An anti-fact causal reasoning knowledge tracking method based on a hypergraph neural network

Abstract

The application discloses a kind of based on hypergraph neural network's counterfactual causal inference knowledge tracking method, according to the relationship of test questions and knowledge points, the same difficulty test question relationship, the same popularity test question relationship and test question association relationship constructs hypergraph network, obtains the semantic representation of test questions and knowledge points by hypergraph neural network and captures the connection of node and hyperedge, by counterfactual causal inference framework constructs student feature prediction branch, test question feature prediction branch and test question feature matching degree prediction branch, in test question feature matching degree prediction branch, by forgetting module and learning module tracking student in the process of learning the changing knowledge state, can obtain the knowledge state growth that more close to actual doing problem situation.Finally, by the high-order representation of test information and accurate tracking knowledge state, the performance of answering question is accurately predicted.

Description

Technical Field

[0001] This invention belongs to the fields of artificial intelligence and educational data mining, specifically relating to a counterfactual causal reasoning knowledge tracking method based on hypergraph neural networks. Background Technology

[0002] The emergence of online education platforms has eliminated the limitations of time and space in learning, accelerating the digital transformation of education systems. However, this has also brought new challenges. One such challenge is how to effectively track students' learning progress through online interaction with textbooks—a problem known as knowledge tracking. Generally, the purpose of knowledge tracking is to utilize students' historical learning interaction data to observe, represent, and quantify their knowledge status—that is, their mastery of the knowledge points contained in the textbook—while accurately predicting their performance in future learning. In recent years, knowledge tracking models have received considerable attention due to their importance in education and have been widely applied in intelligent tutoring systems, online education platforms, and personalized exercise recommendation systems.

[0003] Existing knowledge tracing models can be broadly categorized into two types: traditional knowledge tracing models and deep learning knowledge tracing models. Traditional knowledge tracing models, particularly Bayesian Knowledge Tracing (BKT), map student performance (observable variables) to estimates of knowledge levels (unobservable or latent variables). BKT assumes the state of a knowledge point as a known and unknown binary latent variable and uses a Hidden Markov Model (HMM) to update the probabilities of these binary variables as the student answers. Item Response Theory (IRT)-based models consider students' latent traits and item attributes, such as item difficulty or discrimination, and use logistic functions to simulate the probability of a student answering correctly.

[0004] With the rapid development of neural networks, deep learning-based knowledge tracking models have achieved remarkable results. For example, the DKT and LPKT models, based on recurrent neural networks, use hidden layer states to represent knowledge states and predict answer performance through multilayer perceptrons. The AKT and SAKT models use attention mechanisms to capture students' performance on similar questions to predict answer performance. In knowledge tracking tasks, various relational structures often exist, such as the inclusion relationship between questions and knowledge points, the dependency relationship between knowledge points, and the similarity relationship between questions. To capture these relational structures to better solve knowledge problems, a recent trend is to explore the power of graph representation learning techniques (such as graph neural networks (GNNs)). The GIKT model (GNN) constructs a bipartite graph of knowledge point nodes and question nodes, aggregates question and knowledge point embeddings according to the relationship between questions and knowledge points in the graph, and passes the embedding of each question to the RNN model in a series of interactions to predict the student's answer to the next question. The PEBG model constructs a bipartite graph of questions and knowledge points, capturing explicit question-knowledge point relationships, implicit question similarity, and knowledge point similarity to obtain pre-trained embedding representations to improve model performance.

[0005] However, currently, no model utilizes a hypergraph, a graph representation structure, to describe the question relationship structure in knowledge tracing tasks. Hypergraph structures are highly effective when processing data that can be represented as graphs or networks, excelling at capturing and modeling complex relationships between entities in the data. Secondly, many deep learning-based knowledge tracing models aim to more accurately track knowledge states by constructing learning and forgetting modules. However, these models suffer from issues such as incorrectly calculating knowledge growth by treating students' correct guesses as correct answers and excessive forgetting. This method introduces counterfactual causal inference into the knowledge tracing task to obtain reasonable learning gains in the learning module and employs a time-based forgetting method to mitigate excessive forgetting. Summary of the Invention

[0006] The purpose of this invention is to provide a counterfactual causal reasoning knowledge tracking method based on a hypergraph neural network. The method involves constructing a hypergraph network based on the relationships between test questions and knowledge points, test questions of similar difficulty, test questions of similar popularity, and test question associations. The hypergraph neural network captures the connections between nodes and hyperedges to obtain semantic representations of test questions and knowledge points. A counterfactual causal inference framework is used to construct student feature prediction branches, test question feature prediction branches, and test question feature matching degree prediction branches. In the test question feature matching degree prediction branch, forgetting and learning modules are used to track the constantly changing knowledge state of students during the learning process.

[0007] A counterfactual causal reasoning knowledge tracking method based on hypergraph neural networks includes:

[0008] 1) Obtain the knowledge tracking task dataset, evaluate the difficulty of the questions, the difficulty of the knowledge points, and the popularity of the questions by using the historical answer records of students in the knowledge tracking task dataset, associate questions based on difficulty to obtain the relationship between questions of the same difficulty, associate questions based on popularity to obtain the relationship between questions of the same popularity, extract the answer interval time and answer frequency features, and embed the feature data in the knowledge tracking task dataset to obtain the question features and learning behavior features;

[0009] 2) Generate hyperedges based on the relationship between questions and knowledge points in the knowledge tracing task dataset, the relationship between questions of the same difficulty and the relationship between questions of the same popularity obtained in step 1), and the relationship between questions in the knowledge tracing dataset, and construct a hypergraph neural network with questions as nodes;

[0010] 3) The semantic representations of questions and knowledge points are obtained by capturing the relationships between questions through the hypergraph neural network constructed in step 2);

[0011] 4) Using a counterfactual causal inference framework, the student characteristic prediction branch predicts the student's performance on future test questions based on the learning behavior characteristics and knowledge status in step 1), and the test question feature prediction branch predicts the student's performance on future test questions based on the test question features.

[0012] In the student test question matching prediction branch, the forgetting effect in the learning process is first modeled to obtain the student's current knowledge state. Then, the student's performance on future test questions is predicted based on the student's current knowledge state to obtain the student test question matching prediction branch result.

[0013] The final prediction result is obtained by multiplying the student feature prediction branch result, the test item feature prediction branch result, and the student test item matching degree prediction branch result. The final prediction result is combined with the student feature prediction branch result to obtain the student's learning gain and complete knowledge tracking.

[0014] In this invention, the hypergraph neural network structure represents high-level connections between question nodes, helping us to find similarities between questions. Compared to ordinary bipartite graphs, the simultaneous hypergraph neural network can pass messages not only between two nodes, but also between many nodes and between nodes and hyperedges. This helps us better learn the model's representation of questions and knowledge points. Question and knowledge point representations are crucial factors in knowledge tracing tasks, influencing model prediction performance and knowledge state tracking.

[0015] In this invention, the student feature prediction branch in the counterfactual causal framework predicts answer performance based on the number of student attempts, reflecting the probability of a student guessing correctly. The final prediction result, combined with the prediction result from the student feature branch, eliminates the influence of correct guesses when calculating student knowledge gain, achieving counterfactual growth of knowledge state and more accurate knowledge tracking. The question feature branch predicts answer performance based on question ID, the ID of the knowledge points contained in the question, the difficulty of the knowledge points, the popularity of the question, and the question difficulty, which helps in updating the representation of question features.

[0016] In step 1), the test item features include the test item ID, the knowledge point ID contained in the test item, the test item difficulty feature, the knowledge point difficulty feature, and the test item popularity feature.

[0017] In step 1), the learning behavior characteristics include the interval between answering questions and the number of times questions are answered.

[0018] Step 4) of the counterfactual causal inference framework specifically includes:

[0019] The branches include student feature prediction, test item feature prediction, and student-test item matching prediction.

[0020] In step 4), the forgetting effect during the answering process is first modeled in the student test item matching prediction branch to obtain the student's current knowledge state, specifically including:

[0021] Forgetting is achieved by using time periods, specifically by only considering categories based on the interval size. k Forgetting occurs when the value is ≥1:

[0022]

[0023] Where W4 is the weight matrix, T is the matrix transpose, b4 is the bias term, and H... k-1 It is the knowledge state at time step k-1. k It is the embedding vector of the interval size category at time step k, and σ is the sigmoid activation function. It is a vector concatenation operation;

[0024] Then forget the gate f k Multiply by the previous knowledge state H k-1 Get the student's current knowledge status

[0025]

[0026] In this invention, the forgetting effect can simulate the phenomenon that students forget knowledge points due to time intervals during the learning process, resulting in a decline in their mastery of knowledge points. This allows for more accurate tracking of changes in students' knowledge status. At the same time, using forgetting by time period can effectively prevent the excessive forgetting caused by forgetting by time step in previous methods, which would lead to an excessive decline in the mastery of knowledge points.

[0027] In step 4), the final prediction result is combined with the student feature prediction branch result to obtain the student's learning gain, specifically including:

[0028] Use the final prediction result y k and student feature prediction branch results To calculate students' mastery of actual test questions

[0029]

[0030] Where τ is a hyperparameter, representing the minimum learning gain coefficient when answering a question correctly, r k For the answer status, r k This is the embedding vector of the answer responses, and max is the maximum value operation.

[0031] Then, the complete information of the test questions is embedded in i. k Students' mastery of real exam questions and the mastery of the relevant knowledge points in the test questions. The student's learning gain g is obtained by modeling the learning gain using a multilayer perceptron. k :

[0032]

[0033] Where W6 is the weight matrix and b6 is the bias term;

[0034] The knowledge point related vector of the current test question Multiply by the learning gain g k With the current state of knowledge Adding them together gives the knowledge state H after learning. k :

[0035]

[0036] This invention, by combining the final prediction result with the prediction results of the student feature branch, can to some extent eliminate the influence of students guessing correctly or blindly selecting the correct answer, reflect the students' true answering level, and model a more reasonable learning gain.

[0037] Specifically, a comprehensive knowledge tracking method with increased test difficulty includes:

[0038] This paper utilizes a hypergraph neural network to capture complex relationships between entities, obtaining semantic representations of test questions and knowledge points. A counterfactual causal framework is constructed to assess students' true knowledge state based on their historical answer records, thereby predicting their test performance. The difficulty of test questions, the difficulty of knowledge points, and the popularity of test questions are evaluated using historical answer record data. Features such as answer interval time and answer frequency are extracted and embedded. A hypergraph network is constructed based on the inclusion relationship between test questions and knowledge points, the relationship between test questions of similar difficulty, the relationship between test questions of similar popularity, and the relationship between test questions. Semantic representations of test questions and knowledge points are obtained through the hypergraph neural network. Based on the counterfactual causal inference framework, student feature prediction, test question feature prediction, and student-test question matching prediction branches are constructed. In the student-test question matching prediction branch, the forgetting effect during the answering process is first modeled to obtain the student's current knowledge state. Then, the student's performance on future test questions is predicted based on the current knowledge state. The final prediction result is obtained by combining the results of the three branches. Finally, the student's learning gain is modeled based on the prediction results of the student feature branch.

[0039] The student's historical answer record data includes: question number, question answer, knowledge points covered in the question, and answer timestamp;

[0040] In an online education system, there is a set S = {s1, s2, ..., sn} containing V students. V}, containing a set P = {p1, p2, ..., p} of M test questions. M} and a set of N knowledge points C = {c1, c2, ..., c N The test contains R historical question-answering interactions. Each question is pre-labeled with the knowledge points it contains, and the relationship between questions and knowledge points is represented by a Q-matrix, where Q∈R. M×N The matrix consists of 1s and 0s, Q ij =1 indicates that question p i Includes knowledge point c j Q ij =0 Conversely, question p i The relevant knowledge point vector can be used This represents the i-th row of the Q matrix. The student's historical question-and-answer interaction sequence, arranged chronologically, is defined as... Each tuple Represents a question-and-answer interaction unit, where p k Representative test questions, Representative and test question p k The set of knowledge points included, r k r represents whether the answer is correct or not. k ∈{1, 0}, where 1 represents a correct answer and 0 represents an incorrect answer, t k This represents the timestamp of the answer.

[0041] The difficulty of test questions, the difficulty of knowledge points, and the popularity of test questions are assessed using students' historical answer records, specifically including:

[0042] Test p i Difficulty PD i The calculation formula is as follows:

[0043]

[0044] Where S i The representative answered question p. i The student set, where |S i | represents the size of the student set, r ji ∈{0,1} represents student s j Answer question p i Correct or incorrect, D is the preset difficulty level number;

[0045] Knowledge point c j Difficulty CD j The calculation formula is as follows:

[0046]

[0047] in This represents a set of test questions that cover this knowledge point. This represents the size of the set of test questions. In other words, the difficulty of a knowledge point is the average of the difficulties of all test questions containing that knowledge point.

[0048] Test p i popularity pl i The calculation formula is as follows:

[0049]

[0050] in Indicates answering question p i The size of the interaction set, where R represents the total number of interactions and Z is the preset popularity level.

[0051] Extracting the features of the answer interval and the number of answers, and embedding the data features, includes:

[0052] Calculate the number of consecutive answers (ca) and the total number of answers (hr) of the questions within the interactive answer unit in the historical answer record. Assuming there is a question sequence {p2, p3, p3, p3, p2, p2, p3} in the complete interactive answer unit, the total number of answers for the corresponding questions in the historical answer record at each time step is {0, 0, 1, 2, 1, 2, 3}, and the number of consecutive answers for the corresponding questions in the interactive answer unit at each time step is {0, 0, 1, 2, 0, 1, 0}.

[0053] The time interval (it) between adjacent answer interaction units is calculated using the answer timestamp, and then discretized into six time interval length categories based on the interval size, as follows:

[0054]

[0055] The student's interactive answer unit has been expanded to Where p k Representative test questions, The set of knowledge points represented in the comparison between the test questions and the CR test. k Represents the number of consecutive times a question is answered, hr k It represents the total number of times the history question was answered. k r represents the interval between answering questions. k r represents whether the answer is correct or not. k ∈{1,0}, where 1 represents a correct answer and 0 represents an incorrect answer.

[0056] Using an embedding matrix on the question set P Embedded representation, where M represents the number of test items, d p This represents the dimension of the embedded question vector, followed by the question p in each interactive unit. k Vectors can be used To indicate;

[0057] Using an embedding matrix on the knowledge point set C Embedded representation, where N represents the number of knowledge points, d c This represents the dimension of the embedded knowledge point vector, followed by each knowledge point c. k Using vectors This indicates that the test question p for each interactive unit is... k The collection of knowledge points The set of knowledge points is represented by the average of the sums of the embedding vectors of the knowledge points in the set. Vectors can be used To represent this, the formula is as follows:

[0058]

[0059] in Representative knowledge points The size of the set.

[0060] Using embedding matrix Embedding operation on the difficulty of test questions, where d l This represents the dimension of the embedded question difficulty vector, i.e., question p. k Difficulty using vectors To express.

[0061] Using embedding matrix The difficulty of the knowledge points is embedded, where d l This represents the dimension of the embedded knowledge point difficulty vector, i.e., knowledge point c. k Difficulty using vectors To express.

[0062] Each interactive question unit contains p questions. k The collection of knowledge points The difficulty is obtained by average pooling of the knowledge point difficulty vector, i.e., the knowledge point set. Difficulty using vectors To represent this, the formula is as follows:

[0063]

[0064] Finally, a multilayer perceptron is used to process the question vector p. k The difficulty vector of the test questions, pd k The test questions contain a vector of knowledge points. The test questions include a set of knowledge points and a difficulty vector. The fusion process yields complete embedded test question information.

[0065]

[0066] in Represents the splicing operation, d x For vector dimensions, It is the weight matrix, and T is the matrix transpose. It is a bias term;

[0067] Using embedding matrix Embed the answer, where d r This represents the dimension of the embedded answer vector, followed by the answer r for each learning unit. k Use vectors To express.

[0068] Using embedding matrix Embedding operation on the popularity of test items, where d pl This represents the dimension of the embedded item popularity vector, i.e., item p. k popularity pl k Using vectors To express.

[0069] Using embedding matrix An embedding operation is performed on the number of consecutive answers, where J represents the maximum number of consecutive answers in the record, and d cr The dimension of the vector representing the number of consecutive answers after embedding is cr. kUsing vectors To express.

[0070] Using embedding matrix An embedding operation is performed on the total number of historical answers, where U represents the maximum total number of historical answers in the record, and d hr This represents the dimension of the embedded historical total number of answers vector, i.e., the historical total number of answers hr. k Using vectors To express.

[0071] Using embedding matrix Embed the answer interval time, where d it This represents the dimension of the embedded question-answering interval time vector, i.e., the question-answering interval time it. k Using vectors To express.

[0072] Use a random initialization matrix The knowledge status of students is used to store their level of knowledge mastery, where N is the number of knowledge points, i.e., the vector in the i-th row of the matrix. Represents the corresponding knowledge point c i Level of mastery, d h For vector dimensions.

[0073] A hypergraph network is constructed based on the relationships between test questions and knowledge points, the relationships between test questions of similar difficulty, the relationships between test questions of similar popularity, and the relationships between test questions. The semantic representations of test questions and knowledge points are obtained through the hypergraph neural network, specifically including:

[0074] Treating test questions as nodes in a hypergraph, we define four types of hyperedges: knowledge point hyperedges, test question association hyperedges, test question popularity hyperedges, and test question difficulty hyperedges.

[0075] The relationship between test questions and knowledge points is many-to-many. A test question may contain multiple knowledge points, and multiple test questions may contain the same knowledge point. Therefore, a knowledge point hyperedge can contain multiple test question nodes.

[0076] A time interval of less than one hour is defined as the same time period for answering questions. Questions within the same time period are then classified as related. For example, given the answer sequence x = {(p3, it1), (p1, it2), (p2, it3), (p5, it4), (p7, it5)}, if it3 > 1 hour and the remaining intervals are all less than 1 hour, the time is divided into two periods. Questions p3 and p1 are related, forming a related question set pa1 = {p3, p1}, and questions p2, p5, and p7 are related, forming a related question set pa2 = {p2, p5, p7}. For all related question sets, the Apriori algorithm is used for association mining to calculate frequent itemsets with minimum support θ. Frequent itemsets without supersets are added to the final related question set PA = {pa1, pa2, ..., pa1}. A Questions within the same associated question set can be connected by corresponding question-associated hyperedges.

[0077] Question nodes of the same difficulty can be connected by hyperedges of the corresponding question difficulty.

[0078] Question nodes with the same difficulty and popularity can be connected by corresponding question popularity hyperedges.

[0079] Construct a hypergraph network of test questions and knowledge points G = (V, E), where V = {p1, p2, ..., p...} M Let E = {E1, E2, E3, E4} be the set of nodes, where each node represents a question. The hyperedge subset E1 = {c1, c2, ..., c4} is also defined. N Each hyperedge represents a knowledge point, and the hyperedge subset E2 = {pd1, pd2, ..., pd} D Each hyperedge represents a question difficulty level, and the hyperedge subset E3 = {pa1, pa2, ..., pa3} A Each hyperedge represents a set of related test questions, and the hyperedge subset E4 = {pl1, pl2, ..., pl...} Z Each hyperedge represents the popularity of a question. Each hyperedge has no degree and contains any number of question nodes.

[0080] The representation is updated using a hypergraph neural network, where node representations are updated via an attention-based hyperedge aggregator:

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[0090]

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[0094] Where σ represents the activation function sigmoid. This represents the concatenation operation, and exp represents an exponential function with base e. as well as They respectively represent the node p i The set of knowledge point hyperedges, the set of question difficulty hyperedges, the set of question association hyperedges, and the set of question popularity hyperedges. as well as They are nodes p respectively i With the set of superedges as well as The aggregate vector, as well as Representing node p respectively i Attention scores for hyperedges related to knowledge points, question difficulty, question relevance, and question popularity. as well as Represents the weight vector. as well as Represents a linear transformation matrix. as well as This represents the attention vector. θ, ρ, μ, and ε are hyperparameters that control the importance of different types of hyperedges.

[0095] Update the hyperedge representation using an attention-weighted node aggregator:

[0096]

[0097]

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[0100]

[0101]

[0102]

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[0105]

[0106]

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[0108] in as well as Represents the weight vector. Represents the node p i The number of superedges, as well as This represents the attention vector.

[0109] Based on a counterfactual causal inference framework, three branches are constructed: student feature prediction, question feature prediction, and student-question matching prediction. In the student-question matching prediction branch, the forgetting effect during the answering process is first modeled to obtain the student's current knowledge state. Then, the student's performance on future questions is predicted based on this current knowledge state. The final prediction result is obtained by combining the results of the three branches. Finally, the student's learning gain is modeled based on the prediction results of the student feature branch, specifically including:

[0110] The counterfactual causal reasoning framework mainly includes three branches: student characteristics branch, test item characteristics branch, and student-test item matching degree branch.

[0111] Student characteristic branches are based on the overall knowledge status of students. and the number of consecutive answers (cr) t Total number of history questions answered (hr) t Feature prediction of answer performance represents the student's own influence on answer performance:

[0112]

[0113]

[0114] in It is a weight matrix, b2∈R 1 It is a bias term. Given the current state of knowledge, Predict answer values ​​for student feature branches.

[0115] Item feature branches are analyzed based on item popularity (pl). k and complete test information i k Feature prediction of answer performance represents the impact of the test questions themselves on answer performance:

[0116]

[0117] in It is a weight matrix, b3∈R 1 It is a bias term. Predicting answer values ​​for question feature branches

[0118] The student test question matching branch mainly predicts answers based on the matching degree between the student's corresponding knowledge status and the complete information of the test question. It mainly includes the forgetting module, the learning module, and the prediction module.

[0119] Forgetting Mechanism Module: This module uses forgetting gates to simulate the forgetting effect of knowledge during the learning process. To prevent excessive forgetting of knowledge states caused by step-by-step forgetting, a time-based forgetting approach is adopted. Specifically, forgetting only occurs when the interval between categories is large or small. k Forgetting occurs when the value is ≥1:

[0120]

[0121] in It is a weight matrix. It is a bias term;

[0122] Then forget the gate f k Multiply by the previous knowledge state H k-1 Obtain the current knowledge state

[0123]

[0124] Prediction Module: In the prediction module, based on the knowledge point relevance vectors of the current test question... Query the knowledge state matrix and perform average pooling on multiple knowledge points to obtain the student's mastery level of the corresponding knowledge points.

[0125]

[0126] Where · represents the element-wise product between vectors.

[0127] Then we embed i with the complete information of the current test question. k and the students' mastery of the corresponding knowledge points The matching degree between students' knowledge status and test question information is obtained through a multilayer perceptron:

[0128]

[0129] in It is a weight matrix, b5∈R 1 It is a bias term. Predict answer values ​​for students based on their test question matching degree;

[0130] The matching degree between the student's knowledge status and the test question information is then multiplied by the predicted values ​​of the student's features and the predicted values ​​of the test question branch features, and the final predicted value is obtained by applying the sigmoid function:

[0131]

[0132] Learning Module: To eliminate the possibility of students guessing questions correctly and updating their knowledge state to include correct answers, the final predicted value minus the predicted value of the student's feature branch is used as the student's true level of knowledge.

[0133]

[0134] Where τ is a hyperparameter representing the minimum learning gain coefficient, and max is the maximum value operation.

[0135] Then, the complete information of the test questions is embedded in i. k Students' mastery of real exam questions and the corresponding knowledge points mastery status The learning gain g is obtained by modeling the learning gain using a multilayer perceptron. k :

[0136]

[0137] in It is a weight matrix. It is a bias term;

[0138] The knowledge point relevance vector of the current test question Multiply by the learning gain g k With the current state of knowledge Add

[0139] During model training, the binary cross-entropy loss of the predicted student feature branches is used. s The binary cross-entropy loss of the predicted value of the feature branches of the test questions. p The binary cross-entropy loss of the final predicted valuesp As the joint optimization objective loss:

[0140]

[0141]

[0142]

[0143] loss = loss sp +αloss s +βloss p

[0144] Where α and β are hyperparameters that control the importance of the loss.

[0145] Compared with the prior art, the present invention has the following advantages:

[0146] The solution provided by this invention uses a hypergraph to represent the complex relationships between test questions and knowledge points, related test questions, test questions of the same difficulty, and test questions of the same popularity. It can obtain semantic representations of nodes (test questions) and hyperedges (knowledge points) through hypergraph neural network aggregation. Based on a counterfactual causal inference framework, it constructs student feature prediction branches, test question feature prediction branches, and student-test question matching degree prediction branches. In the student-test question matching degree prediction branch, it avoids excessive weakening of knowledge state by using forgetting over time periods. The results of the student feature prediction branch guide the updating of knowledge state, resulting in knowledge state growth that more closely reflects actual test-taking performance. Finally, through the high-order representation of test question information and the precise tracking of knowledge state, it achieves accurate prediction of test-taking performance. Attached Figure Description

[0147] Figure 1 This is a flowchart of the method proposed in this invention;

[0148] Figure 2 This is a model architecture diagram of the present invention. Detailed Implementation

[0149] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0150] The objective of this invention is achieved through the following technical solution:

[0151] like Figure 1As shown, a counterfactual causal reasoning knowledge tracking method based on hypergraph neural networks specifically includes:

[0152] Step 1: Obtain the student's historical answer records:

[0153] The student's historical answer record data includes: question number, question answer, knowledge points covered in the question, and answer timestamp;

[0154] In an online education system, there is a set S = {s1, s2, ..., sn} containing V students. V}, containing a set P = {p1, p2, ..., p} of M test questions. M} and a set of N knowledge points C = {c1, c2, ..., c N The test contains R historical question-answering interactions. Each question is pre-labeled with the knowledge points it contains, and the relationship between questions and knowledge points is represented by a Q-matrix, where Q∈R. M×N The matrix consists of 1s and 0s, Q ij =1 indicates that question p i Includes knowledge point c j Q ij =0 Conversely, question p i The relevant knowledge point vector can be used This represents the i-th row of the Q matrix. The student's historical question-and-answer interaction sequence, arranged chronologically, is defined as... Each tuple Represents a question-and-answer interaction unit, where p k Representative test questions, Representative and test question p k The set of knowledge points included, r k r represents whether the answer is correct or not. k ∈{1, 0}, where 1 represents a correct answer and 0 represents an incorrect answer, t k This represents the timestamp of the answer.

[0155] Step 2: Assess the difficulty of the test questions, the difficulty of the knowledge points, and the popularity of the questions; extract features such as the number of times questions were answered and the time interval between answers; and perform embedding processing on the data features, specifically including:

[0156] Test p i Difficulty PD i The calculation formula is as follows:

[0157]

[0158] Where S i The representative answered question p. i The student set, where |S i | represents the size of the student set, r ji∈{0,1} represents student s j Answer question p i Correct or incorrect, D is the preset difficulty level number;

[0159] Knowledge point c j Difficulty CD j The calculation formula is as follows:

[0160]

[0161] in This represents a set of test questions that cover this knowledge point. This represents the size of the set of test questions. In other words, the difficulty of a knowledge point is the average of the difficulties of all test questions containing that knowledge point.

[0162] Test p i popularity pl i The calculation formula is as follows:

[0163]

[0164] in Indicates answering question p i The size of the interaction set, where R represents the total number of interactions and Z is the preset popularity level.

[0165] Extracting the features of the answer interval and the number of answers, and embedding the data features, includes:

[0166] Calculate the number of consecutive answers (ca) and the total number of answers (hr) of the questions within the interactive answer unit in the historical answer record. Assuming there is a question sequence {p2, p3, p3, p3, p2, p2, p3} in the complete interactive answer unit, the total number of answers for the corresponding questions in the historical answer record at each time step is {0, 0, 1, 2, 1, 2, 3}, and the number of consecutive answers for the corresponding questions in the interactive answer unit at each time step is {0, 0, 1, 2, 0, 1, 0}.

[0167] The time interval (it) between adjacent answer interaction units is calculated using the answer timestamp, and then discretized into six time interval length categories based on the interval size, as follows:

[0168]

[0169] The student's interactive answer unit has been expanded to Where p k Representative test questions, Representative and test question p k The set of knowledge points included, cr k Represents the number of consecutive times a question is answered, hr kIt represents the total number of times the history question was answered. k r represents the interval between answering questions. k r represents whether the answer is correct or not. k ∈{1,0}, where 1 represents a correct answer and 0 represents an incorrect answer.

[0170] Using an embedding matrix on the question set P Embedded representation, where M represents the number of test items, d p This represents the dimension of the embedded question vector, followed by the question p in each interactive unit. k Vectors can be used To indicate;

[0171] Using an embedding matrix on the knowledge point set C Embedded representation, where N represents the number of knowledge points, d c This represents the dimension of the embedded knowledge point vector, followed by each knowledge point c. k Using vectors This indicates that the test question p for each interactive unit is... k The collection of knowledge points The set of knowledge points is represented by the average of the sums of the embedding vectors of the knowledge points in the set. Vectors can be used To represent this, the formula is as follows:

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[0173] in Representative knowledge points The size of the set.

[0174] Using embedding matrix Embedding operation on the difficulty of test questions, where d l This represents the dimension of the embedded question difficulty vector, i.e., question p. k Difficulty using vectors To express.

[0175] Using embedding matrix The difficulty of the knowledge points is embedded, where d l This represents the dimension of the embedded knowledge point difficulty vector, i.e., knowledge point c. k Difficulty using vectors To express.

[0176] Each interactive question unit contains p questions. k The collection of knowledge points The difficulty is obtained by average pooling of the knowledge point difficulty vector, i.e., the knowledge point set. Difficulty using vectors To represent this, the formula is as follows:

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[0178] Finally, a multilayer perceptron is used to process the question vector p. k The difficulty vector of the test questions, pd k The test questions contain a vector of knowledge points. The test questions include a set of knowledge points and a difficulty vector. The fusion process yields complete embedded test question information.

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[0180] in Represents the splicing operation, d x For vector dimensions, It is a weight matrix. It is a bias term;

[0181] Using embedding matrix Embed the answer, where d r This represents the dimension of the embedded answer vector, followed by the answer r for each learning unit. k Use vectors To express.

[0182] Using embedding matrix Embedding operation on the popularity of test items, where d pl This represents the dimension of the embedded item popularity vector, i.e., item p. k popularity pl k Using vectors To express.

[0183] Using embedding matrix An embedding operation is performed on the number of consecutive answers, where J represents the maximum number of consecutive answers in the record, and d cr The dimension of the vector representing the number of consecutive answers after embedding is cr. k Using vectors To express.

[0184] Using embedding matrix An embedding operation is performed on the total number of historical answers, where U represents the maximum total number of historical answers in the record, and d hr This represents the dimension of the embedded historical total number of answers vector, i.e., the historical total number of answers hr. k Using vectors To express.

[0185] Using embedding matrix Embed the answer interval time, where d itThis represents the dimension of the embedded question-answering interval time vector, i.e., the question-answering interval time it. k Using vectors To express.

[0186] Use a random initialization matrix The knowledge status of students is used to store their level of knowledge mastery, where N is the number of knowledge points, i.e., the vector in the i-th row of the matrix. Represents the corresponding knowledge point c i Level of mastery, d h For vector dimensions.

[0187] Step 3: Construct a hypergraph network based on the relationships between questions and knowledge points, questions of similar difficulty, questions of similar popularity, and question associations. Obtain semantic representations of questions and knowledge points through the hypergraph neural network, specifically including:

[0188] Treating test questions as nodes in a hypergraph, we define four types of hyperedges: knowledge point hyperedges, test question association hyperedges, test question popularity hyperedges, and test question difficulty hyperedges.

[0189] The relationship between test questions and knowledge points is many-to-many. A test question may contain multiple knowledge points, and multiple test questions may contain the same knowledge point. Therefore, a knowledge point hyperedge can contain multiple test question nodes.

[0190] A time interval of less than one hour is defined as the same time period for answering questions. Questions within the same time period are then classified as related. For example, given the answer sequence x = {(p3, it1), (p1, it2), (p2, it3), (p5, it4), (p7, it5)}, if it3 > 1 hour and the remaining intervals are all less than 1 hour, the time is divided into two periods. Questions p3 and p1 are related, forming a related question set pa1 = {p3, p1}, and questions p2, p5, and p7 are related, forming a related question set pa2 = {p2, p5, p7}. For all related question sets, the Apriori algorithm is used for association mining to calculate frequent itemsets with minimum support θ. Frequent itemsets without supersets are added to the final related question set PA = {pa1, pa2, ..., pa1}. A Questions within the same associated question set can be connected by corresponding question-associated hyperedges.

[0191] Question nodes of the same difficulty can be connected by hyperedges of the corresponding question difficulty.

[0192] Question nodes with the same difficulty and popularity can be connected by corresponding question popularity hyperedges.

[0193] like Figure 2As shown in the hypergraph construction module, a hypergraph network G = (V, E) is constructed for the test question knowledge points, where V = {p1, p2, ..., p...}. M Let E = {E1, E2, E3, E4} be the set of nodes, where each node represents a question. The hyperedge subset E1 = {c1, c2, ..., c4} is also defined. N Each hyperedge represents a knowledge point, and the hyperedge subset E2 = {pd1, pd2, ..., pd} D Each hyperedge represents a question difficulty level, and the hyperedge subset E3 = {pa1, pa2, ..., pa3} A Each hyperedge represents a set of related test questions, and the hyperedge subset E4 = {pl1, pl2, ..., pl...} Z Each hyperedge represents the popularity of a question. Each hyperedge has no degree and contains any number of question nodes.

[0194] The representation is updated using a hypergraph neural network. For example... Figure 2 The hyperedge aggregator demonstrates how attention-based hyperedge aggregators can be used to represent nodes more effectively.

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[0208] Where σ represents the activation function sigmoid. This represents the concatenation operation, and exp represents an exponential function with base e. as well as They respectively represent the node p i The set of knowledge point hyperedges, the set of question difficulty hyperedges, the set of question association hyperedges, and the set of question popularity hyperedges. as well as They are nodes p respectively i With the set of superedges as well as The aggregate vector, as well as Representing node p respectively i Attention scores for hyperedges related to knowledge points, question difficulty, question relevance, and question popularity. as well as Represents the weight vector. as well as Represents a linear transformation matrix. as well as This represents the attention vector. θ, ρ, μ, and ε are hyperparameters that control the importance of different types of hyperedges.

[0209] like Figure 2 As shown in the node aggregator diagram, the hyperedge representation is updated using an attention-weighted node aggregator:

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[0222] in as well as Represents the weight vector. Represents the node p i The number of superedges, as well as This represents the attention vector.

[0223] Step 4: Construct a counterfactual causal inference framework. The student feature branch predicts performance based on student characteristics, and the test item feature branch predicts performance based on test item characteristics.

[0224] like Figure 2 The counterfactual causal reasoning framework module, as shown in the module section, mainly includes three branches: student characteristics branch, test item characteristics branch, and student-test item matching degree branch.

[0225] like Figure 2 As shown in the student feature branch section, the student feature branches are based on the student's overall knowledge status. and the number of consecutive answers (cr) t Total number of history questions answered (hr) t Feature prediction of answer performance represents the student's own influence on answer performance:

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[0228] in It is a weight matrix, b2∈R 1 It is a bias term. Given the current state of knowledge, Predict answer values ​​for student feature branches.

[0229] like Figure 2 As shown in the item feature branch section, the item feature branch is based on item popularity (pl). k and complete test information i k Feature prediction of answer performance represents the impact of the test questions themselves on answer performance:

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[0231] in It is a weight matrix, b3∈R 1 It is a bias term. Predicting answer values ​​for question feature branches

[0232] Step 5: In the student test question matching branch, obtain the current knowledge status by forgetting over a time period, specifically including:

[0233] The student-question matching branch primarily predicts answers based on the degree of match between the student's corresponding knowledge level and the complete information in the question. Figure 2 The student test item matching branch mainly includes the forgetting module, the learning module, and the prediction module.

[0234] Forgetting Mechanism Module: This module uses forgetting gates to simulate the forgetting effect of knowledge during the learning process. To prevent excessive forgetting of knowledge states caused by step-by-step forgetting, a time-based forgetting approach is adopted. Specifically, forgetting only occurs when the interval between categories is large or small. k Forgetting occurs when the value is ≥1:

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[0236] in It is a weight matrix. It is a bias term;

[0237] Then forget the gate f k Multiply by the previous knowledge state H k-1 Obtain the current knowledge state

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[0239] Step 6: Based on the student's mastery of relevant knowledge points and the predicted matching degree of the test question information, and combined with the student's feature branch results and the test question feature branch results, the final prediction result is obtained, which specifically includes:

[0240] Prediction Module: In the prediction module, based on the knowledge point relevance vectors of the current test question... Query the knowledge state matrix and perform average pooling on multiple knowledge points to obtain the student's mastery level of the corresponding knowledge points.

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[0242] Where · represents the element-wise product between vectors.

[0243] Then we embed i with the complete information of the current test question. k and the students' mastery of the corresponding knowledge points The matching degree between students' knowledge status and test question information is obtained through a multilayer perceptron:

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[0245] in It is a weight matrix, b5∈R 1 It is a bias term. Predict answer values ​​for students based on their test question matching degree;

[0246] The matching degree between the student's knowledge status and the test question information is then multiplied by the predicted values ​​of the student's features and the predicted values ​​of the test question branch features, and the final predicted value is obtained by applying the sigmoid function:

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[0248] Step 7: Obtain the true answer embedding by analyzing the final prediction results and student characteristic branch results, and calculate the student's knowledge gain by combining the test information and the student's mastery of related knowledge points. Specifically, this includes:

[0249] Learning Module: To eliminate the possibility of students guessing questions correctly and updating their knowledge state to include correct answers, the final predicted value minus the predicted value of the student's feature branch is used as the student's true level of knowledge.

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[0251] Where τ is a hyperparameter representing the minimum learning gain coefficient, and max is the maximum value operation.

[0252] Then, the complete information of the test questions is embedded in i. k Students' mastery of real exam questions and the corresponding knowledge points mastery status The learning gain g is obtained by modeling the learning gain using a multilayer perceptron. k :

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[0254] in It is a weight matrix. It is a bias term;

[0255] The knowledge point related vector of the current test question Multiply by the learning gain g k With the current state of knowledge Adding them together gives the knowledge state H after learning. k :

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[0257] Step 8: Train the model using joint loss, specifically including:

[0258] During model training, the binary cross-entropy loss of the predicted student feature branches is used. s The binary cross-entropy loss of the predicted value of the feature branches of the test questions. p The binary cross-entropy loss of the final predicted value sp As the joint optimization objective loss:

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[0262] loss = loss sp +αloss s +βloss p

[0263] Where α and β are hyperparameters that control the importance of the loss.

[0264] Experimental Setup: The experiment uses three real-world datasets to evaluate the model's performance. The datasets are described below:

[0265] ASSIST2012: Collected from records of the 2012-2013 academic year of the ASSISTments online educational tutoring system. The data comes from the Skills Trainer Exercise Set, and students need to do similar exercises to master these skills.

[0266] ASSISTChall: From the 2017 ASSISTments platform data mining competition. This dataset records student learning activities from the academic year 2004 to 2007. Compared to ASSIST2012, the student interaction sequences in this dataset are longer.

[0267] EdNet: From Santa, a multi-platform AI tutoring service with over 780,000 users in South Korea. The dataset includes all student system interactions collected over two years. It provides different datasets with varying abstractions. We used the simplest dataset form, EdNet-KT1, which consists of student practice interaction logs and basic practice information.

[0268] In the experiments, all interactions with missing values ​​were removed. To avoid the influence of outlier sequences, we removed sequences shorter than 10. For the ASSISTChall dataset, we further truncated the maximum sequence length to 500. For the Ednet and ASSIST2012 datasets, we randomly selected 10,000 students with between 10 and 500 interactions.

[0269] The experiment used seven control models to compare the model performance. The models are described below:

[0270] DKT: The first knowledge tracking model based on deep learning, which uses recurrent neural networks (RNNs) to track students' knowledge status.

[0271] DKT+: An extended version of the DKT model that improves predictions by introducing a regularization term.

[0272] DKVMN: Utilizes external memory structures to better track students' mastery of complex knowledge points. It uses a static key matrix to store latent knowledge concepts and a dynamic value matrix to store and update students' corresponding knowledge states through read and write operations.

[0273] SAKT: The first model to apply multi-head self-attention to knowledge tracking tasks, making predictions based on the performance of related exercises in past interactions.

[0274] AKT employs two self-attention encoders to learn context-aware representations of practice and responses, and utilizes a knowledge retrieval unit to retrieve previously acquired knowledge relevant to the current practice.

[0275] LPKT: It uses response time and interval time features to design a learning gate and a forgetting gate to simulate the gain and decay of knowledge state during the learning process.

[0276] DTransformer: Employs the Transformer architecture, internally incorporating time and cumulative attention, and constructs an architecture from the question level to the knowledge point level.

[0277] Training Setup: For all datasets, we sorted all interaction records for each student according to the interaction timestamps. Then, we split the data into three groups: the first 80% of the interaction sequences as the training set, the last 20% as the test set, and the last 20% of the training set as the validation set. The hyperparameters of the control model were set according to relevant papers. The area under the curve (AUC), root mean square error (RMSE), and accuracy (ACC) were used as evaluation metrics to assess the model's performance.

[0278] Experimental results:

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[0281] As shown in the figure above, the method presented in this patent outperforms the control model on all three datasets and three metrics. The results demonstrate that this method, through a counterfactual causal inference framework, can capture the complex effects of learning behavior and more accurately track learners' knowledge states. Furthermore, this method utilizes a hypergraph neural network to capture representations of test questions and knowledge points, improving its performance. This demonstrates the value of introducing hypergraph neural networks into knowledge tracking tasks and the correctness of the hypergraph neural network construction method used in this patent.

Claims

1. A counterfactual causal reasoning knowledge tracking method based on hypergraph neural networks, characterized in that, include: 1) Obtain the knowledge tracking task dataset, evaluate the difficulty of the questions, the difficulty of the knowledge points, and the popularity of the questions by using the historical answer records of students in the knowledge tracking task dataset, associate questions based on difficulty to obtain the relationship between questions of the same difficulty, associate questions based on popularity to obtain the relationship between questions of the same popularity, extract the answer interval time and answer frequency features, and embed the feature data in the knowledge tracking task dataset to obtain the question features and learning behavior features; 2) Generate hyperedges based on the relationship between questions and knowledge points in the knowledge tracing task dataset, the relationship between questions of the same difficulty and the relationship between questions of the same popularity obtained in step 1), and the relationship between questions in the knowledge tracing dataset, and construct a hypergraph neural network with questions as nodes; 3) The semantic representations of questions and knowledge points are obtained by capturing the relationships between questions through the hypergraph neural network constructed in step 2); 4) Using a counterfactual causal inference framework, the student characteristic prediction branch predicts the student's performance on future test questions based on the learning behavior characteristics and knowledge status in step 1), and the test question feature prediction branch predicts the student's performance on future test questions based on the test question features. In the student test question matching prediction branch, the forgetting effect in the learning process is first modeled to obtain the student's current knowledge state. Then, the student's performance on future test questions is predicted based on the student's current knowledge state to obtain the student test question matching prediction branch result. The final prediction result is obtained by multiplying the student feature prediction branch result, the test item feature prediction branch result, and the student test item matching degree prediction branch result. The final prediction result is combined with the student feature prediction branch result to obtain the student's learning gain and complete knowledge tracking.

2. The counterfactual causal reasoning knowledge tracking method based on hypergraph neural networks according to claim 1, characterized in that, In step 1), the test item features include the test item ID, the knowledge point ID contained in the test item, the test item difficulty feature, the knowledge point difficulty feature, and the test item popularity feature.

3. The counterfactual causal reasoning knowledge tracking method based on hypergraph neural networks according to claim 1, characterized in that, In step 1), the learning behavior characteristics include the interval between answering questions and the number of times questions are answered.

4. The counterfactual causal reasoning knowledge tracking method based on hypergraph neural networks according to claim 1, characterized in that, Step 4) of the counterfactual causal inference framework specifically includes: The branches include student feature prediction, test item feature prediction, and student-test item matching prediction.

5. The counterfactual causal reasoning knowledge tracking method based on hypergraph neural networks according to claim 1, characterized in that, In step 4), the forgetting effect during the answering process is first modeled in the student test item matching prediction branch to obtain the student's current knowledge state, specifically including: Forgetting is achieved by using time periods, specifically by only considering categories based on the interval size. k Forgetting occurs when the value is ≥1: Where W4 is the weight matrix, T is the matrix transpose, b4 is the bias term, and H... k-1 It is the knowledge state at time step k-1. k It is the embedding vector of the interval size category at time step k, and σ is the sigmoid activation function. It is a vector concatenation operation; Then forget the gate f k Multiply by the previous knowledge state H k-1 Get the student's current knowledge status 6. The counterfactual causal reasoning knowledge tracking method based on hypergraph neural networks according to claim 1, characterized in that, In step 4), the final prediction result is combined with the student feature prediction branch result to obtain the student's learning gain, specifically including: Use the final prediction result y k and student feature prediction branch results To calculate students' mastery of actual test questions Where τ is a hyperparameter, representing the minimum learning gain coefficient when answering a question correctly, r k For the answer status, r k This is the embedding vector of the answer responses, and max is the maximum value operation; Then, the complete information of the test questions is embedded in i. k Students' mastery of real exam questions and the mastery of the relevant knowledge points in the test questions. The student's learning gain g is obtained by modeling the learning gain using a multilayer perceptron. k : Where W6 is the weight matrix and b6 is the bias term; The knowledge point related vector of the current test question Multiply by the learning gain g k With the current state of knowledge Adding them together gives the knowledge state H after learning. k :

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