps include: Step a: Assume that in the knowledge tracking task there is an exercise set ε containing M exercises and a knowledge point set containing N knowledge points And an exercise-knowledge point association matrix Q, if exercise i contains knowledge point j, then Q ij =1; Step b: Use a pre-training method based on the mutual information maximization criterion to obtain the feature representation of the associated information between the introduced exercises and knowledge points; Step c: Extract knowledge commonality from the pre-trained knowledge point feature representation to obtain the knowledge commonality vector used for modeling the student knowledge state at the knowledge commonality level, i.e., the knowledge commonality matrix V; Step d: Use the knowledge commonality matrix V to establish an evolution tracking module for the student's knowledge state. This module includes: using the current student's knowledge state to predict the student's next performance, and updating the student's knowledge state according to the student's current performance; Step e: Execute the above prediction and update parts at each time step, and finally calculate the loss function based on the predicted results and actual results. By minimizing the loss function, update the parameters in the entire method to complete the prediction of the student's future learning performance; The extraction of knowledge commonality in step c adopts the method of dynamic routing in capsule network as the knowledge commonality extractor, and uses the result obtained by clustering as the knowledge commonality. The process is carried out in the following iterative form: c-1: Using the preset mapping matrix W j Each knowledge point c i Mapped to the contribution factor u to the jth knowledge commonality i|j ; c-2: At the rth iteration, calculate the weighted sum of all contribution factors to obtain the candidate knowledge commonality vector Then divide it by its own modulus to normalize it and get the commonality vector of this iteration c-3: Weight of weighted calculation Dynamically updated at the end of each iteration for the next iteration. At the beginning of the first iteration, all weights are initialized to the same value. Then, in each iteration, the weights are accumulated with the current knowledge commonality vector. and the contribution factor u of knowledge commonality i|j degree of consistency; c-4: After multiple iterations, the knowledge commonality extractor obtains multiple knowledge commonality vectors v j , stack them up to form the knowledge commonality matrix V; The specific steps of predicting the student's next performance based on the current student's knowledge status in step d and updating the student's knowledge status, i.e., the knowledge point level and the knowledge commonality level, according to the student's current performance are as follows: d-1: Initialize the knowledge point state matrix H t and knowledge commonality state matrix G t ; d-2: Prediction part: At the current time step t, assuming that the question the student has to do is e t , first use e t The feature representation Calculate the weight coefficient with the knowledge commonality matrix V Then use this coefficient and the knowledge commonality state matrix G t Perform weighted sum calculation to obtain the knowledge commonality state r relative to the question t ; At the same time, assuming that the knowledge point c contained in the question is in H t The corresponding part is The combination of the two is sent into a single-layer neural network to obtain the student’s prediction y for the current question performance. t ; d-3: State update part: At the current time step t, assuming that the student's answer is x t =(et,rt), where r t Indicates the correctness of the result. For the knowledge point state matrix H t , use a gated recurrent unit to update; for the knowledge commonality state matrix G t , discard the invalid information in the historical state, introduce the latest information, and calculate an erasure vector z t and increase vector a t , and then according to the calculated weight coefficient For G t The corresponding parts will be updated.

2. According to the two-state co-evolution method for predicting student performance in the knowledge tracking process of claim 1, Features The pre-training method based on the mutual information maximization criterion used in step b is used to obtain feature representations that introduce information related to exercises and knowledge points. This is based on the inclusion relationship between exercises and knowledge points, and positive and negative examples of knowledge points for specific exercises are obtained. Then, effective feature representations are learned by optimizing the InfoNCE loss calculated from their representations.

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