Probabilistic Gaussian embedding knowledge tracking method based on knowledge relation perception

Abstract

The invention discloses a probability Gaussian embedded knowledge tracking method based on knowledge relation perception, which comprises the following steps of: modeling a relation between questions, and deducing the relation between the questions by counting historical records of students answering different questions. And constructing a question-knowledge concept mixed graph, and mapping the knowledge concepts into probability distribution to model a hierarchical inclusion relationship among different knowledge concepts. According to the method, knowledge concepts are modeled into Gaussian distribution to express a hierarchical inclusion relationship between the knowledge concepts, so that each knowledge concept is regarded as a Gaussian distribution, the mean value of the Gaussian distribution represents the central position of the concept, and the standard deviation reflects the range of the concept. In order to represent partial mapping relations between questions and knowledge concepts, the questions and the knowledge concepts are mapped to the same representation space, and then Gaussian mixture distribution is adopted to achieve the purpose. The overall knowledge state of the students is modeled through historical answer records of the students, so that the answer conditions of the students at the next moment are deduced. According to the method, the accuracy of predicting the answer condition of the student is obvious, and more accurate and personalized learning content recommendation can be provided for the student.

Description

Technical Field

[0001] The present invention belongs to the technical field of educational data mining, and relates to a probabilistic Gaussian embedding knowledge tracking method based on knowledge relationship perception. Background Art

[0002] With the rapid development of digital technology, online education platforms such as intelligent assistance systems (ITS) and massive open online courses (MOOCS) are emerging. In order to improve the performance and interpretability of existing knowledge tracing models, the following issues should be addressed:

[0003] First, the hierarchical inclusion relationship between knowledge concepts is not considered.

[0004] Knowledge concepts not only have implicit multidimensional relationships, but also contain hierarchical inclusion relationships. Similar knowledge concepts, while showing semantic similarity, also involve more complex inclusion and implication relationships, resulting in different knowledge contents represented by different knowledge concepts. When students master a wider range of knowledge content, that is, higher-order knowledge concepts, they can obtain richer knowledge benefits. This is because students who can understand and apply higher-order knowledge concepts usually have a good grasp of the basic knowledge concepts contained in the above higher-order knowledge concepts. In the real world, two related knowledge concepts can be randomly selected and marked as A and B. Suppose A represents "Rounding" and B represents "Estimation". Since "Rounding" is a specific method of "Estimation", that is, an inclusion relationship, when students have mastered the knowledge concept B of estimation, it can be inferred that they have a great understanding of the knowledge concept A of rounding.

[0005] Second, some mapping relationships between knowledge concepts and questions are not considered.

[0006] There is not only a direct multi-dimensional relationship between questions and knowledge concepts. Questions and the knowledge concepts involved are not completely and simply mapped one-to-one. Different knowledge concepts may represent different knowledge content in the same question. The existence of this relationship makes students have different levels of mastery of the different knowledge concepts involved in a question after completing it. For example, the question "10000+1000×10%=?" involves both "integer addition" and "percentage". However, "integer addition" belongs to more basic knowledge and is the most basic content in algebra learning, while "percentage" is a higher-level concept involving the conversion and application between fractions, decimals and percentages. Therefore, in the process of solving this question, students will have different mastery and benefits of these two different levels of knowledge concepts.

[0007] Third, the fine-grained dynamic characteristics of students are not considered

[0008] Students’ learning activities are a dynamic process, and their knowledge status will change as the learning process progresses. Specifically, the knowledge status mainly reflects the students’ mastery of different knowledge concepts. Therefore, when modeling knowledge concepts, it is necessary to consider the hierarchy and inclusion relationship between them, and use fine-grained knowledge concept features to more accurately characterize the students’ knowledge status, thereby improving the interpretability of the model. Summary of the invention

[0009] In order to effectively solve the above problems, the present invention proposes a probabilistic Gaussian embedding knowledge tracking method based on knowledge relationship perception. This method can provide students with more accurate and personalized learning content recommendations, and can also adjust the difficulty of learning tasks according to students' actual mastery, ensuring a balance between learning challenges and abilities, avoiding students' anxiety, and significantly improving learning outcomes.

[0010] The technical solution adopted by the present invention is as follows:

[0011] A probabilistic Gaussian embedding knowledge tracking method based on knowledge relationship perception includes the following steps:

[0012] Step 1: Model the relationship between questions

[0013] The relationship between questions can be inferred by counting students' historical answers to different questions. When the same student answers two different questions, if he gets question A wrong, he is more likely to get question B wrong; or if he gets question A right, he is more likely to get question B right, which indicates that there is a certain connection between the two questions. Through the overall analysis and statistics of the answer records, the relationship diagram between questions can be inferred and constructed.

[0014] Step 2: Construct a mixed graph of questions and concepts

[0015] In knowledge tracking, there is a multi-dimensional complex relationship between questions and knowledge concepts. There are not only various levels of associations between questions, but also various connections between knowledge concepts. Questions and knowledge concepts are also intertwined, representing which knowledge concepts are involved in the problem, forming a complex relationship graph. In order to fully depict the complex relationship between the above questions and knowledge concepts, it is particularly important to construct a question-knowledge concept hybrid graph. By integrating the question relationship graph and the question-knowledge concept relationship graph, the construction of the question-knowledge concept hybrid graph is realized. The details are as follows:

[0016] Step 2-1: Topic relationship graph construction: In order to obtain effective topic representation, the relationship obtained in step 1 is converted into a graph representation, and a threshold ω is set to control whether there is an edge between two topics.

[0017] The title graph can be defined as in:

[0018] Topic edge weight W: represents the strength of the relationship between different topics.

[0019] W={w ij |e ij ∈E} (1)

[0020] w ij =Relate(v i ,v j ) (2)

[0021] In formula (1) and (2), w ij Represents edge e ij The weight of Relate(v i ,v j ) is to infer the similarity between questions by counting students' historical interaction data.

[0022] Edge set E: represents the relationship between questions. If question q i and topic q j If there is a relationship between i and q j There is an undirected edge between them, namely: E = {e ij |w ij ≥ω}(3)

[0023] In formula (3), ω represents a threshold hyperparameter, which is used to measure the strength of the relationship between questions. Only when the relationship coefficient exceeds the threshold, it is considered that there is a significant correlation between the questions.

[0024] Node set V: represents the set of question nodes. That is: V = Q (4)

[0025] In formula (4), Q represents the set of questions.

[0026] Step 2-2: Constructing the question-knowledge concept relationship graph: By analyzing the knowledge points involved in each question, establish the mapping relationship between the question and the knowledge concept, and connect the question node and the knowledge concept node in the form of a bipartite graph. The construction process is:

[0027] Step 2-3: Construction of a question-knowledge concept hybrid graph: It contains the direct connection between questions and knowledge concepts, and also reflects the similarity between questions based on content or structure. In the hybrid graph, nodes are divided into two categories: question nodes and knowledge concept nodes. Question nodes are connected by edges, indicating the similarity in question content, difficulty, etc.; while the edges between question and knowledge concept nodes indicate that the questions involve or test specific knowledge concepts. In this way, the hybrid graph not only reveals the intrinsic relationship between questions, but also clarifies the knowledge points corresponding to each question, thereby providing rich structural information for the knowledge tracking model and supporting more accurate evaluation and prediction of students' learning status. The construction process of the hybrid graph is:

[0028] For v H ∈V H :If v H ∈Q, then v H Is the topic node. If v H ∈C, then v H It is a knowledge concept node.

[0029] For e H ∈E H :If e H = i ,q j >, where i,j={1,2,…,num q ,i≠j}, then it means question q i With the topic q j There is a similarity relationship. If e H =q i ,c k , where i = {1,2,…,num q}, k = {1,2,…,num c}, then it means e H It is the topic q i Involving c k Knowledge concept.

[0030] Step 3: Map knowledge concepts into probability distributions to model the hierarchical inclusion relationship between different knowledge concepts.

[0031] The hierarchical inclusion relationship between knowledge concepts is expressed by modeling them as Gaussian distribution. Each knowledge concept is thus regarded as a Gaussian distribution, whose mean represents the central position of the concept and the standard deviation reflects the scope of the concept. The details are as follows:

[0032] ​Step 3-1: By walking in the question-knowledge concept mixed graph, the semantic similarity between knowledge concepts can be effectively captured. The walk starts from a starting knowledge concept, passes through the question nodes related to it, and then finds other question nodes with higher relevance in the question nodes, and continues to walk until it finally returns to the target knowledge concept. Through this walking process, a "knowledge concept related sequence" is generated, in which the starting and ending parts of the sequence correspond to semantically similar knowledge concepts, and the middle part contains questions associated with these knowledge concepts.

[0033]

[0034] In formula (5), when the walk starts, Γ(v 0 )=0, indicating that the walking pointer is at the knowledge concept node at this time, and the walking process ends with Γ(v L )=0.

[0035] The transition probability p(v i+1 |v i ) is defined as follows:

[0036] p(v i+1 |v i )=p(t|v i )p(v i+1 |t,v i ) (6)

[0037] In formula (6), the formulas of each sub-item are:

[0038] t=Γ(v i ) (7)

[0039]

[0040] In formula (7), (8), (9), (10), w i ,w i+1 represents the weight of the edge between topics, represents the weight of the edge between the question and the knowledge concept, and c is a damping coefficient used to penalize the length of the walk sequence. The essence of this walk strategy is to learn the similarity between different knowledge concepts and simultaneously represent their contextual relationship from the perspective of the question. The more similar the semantic relationship between two knowledge concepts is, the greater the probability that they appear in the same sequence.

[0041] Step 3-2: Get positive and negative sample noise related to the topic from the generated "knowledge concept related sequence". Specifically, positive samples refer to the topics related to the knowledge concepts obtained by hybrid graph walking in step 3-1, and the strength of the relationship is controlled by adjusting the hyperparameters, while negative samples are topics unrelated to the above knowledge concepts.

[0042] Step 3-3: In order to intuitively represent the hierarchical relationship of different concepts in the probability space, so as to more naturally capture the inclusion relationship between concepts, the knowledge concepts are mapped to the probability space. Specifically: the loss of positive sample pairs is brought closer and the loss of negative sample pairs is alienated through KL divergence. The goal is to push the score of positive sample pairs higher than that of negative sample pairs by setting the margin. In order to further optimize this process, the Max Margin Ranking strategy is adopted. This strategy ensures that the model has stronger discriminative ability in distinguishing related and unrelated knowledge concepts by maximizing the marginal difference between positive and negative sample pairs. Finally, the knowledge concepts are mapped to the Gaussian distribution in the same representation space.

[0043]

[0044] In formula (11) and (12), KL divergence is used to measure knowledge concepts The probabilistic similarity between them can be used to learn the hierarchical inclusion relationship between knowledge concepts.

[0045] Step 4: To represent the partial mapping relationship between questions and knowledge concepts, first map them to the same representation space, and then use Gaussian mixture distribution to achieve the purpose. The details are as follows:

[0046] Step 4-1: Since different knowledge concepts in the questions involve different knowledge categories, and the contents expressed by different knowledge concepts in the same question are also different, in order to obtain the weights of the knowledge concepts contained in different questions, a graph convolutional neural network (GCN) based on question relations is used to perceive the similarity between different questions by aggregating the neighbors of different question nodes.

[0047]

[0048] In formula (13), w l and b l are learnable weights and bias coefficients. σ is a nonlinear activation function.

[0049]

[0050] In formula (14), W is the initialized weight matrix, and α is the weight fraction of the Gaussian mixture, which should satisfy α i >0 and

[0051] Step 4-2: Use the mixing coefficient obtained in step 4-1 to distinguish the performance of different knowledge concepts in the question. Specifically, use Gaussian mixture distribution to merge the distribution of each knowledge concept, so as to more accurately represent the comprehensive impact of different knowledge concepts in the question.

[0052]

[0053] In formula (15), C i It is the topic q i The set of knowledge concepts involved, α i It is the weight of the knowledge concepts involved in the question, which means that different knowledge concepts in the question represent different knowledge categories. Representing knowledge concepts The representation of the kth knowledge concept in .

[0054] Step 5: When modeling the dynamic changes in students’ knowledge status, not only the students’ performance results on future questions are considered, but also the students’ performance in answering different knowledge concepts is comprehensively considered.

[0055] First, the overall knowledge state of students is modeled through their historical answer records, so as to infer their answers at the next moment. In order to fully consider the contextual relationship during the students' practice, the present invention introduces the attention mechanism as an encoder, which aims to capture the long-term contextual dependencies in students' historical learning, so as to more accurately understand the students' learning trajectory.

[0056] Secondly, we introduce probabilistic embedding of knowledge concepts with hierarchical inclusion relations and probabilistic embedding of questions with partial mapping relations to supplement students’ historical answer information. Probabilistic embedding representation can more carefully depict the state changes of students on various knowledge concepts and questions, and effectively integrate the hierarchical relationships between different concepts, thus providing more accurate predictions for students’ future performance.

[0057] Finally, the model is supervised and trained through the cross entropy loss function to optimize the prediction effect of the model.

[0058] Step 5-1: Generate the student's dynamic knowledge state representation through the sampled probability distribution embedding, where each Gaussian distribution represents the student's knowledge state under a specific knowledge concept. The mean and variance of the Gaussian distribution reflect the student's mastery of the knowledge concept and the distribution range of the knowledge, respectively. With the help of the mixed Gaussian model, it is possible to quantify the student's mastery of the question at the fine-grained level, and the mixed probability model of the question reflects the various parts represented by different knowledge concepts. In order to reasonably represent the embedded information, the reparameterization trick is used to sample and embed the probability distribution to obtain its embedded information. Specifically, by reparameterizing and sampling the Gaussian distribution of the knowledge concept and the Gaussian mixture model of the question, their specific embedded representations are obtained. At this point, the embedded information incorporates the high-dimensional information of the above-mentioned hierarchical structure, inclusion relationship, and partial mapping relationship.

[0059] Step 5-2: Then, the knowledge concept embedding and question embedding of the hierarchical inclusion relationship and partial mapping relationship are used as the representation of the student’s current learning content, and then the student’s historical learning record is modeled through the long short-term memory network (LSTM) to obtain the student’s knowledge status.

[0060] Step 5-3: Finally, a two-layer fully connected neural network is used to further optimize the student’s knowledge state and better align it with the knowledge concept. The verification is performed by combining the student’s current knowledge state and the question performance at the next moment, thereby predicting the student’s answer performance on the next question.

[0061] Step 5-4: In order to more accurately model the student's knowledge status, the loss function is used to jointly optimize the model: supervised cross entropy loss is applied to the student's performance on the question, and its optimization goal is to minimize the loss between the student's answer and the correctness prediction probability. The model is trained by minimizing the loss function using the Adam optimizer.

[0062] The beneficial effect of the present invention is that compared with the traditional method, the present method has obvious accuracy in predicting students' answers and can provide students with more accurate and personalized learning content recommendations. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 An overall flow chart of the method provided by an embodiment of the present invention.

[0064] Figure 2 A topic relationship diagram of the method provided by an embodiment of the present invention.

[0065] Figure 3 A topic-knowledge concept relationship diagram of the method provided by an embodiment of the present invention.

[0066] Figure 4 A topic-knowledge concept hybrid graph of the method provided in an embodiment of the present invention.

[0067] Figure 5 A schematic diagram of a knowledge concept related sequence used by the method provided in an embodiment of the present invention.

[0068] Figure 6 The method provided in the embodiment of the present invention adopts a knowledge concept probability embedding distribution graph.

[0069] Figure 7 A schematic diagram of neighbor topic aggregation in graph convolution adopted by the method provided in an embodiment of the present invention.

[0070] Figure 8 The method provided in the embodiment of the present invention adopts a structural diagram of the dynamic process of modeling students.

[0071] Fig. 9 The method provided by the embodiment of the present invention includes a modeling result diagram for the actual level of knowledge concepts.

[0072] Fig.10 A schematic diagram of the knowledge state of learning a small amount of interactive data by the method provided by an embodiment of the present invention.

[0073] Fig.11 Comparison chart of the performance of predicting students' future knowledge performance by the method provided by the embodiment of the present invention DETAILED DESCRIPTION

[0074] The specific embodiments of the present invention are described in detail below in combination with the technical solutions and the accompanying drawings.

[0075] Example 1

[0076] This embodiment is as follows: Figure 1 As shown, the following steps are included:

[0077] Step 1: Model the relationship between questions: Infer the relationship between questions by counting the student's historical answers to different questions. Specifically, when the same student answers two different questions, if he gets question A wrong, he is more likely to get question B wrong, or if he gets question A right, he is more likely to get question B right, which indicates that there is a certain connection between the two questions. By analyzing the answer records as a whole, a relationship diagram between questions can be constructed. Use Relate(q 1 →q 2 ) to represent two questions q 1 and q 2 The higher the relationship coefficient, the higher the similarity between the two questions. The specific calculation formula is as follows:

[0078]

[0079] In formula (1), max is used to ensure the non-negativity of the correlation coefficient. is the probability score, corresponding to the same answer and the overall answer, ln(x) represents the natural logarithm, which is used to measure the relative size of the relationship coefficient. It is calculated by counting the performance of students in answering two different questions. The specific calculation method is as follows:

[0080]

[0081] In formula (2) and (3), Count((q i ,q j )=(r i ,r j )) means that in the process of students answering, first i Answer i , then q j Answer j The number of times. and Indicates the student's answer to question q i Answer true or false. To prevent the denominator from being too small, a Laplace smoothing parameter of 0.01 is added.

[0082] Step 2: Construct a mixed graph of questions and knowledge concepts: In knowledge tracking, there are complex multi-dimensional relationships between questions and knowledge concepts. Not only are there various levels of associations between questions, but there are also various connections between knowledge concepts. Questions and knowledge concepts are also intertwined, representing which knowledge concepts are involved in the problem, forming a complex relationship graph. In order to fully depict the complex relationship between the above questions and knowledge concepts, it is particularly important to construct a mixed graph of questions and knowledge concepts. By integrating the question relationship graph and the question-knowledge concept relationship graph, the construction of the question-knowledge concept mixed graph is realized. Specifically:

[0083] Step 2-1: Topic relationship diagram construction: In order to obtain effective topic representation, such as Figure 2 As shown, the relationship obtained in step 1 is converted into a graph representation. Specifically, a threshold ω is set to control whether there is an edge between two questions. The formal representation is:

[0084] The title graph can be defined as The topic edge weight W represents the strength of the relationship between different topics, w ij

[0085] Represents edge e ij The weight of Relate(v i ,v j ) is to infer the similarity between questions by counting students' historical interaction data.

[0086] W={w ij |e ij ∈E} (4)

[0087] w ij =Relate(v i ,v j ) (5)

[0088] Edge set E: represents the relationship between questions. If question q i and topic q j If there is a relationship between i and q j There is an undirected edge between them, namely: E = {e ij |w ij ≥ω}(6)

[0089] In formula (6), ω represents a threshold hyperparameter, which is used to measure the strength of the relationship between questions. Only when the relationship coefficient exceeds the threshold, it is considered that there is a significant correlation between the questions.

[0090] Node set V: represents the set of question nodes. That is: V = Q (7)

[0091] Among them, Q represents the set of questions.

[0092] Step 2-2: Constructing the question-knowledge concept relationship graph: By analyzing the knowledge points involved in each question, establish the mapping relationship between the question and the knowledge concept, and connect the question node and the knowledge concept node in the form of a bipartite graph. Figure 3 As shown, the question-knowledge concept graph can be defined as a bipartite graph: The specific formalization is:

[0093] Binary relation adjacency matrix R: represents the relationship between the question and the knowledge concept, that is:

[0094] R=[r ij ]∈{0,1} |Q|×|C| (8)

[0095] Among them, if the question q i With knowledge concept c j If there is a relationship between ij =1, otherwise r ij =0.

[0096] Node set V: It includes knowledge concepts and topic nodes. That is: V = Q∪C (9)

[0097] Among them, Q represents the set of question nodes, and C represents the set of knowledge concept nodes.

[0098] Edge set E: represents the relationship between nodes. If question q i With knowledge concept c j is related (that is, the question examines this knowledge concept), then q i and c j There is an undirected edge between them. That is: E={(q i ,c j )|r ij =1}(10)

[0099] Step 2-3: Construct a mixed graph of questions and knowledge concepts: It contains the direct connection between questions and knowledge concepts, and also reflects the similarity between questions based on content or structure. In the mixed graph, nodes are divided into two categories: question nodes and knowledge concept nodes. Question nodes are connected by edges, indicating the similarity in question content, difficulty, etc.; and the edges between question and knowledge concept nodes indicate that the questions involve or test specific knowledge concepts. In this way, the mixed graph not only reveals the intrinsic relationship between questions, but also clarifies the knowledge points corresponding to each question, thereby providing rich structural information for the knowledge tracking model, helping to more accurately evaluate and predict students' learning status. Figure 4 As shown, the question-knowledge concept mixed graph is represented as Specifically:

[0100] For v H ∈V H :If v H ∈Q, then v H is the topic node; if v H ∈C, then v H It is a knowledge concept node.

[0101] For e H ∈E H :If e H = i ,q j >, where i,j={1,2,…,num q ,i≠j}, then it means question q i With the topic q j There is a similarity relationship. If e H =q i ,c k , where i = {1,2,…,num q}, k = {1,2,…,num c}, then it means e H It is the topic q i Involving c k Knowledge concept.

[0102] ​Step 3: Map knowledge concepts into probability distributions to model the hierarchical inclusion relationship between different knowledge concepts. The hierarchical inclusion relationship between knowledge concepts is expressed by modeling them as Gaussian distributions. Each knowledge concept is thus considered as a Gaussian distribution, whose mean represents the central position of the concept and the standard deviation reflects the range of the concept. Specifically:

[0103] Step 3-1: By walking in the question-knowledge concept mixed graph, the semantic similarity between knowledge concepts can be effectively captured. The walk starts from a starting knowledge concept, passes through the question nodes related to it, and then finds other question nodes with higher relevance in the question nodes, and continues to walk until it finally returns to the target knowledge concept. Through this walking process, a "knowledge concept related sequence" is generated, such as Figure 5 As shown in the figure, the beginning and end of the sequence correspond to knowledge concepts with similar semantics, while the middle part contains questions related to these knowledge concepts. The specific walking strategy is as follows:

[0104]

[0105] In formula (11), when the walk starts, Γ(v 0 )=0, indicating that the walking pointer is at the knowledge concept node at this time, and the walking process ends with Γ(v L )=0.

[0106] The transition probability p(v i+1 |v i ) is defined as follows:

[0107] p(v i+1 |v i )=p(t|v i )p(v i+1 |t,v i ) (12)

[0108] In formula (12), the formulas of each sub-item are:

[0109] t=Γ(v i ) (13)

[0110]

[0111] In formulas (13), (14), (15), and (16), w i ,w i+1 represents the weight of the edge between topics, represents the weight of the edge between the question and the knowledge concept, and c is a damping coefficient used to penalize the length of the walk sequence. The essence of this walk strategy is to learn the similarity between different knowledge concepts and simultaneously represent their contextual relationship from the perspective of the question. The more similar the semantic relationship between two knowledge concepts is, the greater the probability that they appear in the same sequence.

[0112] Step 3-2: Get positive and negative sample noise related to the topic from the generated "knowledge concept related sequence". Specifically, positive samples refer to the topics related to the knowledge concepts obtained by hybrid graph walking in step 3-1, and the strength of the relationship is controlled by adjusting the hyperparameters, while negative samples are topics unrelated to the above knowledge concepts.

[0113]

[0114] Where: Sample v concept From P sim (u * ), determined by the probability of the knowledge concept appearing in the above walk algorithm, negative samples Sampling from uncorrelated noise.

[0115] Step 3-3: In order to intuitively represent the hierarchical relationship between different concepts in the probability space, so as to more naturally capture the inclusion relationship between concepts, the knowledge concepts are mapped to the probability space. Specifically: the KL divergence is used to bring the loss of positive sample pairs closer and alienate the loss of negative sample pairs. The goal is to push the score of positive sample pairs higher than that of negative sample pairs by setting the margin. In order to further optimize this process, the Max Margin Ranking strategy is adopted. This strategy ensures that the model has stronger discriminative ability in distinguishing related and unrelated knowledge concepts by maximizing the marginal difference between positive and negative sample pairs. Finally, the knowledge concepts are mapped to the Gaussian probability distribution in the same representation space, such as Figure 6 shown.

[0116]

[0117]

[0118] In formula (18) and (19), KL divergence is used to measure knowledge concepts The similarities between them are used to learn the hierarchical inclusion relationship between knowledge concepts.

[0119] Step 4: To represent the partial mapping relationship between questions and knowledge concepts, first map them to the same representation space, and then use Gaussian mixture distribution to achieve the purpose. The specific process is as follows:

[0120] Step 4-1: Since different knowledge concepts in the questions involve different knowledge categories, and the contents expressed by different knowledge concepts in the same question are also different, in order to obtain the weights of the knowledge concepts contained in different questions, a graph convolutional neural network (GCN) based on question relations is used to perceive the similarity between different questions by aggregating the neighbors of different question nodes, such as Figure 7 As shown. In the topic relationship graph, its neighbor node set is Then the GCN formula of the lth layer can be expressed as:

[0121]

[0122] In formula (20), w l and b l are learnable weights and bias coefficients. σ is a nonlinear activation function.

[0123]

[0124] In formula (21), W is the initialized weight matrix, and α is the weight fraction of the Gaussian mixture, which should satisfy α i >0 and

[0125] Step 4-2: For any question Gaussian mixture model P(x):

[0126]

[0127] E can be obtained by P (x) Expectation: First, from the Gaussian distribution of each knowledge concept We then use the weight α to mix these expectations to get E P (x). The proof is as follows:

[0128]

[0129] Therefore, the mixing coefficient obtained in step 4-1 is used to distinguish the performance of different knowledge concepts in the questions. Specifically, the distribution of each knowledge concept is fused using Gaussian mixture distribution, so as to more accurately represent the comprehensive influence of different knowledge concepts in the question.

[0130]

[0131] In formula (24), C i It is the topic q i The set of knowledge concepts involved, α i It is the weight of the knowledge concepts involved in the question, which means that different knowledge concepts in the question represent different knowledge categories. Representing knowledge concepts The representation of the kth knowledge concept in .

[0132] Step 5: When modeling the dynamic knowledge state changes of students, the present invention not only considers the performance results of students in future questions, but also comprehensively considers the performance of students in answering different knowledge concepts. Specifically, first, the overall knowledge state of students is modeled through their historical answer records, so as to infer the students' answers at the next moment. In order to fully consider the contextual relationship during the students' practice process, the present invention introduces the attention mechanism (Attention) as an encoder, aiming to capture the long-term contextual dependencies in students' historical learning, so as to more accurately understand the students' learning trajectory. Secondly, the knowledge concept probability embedding that introduces hierarchical inclusion relationships and the question probability embedding that introduces partial mapping relationships are used to supplement the students' historical answer information. The probabilistic embedding representation can more carefully characterize the state changes of students in various knowledge concepts and questions, and effectively integrate the hierarchical relationships between different concepts, thereby providing more accurate predictions for students' future performance. Finally, the model is supervised and trained through the cross entropy loss function to optimize the prediction effect of the model.

[0133] Step 5-1: First, we construct the representation x of the initial question by combining the embeddings of the question Q and the knowledge concept C in the student’s historical practice record S t , that is, x t =q t +c t , then based on each student’s historical answers, an encoder based on the attention mechanism is used to capture the long-term contextual dependencies of knowledge concepts in the student’s historical learning, thereby finding the potential dependencies between knowledge concepts. Specifically, in order to model the current answer question x t Same as previously answered question x i of relevance.

[0134] Step 5-2: Generate the student's dynamic knowledge state representation through the probability distribution embedding after sampling, where each Gaussian distribution represents the student's knowledge state under a specific knowledge concept. The mean and variance of the Gaussian distribution reflect the student's mastery of the knowledge concept and the distribution range of the knowledge, respectively. With the help of the mixed Gaussian model, it is possible to quantify the student's mastery of the question at a fine-grained level, while the mixed probability model of the question reflects the various parts represented by different knowledge concepts. Specifically, by reparameterizing and sampling the Gaussian distribution of the knowledge concept and the Gaussian mixture model of the question, their specific embedding representation is obtained. At this point, the embedded information incorporates the high-dimensional information of the above-mentioned hierarchical structure, inclusion relationship, and partial mapping relationship.

[0135] Given a Gaussian distribution with mean μ and covariance Σ, we can get Sampling x: First, from the standard normal distribution Then calculate

[0136]

[0137] So far, the sampling embedding results E of the probability distribution of the topic and knowledge concept are obtained respectively. N (q), E N (c) The embedding contains the hierarchical inclusion relationship between the topics and the partial mapping information between the topics and the knowledge concepts.

[0138] Step 5-3: The knowledge concept embedding and question embedding of the hierarchical inclusion relationship and partial mapping relationship are used as the representation of the student’s current learning content, and then the student’s historical learning records are modeled through the long short-term memory network (LSTM) to obtain the student’s knowledge status.

[0139] First, at each time step t, the topic is embedded into q t and knowledge concept embedding c t Combine students' answers to questions and embed them into t Splice and expand t is a feature vector Get the final problem representation

[0140]

[0141] In formula (26), Represents a vector concatenation operation.

[0142] The following is the detailed process of the Long Short-Term Memory Network (LSTM), such as Figure 8 As shown in Figure 1, LSTM uses three gating mechanisms and two states to implement the flow and update of information internally. At time step t, LSTM uses the input vector x t and the hidden state vector h at the previous moment t-1 , after four different neural network layers, the input gate i is generated t 、Forget gate t , output gate o t and the current information flow Specifically, t , f t and t Represent the three gating mechanisms of input gate, forget gate and output gate respectively, and Represents the information flow at the current moment.

[0143] These gating mechanisms and Together they control the memory, forgetting and output of information. t and the memory state c of the previous moment t-1 The interaction of f determines the degree to which the model forgets the state of the previous moment. Specifically, f t ∈[0,1], if f t A value of 0 means complete forgetting Similarly, the input gate i t and The interaction controls the memory of the current state. Then, the results of the input gate and the forget gate are combined to obtain the memory state c at the current moment. t .

[0144] Finally, the output gate o t Interact with the memory state c_t to generate the current hidden state h t , used for subsequent calculations.

[0145] i t =σ(W i [x t ,h t-1 ]+b i ) (26)

[0146] f t =σ(W f [x t ,h t-1 ,]+b f ) (27)

[0147] o t =σ(W o [x t ,h t-1 ]+b o ) (28)

[0148]

[0149] h t =o t tanh(c t ) (31)

[0150] Wherein formula (26), (27), (28), (29), (30), (31), W i , W f , W o , W c is the learnable weight matrix, b i 、b f 、b o 、b cis a learnable bias, σ(·) and tanh(·) are nonlinear activation functions.

[0151] Step 5-4: Finally, a two-layer fully connected neural network is used to further optimize the student’s knowledge state and better align it with the knowledge concept. The verification is performed by combining the student’s current knowledge state and the question performance at the next moment to predict the student’s answer performance on the next question.

[0152] h t =ReLU(W 2 ReLU(W 1 ·h t +b 1 )+b 2 )) (32)

[0153] r t+1 =σ(W r ·(h t ·x t+1 )+b r ) (33)

[0154] In formula (32), (33), W 1 , W 2 , b 1 , b 2 , W r , b r are the learnable bias and weight matrices respectively. ReLU(·), σ(·) are the activation functions.

[0155] Step 5-5: In order to more accurately model the student's knowledge status, the loss function is used to jointly optimize the model: supervised cross entropy loss is applied to the student's performance on the question, and its optimization goal is to minimize the loss between the student's answer and the correctness prediction probability. Specifically:

[0156]

[0157] In formula (34), r t+1 It is 1 or 0, 1 means the answer is correct, 0 means the answer is wrong. The model predicts the student's answer results. The model is trained by minimizing the loss function using the Adam optimizer.

[0158] The results of this example are Fig. 9As shown, by setting the expected value of the Gaussian distribution as the center position of the knowledge concept, the covariance matrix defines the knowledge category covered by the knowledge concept. Through the visualization of probability distribution, the hierarchical structure of knowledge concepts and their inclusion relationships can be more intuitively displayed. Taking algebra in mathematics as an example, "natural numbers" refers to a set of non-negative integers starting from 0, so it is included in the broader "integer" set. In addition, the area that partially overlaps with the "integer" knowledge concept represents the knowledge concept of "negative number addition", indicating that "negative number addition" mainly acts on the "negative number" sub-concept part in the integer set. At the same time, the "negative fraction addition" sub-knowledge concept in "negative number addition" may be involved in the non-overlapping area. Therefore, the method of the present invention can make complex hierarchical structures and inclusion relationships clearer and easier to understand.

[0159] Example 2: Path optimization and construction of knowledge hierarchy relationships on intelligent learning platform

[0160] In existing online learning platforms, although the platforms can provide certain personalized learning recommendations, the relationship between knowledge concepts cannot be accurately captured, which often leads to inaccurate recommendations for learning paths. Students may miss the consolidation of basic knowledge or enter an overly complex learning stage during the learning process. Through this patented method, the platform can accurately organize the knowledge structure based on the hierarchical relationship of knowledge concepts, capture the learning order, and thus develop a more personalized learning route for students. This method not only helps the platform optimize the learning path, ensures that students master the basic knowledge at the appropriate stage and gradually transition to more advanced learning content, but also effectively improves learning outcomes, avoids gaps in students' knowledge mastery, and achieves steady knowledge progress. Through precise knowledge tracking and dynamic adjustment, this patented method can provide existing platforms with a powerful tool to enhance personalized learning experience and solve the problem of insufficient learning path planning in traditional platforms.

[0161] Example 3: Personalized knowledge mastery assessment and learning path optimization based on a small amount of learning interaction data

[0162] In existing online learning platforms, the platform usually records students' answers, accuracy, answering time and other data in each exercise to count and analyze students' overall knowledge mastery. However, this method often requires students to study on the platform for a period of time before their knowledge mastery level can be more accurately assessed. In fact, with the help of this patented method, students can accurately reflect their mastery of certain basic concepts through a small amount of interactive data in the early learning stage, thereby achieving earlier knowledge level assessment and personalized learning recommendations.

[0163] By capturing and analyzing students' learning interaction records, this patented method can accurately identify students' mastery of basic knowledge and automatically infer the knowledge points they have mastered, such as Fig.10 As shown, combined with the patent method, it can be seen that after the student interacts with the knowledge concept for the first time, the platform can quickly understand the student's mastery of other related basic knowledge. Traditional methods usually use random initialization for knowledge concepts, so that the difference between the mastery of knowledge concepts and related knowledge concepts may be as high as 70% or even higher, while the patent method can quickly adjust its mastery after capturing the relevant knowledge concept, so that the difference is reduced to less than 10%. This means that although students may not have directly learned a certain knowledge concept, the platform can still accurately infer that the student has mastered the relevant basic knowledge through their excellent performance in more advanced knowledge concepts. At the same time, the platform can continue to track the student's learning progress and keep abreast of their mastery of different knowledge concepts. If the platform finds that the student performs well in higher-level tasks, it will infer that the student has mastered the corresponding basic knowledge, thereby avoiding students from repeating the content they have mastered and improving learning efficiency.

[0164] By modeling the dynamic knowledge status of students, this patented method can accurately and effectively predict how students will perform in answering future questions. This not only helps to personalize the recommendation of learning content, but also adjusts teaching strategies in real time and provides targeted feedback. By deeply analyzing the knowledge mastery progress of each student, the system can tailor a personalized learning path for the student.

[0165] Example 4: Dynamically track students' knowledge mastery level and personalize students' learning content

[0166] In existing online learning platforms, students’ mastery of different knowledge points is usually inferred through the questions they have interacted with in the past and the knowledge concepts involved. However, these platforms often ignore the dynamic changes in students’ knowledge status and personalized needs, resulting in recommended content and learning paths that are too fixed and single, and unable to adapt to the unique progress and interests of each student. As a result, students’ learning experience may be limited, and they may even feel frustrated or dislike learning when faced with questions that are too difficult or too easy. In contrast, the patented method can accurately track and predict students’ learning progress in real time by dynamically modeling their knowledge status. Fig.11 As shown, compared with the traditional method, the patented method has improved the accuracy of predicting students' answers by 4.32%. Based on this advantage, the system can provide students with more accurate and personalized learning content recommendations. In addition to recommending appropriate learning content, the patented method can also adjust the difficulty of learning tasks according to the students' actual mastery, thereby ensuring a balance between learning challenges and abilities, avoiding students from becoming anxious due to excessive challenges, or losing interest due to overly simple tasks, thereby significantly improving students' learning outcomes and enthusiasm.

Claims

1. A probabilistic Gaussian embedding knowledge tracking method based on knowledge relationship perception, characterized in that: The following steps are involved: Step 1: Model the relationship between questions The relationship between the questions is inferred by counting the students' historical answers to different questions. When the same student answers two different questions, if he gets question A wrong, he is more likely to get question B wrong, or if he gets question A right, he is more likely to get question B right, which indicates that there is a certain connection between the two questions. Through the overall analysis and statistics of the answer records, the relationship diagram between the questions is inferred and constructed. Step 2: Construct a mixed graph of questions and concepts In knowledge tracking, there is a multi-dimensional complex relationship between questions and knowledge concepts. There are not only various levels of associations between questions, but also various connections between knowledge concepts. Questions and knowledge concepts are also intertwined, representing which knowledge concepts are involved in the problem, forming a complex relationship graph. In order to fully describe the complex relationship between the above questions and knowledge concepts, it is particularly important to construct a question-knowledge concept hybrid graph. By integrating the question relationship graph and the question-knowledge concept relationship graph, the construction of the question-knowledge concept hybrid graph is realized. Step 3: Map the knowledge concepts into probability distributions to model the hierarchical inclusion relationship between different knowledge concepts; express the hierarchical inclusion relationship between knowledge concepts by modeling them as Gaussian distributions; thus, each knowledge concept is regarded as a Gaussian distribution, whose mean represents the central position of the concept and the standard deviation reflects the range of the concept; Step 4: To represent the partial mapping relationship between questions and knowledge concepts, first map them to the same representation space, and then use Gaussian mixture distribution to achieve the purpose; Step 5: When modeling the dynamic knowledge state changes of students, not only the performance results of students on future questions are considered, but also the performance of students' answers on different knowledge concepts are comprehensively considered; First, we model the overall knowledge state of students through their historical answer records, so as to infer their answers at the next moment. In order to fully consider the contextual relationship during students’ practice, we introduce an attention mechanism as an encoder, which aims to capture the long-term contextual dependencies in students’ historical learning, so as to understand students’ learning trajectories more accurately. Secondly, we introduce probabilistic embedding of knowledge concepts with hierarchical inclusion relations and probabilistic embedding of questions with partial mapping relations to supplement students’ historical answer information. Probabilistic embedding representation can more carefully describe the changes in students’ status on various knowledge concepts and questions, and effectively integrate the hierarchical relations between different concepts, thus providing more accurate predictions for students’ future performance. Finally, the model is supervised and trained through the cross entropy loss function to optimize the prediction effect of the model.

2. According to the probabilistic Gaussian embedding knowledge tracking method based on knowledge relationship perception in claim 1, it is characterized in that: The step 2 comprises the following steps: Step 2-1: Topic relationship graph construction: In order to obtain effective topic representation, the relationship obtained in step 1 is converted into a graph representation, and a threshold ω is set to control whether there is an edge between two topics; The question graph is defined as Q =<V,E,W> ,in: Topic edge weight W: represents the strength of the relationship between different topics; W={w ij i.e ij ∈E} (1) w ij =Relate(v i ,v j ) (2) In formula (1) and (2), w ij Represents edge e ij The weight of Relate(v i ,v j ) is to infer the similarity between questions by counting students' historical interaction data; Edge set E: represents the relationship between questions. If question q i and topic q j If there is a relationship between i and q j There is an undirected edge between them, namely: E = {e ij |w ij ≥ω}(3) In formula (3), ω represents a threshold hyperparameter, which is used to measure the strength of the relationship between questions. Only when the relationship coefficient exceeds the threshold, it is considered that there is a significant correlation between the questions. Node set V: represents the set of question nodes; that is, V = Q (4) where Q represents the set of questions; Step 2-2: Constructing the question-knowledge concept relationship graph: By analyzing the knowledge points involved in each question, establish the mapping relationship between the question and the knowledge concept, and connect the question node and the knowledge concept node in the form of a bipartite graph; the construction process is: Step 2-3: Construction of a mixed graph of questions and knowledge concepts: This graph contains the direct relationship between questions and knowledge concepts, and also reflects the similarity between questions based on content or structure. In the mixed graph, nodes are divided into two categories: question nodes and knowledge concept nodes. Question nodes are connected by edges, indicating the similarity in question content, difficulty, etc. The edges between question and knowledge concept nodes indicate that the question involves or tests specific knowledge concepts. In this way, the mixed graph not only reveals the intrinsic relationship between questions, but also clarifies the knowledge points corresponding to each question, thereby providing rich structural information for the knowledge tracking model and supporting more accurate evaluation and prediction of students' learning status. The construction process of the mixed graph is as follows: For v H ∈V H :If v H ∈Q, then v H is the topic node; if v H ∈C, then v H It is a knowledge concept node; For e H ∈E H :If e H = i ,q j >, where i,j={1,2,…,num q ,i≠j}, then it means question q i With the topic q j There is a similarity relationship; if e H =q i ,c k , where i = {1,2,…,num q }, k = {1,2,…,num c }, then it means e H It is the topic q i Involving c k Knowledge concept.​ 3. A probabilistic Gaussian embedding knowledge tracking method based on knowledge relationship perception according to claim 1 or 2, characterized in that: The step 3 comprises the following steps: Step 3-1: By walking in the question-knowledge concept mixed graph, the semantic similarity between knowledge concepts can be effectively captured; the walk starts from a starting knowledge concept, passes through the question nodes related to it, and then finds other question nodes with high relevance in the question nodes, and continues to walk until it finally returns to the target knowledge concept; through this walking process, a "knowledge concept related sequence" is generated, in which the start and end parts of the sequence correspond to semantically similar knowledge concepts, and the middle part contains questions related to these knowledge concepts; In formula (5), when the walk starts, Γ(v 0 )=0, indicating that the walking pointer is at the knowledge concept node at this time, and the walking process ends with Γ(v L ) = 0; The transition probability p(v i+1 |v i ) is defined as follows: p(v i+1 |v i )=p(t|v i )p(v i+1 |t,v i ) (6) In formula (6), the formulas of each sub-item are: t=Γ(v i ) (7) In formula (7), (8), (9), (10), w i ,w i+1 represents the weight of the edge between topics, represents the weight of the edge between the question and the knowledge concept, and c is a damping coefficient used to penalize the length of the walking sequence. The essence of this walking strategy is to learn the similarity between different knowledge concepts and simultaneously represent their contextual relationship from the perspective of the question. If the semantic relationship between two knowledge concepts is more similar, then the probability that they appear in the same sequence is greater. Step 3-2: Obtain positive and negative sample noise related to the questions from the generated "knowledge concept related sequence"; specifically, positive samples refer to questions related to the knowledge concepts obtained by hybrid graph walking in step 3-1, and the strength of the relationship is controlled by adjusting hyperparameters, while negative samples refer to questions that are unrelated to the above knowledge concepts; Step 3-3: Use KL divergence to bring the loss of positive sample pairs closer and alienate the loss of negative sample pairs; The goal is to push the score of the positive sample pair higher than that of the negative sample pair by setting the margin. To further optimize this process, the maximum margin sorting strategy is adopted. This strategy ensures that the model has stronger discrimination ability in distinguishing related and irrelevant knowledge concepts by maximizing the marginal difference between positive and negative sample pairs. Finally, the knowledge concepts are mapped to the Gaussian distribution in the same representation space. In formula (11) and (12), KL divergence is used to measure knowledge concepts The probabilistic similarity between them can be used to learn the hierarchical inclusion relationship between knowledge concepts.

4. According to the probabilistic Gaussian embedding knowledge tracking method based on knowledge relationship perception of claim 3, it is characterized in that: The step 4 comprises the following steps: Step 4-1: Use a graph convolutional neural network (GCN) based on question relationships to perceive the similarity between different questions by aggregating the neighbors of different question nodes; In formula (13), w l and b l are learnable weights and bias coefficients; σ is a nonlinear activation function; α=softmax(W·x i l ) (14) In formula (14), W is the initialized weight matrix, and α is the weight fraction of the Gaussian mixture, which should satisfy α i >0 and Step 4-2: Use the mixture coefficient obtained in step 4-1 to distinguish the performance of different knowledge concepts in the question; specifically, use Gaussian mixture distribution to merge the distribution of each knowledge concept, so as to more accurately represent the comprehensive impact of different knowledge concepts in the question; In formula (15), C i It is the topic q i The set of knowledge concepts involved, α i It is the weight of the knowledge concepts involved in the question, which means that different knowledge concepts in the question represent different knowledge categories; Gaussian distribution Representing knowledge concepts The representation of the kth knowledge concept in .

5. A probabilistic Gaussian embedding knowledge tracking method based on knowledge relationship perception according to claim 1 or 2, characterized in that: The step 5 comprises the following steps: Step 5-1: Generate the student's dynamic knowledge state representation through the probability distribution embedding after sampling, where each Gaussian distribution represents the student's knowledge state under a specific knowledge concept; the mean and variance of the Gaussian distribution reflect the student's mastery of the knowledge concept and the distribution range of the knowledge respectively; with the help of the mixed Gaussian model, it is possible to quantify the student's mastery of the question at the fine-grained level, and the mixed probability model of the question reflects the various parts represented by different knowledge concepts; in order to reasonably represent the embedded information, the probability distribution is sampled and embedded with the help of the reparameterization technique to obtain its embedded information; specifically, by reparameterizing and sampling the Gaussian distribution of the knowledge concept and the Gaussian mixture model of the question, their specific embedded representation is obtained; at this time, the embedded information integrates the high-dimensional information of the above-mentioned hierarchical structure, inclusion relationship and partial mapping relationship; Step 5-2: Then, the knowledge concept embedding and question embedding of the hierarchical inclusion relationship and partial mapping relationship are used as the representation of the student's current learning content, and then the student's historical learning record is modeled through the long short-term memory network to obtain the student's knowledge state; Step 5-3: Finally, a two-layer fully connected neural network is used to further optimize the student's knowledge state and better align it with the knowledge concept; verification is performed by combining the student's current knowledge state and the question performance at the next moment, thereby predicting the student's answer performance on the next question; Step 5-4: In order to more accurately model the student's knowledge status, the loss function is used to jointly optimize the model: supervised cross entropy loss is applied to the student's performance on the question, and its optimization goal is: Minimize the loss between the student's answer and the predicted probability of correctness; train the model by minimizing the loss function using the Adam optimizer.

6. The probabilistic Gaussian embedding knowledge tracking method based on knowledge relationship perception according to claim 3 is characterized in that: The step 5 comprises the following steps: Step 5-1: Generate the student's dynamic knowledge state representation through the sampled probability distribution embedding, where each Gaussian The distribution represents the knowledge status of students under a specific knowledge concept; the mean and variance of the Gaussian distribution reflect the students' mastery of the knowledge concept and the distribution range of the knowledge respectively; with the help of the mixed Gaussian model, it is possible to quantify the students' mastery of the question at the fine-grained level, and the mixed probability model of the question reflects the various parts represented by different knowledge concepts; in order to reasonably represent the embedded information, the probability distribution is sampled and embedded with the help of the reparameterization technique to obtain its embedded information; specifically, by reparameterizing the Gaussian distribution of the knowledge concept and the Gaussian mixture model of the question, their specific embedded representation is obtained; at this time, the embedded information integrates the high-dimensional information of the above-mentioned hierarchical structure, inclusion relationship and partial mapping relationship; Step 5-2: Then, the knowledge concept embedding and question embedding of the hierarchical inclusion relationship and partial mapping relationship are used as the representation of the student's current learning content, and then the student's historical learning record is modeled through the long short-term memory network to obtain the student's knowledge state; Step 5-3: Finally, a two-layer fully connected neural network is used to further optimize the student's knowledge state and better align it with the knowledge concept; verification is performed by combining the student's current knowledge state and the question performance at the next moment, thereby predicting the student's answer performance on the next question; Step 5-4: In order to more accurately model the student's knowledge status, the loss function is used to jointly optimize the model: supervised cross entropy loss is applied to the student's performance on the question, and its optimization goal is: Minimize the loss between the student's answer and the predicted probability of correctness; train the model by minimizing the loss function using the Adam optimizer.

7. The probabilistic Gaussian embedding knowledge tracking method based on knowledge relationship perception according to claim 4 is characterized in that: The step 5 comprises the following steps: Step 5-1: Generate the student's dynamic knowledge state representation through the sampled probability distribution embedding, where each Gaussian The distribution represents the knowledge status of students under a specific knowledge concept; the mean and variance of the Gaussian distribution reflect the students' mastery of the knowledge concept and the distribution range of the knowledge respectively; with the help of the mixed Gaussian model, it is possible to quantify the students' mastery of the question at the fine-grained level, and the mixed probability model of the question reflects the various parts represented by different knowledge concepts; in order to reasonably represent the embedded information, the probability distribution is sampled and embedded with the help of the reparameterization technique to obtain its embedded information; specifically, by reparameterizing the Gaussian distribution of the knowledge concept and the Gaussian mixture model of the question, their specific embedded representation is obtained; at this time, the embedded information integrates the high-dimensional information of the above-mentioned hierarchical structure, inclusion relationship and partial mapping relationship; Step 5-2: Then, the knowledge concept embedding and question embedding of the hierarchical inclusion relationship and partial mapping relationship are used as the representation of the student's current learning content, and then the student's historical learning record is modeled through the long short-term memory network to obtain the student's knowledge state; Step 5-3: Finally, a two-layer fully connected neural network is used to further optimize the student's knowledge state and better align it with the knowledge concept; verification is performed by combining the student's current knowledge state and the question performance at the next moment, thereby predicting the student's answer performance on the next question; Step 5-4: In order to more accurately model the student's knowledge status, the loss function is used to jointly optimize the model: supervised cross entropy loss is applied to the student's performance on the question, and its optimization goal is: Minimize the loss between the student's answer and the predicted probability of correctness; train the model by minimizing the loss function using the Adam optimizer.

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