A knowledge relationship perception-based probabilistic gaussian embedding knowledge tracking method

Abstract

The application discloses a kind of probability Gaussian embedding knowledge tracking methods based on knowledge relationship perception, comprising the following steps: modeling the relationship between questions, the relationship between questions is inferred by the record of the history of students in different questions answer.Statistical question-knowledge concept hybrid graph is constructed, and knowledge concept is mapped to probability distribution to model the hierarchical containing relationship between different knowledge concepts. The hierarchical containing relationship between knowledge concepts is expressed by modeling them as Gaussian distribution, so that each knowledge concept is regarded as a Gaussian distribution, and the mean value represents the central position of the concept, and the standard deviation reflects the range of the concept.To represent the partial mapping relationship between questions and knowledge concepts, they are first mapped to the same representation space, and then a Gaussian mixture distribution is used to achieve the goal.The overall knowledge state of students is modeled by their historical answer records, so as to infer the answering situation of students at the next moment.The application is obviously accurate in predicting the answering situation of students, and can provide more accurate and personalized learning content recommendation for students.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of educational data mining, and relates to a knowledge tracking method based on knowledge relationship perception and probability Gaussian embedding. BACKGROUND

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

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

[0004] Knowledge concepts not only have implicit multi-dimensional relationships, but also contain hierarchical inclusion relationships. Similar knowledge concepts not only show semantic similarity, but also involve more complex inclusion and entailment relationships, resulting in different knowledge content represented by different knowledge concepts. When students master more knowledge content, i.e., higher-order knowledge concepts, they can gain more knowledge benefits. This is because students who can understand and use high-order knowledge concepts have usually mastered the basic knowledge concepts contained in the high-order knowledge concepts. In the real world, two related knowledge concepts can be randomly selected and labeled as A and B. Suppose A represents "Rounding" and B represents "Estimation". Since "Rounding" is a specific method of "Estimation", i.e., an inclusion relationship, when students have mastered the knowledge concept B of Estimation, it can be inferred that they have a good understanding of the knowledge concept A of Rounding.

[0005] Second, the partial mapping relationship between knowledge concepts and questions is not considered

[0006] There is not only a direct multi-dimensional relationship between questions and knowledge concepts. The relationship between questions and knowledge concepts is not a simple one-to-one mapping. Different knowledge concepts may represent different knowledge content in the same question. The existence of this relationship makes the students' mastery of different knowledge concepts involved in a question different after completing the question. For example, the question "10000+1000x10%=?" involves two knowledge concepts "Integer Addition" and "Percentage". However, "Integer Addition" is a more basic knowledge and is the most basic content in algebra learning, while "Percentage" is a higher-order concept involving the conversion and application between fractions, decimals and percentages. Therefore, students' mastery and benefits of these two different levels of knowledge concepts will be different in the process of answering the question.

[0007] Third, the dynamic characteristics of students are not considered in detail

[0008] The learning activities of students are a dynamic process, and the knowledge state will change continuously as the learning process advances. Specifically, the knowledge state mainly reflects the mastery of students on different knowledge concepts. Therefore, when modeling knowledge concepts, the hierarchy and inclusion relationship between them need to be considered, and the knowledge state of students can be more accurately described through detailed knowledge concept features, thereby improving the interpretability of the model. SUMMARY

[0009] To effectively solve the above problems, the present application provides a probability Gaussian embedding knowledge tracking method based on knowledge relationship perception. This method can provide more accurate and personalized learning content recommendations for students, and can also adjust the difficulty of learning tasks according to the actual mastery of students, ensure the balance between learning challenges and abilities, avoid student anxiety, and significantly improve learning effectiveness.

[0010] The technical scheme adopted by the present application is as follows:

[0011] A probability Gaussian embedding knowledge tracking method based on knowledge relationship perception, comprising the following steps:

[0012] Step 1: Modeling the relationship between questions

[0013] The relationship between questions is inferred by analyzing the historical records of students' answers to different questions. When a student answers two different questions, the probability of making a mistake in question B is high after making a mistake in question A, or the probability of making a mistake in question B is high after making a mistake in question A, which indicates that there is a certain relationship between the two questions. Through overall analysis and statistics of the answer records, the relationship graph between the questions is inferred and constructed.

[0014] Step 2: Constructing a question-knowledge concept hybrid graph

[0015] In knowledge tracking, there are multiple dimensions of complex relationships between questions and knowledge concepts. Not only are there various levels of association between questions, but there are also various connections between knowledge concepts, and questions and knowledge concepts are intertwined, representing the knowledge concepts involved in the questions, 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 fusing the question relationship graph and the question-knowledge concept relationship graph, the construction of the question-knowledge concept hybrid graph is realized. Specifically as follows:

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

[0017] A topic graph can be defined as wherein:

[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] wherein formula (1), (2), w ij represents the weight of edge e ij , Relate(v i , v j ) is the similarity relationship between topics inferred by statistical analysis of historical interaction data of students.

[0022] Edge set E: represents the relationship between topics. If topic q i and topic q j have a relationship, then q i and q j exist a undirected edge, that is: E = {e ij | w ij ≥ ω} (3)

[0023] wherein formula (3), ω represents the threshold parameter, used to measure the strength of the relationship between topics. Only when the relationship coefficient exceeds the threshold, it is considered that there is a significant association between topics.

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

[0025] wherein formula (4), Q represents the set of topics.

[0026] Step 2-2: Topic-knowledge concept relationship graph construction: by analyzing the knowledge points involved in each question, the mapping relationship between the question and the knowledge concept is established, and the question node and the knowledge concept node are connected in the form of bipartite graph. The construction process is:

[0027] Step 2-3: Constructing a hybrid graph of questions and knowledge concepts, which contains direct associations 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, representing the similarity of question content, difficulty, etc. Edges between question and knowledge concept nodes represent that the question involves or tests a specific knowledge concept. In this way, the hybrid graph not only reveals the internal relationship between questions, but also clearly identifies the knowledge points corresponding to each question, providing rich structural information for the knowledge tracking model to support more accurate assessment and prediction of student learning status. The construction process of the hybrid graph is as follows:

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

[0029] For e H ∈ E H : If e H = <q i , q j >, where i, j = {1, 2,..., num q , i ≠ j}, then it represents that question q i has a similarity relationship with question q j . If e H = <q i , c k >, where i = {1, 2,..., num q} and k = {1, 2,..., num c}, then it represents that e H is a question q i involving c k knowledge concept.

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

[0031] Model the hierarchical inclusion relationship between knowledge concepts by modeling them as Gaussian distributions. Thus, each knowledge concept is 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 as follows:

[0032] Step 3-1: The semantic similarity between knowledge concepts can be effectively captured by conducting a walk in the topic-knowledge concept hybrid graph. The walk starts from a starting knowledge concept, goes through the topic nodes related to it, then finds other topic nodes with high relevance in the topic nodes, and continues the walk until it finally returns to the target knowledge concept. Through this walk 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 topics associated with these knowledge concepts.

[0033]

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

[0035] The transition probability p(v i+1 |v i ) of the i-th step is defined as follows:

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

[0037] where formula (6), each sub-formula is:

[0038] t = Γ(v i ) (7)

[0039]

[0040] where formula (7), (8), (9), (10), w i , w i+1 represent the weights of the edges between topics, represent the weights of the edges between topics and knowledge concepts, and c is a damping coefficient to punish the length of the walk sequence. The essence of this walk strategy is to learn the similarity relationship between different knowledge concepts and at the same time represent their contextual relationship in the topic perspective. If the semantic relationship between two knowledge concepts is more similar, the probability of their appearing in the same sequence will be greater.

[0041] Step 3-2: Obtain positive and negative samples from the generated "knowledge concept related sequence" related to the question. Specifically, the positive sample refers to the question related to the knowledge concept obtained by mixing the graph walk in step 3-1, and the strength of the relationship is controlled by adjusting the hyperparameters, while the negative sample is the question unrelated to the above knowledge concept.

[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 concept is mapped to the probability space. Specifically: the loss of the positive sample pair is pulled closer by KL divergence, and the loss of the negative sample pair is distant. The goal is to push the score of the positive sample pair higher than that of the negative sample pair by setting the margin. In order to further optimize this process, the Max Margin Ranking strategy is adopted. This strategy maximizes the margin difference between positive and negative sample pairs to ensure that the model has stronger discriminant ability when distinguishing between related and unrelated knowledge concepts. Finally, the knowledge concept is mapped to the Gaussian distribution in the same representation space.

[0043]

[0044] wherein formula (11), (12), KL divergence is used to measure the probability similarity between knowledge concepts , so as 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. Specifically as follows:

[0046] Step 4-1: Since different knowledge concepts involved in the question are different, and the content expressed by different knowledge concepts in the same question is also different. Therefore, in order to obtain the weight of the knowledge concept contained in different questions, the graph convolutional neural network (GCN) based on question relationship is adopted, which aggregates the neighbors of different question nodes to perceive the similarity between different questions.

[0047]

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

[0049]

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

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

[0052]

[0053] wherein formula (15), C i is the question q i involved knowledge concept set, α i is the weight of the knowledge concept involved in the question, representing the different knowledge categories represented by different knowledge concepts in the question. Gaussian distribution represents the knowledge concept representation of the kth knowledge concept.

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

[0055] First, the overall knowledge state of the student is modeled through the student's historical answer record, so as to infer the student's answer at the next moment. In order to fully consider the context relationship in the student's practice process, the invention introduces an attention mechanism (Attention) as an encoder, aiming to capture the long-term context dependency in the student's historical learning, so as to more accurately understand the student's learning trajectory.

[0056] Secondly, the knowledge concept probability embedding with hierarchical inclusion relationship and the question probability embedding with partial mapping relationship are introduced to supplement the student's historical answer information. The state change of the student on each knowledge concept and the question can be described in more detail through probability embedding representation, and the hierarchical relationship between different concepts can be effectively integrated, so as to provide more accurate prediction for the future performance of the student.

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

[0058] Step 5-1: Generate the dynamic knowledge state representation of the student by sampling the probability distribution embedding, wherein each Gaussian distribution represents the knowledge state of the student on a certain knowledge concept. The mean and variance of the Gaussian distribution reflect the mastery of the student on the knowledge concept and the distribution range of the knowledge, respectively. With the help of the Gaussian mixture model, the mastery of the student on the topic at the fine granularity can be quantified, and the mixed probability model of the topic reflects each part represented by different knowledge concepts. In order to reasonably represent the embedding information, the reparameterization trick is used to sample the embedding of the probability distribution to obtain the embedding information thereof. Specifically, by reparameterizing and sampling the Gaussian distribution of the knowledge concept and the Gaussian mixture model of the topic, the specific embedding representation thereof is obtained. At this time, the embedding information integrates the high-dimensional information of the above hierarchical structure, inclusion relationship and part mapping relationship.

[0059] Step 5-2: Then, the knowledge concept embedding of the hierarchical inclusion relationship and the part mapping relationship is combined with the topic embedding as the representation of the current learning content of the student, and then the historical learning record of the student is modeled by using the long short-term memory network (LSTM) to obtain the knowledge state of the student.

[0060] Step 5-3: Finally, a two-layer fully connected neural network is used to further optimize the knowledge state of the student to better align the knowledge concept. By combining the current knowledge state of the student and the performance of the next topic, the performance of the student on the next topic is verified and predicted.

[0061] Step 5-4: In order to more accurately model the knowledge state of the student, the model is jointly optimized by using a loss function: for the performance of the student on the topic, a supervised cross-entropy loss is used, and the optimization goal is to minimize the loss between the answer of the student and the correctness prediction probability. The model is trained by minimizing the loss function by using the Adam optimizer.

[0062] The beneficial effects of the present application are that, compared with the traditional method, the present method is obviously accurate in predicting the answering situation of the student, and can provide more accurate and personalized learning content recommendation for the student. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 The overall flowchart of the method provided by the embodiment of the present application.

[0064] Figure 2 The topic relationship diagram of the method provided by the embodiment of the present application.

[0065] Figure 3 The topic-knowledge concept relationship diagram of the method provided by the embodiment of the present application.

[0066] Figure 4 The method provided by the embodiment of the present application provides a topic-knowledge concept hybrid graph.

[0067] Figure 5 The method provided by the embodiment of the present application adopts a knowledge concept related sequence schematic diagram.

[0068] Figure 6 The method provided by the embodiment of the present application adopts a knowledge concept probability embedding distribution diagram.

[0069] Figure 7 The method provided by the embodiment of the present application adopts a schematic diagram of neighbor topic aggregation in graph convolution.

[0070] Figure 8 The method provided by the embodiment of the present application adopts a modeling student dynamic process structure diagram.

[0071] Figure 9 The method provided by the embodiment of the present application contains a modeling result diagram for the actual level of knowledge concept.

[0072] Figure 10 The method provided by the embodiment of the present application adopts a knowledge state schematic diagram of a small amount of learning interaction data.

[0073] Figure 11 The method provided by the embodiment of the present application adopts a comparison diagram of predicting student future knowledge performance DETAILED DESCRIPTION

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

[0075] Embodiment 1

[0076] The embodiment is like a flow Figure 1 As shown, comprising the following steps:

[0077] Step 1: modeling the relationship between questions: the relationship between questions is inferred by statistically analyzing the historical records of students' answers to different questions. Specifically, when a student answers two different questions, the probability of making a mistake in question B is higher after making a mistake in question A, or the probability of making a mistake in question B is higher after making a mistake in question A, which indicates that there is a certain relationship between the two questions. By analyzing the answer records as a whole, a relationship graph between questions is constructed. Relate(q1→q2) is used to represent the relationship between two questions q1 and q2, and the higher the relationship coefficient, the higher the similarity between the two questions. The specific 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 result and the overall answer, respectively, ln(x) represents the natural logarithm, used to measure the relative size of the correlation coefficient. It is calculated by counting the performance of two different questions in the process of students' answering, and the specific calculation method is as follows:

[0080]

[0081] wherein formula (2), (3), Count((q i ,q j )=(r i ,r j )) represents the number of times that the student answers r i to q i and then answers r j to q j in the process of answering. and represent that the student answers correctly or incorrectly to the question q i . In order to prevent the denominator from being too small, a Laplace smoothing parameter of 0.01 is added.

[0082] Step 2: Constructing a question-knowledge concept hybrid graph: In knowledge tracking, there are multiple dimensions of complex relationships between questions and knowledge concepts. Questions are not only associated with various levels, but knowledge concepts also have various connections, and questions and knowledge concepts are intertwined, representing which knowledge concepts the question involves, forming a complex relationship graph. In order to fully depict the complex relationship between 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. Specifically:

[0083] Step 2-1: Question relationship graph construction: In order to obtain effective question representation, as shown in Figure 2 , the obtained relationship in step 1 is converted into a graph form, specifically, by setting a threshold ω to control whether there is an edge between two questions. The formal representation is:

[0084] The question graph can be defined as The question edge weight W represents the relationship strength between different questions, w ij

[0085] represents the weight of edge e ij , Relate(v i ,v j ) is the similarity relationship between questions inferred by counting the historical interaction data of students.

[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 has a relationship with question q j , then there is an undirected edge between q i and q j , that is: E = {e ij | w ij ≥ ω} (6)

[0089] wherein formula (6), ω represents a threshold hyperparameter, 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 association between questions.

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

[0091] wherein Q represents the set of questions.

[0092] Step 2-2: Question-knowledge concept relationship graph construction: by analyzing the knowledge points involved in each question, the mapping relationship between questions and knowledge concepts is established, and the question nodes and knowledge concept nodes are connected in the form of a bipartite graph. As shown in Figure 3 the question-knowledge concept graph can be defined as a bipartite graph: The specific formal representation is:

[0093] Binary relationship adjacency matrix R: represents the relationship between questions and knowledge concepts, that is:

[0094] R = [r ij ] ∈ {0, 1} |Q|×|C| (8)

[0095] wherein if question q i has a relationship with knowledge concept c j , then r ij = 1, otherwise r ij = 0.

[0096] Node set V: which includes knowledge concept and question nodes. That is: V = Q ∪ C (9)

[0097] wherein 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 has a relationship with knowledge concept c jThere is an undirected edge between q i and c j if and only if the topic examines the knowledge concept. That is, E = {(q i , c j ) | r ij = 1} (10)

[0099] Step 2-3: Topic-knowledge concept hybrid graph construction: This step involves constructing a hybrid graph that combines both direct associations between topics and knowledge concepts, as well as reflecting the similarity between topics based on content or structure. In the hybrid graph, nodes are divided into two categories: topic nodes and knowledge concept nodes. Edges between topic nodes represent the similarity in content, difficulty, or other aspects of the topics. Edges between a topic node and a knowledge concept node represent that the topic involves or tests a specific knowledge concept. This way, the hybrid graph reveals both the internal relationships between topics and the knowledge points corresponding to each topic, providing rich structural information for the knowledge tracking model and helping to more accurately assess and predict students' learning states. As shown in Figure 2, the topic-knowledge concept hybrid graph is represented as G = (V, E). Figure 4 Specifically:

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

[0101] For e H ∈ E H : If e H = <q i , q j >, where i, j = {1, 2,..., num q , i ≠ j}, then it represents that topic q i has a similarity relationship with topic q j . If e H = q i , c k , where i = {1, 2,..., num q} and k = {1, 2,..., num c}, then it represents that e H is a topic q i involving c k knowledge concept.

[0102] ​Step 3: Map knowledge concepts to probability distributions to model hierarchical inclusion relationships among different knowledge concepts. The hierarchical inclusion relationships among knowledge concepts are expressed by modeling them as Gaussian distributions. Thus, each knowledge concept is viewed 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 topic-knowledge concept mixed graph, the semantic similarity between knowledge concepts can be effectively captured. Walking starts from a starting knowledge concept, passes through the topic nodes related to it, then finds other topic nodes with high relevance in the topic 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, as shown in Figure 5 The starting and ending parts of the sequence correspond to semantically similar knowledge concepts, and the middle part contains topics associated with these knowledge concepts. The specific walking strategy is as follows:

[0104]

[0105] where formula (11), when walking 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 ) of the i-th step is defined as follows:

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

[0108] where formula (12), the sub-formula is:

[0109] t = Γ(v i ) (13)

[0110]

[0111] where formula (13), (14), (15), (16), w i , w i+1 represent the weights of the edges between topics, where c is a damping factor to penalize the length of the walk sequence. The essence of this walk strategy is to learn the similarity relationship between different knowledge concepts and represent their contextual relationship in the perspective of the question at the same time. If the semantic relationship between two knowledge concepts is more similar, the probability of them appearing in the same sequence will be greater.

[0112] Step 3-2: Obtain positive and negative samples related to the question from the generated "knowledge concept related sequence". Specifically, the positive sample refers to the question related to the knowledge concept obtained by the mixed graph walk in step 3-1, and the strength of the relationship is controlled by adjusting the hyperparameter, while the negative sample is the question unrelated to the above knowledge concept.

[0113]

[0114] where: sample v concept from P sim (u * ), the probability of the appearance of the knowledge concept in the above walk algorithm determines the negative sample from unrelated noise.

[0115] 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, map the knowledge concept to the probability space. Specifically: through the KL divergence to pull the loss of the positive sample pair and to distance the loss of the negative sample pair. The goal is to push the score of the positive sample pair higher than that of the negative sample pair by setting the edge margin. In order to further optimize this process, the Max Margin Ranking strategy is adopted. This strategy maximizes the margin difference between positive and negative sample pairs to ensure that the model has stronger discriminant ability when distinguishing between related and unrelated knowledge concepts. Finally, the knowledge concept is mapped to the Gaussian probability distribution in the same representation space, as shown in Figure 6 .

[0116]

[0117]

[0118] where formula (18), (19), the KL divergence is used to measure the similarity between knowledge concepts , so as to learn the hierarchical inclusion relationship between knowledge concepts.

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

[0120] Step 4-1: Since different knowledge concepts in the topic involve different knowledge categories, and the content expressed by different knowledge concepts in the same topic is also different. Therefore, in order to obtain the weight of the knowledge concept contained in different topics, the graph convolutional neural network (GCN) based on the relationship of the topic is used to perceive the similarity between different topics by aggregating the neighbors of different topic nodes, as shown in Figure 7 The neighbor node set of the topic relationship graph is The GCN formula of the l-th layer can be expressed as:

[0121]

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

[0123]

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

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

[0126]

[0127] E P (x) expectation can be obtained in the following way: first sample from the Gaussian distribution of each knowledge concept to obtain the expectation, and then mix these expectations using the weight α to obtain 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 topic. Specifically, the Gaussian mixture distribution is used to fuse the distribution of each knowledge concept, so as to more accurately represent the comprehensive influence of different knowledge concepts in the topic.

[0130]

[0131] Wherein formula (24), C i is the set of knowledge concepts involved in the topic q i , α i is the weight of the knowledge concept involved in the topic, representing the different knowledge categories represented by different knowledge concepts in the topic. The Gaussian distribution Representation of knowledge concepts Representation of the k-th knowledge concept.

[0132] Step 5: In modeling the dynamic knowledge state changes of students, the present invention not only considers the performance results of students on future questions, but also comprehensively considers the performance of students on different knowledge concepts. Specifically, first, the overall knowledge state of the student is modeled through the student's historical answer records, so as to infer the student's answer at the next moment. In order to fully consider the context relationship in the student's practice process, the present invention introduces an attention mechanism (Attention) as an encoder, aiming to capture the long-term context dependency in the student's historical learning, so as to more accurately understand the student's learning trajectory. Secondly, the knowledge concept probability embedding introducing hierarchical inclusion relationship and the question probability embedding introducing partial mapping relationship are introduced to supplement the student's historical answer information. Through the probability embedding representation, the state changes of the student on each knowledge concept and question can be more detailedly described, and the hierarchical relationship between different concepts can be effectively integrated, thereby providing more accurate prediction for the future performance of the student. 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, through the historical practice records S of the student, the initial question representation x is constructed by combining the embedding of the question Q and the knowledge concept C t , i.e. t = q t + c t , then based on the historical answers of each student, an attention mechanism-based encoder is used to capture the long-term context dependency of the knowledge concept in the student's historical learning, thereby finding the potential dependency between the knowledge concepts. Specifically, in order to model the correlation between the current answer question x t and the previously answered question x i .

[0134] Step 5-2: The dynamic knowledge state representation of the student is generated by sampling the probability distribution embedding, where each Gaussian distribution represents the knowledge state of the student on a certain specific knowledge concept. The mean and variance of the Gaussian distribution respectively reflect the mastery degree of the student on the knowledge concept and the distribution range of the knowledge. With the help of the Gaussian mixture model, the mastery of the student on the question can be quantified, and the mixed probability model of the question reflects each part represented by different knowledge concepts. Specifically, by reparameterization sampling on the Gaussian distribution of the knowledge concept and the Gaussian mixture model of the question, their specific embedding representation is obtained. At this time, the embedding information integrates the high-dimensional information of the above hierarchical structure, inclusion relationship and partial mapping relationship.

[0135] Given the mean μ and covariance Σ of the Gaussian distribution, it can be obtained from Mid-sampling x: First sample from standard normal distribution Mid-sampling ε, then compute

[0136]

[0137] So far, the embedding results E of the samples of the probability distribution of the questions and knowledge concepts are obtained respectively N (q), E N (c), which contains the hierarchical inclusion relationship between questions and the partial mapping information involved by the questions and knowledge concepts.

[0138] Step 5-3: Embedding the knowledge concepts of hierarchical inclusion relationship and partial mapping relationship with the question embedding as the representation of the student's current learning content, and then modeling the student's historical learning records through a long short-term memory network (LSTM) to obtain the student's knowledge state.

[0139] First, at each time step t, the question embedding q t and the knowledge concept embedding c t are combined with the student's answer embedding r t to splice r t into a feature vector to obtain the final question representation

[0140]

[0141] where formula (26), represents the splicing operation of the vector.

[0142] The detailed process of the long short-term memory network (LSTM) is as follows, as shown in Figure 8 . LSTM realizes the flow and update of information inside through three gating mechanisms and two states. At time step t, LSTM uses the input vector x t and the hidden state vector h t-1 at the last moment to pass through four different neural network layers to generate the input gate i t , the forget gate f t , the output gate o t and the information flow at the current moment . Specifically, i t , f t and o t represent the input gate, the forget gate and the output gate respectively, and represents the information flow at the current moment.

[0143] These gating mechanisms and controls the memory, the forgetting and the output of information. Among them, the forgetting gate f t interacts with the memory state c t-1 of the last moment, determines the forgetting degree of the model to the state of the last moment. Specifically, f t ∈[0, 1], if the value of f t is 0, it means completely forgetting the content. Similarly, the input gate i t controls the memory of the current moment state by interacting with c . Then, the results of the input gate and the forgetting gate are combined to obtain the memory state c t of the current moment.

[0144] Finally, the output gate o t interacts with the memory state c_t to generate the hidden state h t of the current moment, which is used for subsequent calculation.

[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 are learnable weight matrices, b i , b f , b o , b cσ(·), tanh(·) are non-linear activation functions.

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

[0152] h t = ReLU(W2 ReLU(W1 h t + b1) + b2) (32)

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

[0154] wherein formula (32), (33), W1, W2, b1, b2, W r , b r are learnable bias and weight matrix respectively. ReLU(·), σ(·) are activation functions.

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

[0156]

[0157] wherein formula (34), r t+1 is 1 or 0, 1 represents correct answer, and 0 represents incorrect answer. is the model prediction of the student's answer result. The model is trained by minimizing the loss function through the Adam optimizer.

[0158] The results of the present example are shown in FIG. 1. Figure 9As shown, by setting the expectation 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 the probability distribution, the hierarchical structure of the knowledge concept and its inclusion relationship can be more intuitively demonstrated. Taking algebra in mathematics as an example, "natural number" refers to the set of non-negative integers starting from 0, so it is included in the more extensive "integer" set. In addition, the area partially overlapping with the "integer" knowledge concept represents the "negative number addition" knowledge concept, indicating that "negative number addition" mainly acts on the "negative number" sub-concept part in the integer set. At the same time, the non-overlapping area may involve the "negative fraction addition" sub-knowledge concept in "negative number addition". Therefore, the method of the present application can make the complex hierarchical structure and inclusion relationship clearer and easier to understand.

[0159] Example 2: Path optimization and construction of knowledge hierarchical relationship of intelligent learning platform

[0160] In existing online learning platforms, although the platform can provide certain personalized learning recommendations, the relationship between knowledge concepts is not accurately captured, often leading to inaccurate learning path recommendations, and students may miss the consolidation of basic knowledge or enter too complex a learning stage during the learning process. Through the method of the present application, the platform can accurately organize the knowledge structure based on the hierarchical relationship of knowledge concepts and capture the learning order, thereby developing a more personalized learning route for students. This method not only helps the platform optimize the learning path to ensure that students master basic knowledge at the appropriate stage and gradually transition to higher-level learning content, but also effectively improves learning effectiveness and avoids knowledge gaps in students' knowledge mastery, enabling steady knowledge progress. Through precise knowledge tracking and dynamic adjustment, the method of the present application can provide a powerful tool for existing platforms to enhance personalized learning experience and solve the problem of insufficient learning path planning in traditional platforms.

[0161] Example 3: Personalized knowledge mastery evaluation and learning path optimization with small amount of learning interaction data

[0162] In existing online learning platforms, the platform usually records students' answer situations, accuracy, answer time, and other data in each practice to statistically and analytically evaluate students' overall knowledge mastery. However, this method often requires students to learn on the platform for a period of time to accurately assess their knowledge mastery level. In fact, with the help of the present application, students can accurately reflect their mastery of certain basic concepts in the early learning stage through a small amount of interaction data, thereby achieving earlier knowledge level evaluation and personalized learning recommendations.

[0163] By capturing and analyzing students' learning interaction records, the present application can accurately identify students' basic knowledge mastery and automatically infer the knowledge points they have mastered, such asFigure 10 As shown, with the present method, the platform can quickly understand the student's mastery of other related basic knowledge after the first interaction with the knowledge concept. Traditional methods usually use random initialization for knowledge concepts, which can result in a difference of up to 70% or even higher between the knowledge concept and the related knowledge concept. However, the present method can quickly adjust the mastery level after capturing the related knowledge concept, reducing the difference to within 10%. This means that although the student may not have directly learned a certain knowledge concept, the platform can accurately infer that the student has already mastered the related basic knowledge through their excellent performance in higher-level knowledge concepts. At the same time, the platform can continuously track the student's learning progress and understand their mastery of different knowledge concepts in a timely manner. If the platform finds that the student performs well in higher-level tasks, it will infer that the student has already mastered the corresponding basic knowledge, thereby avoiding the student from repeating learning of already mastered content and improving learning efficiency.

[0164] By modeling the dynamic knowledge state of students, the present method can accurately and effectively predict the student's performance in answering future questions. This not only helps to individualize learning content, but also allows for real-time adjustment of teaching strategies and provides targeted feedback. By deeply analyzing the knowledge mastery progress of each student, the system can tailor individualized learning paths for students.

[0165] Embodiment 4: Dynamically tracking student knowledge mastery level and individualizing student learning content

[0166] In existing online learning platforms, the student's mastery of different knowledge points is usually inferred from their historical interactions with questions and the knowledge concepts involved. However, these platforms often overlook the dynamic changes in students' knowledge states and individualized needs, resulting in overly fixed and single learning content and paths that cannot adapt to each student's unique progress and interests. Therefore, students' learning experience may be limited, and even when faced with overly difficult or easy questions, they may feel frustrated or lose interest. In contrast, the present method dynamically models students' knowledge states to accurately and timely track and predict students' learning progress. As shown, Figure 11 As shown, compared with traditional methods, the present method improves the accuracy of predicting students' answers by 4.32%. Based on this advantage, the system can provide more accurate and individualized learning content recommendations for students. In addition to recommending appropriate learning content, the present method can also adjust the difficulty of learning tasks based on the student's actual mastery, ensuring a balance between learning challenges and abilities, and avoiding students feeling anxious due to excessive challenges or losing interest due to overly simple tasks, thereby significantly improving students' learning effectiveness and enthusiasm.

Claims

1. A probabilistic Gaussian embedding knowledge tracing method based on knowledge relationship awareness, characterized in that, Includes the following steps: Step 1: Model the relationships between the problems By statistically analyzing students' historical records of answering different questions, the relationships between questions can be inferred. When the same student answers two different questions, if they answer question A incorrectly, they are more likely to answer question B incorrectly, or if they answer question A correctly, they are more likely to answer question B correctly. This indicates that there is a certain connection between the two questions. Through overall analysis and statistical analysis of the answer records, a relationship graph between the questions can be inferred and constructed. Step 2: Construct a hybrid diagram of questions and knowledge concepts In knowledge tracing, there are complex, multi-dimensional relationships between questions and knowledge concepts. Questions are not only linked at various levels, but knowledge concepts also have diverse connections. Furthermore, questions and knowledge concepts are intertwined, representing which knowledge concepts are involved in the question, forming a complex relationship diagram. To fully depict the complex relationships between questions and knowledge concepts, it is particularly important to construct a hybrid question-knowledge concept diagram. By integrating the question relationship diagram and the question-knowledge concept relationship diagram, the construction of the hybrid question-knowledge concept diagram is achieved. Step 3: Map knowledge concepts to probability distributions to model the hierarchical inclusion relationship between different knowledge concepts; express the hierarchical inclusion relationship between them by modeling knowledge concepts as Gaussian distributions; thus, each knowledge concept is regarded as a Gaussian distribution, whose mean represents the central position of the concept and whose standard deviation reflects the range of the concept; Step 4: To represent the partial mapping relationship between questions and knowledge concepts, we first map them to the same representation space, and then use a Gaussian mixture distribution to achieve the purpose; Step 5: When modeling the dynamic changes in students' knowledge status, we not only consider the students' performance on future questions, but also comprehensively consider the students' performance on different knowledge concepts. First, the overall knowledge state of students is modeled by their historical answer records, thereby inferring their answer in the next moment. In order to fully consider the contextual relationships in the students' practice process, an attention mechanism is introduced as an encoder, which aims to capture the long-term contextual dependencies in students' historical learning, so as to understand the students' learning trajectory more accurately. Secondly, we will supplement students' historical answer information by introducing the probabilistic embedding of knowledge concepts with hierarchical inclusion relationships and the probabilistic embedding of questions with partial mapping relationships. Through probabilistic embedding, we can more meticulously depict the changes in students' status 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 trained under supervision using the cross-entropy loss function to optimize its prediction performance.

2. The probabilistic Gaussian embedding knowledge tracing method based on knowledge relationship awareness according to claim 1, characterized in that, Step 2 includes the following steps: Step 2-1: Problem Relationship Graph Construction: In order to obtain an effective problem representation, the relationship obtained in Step 1 is transformed into a graph representation, and a threshold ω is set to control whether there is an edge between two problems; The problem diagram is defined as Q =<V,E,W> ,in: Edge weight W: represents the strength of the relationship between different questions; W={w ij i.e ij ∈E} (1) w ij =Relate(v i ,v j ) (2) In equations (1) and (2), w ij Representing edge e ij The weights, Relate(v) i ,v j The similarity between questions is inferred by statistically analyzing students' historical interaction data. Edge set E: Represents the relationship between problems; if problem q i And the question q j If there is a relationship between them, then q i and q j There exists an undirected edge, namely: E = {e ij |w ij ≥ω}(3) where ω represents the threshold hyperparameter, which is used to measure the strength of the relationship between questions; only when the relationship coefficient exceeds the threshold is it considered that there is a significant correlation between the questions; Node set V: represents the set of problem nodes; that is: V = Q (4) where in equation (4), Q represents the set of problems; Step 2-2: Construction of the Question-Knowledge Concept Relationship Graph: By analyzing the knowledge points involved in each question, a mapping relationship between questions and knowledge concepts is established, and question nodes and knowledge concept nodes are connected in the form of a bipartite graph; the construction process is as follows: Steps 2-3: Construction of the Question-Knowledge Concept Hybrid Graph: This includes the direct relationship 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, representing similarity in terms of question content and difficulty. The edges between question and knowledge concept nodes indicate that the question involves or tests specific knowledge concepts. In this way, the hybrid graph not only reveals the inherent relationship between questions, but also clarifies the knowledge points corresponding to each question, thus providing rich structural information for the knowledge tracing model and supporting more accurate assessment and prediction of students' learning status. The construction process of the hybrid graph is as follows: For v H ∈V H If v H ∈Q, then v H It is a problem node; if v H ∈C, then v H These are knowledge concept nodes; For e H ∈E H If e H = i ,q j > where i,j={1,2,…,num q If i ≠ j, then it means that the problem q i With question 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 The question is q i Involving c k Knowledge concept.​ 3. A probabilistic Gaussian embedding knowledge tracing method based on knowledge relationship awareness according to claim 1 or 2, characterized in that, Step 3 includes the following steps: Step 3-1: By traversing the question-knowledge concept hybrid graph, the semantic similarity between knowledge concepts can be effectively captured. The traversal starts from a knowledge concept, passes through the question nodes it involves, and then searches for other question nodes with high relevance among the question nodes, and continues traversing until it finally returns to the target knowledge concept. Through this traversal process, a "knowledge concept related sequence" is generated, where the beginning and end parts of the sequence correspond to semantically similar knowledge concepts, while the middle part contains questions associated with these knowledge concepts. In equation (5), when the walk begins, Γ(v) 0 If ) = 0, it means that the wandering pointer is currently at a knowledge concept node, and the wandering process will eventually end with Γ(v L The process ends when ) = 0; The transition probability p(v) at step i i+1 |v i The definition of ) is as follows: p(v i+1 |v i )=p(t|v i )p(v i+1 |t,v i ) (6) In equation (6), the formulas for each sub-item are: t=Γ(v i ) (7) Among them, equations (7), (8), (9), and (10), w i ,w i+1 This indicates the weight of the edges between the questions. The weight of the edge between the question and the knowledge concept is represented by c, which is a damping coefficient used to penalize the length of the walk sequence. The essence of this walk strategy is to learn the similarity relationship between different knowledge concepts and at the same time represent their contextual relationship from the perspective of the question. If the semantic relationship between two knowledge concepts is more similar, then the probability of them appearing 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 knowledge concepts obtained in step 3-1 through mixed graph walk, and the strength of the relationship is controlled by adjusting hyperparameters, while negative samples are questions unrelated to the above knowledge concepts. Step 3-3: Use KL divergence to narrow the loss of positive sample pairs and widen the loss of negative sample pairs; The goal is to push the scores of positive sample pairs higher than those of negative sample pairs by setting margins. To further optimize this process, a maximum margin ranking strategy is adopted. This strategy ensures that the model has a stronger discriminative ability to distinguish between relevant and irrelevant knowledge concepts by maximizing the marginal difference between positive and negative sample pairs. Finally, knowledge concepts are mapped to a Gaussian distribution in the same representation space. In equations (11) and (12), the KL divergence is used to measure knowledge concepts. By studying the probabilistic similarity between concepts, we can learn the hierarchical inclusion relationships between knowledge concepts.

4. The knowledge tracing method based on knowledge relationship awareness using probabilistic Gaussian embedding according to claim 3, characterized in that, Step 4 includes 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 equation (13), w l and b l These are the learnable weights and bias coefficients; σ is the non-linear activation function. α=softmax(W·x i l ) (14) In equation (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 mixing coefficients obtained in Step 4-1 to distinguish the performance of different knowledge concepts in the questions; specifically, use Gaussian mixture distribution to fuse the distributions of various knowledge concepts, so as to more accurately represent the comprehensive influence of different knowledge concepts in the questions. Wherein equation (15), C i The question is q i The set of knowledge concepts involved, α i It represents the weight of the knowledge concepts involved in the question, indicating that different knowledge concepts in the question represent different knowledge categories; Gaussian distribution. Representing knowledge concepts The representation of the k-th knowledge concept.

5. A probabilistic Gaussian embedding knowledge tracing method based on knowledge relationship awareness according to claim 1 or 2, characterized in that, Step 5 includes the following steps: Step 5-1: Generate a dynamic knowledge state representation for students by embedding the sampled probability distributions. Each Gaussian distribution represents a student's knowledge state under a specific knowledge concept. The mean and variance of the Gaussian distributions reflect the student's mastery of the knowledge concept and the distribution range of the knowledge, respectively. Using a Gaussian mixture model, students' mastery of the questions at a fine-grained level can be quantified, while the mixture probability model of the questions reflects the various parts represented by different knowledge concepts. To reasonably represent the embedded information, a reparameterization technique is used to sample and embed the probability distributions to obtain their embedding information. Specifically, by reparameterizing the Gaussian distributions of the knowledge concepts and the Gaussian mixture model of the questions, their specific embedding representations are obtained. At this point, the embedded information integrates the high-dimensional information of the aforementioned hierarchical structure, inclusion relationships, and partial mapping relationships. Step 5-2: Then, embed the knowledge concepts and questions based on hierarchical inclusion and partial mapping relationships as representations of the student's current learning content. Then, model the student's historical learning records through a 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, making it better aligned with the knowledge concepts; by combining the student's current knowledge state with the performance on the questions at the next moment, the prediction of the student's performance on the next questions is made. Step 5-4: To more accurately model students' knowledge status, the model is jointly optimized using a loss function: a supervised cross-entropy loss is applied to students' performance on the questions, with the optimization objective being: Minimize the loss between the student's answer and the probability of correct prediction; train the model by minimizing the loss function using the Adam optimizer.

6. The knowledge tracing method based on knowledge relationship awareness using probabilistic Gaussian embedding according to claim 3, characterized in that, Step 5 includes the following steps: Step 5-1: Generate a dynamic knowledge state representation for the student by embedding the sampled probability distribution, where each Gaussian... The distribution represents a 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; the Gaussian mixture model can quantify the student's mastery of the questions at a fine-grained level, while the mixture probability model of the questions reflects the various parts represented by different knowledge concepts; in order to reasonably represent the embedded information, the reparameter technique is used to sample and embed the probability distribution to obtain its embedded information; specifically, by reparameterizing the Gaussian distribution of the knowledge concept and the Gaussian mixture model of the questions, their specific embedded representations are obtained; at this time, the embedded information integrates the high-dimensional information of the above hierarchical structure, inclusion relationship, and partial mapping relationship; Step 5-2: Then, embed the knowledge concepts and questions based on hierarchical inclusion and partial mapping relationships as representations of the student's current learning content. Then, model the student's historical learning records through a 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, making it better aligned with the knowledge concepts; by combining the student's current knowledge state with the performance on the questions at the next moment, the prediction of the student's performance on the next questions is made. Step 5-4: To more accurately model students' knowledge status, the model is jointly optimized using a loss function: a supervised cross-entropy loss is applied to students' performance on the questions, with the optimization objective being: Minimize the loss between the student's answer and the probability of correct prediction; train the model by minimizing the loss function using the Adam optimizer.

7. The knowledge tracing method based on knowledge relationship awareness using probabilistic Gaussian embedding according to claim 4, characterized in that, Step 5 includes the following steps: Step 5-1: Generate a dynamic knowledge state representation for the student by embedding the sampled probability distribution, where each Gaussian... The distribution represents a 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; the Gaussian mixture model can quantify the student's mastery of the questions at a fine-grained level, while the mixture probability model of the questions reflects the various parts represented by different knowledge concepts; in order to reasonably represent the embedded information, the reparameter technique is used to sample and embed the probability distribution to obtain its embedded information; specifically, by reparameterizing the Gaussian distribution of the knowledge concept and the Gaussian mixture model of the questions, their specific embedded representations are obtained; at this time, the embedded information integrates the high-dimensional information of the above hierarchical structure, inclusion relationship, and partial mapping relationship; Step 5-2: Then, embed the knowledge concepts and questions based on hierarchical inclusion and partial mapping relationships as representations of the student's current learning content. Then, model the student's historical learning records through a 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, making it better aligned with the knowledge concepts; by combining the student's current knowledge state with the performance on the questions at the next moment, the prediction of the student's performance on the next questions is made. Step 5-4: To more accurately model students' knowledge status, the model is jointly optimized using a loss function: a supervised cross-entropy loss is applied to students' performance on the questions, with the optimization objective being: Minimize the loss between the student's answer and the probability of correct prediction; train the model by minimizing the loss function using the Adam optimizer.

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