Knowledge Tracing Method and System Based on Dynamic Memory Key-Value Pair Network

Abstract

The present invention discloses a knowledge tracing method and system based on a dynamic memory key-value pair network. The method includes: obtaining exercise tags and corresponding exercise difficulties; constructing a knowledge tracing network model including an embedding layer, a key-value pair memory layer, a cognitive behavior layer, and an output layer; training the network model using the exercise difficulty and the exercise tags, and implementing knowledge tracing using the trained network model. The knowledge tracing method based on the dynamic memory key-value pair network proposed by the present invention constructs a knowledge tracing model by integrating cognitive behaviors. This model can trace the impacts brought by cognitive behaviors such as changes in users' knowledge point mastery levels, guesses, and mistakes, thereby predicting users' performances in answering exercises, clustering the exercises based on users' answering records, having good interpretability, being applicable to different types of users, and having a high accuracy rate.

Description

Technical Field

[0001] The present invention belongs to the technical field of knowledge tracing, and particularly relates to a knowledge tracing method and system based on a dynamic memory key-value pair network. Background Art

[0002] With the continuous development of science and technology, many online education platforms have emerged. Compared with offline education methods, online education platforms have the advantages of rich resources and being less restricted by factors such as learning locations and learning times, attracting the attention of a large number of users. Currently, more and more users are starting to use online education platforms for learning.

[0003] Intelligent tutoring is an important function of online education platforms. It collects and analyzes users' learning data and can provide corresponding learning guidance to users. An important implementation of intelligent tutoring is knowledge tracing. Knowledge tracing builds a learning model for users based on their answering history, tracks users' mastery levels of different knowledge points during the learning process. In addition, knowledge tracing can also predict users' next answering performance based on their learning history. The detection and tracking of these learning states are of great significance to users' learning guidance and are an indispensable part of improving users' learning efficiency.

[0004] Existing knowledge tracing methods mainly fall into two categories: traditional knowledge tracing methods and neural network-based knowledge tracing methods. Traditional knowledge tracing methods mainly use predefined formulas to model the learning process. For example, the IRT (Item Response Theory) model uses the formula to model the state of each knowledge point, where D is a constant 1.7, c is the guessing parameter, θ is the mastery level of the knowledge point, and a and b are the discrimination and difficulty of the exercise respectively. The DINA (Deterministic Input, Noisy and Gate) model adds a Q matrix to represent the relationship between each exercise and knowledge point when modeling.

[0005] Neural network-based knowledge tracing methods mainly use machine learning methods to model users' learning states. For example, Jiani Zhang et al. proposed the DKVMN (Dynamic Key-Value Memory Network) model based on MANN (Memory-Augmented Neural Networks). This model stores the relationships between knowledge points and the states of knowledge points through a key-value pair network and has achieved good results.

[0006] However, due to the relatively simple interaction function defined by traditional knowledge tracing models, it is difficult to finely model the learning process of users. Therefore, when predicting users' problem-solving performance, the accuracy is relatively low. At the same time, traditional knowledge tracing models do not take into account the differences between different users. Therefore, in the face of different types of users, this type of method cannot achieve personalized modeling. Existing neural network-based knowledge tracing models benefit from the high complexity of neural networks and can track the change process of users' knowledge points well in a big data environment. However, due to the black-box nature of neural networks, the models lack interpretability. Summary of the Invention

[0007] To solve the above problems existing in the prior art, the present invention provides a knowledge tracing method and system based on a dynamic memory key-value pair network. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0008] The present invention provides a knowledge tracing method and system based on a dynamic memory key-value pair network, and the method includes:

[0009] Obtain exercise tags and corresponding exercise difficulties;

[0010] Construct a knowledge tracing network model including an embedding layer, a key-value pair memory layer, a cognitive behavior layer, and an output layer;

[0011] Train the network model using the exercise difficulty and the exercise tags, and use the trained network model to achieve knowledge tracing;

[0012] Among them, the embedding layer performs dimensional embedding on the exercise tags and the exercise difficulty using an embedding matrix, and correspondingly obtains a tag vector and a difficulty vector;

[0013] The key-value pair memory layer calculates the associated vector of the implicit knowledge points of the current exercise from the key matrix based on the tag vector, and reads the learning state vector from the value matrix according to the associated vector; at the same time, after the user completes the current question, the true answer result of the user is used to update the value network;

[0014] The cognitive behavior layer predicts the cognitive process of the user during answering according to the learning state vector and the difficulty vector, and obtains a cognitive result;

[0015] The output layer predicts the user's answer result based on the cognitive result and the exercise difficulty.

[0016] Advantages of the present invention:

[0017] The knowledge tracing method based on the dynamic memory key-value pair network proposed by the present invention constructs a knowledge tracing model by integrating cognitive behaviors. This model can track the changes in the user's knowledge point mastery level and consider the impacts brought by cognitive behaviors such as guessing and mistakes, so as to predict the user's performance in answering exercises and cluster the exercises based on the user's answering records. It has good interpretability, is applicable to different types of users, and has a high accuracy rate. In addition, this model also has a better AUC performance compared with other knowledge tracing models.

[0018] The following will further elaborate on the present invention in conjunction with the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a schematic flowchart of a knowledge tracing method based on the dynamic memory key-value pair network provided by an embodiment of the present invention;

[0020] Figure 2 is a framework diagram of the knowledge tracing network model provided by an embodiment of the present invention;

[0021] Figure 3 shows the output results of the model in the scenario where the user has not learned the exercise tags at all;

[0022] Figure 4 shows the output results of the model in the scenario where the user is slowly learning and trying to master the exercise tags;

[0023] Figure 5 shows the output results of the model in the scenario where the user has completely mastered the exercise tags;

[0024] Figure 6 shows the output comparison results between this model and DKVMN;

[0025] Figure 7 shows the exercise tag clustering results using this model. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0026] The following further describes the present invention in detail in conjunction with specific embodiments, but the implementation manners of the present invention are not limited thereto.

[0027] Embodiment 1

[0028] Please refer to Figure 1 , Figure 1 which is a schematic flowchart of a knowledge tracing method based on the dynamic memory key-value pair network provided by an embodiment of the present invention, and it includes:

[0029] Step 1: Obtain exercise tags and the corresponding exercise difficulties.

[0030] Specifically, for a given exercise Q, its corresponding exercise label is represented as ct. For the exercise difficulty, this embodiment proposes a method for calculating the exercise difficulty based on the error rate of the exercise. The calculation formula is as follows:

[0031]

[0032] Among them, q t represents the exercise difficulty, Total t represents the total number of times this exercise appears, Total wrong (t) represents the number of times this exercise is done wrong. α is a correction coefficient used to handle the case where the error rate in the exercise is 1. In the subsequent calculation and experiment process, α = 0.8.

[0033] Step 2: Construct a network model including an embedding layer, a key-value pair memory layer, a cognitive behavior layer, and an output layer.

[0034] Please refer to Figure 2 , Figure 2 which is the framework diagram of the knowledge tracing network model provided by the embodiment of the present invention. This model consists of four layers in total: an embedding layer, a key-value pair memory layer, a cognitive behavior layer, and an output layer. The following combines the attached Figure 2 to introduce in detail the algorithm process of each layer of the knowledge tracing network model constructed in this embodiment.

[0035] I. Embedding layer

[0036] In this embodiment, the embedding layer is mainly used to embed the difficulty of the exercise and the corresponding label of the exercise, map it to a high dimension for representation, and obtain the label vector and the difficulty vector correspondingly.

[0037] Specifically, as Figure 2 shown, for the input exercise label c t ∈C (C represents the exercise set), the embedding matrix A completes the embedding. The matrix dimension of A is c×d k , where c is the number of exercise labels to which the exercise belongs. Therefore, the calculation process of the embedded vector m t is as follows:

[0038] m t = c t A

[0039] For the embedding of the exercise difficulty q t , it is obtained by multiplying the embedding matrix E and the one-hot encoded q t , that is:

[0040] q e = q t E

[0041] II. Key-Value Pair Memory Layer

[0042] Please continue to refer to Figure 2 where the key-value pair memory layer includes a static matrix M K and a dynamic matrix M v The sizes of the matrices are N×d k and N×d v respectively, where d k and d v are generally set by the user themselves, and d k = d v N represents the number of implicit knowledge points included in the exercise. These implicit knowledge points will be stored in matrix M k This matrix is also called the key matrix. The values of the key matrix will change during network training, but remain unchanged during the use of the model. The user's mastery level of each implicit knowledge point during the learning process is stored in matrix M v This matrix is also called the value matrix. This matrix will be dynamically updated during the user's learning process to reflect the changes in the user's learning state, that is, the dynamic changes of the implicit knowledge points corresponding to the exercise. In addition, this model also includes a cognitive behavior layer, which is used to model factors such as the guesses and mistakes made by the user during the process of doing questions and predict the answering results.

[0043] In this embodiment, the key-value pair memory layer includes two parts: an association part, a read part, and a write part. The association part is used to calculate the association vector of the implicit knowledge points of the current exercise from the key matrix. The read part is responsible for reading the learning state vector of the dynamic changes of the corresponding implicit knowledge points from the value matrix. The write part is used to update the value network using the user's real answering result after the user completes the current question, so as to reduce the influence caused by prediction errors and ensure that the state of each implicit knowledge point corresponds to the real result.

[0044] Specifically, in this embodiment, the process of the association part of the key-value pair memory layer is as follows:

[0045] Perform an operation on the label vector m t obtained from the embedding layer and the key matrix to obtain the association vector. The calculation formula is:

[0046]

[0047] where n t (i) represents the value of the i-th bit of the association vector n t It represents the information of the implicit knowledge points of the exercise and will play an important role in the subsequent read process and write process. M k (i) represents the elements included in the i-th row of the key matrix.

[0048] Softmax is a normalization exponential function, and its operation rule is as follows:

[0049]

[0050] In this embodiment, the process of the read part of the key-value pair memory layer is as follows:

[0051] After obtaining the n t That is, the associated matrix, the content of the read process can be obtained by multiplying and summing the associated matrix and the matrix slots of each value matrix.

[0052] Specifically, multiply each value of the associated vector n t by the row vector corresponding to the value matrix, and add the obtained vectors to obtain the learning state vector. The formula is expressed as follows:

[0053]

[0054] where, v i represents the learning state vector, N represents the number of rows of the value matrix, that is, the number of categories of implicit knowledge points included in the exercise, represents the elements included in the i-th row of each value matrix.

[0055] Through the read process, the state v i of the implicit knowledge points associated with the corresponding exercise can be obtained, which contains the user's mastery level information of this knowledge point.

[0056] For the description of the write part of the key-value pair memory layer, please refer to the following text.

[0057] III. Cognitive Behavior Layer

[0058] In this embodiment, the cognitive behavior layer includes a long short-term memory network and three fully connected layers. The long short-term memory network is used to enhance the model's processing ability for sequences, and the three fully connected layers are used to map the user's mastery level (L, Learning), guessing probability (G, Guessing), and mistake probability (S, Slipping) from the output results of the long short-term memory network. The specific process is as follows:

[0059] 1. Use a fully connected layer to connect the learning state vector and the difficulty vector to obtain a summary vector.

[0060] Specifically, in order to make full use of the information contained in the user's answer sequence, in this embodiment, the content v t read in the read process and the embedded exercise difficulty vector q e are connected, and the connected vector is used as the input and input into a fully connected layer to obtain the summary vector s t, this process is expressed by the formula as follows:

[0061]

[0062] Wherein, W1 and b1 are respectively the weight matrix and the bias vector of the fully connected layer.

[0063] 2. Process the summary vector by using a long short-term memory network.

[0064] Specifically, input the summary vector s t obtained above into the long short-term memory network for processing, and its expression is as follows:

[0065] g t = Sigmoid(W g [h t-1 , s t + b g )

[0066] i t = Sigmoid(W i [h t-1 , s t + b i )

[0067] o t = Sigmoid(W o [h t-1 , s t + b o )

[0068]

[0069]

[0070] h t = o t ⊙ Tanh(c t )

[0071] Wherein, W g , W i , W o , W c respectively represent the weight vectors of the corresponding neural networks, and b g , b i , b o , b c respectively represent the bias vectors of the corresponding neural networks. g t represents the output of the forget gate, i t represents the output of the update gate, o t represents the output of the output gate, h t represents the hidden state, ct represents the output of the cell gate, represents the output of the unupdated cell gate, and ⊙ represents matrix multiplication.

[0072] 3. Use three fully connected layers to map out the user's mastery level L, guessing probability G, and error probability S of knowledge points from the output results of the long short-term memory network respectively.

[0073] Specifically, after the calculation of the long short-term memory network, the output h t is used as the input of the three fully connected layers to calculate L, S, and G. The calculation formulas are as follows:

[0074]

[0075]

[0076]

[0077] Among them, L represents the mastery level of knowledge points, S represents the probability of answering a question wrong due to mistakes, G represents the probability of answering a question correctly due to guessing, W l , W s , W g represent the weight matrices of the fully connected layers respectively, and b l , b s , b g represent the bias vectors of the fully connected layers respectively.

[0078] IV. Output layer

[0079] In this embodiment, the output layer uses the results of the cognitive behavior layer as the input and combines the knowledge points of the current question to calculate the probability that the user answers the current question correctly.

[0080] Specifically, the output layer predicts the user's answer result according to the following formula based on the cognitive results L, G, S and the question difficulty:

[0081] P = L * (1 - R) * (1 - S) + (1 - L * (1 - R)) * G

[0082] Among them, P represents the probability that the user answers the question correctly, and R represents the question difficulty.

[0083] The knowledge tracing network model constructed in this embodiment for the difficulty q t of the given question Q t, the model obtains the knowledge points implied by the exercise and the mastery level of the implied knowledge points from the key-value pair network, and generates the mastery level, guess probability, and error probability of the user for the knowledge points implied by the current exercise through knowledge tracing. Finally, combined with the difficulty of the question, the probability of answering the exercise correctly is obtained.

[0084] It should be noted that after predicting the probability that the user correctly answers exercise q t , this model also needs to use the true answer result r t to update the value matrix to ensure that the mastery level of the current implied knowledge points changes with the true answer result, that is, the write process in the key-value pair memory layer. The following is a detailed introduction to this process.

[0085] 1. Use the embedding matrix B with dimension 2C×d v to map the user's true answer result y t and the exercise label c t . The expression is:

[0086] w t = [c t , y t T ·B

[0087] where w t represents the knowledge level change vector, and c represents the number of exercise labels.

[0088] 2. Process w t using the erasure gate and the enhancement gate to obtain the erasure vector f t and the enhancement vector a t respectively.

[0089] Since w t contains the knowledge level change information after the user answers the question, inspired by the input and forget gates in the long short-term memory network, this model also constructs an enhancement and erasure gate in the write process to simulate the change of the knowledge level during the process of the user trying to answer c t . Among them, the erasure gate is used to control the elimination of the corresponding information from the value matrix, that is, to reduce the mastery level of some knowledge points; the enhancement gate is used to control the enhancement of the corresponding information from the value matrix, that is, to improve the mastery level of some knowledge points. In the read process, before improving the mastery level of the knowledge points, this model first needs to reduce the mastery level of some knowledge points, that is, erase first before enhancing.

[0090] Specifically, given the w t vector, the calculation method of the erasure vector f t is:

[0091]

[0092] Among them, Sigmoid is the activation function, and its operation rule is:

[0093]

[0094] After the erasure process is completed, the enhanced vector a t The calculation formula is:

[0095]

[0096] W e and W a respectively represent the weight matrices of the corresponding fully connected layers, and b e and b a respectively represent the bias vectors of the corresponding fully connected layers; Tanh is the hyperbolic tangent function.

[0097] 3. Update the value matrix according to the erasure vector f t and the enhanced vector a t Update the value matrix.

[0098] First, after obtaining the erasure vector f t , update the value matrix according to the following update method:

[0099]

[0100] Then, the value matrix improves the mastery level of the corresponding implicit knowledge points through the enhanced vector a t , and its formula is:

[0101]

[0102] Thus, the update of the value matrix is completed.

[0103] The model constructed in this embodiment can generate a knowledge tracing model based on the user's answering history, predict the user's answering performance, cluster the exercise labels according to the exercise labels, and take into account the influence of cognitive behaviors such as the change of the user's knowledge point mastery level, guessing, and mistakes, and has good interpretability.

[0104] Step 3: Train the network model using the exercise difficulty and the exercise labels, and implement knowledge tracing using the trained network model.

[0105] Specifically, this embodiment constructs four loss functions loss l , loss s , loss g and loss p to form a total loss function to train the model.

[0106] For lossl The loss function, which represents the loss function corresponding to L. L depicts the user's mastery level of the corresponding implicit knowledge point during answering. To constrain the change of L, in this embodiment, the upper and lower bounds of the change level of L are set, then loss l The loss function can be expressed as:

[0107]

[0108] Where, ΔL t =|L t+1 -L t | represents the absolute value of the change in the mastery level of two knowledge points. L t+1 represents the mastery level of the knowledge point after the (t + 1)-th answer, and L t represents the mastery level of the knowledge point after the t-th answer, and τ lower and τ upper respectively represent the lower bound of the change amount of the knowledge point mastery level and the upper bound of the change amount of the knowledge point mastery level.

[0109] In this embodiment, τ lower can be taken as 0.2, and τ upper can be taken as 0.3.

[0110] This embodiment uses loss l to constrain the change in the mastery level of knowledge points during two adjacent answering processes of the user, making the change in the mastery level of knowledge points smoother.

[0111] For the loss function loss s which represents the loss function corresponding to S. S depicts the probability that the user answers wrongly due to mistakes when answering exercises, then loss s The definition of the loss function is as follows:

[0112]

[0113] Where, S t is the probability that the user answers wrongly due to mistakes at time t, len is the length of the user's current answering sequence, and λ s is the average value of the total average wrong-answer probability of this answering sequence. In this embodiment, λ s can be taken as 0.3.

[0114] For the loss function loss g which represents the loss function corresponding to G. G depicts the probability that the user answers correctly due to guessing when answering, then loss g The definition of the loss function is as follows:

[0115]

[0116] Among them, G t is the probability that the user answers correctly due to guessing at time t, len is the length of the user's answer sequence for this question, and λ g is the average value of the probability of answering correctly due to guessing for this answer sequence. In this embodiment, λ g can be taken as 0.3.

[0117] For the loss p function, in this embodiment, the loss p is used to characterize the accuracy ability of this model to predict the final answer result, and it is mainly calculated through cross-entropy, that is:

[0118]

[0119] Among them, p t represents the probability that the exercise is answered correctly predicted by this model at the t-th answer.

[0120] After obtaining the loss functions loss l , loss s , loss g and loss p , the calculation method of the final total loss function is as follows:

[0121] loss = loss p + loss l + loss s + loss g

[0122] In this embodiment, the above loss function is used to supervise the training process of the knowledge tracking network model, and the trained network model is used to implement knowledge tracking for different users.

[0123] The knowledge tracking method based on the dynamic memory key-value pair network proposed by the present invention constructs a knowledge tracking model by integrating cognitive behaviors. This model can track the impact of cognitive behaviors such as changes in the user's knowledge point mastery level, guessing, and mistakes, so as to predict the performance of the user answering exercises, cluster the exercises according to the user's answer records, has good interpretability, is applicable to different types of users, and has high accuracy; in addition, this model also has better AUC performance compared with other knowledge tracking models.

[0124] Embodiment 2

[0125] Based on the above Embodiment 1, this embodiment provides a knowledge tracking system based on a dynamic memory key-value pair network, including:

[0126] A data acquisition module for acquiring exercise tags and corresponding exercise difficulties;

[0127] A model construction module for constructing a knowledge tracing network model including an embedding layer, a key-value pair memory layer, a cognitive behavior layer, and an output layer;

[0128] A training module for training the network model using the exercise difficulty and the exercise tags, and realizing knowledge tracing using the trained network model;

[0129] Among them, the embedding layer performs dimensional embedding on the exercise tags and the exercise difficulty using an embedding matrix, and correspondingly obtains a tag vector and a difficulty vector;

[0130] The key-value pair memory layer calculates an association vector of the implicit knowledge points of the current exercise from a key matrix based on the tag vector, and reads a learning state vector from a value matrix according to the association vector; meanwhile, after the user completes the current question, the true answer result of the user is used to update the value network;

[0131] The cognitive behavior layer predicts the cognitive process when the user answers the question according to the learning state vector and the difficulty vector, and obtains a cognitive result;

[0132] The output layer predicts the user's answer result based on the cognitive result and the exercise difficulty.

[0133] The system provided in this embodiment is used to implement the method provided in the above-mentioned Embodiment 1. For the specific implementation process and the flow of each module in the system, refer to the above-mentioned Embodiment 1, and details are not described here.

[0134] Therefore, the system provided in this embodiment can also trace the influence of cognitive behaviors such as changes in the user's knowledge point mastery level, guessing, and mistakes, thereby predicting the user's performance in answering exercises, clustering the exercises based on the user's answer records, having good interpretability, being applicable to different types of users, and having high accuracy and good AUC performance.

[0135] Embodiment 3

[0136] Next, the knowledge tracing network model of the present invention is used to conduct tests on multiple data sets, and some other knowledge tracing methods are compared to elaborate in detail the beneficial effects such as interpretability and implicit knowledge point clustering in the model of the present invention.

[0137] 1. Experimental conditions:

[0138] In this experiment, three data sets containing user answer records for algebraic questions were used, namely Algebra Data Set 1, Algebra Data Set 2, and Algebra Data Set 3. Among them, the difficulty distribution of the exercises in each data set is shown in Table 1:

[0139] Table 1

[0140]

[0141] To compare the performance of this model with other models, four different knowledge tracing methods were selected as benchmarks in this experiment as the comparison methods. These four knowledge tracing methods are: BKT, DKT, DKT+, and DKVMN. Among them,

[0142] BKT: BKT is a knowledge tracing method based on Bayesian inference proposed by Corbett et al. in 1994.

[0143] DKT: DKT is a model proposed by Piech et al. that first uses neural network methods to perform knowledge tracing tasks.

[0144] DKT+: DKT+ is an improved DKT algorithm proposed by Yeung by adding a series of regularization terms to DKT. It reduces the fluctuations in the knowledge mastery level and makes the changes in the prediction results smoother.

[0145] DKVMN: DKVMN is a knowledge tracing method based on the Memory-Augmented Neural Network (MANN) proposed by Zhang et al.

[0146] In addition, during the model training process, 80% of the dataset was used as the training set and the other 20% as the test set in this embodiment. Adam was used as the optimizer during the training process. During the entire training process, set d k = d v .

[0147] 2. Experimental Contents and Result Analysis

[0148] I. Verification of Model AUC Performance:

[0149] The comparison results of the AUC of the model of the present invention and other models for different datasets are shown in Table 2:

[0150] Table 2

[0151]

[0152] As can be seen from Table 2, the AUC performance of this model on the three datasets is better than that of other benchmark models.

[0153] II. Verification of Model Interpretability

[0154] To illustrate the interpretability of this model, several problem-solving scenarios were selected in this experiment, and all the outputs of this model were tested, including the knowledge point mastery level (L), the error probability (S), the guessing probability (G), and the exercise difficulty (R). The results are as Figures 3 - 5 shown.

[0155] Figure 3 It shows the output changes when the user has not learned the exercise tags 19 and 14 at all. It can be seen that the knowledge point mastery level (L) decreases continuously with the user's multiple wrong answers; Figure 4 It shows the model output when the user is slowly learning and trying to master the exercise tag 66. It can be seen that when the user answers the tag 66 correctly, the value of L will increase, and conversely, L will decrease. It is worth noting that when answering wrongly three times in the figure, the value of S is higher than the normal value, which indicates that the possibility of the user making mistakes is higher at this time; Figure 5 It shows that the user has completely mastered the knowledge points implied by the exercise tags 59 and 60. At this time, due to the user's high mastery level of knowledge points, the probability of the user answering correctly by guessing alone has also increased accordingly. In addition, it can be seen that when the user answers the exercise tag 60 wrongly for the only time, the probability of S, that is, the error probability, is higher at this time, indicating that the user is very likely to answer wrongly due to mistakes.

[0156] In addition, to illustrate that this model has better interpretability than other knowledge tracing models, the output of this invention model was also compared with the output of the existing DKVMN in this experiment. The results are as Figure 6 shown.

[0157] Among them, for better display effect, at this time S = 0.5S, L = 0.5L, G = 0.5G, R = 0.5R, where P represents the probability of answering this question correctly. It can be seen that when attempting to answer the question tag 69 for the first time, this model shows a relatively high error probability, while DKVMN only gives the knowledge point mastery level and the probability of the question being answered correctly; at the same time, when attempting to answer the question tag 15 for the third time, since the user gave the correct answers in the previous two attempts to answer the question tag 15, this model gives a relatively high error probability in the third answer, indicating that the probability of the user answering wrongly due to mistakes is relatively high at this time. At the same time, at this time, the user's knowledge point mastery level L only decreases slightly, while DKVMN shows a large decrease, which is obviously not in line with the law in the real learning process. Therefore, compared with DKVMN, this model has better interpretability and better variation law of knowledge point mastery level.

[0158] III. Verification of Model Clustering Effect

[0159] Since the relationships of implicit knowledge points are stored in the key matrix of this model, where the dimension of the key matrix is N×dk , where N is the number of all implicit knowledge points, that is, N matrix slots. By finding the matrix slot with the largest value in each exercise label, the exercise label can be classified. In the following experiment, N = 10 is set, and the experimental results are shown in Figure 7.

[0160] From Figure 7 It can be seen that according to the clustering results of this model, all exercise labels are divided into 10 categories at this time. It can be seen that the results after plotting by t-SNE show that this model can clearly segment these exercise labels.

[0161] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, which should all be regarded as belonging to the protection scope of the present invention.

Claims

1. A knowledge tracing method based on a dynamic memory key-value pair network, characterized in that, Including: Obtain exercise tags and corresponding exercise difficulties; Construct a knowledge tracing network model including an embedding layer, a key-value pair memory layer, a cognitive behavior layer, and an output layer; Train the network model using the exercise difficulty and the exercise tags, and use the trained network model to achieve knowledge tracing; Among them, the embedding layer performs dimensional embedding on the exercise tags and the exercise difficulty using an embedding matrix, and correspondingly obtains a tag vector and a difficulty vector; The key-value pair memory layer calculates the associated vector of the implicit knowledge points of the current exercise from the key matrix based on the tag vector, and reads the learning state vector from the value matrix according to the associated vector; meanwhile, after the user completes the current question, use the user's real answer result to update the value network; The cognitive behavior layer predicts the cognitive process of the user when answering questions based on the learning state vector and the difficulty vector, and obtains a cognitive result; The output layer predicts the user's answer result based on the cognitive result and the exercise difficulty.

2. The knowledge tracking method based on the dynamic memory key-value pair network according to claim 1, wherein The calculation formula for the exercise difficulty is: Among them, q t represents the difficulty of the exercise, and Total t represents the total number of times the exercise appears. Total wrong (t) represents the number of times the exercise is answered incorrectly, and α is the correction coefficient.

3. The knowledge tracing method based on the dynamic memory key-value pair network according to claim 1, wherein The embedding layer respectively uses the embedding matrix A and the embedding matrix E to achieve dimensional embedding of the exercise tags and the exercise difficulty, and the formula is expressed as follows: m t = c t A; q e = q t E; Among them, m t represents the label vector, c t represents the exercise label, q e represents the difficulty vector, q t represents the exercise difficulty.

4. The knowledge tracing method based on the dynamic memory key-value pair network according to claim 3, characterized in that The key-value pair memory layer calculates the associated vector of the implicit knowledge points of the current exercise from the key matrix based on the tag vector, including: Perform an operation on the label vector m t and the key matrix to obtain an association vector. The calculation formula is as follows: where n t (i) represents the value of the i-th bit of the associated vector n t , Softmax is the normalized exponential function, M k (i) represents the elements contained in the i-th row of the key matrix, and T represents the transpose operation.

5. The knowledge tracing method based on the dynamic memory key-value pair network according to claim 4, characterized in that Reading the learning state vector from the value matrix according to the associated vector, including: Multiply each value of the associated vector n t by the row vector corresponding to the value matrix, and sum the resulting vectors to obtain the learning state vector, which is expressed by the following formula: Among them, v i represents the learning state vector, N represents the number of rows of the value matrix, that is, the number of categories of implicit knowledge points included in the exercise, represents the elements included in the i-th row of each value matrix.

6. The knowledge tracing method based on the dynamic memory key-value pair network according to claim 5, wherein Using the user's real answer result to update the value network includes: Use the embedding matrix B of dimension 2c×d v to map the user's true answer result y t and the exercise label c t The mapping is expressed as: w t = [c t , y t T ·B;​ where, w t represents the change vector of knowledge level, c represents the number of exercise tags, and d v is the value matrix dimension; Process w using an erasure gate and a strengthening gate t to obtain an erasure vector f t and a strengthening vector a t respectively. Two fully connected layers are used in this calculation process, and the formula is expressed as: Among them, W e and W a respectively represent the weight matrices of the corresponding fully connected layers, b e and b a respectively represent the bias vectors of the corresponding fully connected layers; Sigmoid is the activation function, and Tanh is the hyperbolic tangent function; According to the erasure vector f t and the enhancement vector a t update the value matrix, and the update formula is:

7. The knowledge tracing method based on the dynamic memory key-value pair network according to claim 6, wherein The cognitive behavior layer predicts the cognitive process of the user when answering questions based on the learning state vector and the difficulty vector, and obtains a cognitive result, including: Connect the learning state vector and the difficulty vector using a fully connected layer to obtain a summary vector; Process the summary vector using a long short-term memory network; Use three fully connected layers to respectively map the user's mastery level L, guessing probability G, and mistake probability S of the knowledge points from the output result of the long short-term memory network.

8. The knowledge tracing method based on the dynamic memory key-value pair network according to claim 7, wherein, The output layer predicts the user's answer result based on the cognitive results L, G, S and the exercise difficulty according to the following formula: P = L * (1 - R) * (1 - S) + (1 - L * (1 - R)) * G; Among them, P represents the probability that the user answers the exercise correctly, and R represents the exercise difficulty.

9. The knowledge tracing method based on the dynamic memory key-value pair network according to claim 7, wherein During the training process of the network model, the following loss function is adopted: loss = loss p + loss l + loss s + loss g ; Among them, loss represents the total loss function, and loss l represents the loss function corresponding to L, and its expression is: where, ΔL t = |L t+1- L t | represents the absolute value of the change in the mastery level of two knowledge points, L t+1 represents the mastery level of the knowledge point after the (t + 1)-th answer, L t represents the mastery level of the knowledge point after the t-th answer, τ lower and τ upper respectively represent the lower bound and the upper bound of the change in the mastery level of the knowledge point; loss s represents the loss function corresponding to S, and its expression is: wherein, S t is the probability that the user answers wrongly due to a mistake at time t, len is the length of the user's answer sequence this time, and λ s is the average value of the total average wrong answer probability of this answer sequence; loss g denotes the loss function corresponding to G, and its expression is: Among them, G t is the probability that the user answers correctly due to guessing at time t, len is the length of the user's answer sequence for this question, and λ g is the average value of the probability that the answer sequence is answered correctly due to guessing; loss p Indicates the accuracy ability of the model to predict the final answer result, and its expression is: Among them, p t represents the probability that the exercise predicted by this model is answered correctly at the t-th time of answering questions.

10. A knowledge tracking system based on a dynamic memory key-value pair network, characterized in that, Including: A data acquisition module for obtaining exercise tags and corresponding exercise difficulties; A model construction module for constructing a knowledge tracing network model including an embedding layer, a key-value pair memory layer, a cognitive behavior layer, and an output layer; A training module for training the network model using the exercise difficulty and the exercise tags, and using the trained network model to achieve knowledge tracing; Among them, the embedding layer performs dimensional embedding on the exercise tags and the exercise difficulty using an embedding matrix, and correspondingly obtains a tag vector and a difficulty vector; The key-value pair memory layer calculates the correlation vector of the implicit knowledge points of the current exercise from the key matrix based on the label vector, and reads the learning status vector from the value matrix according to the correlation vector; meanwhile, after the user completes the current question, the true answer result of the user is used to update the value network; The cognitive behavior layer predicts the cognitive process of the user during answering according to the learning status vector and the difficulty vector to obtain a cognitive result; The output layer predicts the user's answer result based on the cognitive result and the exercise difficulty.

Images