A knowledge tracking system with cross-granularity representation

Abstract

The present invention provides a knowledge tracking system with cross-granularity representation, which belongs to the field of knowledge technology and includes: a multi-granularity knowledge point network construction module, a knowledge point cross-granularity representation module, and an exercise cross-granularity representation module; the present invention combines the actual knowledge point granularity to increase the effect of granularity on knowledge point representation when modeling knowledge point representation, and constructs a multi-granularity knowledge point network; the present invention applies an attention mechanism in the multi-granularity knowledge point network, focusing on the degree of influence of neighbor nodes of different granularities on the central node, and assigns different attention scores to the knowledge point according to the granularity, and finally obtains the knowledge point cross-granularity representation by aggregating neighbor nodes with different attention scores; the present invention combines the knowledge points contained in the exercises and their cross-granularity representation to increase the influence of granularity on the exercise representation when modeling the exercises.

Description

Technical Field

[0001] The present invention relates to the field of knowledge tracing technology, and in particular to a cross-granularity representation knowledge tracing system. Background Art

[0002] In recent years, knowledge tracing models have made significant progress in representing knowledge points and predicting the accuracy of exercise answers. Deep Knowledge Tracing (DKT) utilizes recurrent neural networks (RNNs) or long short-term memory networks (LSTMs) to track the learner's knowledge state, representing it via a hidden state vector. However, DKT does not consider the direct representation of knowledge points or explicitly model the relationships between them. Dynamic Key-Value Memory Networks for Knowledge Tracing (DKVMN) store concepts using a key matrix and the learner's mastery of these concepts using a value matrix. DKVMN can accurately indicate the learner's specific knowledge state on each concept, but it only uses a static matrix to store knowledge representation and does not consider other information about the knowledge points. Subsequent related work has improved on DKT by incorporating the knowledge points tested in the exercises and introducing new model architectures to enhance the representation of knowledge points and exercises. To further improve the modeling of knowledge points and exercises, subsequent research generally only includes information about the knowledge points themselves. The above methods, based on exercises and knowledge points, model knowledge point representation from different perspectives and achieve good results. However, they also limit the information representing knowledge points to the content of the knowledge points themselves, ignore the impact of knowledge point granularity on knowledge points and their relationships, and fail to consider the exercise representation of knowledge points of different granularities.

[0003] The most similar existing technology solution to the present invention is Dynamic Key-Value Memory Networks for Knowledge Tracing (DKVMN). This model is based on the concept of memory networks and uses dynamic key-value storage to represent the learner's knowledge state. This storage can be regarded as a large dictionary of key-value pairs, where each key corresponds to a knowledge point and the value represents the learner's mastery of the knowledge point. Each time a learner answers a question, the value of the corresponding knowledge point in the memory network is updated based on the learner's answer and the corresponding question features. The memory attention mechanism is used in the update process, and corresponding calculations and operations are performed through the question features and the keys in the storage to update the mastery of the corresponding knowledge point.

[0004] Classic knowledge tracing models, such as Bayesian Knowledge Tracing (BKT), Deep Knowledge Tracing (DKT), and Dynamic Key-Value Memory Networks for Knowledge Tracing (DKVMN), use learners' exercise interaction data to track their knowledge state. However, exercise interaction data only indicates whether a learner answered a question correctly or incorrectly, and the information it contains is relatively limited. In the actual learning process, knowledge points also contain richer granular information. Based on the granularity of knowledge points, the data received by the model can contain richer information, thereby more accurately tracking the learner's knowledge state. For example, two knowledge points in mathematics, "plane geometry" and "triangle," have different granularities, and there will be differences in their representation. Knowledge points of different granularities will influence each other during representation. Most existing knowledge tracking models ignore the impact of knowledge point granularity on knowledge points and their relationships, and do not consider the exercise representation under the influence of knowledge points of different granularities. Obviously, these models cannot obtain the above-mentioned relevant information, and these models ignore the modeling of granularity information when modeling knowledge point representation and exercise representation. Summary of the Invention

[0005] The present invention provides a cross-granularity representation knowledge tracking system to solve the defect of modeling in the prior art that granularity information is ignored.

[0006] The present invention provides a cross-granularity representation knowledge tracking system, comprising: a multi-granularity knowledge point network construction module, a knowledge point cross-granularity representation module, and an exercise cross-granularity representation module;

[0007] The multi-granularity knowledge point network construction module includes: a knowledge point similarity calculation unit, an adjacency matrix update unit, a weight matrix update unit and a knowledge point granularity calculation unit, which are used to construct a multi-granularity knowledge point network. The multi-granularity knowledge point network includes: knowledge points, relationships between knowledge points, and granularity information of knowledge points; wherein the total number of knowledge points is N, and any knowledge point is denoted as c i ,1≤i≤N, the knowledge point set is recorded as C={c1,c2,...,c N}, the feature matrix of the knowledge point is recorded as X∈R N×d , the feature dimension is d, E represents the set of knowledge point relationships, A represents the adjacency matrix, represents the granularity matrix;

[0008] The knowledge point similarity calculation unit is used to calculate the similarity between different knowledge points using a Gaussian kernel function to obtain a similarity matrix S;

[0009] The adjacency matrix updating unit is used to set a threshold ε and update the adjacency matrix A according to the similarity matrix S and the threshold ε;

[0010] The weight matrix updating unit is used to update the weight matrix W using the adjacency matrix A and the similarity matrix S;

[0011] The knowledge point granularity calculation unit is used to map the information entropy of the knowledge point to the knowledge point granularity by using the mapping relationship between the knowledge point granularity and the information entropy, so as to construct a granularity matrix;

[0012] The knowledge point cross-granularity representation module includes an attention coefficient calculation unit and a neighbor node feature aggregation unit, which are used to generate a knowledge point cross-granularity representation; the knowledge point cross-granularity representation is a knowledge point representation obtained by capturing the influence of the knowledge point granularity on the relationship between adjacent knowledge points;

[0013] The attention coefficient calculation unit is used to calculate the attention score of any knowledge point relative to neighboring nodes of different granularities using a nonlinear activation function, and normalize the attention score to obtain the attention coefficient;

[0014] The neighbor node feature aggregation unit is used to multiply the attention coefficient with the corresponding neighbor node feature, and then use linear combination and activation units to aggregate the embeddings of knowledge points of different granularities to obtain the cross-granularity representation of the knowledge points;

[0015] The cross-granularity representation module of the exercises is used to activate the multi-granularity knowledge point network and model the cross-granularity representation of the exercises by fusing the cross-granularity representations of the activated knowledge points and their neighboring nodes.

[0016] The cross-granularity representation knowledge tracking system provided by the present invention has the following advantages over the prior art:

[0017] (1) The present invention introduces knowledge point granularity to construct a multi-granularity knowledge point network when tracking the learner's knowledge status. Most existing models (systems) obtain knowledge point representation through knowledge point content or knowledge point relationship. These methods ignore the impact of the granularity of the knowledge point itself on its representation. The present invention combines the actual knowledge point granularity and increases the effect of granularity on knowledge point representation when modeling knowledge point representation. First, the Gaussian kernel function is used to calculate the similarity between knowledge points to form knowledge point relationships. Second, information entropy is used as the measurement basis of knowledge point granularity, and the knowledge point information entropy is mapped to the knowledge point granularity space. Finally, a multi-granularity knowledge point network composed of knowledge points of different granularities is obtained.

[0018] (2) This paper focuses on the impact of knowledge point granularity on the relationship between adjacent knowledge points when tracking the learner's knowledge status, and models a cross-granularity mechanism for mutual representation between knowledge points of different granularities. The attention mechanism is applied to a multi-granularity knowledge point network, focusing on the degree of influence of neighboring nodes of different granularities on the central node. Different attention scores are assigned to each knowledge point according to its granularity. Finally, the cross-granularity representation of the knowledge point is obtained by aggregating neighboring nodes with different attention scores.

[0019] (3) The present invention performs cross-granularity representation of answering exercises while tracking the learner's knowledge status. Most current models only model exercise representation based on the content of exercises and knowledge points, ignoring the impact of different granularity knowledge points contained in the exercises on the exercise representation. The present invention combines the knowledge points contained in the exercises and their cross-granularity representation to increase the impact of granularity on exercise representation when modeling exercises. First, a multi-granularity knowledge point network is activated, and then the cross-granularity representation of the exercise is modeled by fusing the cross-granularity representation of the activated knowledge points and their neighboring nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the present invention or the prior art, a brief introduction is given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0021] Figure 1 It is a schematic diagram of the framework of the cross-granularity representation knowledge system provided by the present invention. DETAILED DESCRIPTION

[0022] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0023] It should be noted that, in the description of the embodiments of the present invention, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed, or also includes elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.

[0024] Figure 1 This is a schematic diagram of the framework of the cross-granularity representation knowledge system provided by the present invention. Figure 1 The technical solution of the present invention is described.

[0025] Figure 1 It is a cross-granularity representation knowledge tracking model diagram. The method includes:

[0026] (1) Multi-granularity knowledge point network construction module.

[0027] The multi-granularity knowledge point network contains knowledge points c i , the relationship between knowledge points and the granularity information of knowledge points. The total number of knowledge points is N, and any knowledge point is denoted as c i ,1≤i≤N, the knowledge point set is recorded as C={c1,c2,...,c N}, the feature matrix of the knowledge point is recorded as X∈R N×d , the feature dimension is d. The multi-granularity knowledge point network construction module represents the relationship between knowledge points and their granularity information, including: knowledge point similarity calculation unit, adjacency matrix update unit, weight matrix update unit and knowledge point granularity calculation unit.

[0028] First, the knowledge point similarity calculation unit is used to calculate the knowledge point similarity S. The Gaussian kernel function accurately captures the similarity of different knowledge points by mapping them from the input space to the high-dimensional feature space. The calculation is as follows:

[0029]

[0030] Among them, x i and x j They are knowledge points c i ,c j ∈C, σ is the width parameter of the function, S ij Represents the element in the i-th row and j-th column of the similarity matrix, and exp() represents the exponential function.

[0031] Second, the adjacency matrix update unit is used to update the adjacency matrix. Set the threshold ε and update the adjacency matrix A according to S and ε:

[0032]

[0033] Among them, ε is the median of similarity; S ij ≥ε, knowledge point c i ,c j There is an edge between ∈C, namely e ij =(c i ,c j ); otherwise knowledge point ci ,c j There is no edge between A∈C; ij Represents the element in the i-th row and j-th column of the adjacency matrix.

[0034] Third, the weight matrix update unit is used to update the weight matrix. The weight matrix W is updated by the adjacency matrix A and the similarity matrix S:

[0035] W ij =A ij ·S ij

[0036] Among them, c i ,c j If there is a connection between them, the weight W ij Equal to the similarity between them, otherwise the weight is 0; W ij Represents the element in the i-th row and j-th column of the weight matrix.

[0037] Fourth, the knowledge point granularity calculation unit is used to calculate the knowledge point granularity. The knowledge point granularity is the amount of information contained in the knowledge point. Information entropy is used to measure the uncertainty or amount of information in the information source, so it can be used as an effective measure of the amount of information in the knowledge point. Based on the potential mapping relationship between knowledge point granularity and information entropy, MLP is applied to map the information entropy of the knowledge point to the knowledge point granularity. For knowledge point c i Normalize the edge weights to get the corresponding probability vector p ij ,as follows:

[0038]

[0039] Calculation knowledge point c i The information entropy of is as follows:

[0040]

[0041] Among them, p ij It is knowledge point c i The information distribution implied by the relationship with other knowledge points. Then, through the embedding layer, set the embedding matrix B∈R 1×N H(c i ) is mapped into a distributed real-valued vector h i =B·H(c i ), and h i and the knowledge point feature matrix X∈R N×d Multiply by the softmax function as follows:

[0042]

[0043] Through the feed-forward layer Convert to knowledge point c iParticle size g i ∈R 1×d ,as follows:

[0044] g i =MLP(W hi );

[0045] Among them, MLP() represents the feedforward layer, which is used to obtain the knowledge point granularity through nonlinear mapping;

[0046] Calculate the granularity of all knowledge points to form a granularity matrix Thus, the information contained in each knowledge point in the knowledge point network is quantified. Finally, a multi-granularity knowledge point network is obtained. Among them, E represents the set of knowledge point relationships.

[0047] (2) Knowledge point cross-granularity representation module.

[0048] The knowledge point cross-granularity representation module includes an attention coefficient calculation unit and a neighbor node feature aggregation unit, which is used to generate a cross-granularity representation of the knowledge point; the cross-granularity representation of the knowledge point is a knowledge point representation obtained by capturing the influence of the knowledge point granularity on the relationship between adjacent knowledge points.

[0049] In a multi-granularity knowledge point network, the representation of a node is directly affected by its neighboring nodes. The degree of influence of neighboring nodes of different granularities is also different, and this influence changes the representation of the knowledge point. The working principle of the attention mechanism is to dynamically assign weights to each part of the input data by calculating the correlation between them. Based on this, the present invention applies the attention mechanism in a multi-granularity knowledge point network, focusing on the degree of influence of neighboring nodes of different granularities on the central knowledge point, and assigning different attention scores to them according to the granularity of the knowledge point. Finally, by aggregating neighboring nodes with different attention scores, the cross-granularity representation of the knowledge point is obtained.

[0050] First, the attention coefficient calculation unit is used to use a nonlinear activation function to calculate the attention score of any knowledge point relative to neighboring nodes of different granularities, and normalize the attention score to obtain the attention coefficient.

[0051] Specifically, because the influence of neighbor nodes of different granularities is also different, the granularity of the neighbor nodes is Assign different attention scores to them. Use nonlinear activation function to calculate any knowledge point c i The attention scores relative to neighboring nodes of different granularities are as follows:

[0052]

[0053] Among them, α∈R d×1is the attention weight vector, || is the connection operation, · is the inner product operation, σ(·) is the nonlinear activation function, and the present invention can use the LeakyReLU function; Represents knowledge point c i The granularity value of the current neighbor node, Represents knowledge point c i The granularity value of the kth neighbor node.

[0054] Then, use softmax to normalize and get the attention coefficient a ik ,as follows:

[0055]

[0056] Among them, a ik is the attention coefficient.

[0057] Second, the neighbor node feature aggregation unit.

[0058] Specifically, because the contribution of neighbor nodes of different granularities is different, the attention coefficient is multiplied by the corresponding neighbor node features, and then the embedding of knowledge points of different granularities is aggregated using linear combination and activation units, and finally c i The knowledge point cross-granularity representation K ci as follows:

[0059]

[0060] Among them, a ik represents the attention coefficient used to combine neighbor node representations of different granularities, X ik Represents knowledge point c i The corresponding eigenvalue of the kth neighbor node.

[0061] (3) The cross-granularity representation module of exercises is used to activate the multi-granularity knowledge point network and model the cross-granularity representation of exercises by fusing the cross-granularity representations of the activated knowledge points and their neighboring nodes.

[0062] Specifically, the knowledge points learners master originate from a multi-granularity knowledge point network. Therefore, as learners solve problems, the knowledge points contained in the problems activate the multi-granularity knowledge point network. The representation of a problem is directly influenced by the knowledge points it contains, causing the cross-granularity representations of the activated knowledge points and their neighboring nodes to further influence the problem representation, ultimately affecting the problem representation. To more accurately describe the problem, the present invention first activates the multi-granularity knowledge point network and then models the problem cross-granularity representation by fusing the cross-granularity representations of the activated knowledge points and their neighboring nodes.

[0063] First, activate the multi-granularity knowledge point network. The set of knowledge points included in the exercise is Cq The knowledge point in G g The corresponding knowledge point set C is found, and the knowledge point set J activated by the multi-granularity knowledge point network is obtained, that is, J = {c i |c i ∈C q ∧c i ∈C}; where |q| represents the knowledge point set C q The number of knowledge points contained in .

[0064] Second, the cross-granularity representations of the activated knowledge point and its neighbors are fused. The knowledge points contained in the exercise are affected by each incoming neighbor, so the activated knowledge point c in the multi-granularity knowledge point network is i The cross-granularity representation concatenation of ∈J and its neighboring nodes is as follows:

[0065]

[0066] Among them, W o ′ and b o ′ are weight parameters and bias terms respectively; Represents knowledge point c i ∈J is the set of neighbor nodes, Represents knowledge point c i ∈J’s neighbor nodes; ⊕ represents the concatenation operation; Relu represents the Relu activation function;

[0067] Finally, we represent the exercises across granularity. The ID of exercise q is represented as a one-hot encoding O(q)∈R 1×N , set an embedding matrix W q ∈R M×d , map the problem q into an embedding vector q′∈R 1×d :

[0068] q′=O(q)×W q

[0069] In addition, using Z∈R m×n The matrix describes the many-to-many relationship between exercises and knowledge points. Each row in the matrix corresponds to an exercise, and each column in the matrix corresponds to a knowledge point. When an exercise tests a certain knowledge point, the value of the corresponding position in the matrix Z is 1, otherwise it is 0. Multiply q′ by the Z matrix and convert it into the weight W of the exercise q for the knowledge point it contains through the softmax function. t ∈R 1×N ::

[0070] W t =softmax(q′×Z Τ );

[0071] In order to quantify the weight of knowledge points of different granularities in the exercises, that is, to represent cross-granularity reasoning exercises. t ∈R 1 ×N and F calculation exercises cross-granularity representation Q c :

[0072] Q c =softmax(F·W t ).

[0073] (4) Prediction module.

[0074] The prediction module is used to predict the learner's future answer performance. The cross-granular representation of the spliced ​​exercises and the historical answers are input into the fully connected layer activated by the Tanh function to obtain the vector i t :

[0075] i t =Tanh(W t Τ [Q c ⊕q1,...,q t ,a1,...,a t ]+b i )

[0076] Among them, q t represents the tth exercise q answered by the learner t ∈R 1×Q ,t>0;a t represents the learner's t The answer result of a t ∈{1,0}, 0 indicates an incorrect answer, and 1 indicates a correct answer.

[0077] will i t Input the fully connected layer to predict the learner's answer performance on the exercise:

[0078]

[0079] Among them, p t is the predicted value, W p is the weight parameter, b p is the bias term.

[0080] The results of experiments conducted using the cross-granularity representation knowledge tracking system (model) provided by the present invention are shown in Table 1. Table 1 shows the AUC values ​​of different models for different datasets. AUC is the area between the receiver operating characteristic curve and the coordinate axes. This metric is generally used to characterize the predictive performance of a model; a higher AUC value indicates better predictive performance.

[0081] Among them, DKT (Deep Knowledge Tracing) is the first deep knowledge tracing model, DKVMN (Dynamic key-value memory networks for knowledge tracing) is a knowledge tracing model of dynamic key-value memory networks, and GKT (Graph-based knowledge tracing: modeling student proficiency using graph neural network) is a graph-based knowledge tracing model.

[0082] Table 1 AUC comparison of different models

[0083]

[0084] In summary, the cross-granularity representation knowledge tracking system provided by the present invention has the following advantages over the prior art:

[0085] (1) The present invention introduces knowledge point granularity to construct a multi-granularity knowledge point network when tracking the learner's knowledge status. Most existing models obtain knowledge point representation through knowledge point content or knowledge point relationship. These methods ignore the impact of the granularity of the knowledge point itself on its representation. The present invention combines the actual knowledge point granularity and increases the effect of granularity on knowledge point representation when modeling knowledge point representation. First, the Gaussian kernel function is used to calculate the similarity between knowledge points to form knowledge point relationships. Second, information entropy is used as the measurement basis of knowledge point granularity, and the knowledge point information entropy is mapped to the knowledge point granularity space. Finally, a multi-granularity knowledge point network composed of knowledge points of different granularities is obtained.

[0086] (2) This paper focuses on the impact of knowledge point granularity on the relationship between adjacent knowledge points when tracking the learner's knowledge status, and models a cross-granularity mechanism for mutual representation between knowledge points of different granularities. The attention mechanism is applied to a multi-granularity knowledge point network, focusing on the degree of influence of neighboring nodes of different granularities on the central node. Different attention scores are assigned to each knowledge point according to its granularity. Finally, the cross-granularity representation of the knowledge point is obtained by aggregating neighboring nodes with different attention scores.

[0087] (3) The present invention performs cross-granularity representation of answering exercises while tracking the learner's knowledge status. Most current models only model exercise representation based on the content of exercises and knowledge points, ignoring the impact of different granularity knowledge points contained in the exercises on the exercise representation. The present invention combines the knowledge points contained in the exercises and their cross-granularity representation to increase the impact of granularity on exercise representation when modeling exercises. First, a multi-granularity knowledge point network is activated, and then the cross-granularity representation of the exercise is modeled by fusing the cross-granularity representation of the activated knowledge points and their neighboring nodes.

[0088] The above is only an exemplary embodiment of the present disclosure and cannot be used to limit the scope of the present disclosure. That is, any equivalent changes and modifications made according to the teachings of the present disclosure are still within the scope of the present disclosure. After considering the specification and practicing the disclosure herein, those skilled in the art will easily think of the implementation scheme of the present disclosure. This application is intended to cover any variation, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary technical means in the art that are not recorded in the present disclosure. The description and examples are to be regarded as exemplary only, and the scope and spirit of the present disclosure are defined by the claims.

[0089] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0090] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A knowledge tracking system with cross-granularity representation, characterized by: include: Multi-granularity knowledge point network construction module, knowledge point cross-granularity representation module, and exercise cross-granularity representation module; The multi-granularity knowledge point network construction module includes: a knowledge point similarity calculation unit, an adjacency matrix update unit, a weight matrix update unit and a knowledge point granularity calculation unit, which are used to construct a multi-granularity knowledge point network. The multi-granularity knowledge point network includes: knowledge points, relationships between knowledge points, and granularity information of knowledge points; wherein the total number of knowledge points is N, and any knowledge point is denoted as c i ,1≤i≤N, the knowledge point set is recorded as C={c1,c2,...,c N }, the feature matrix of the knowledge point is recorded as X∈R N×d , the feature dimension is d, E represents the set of knowledge point relationships, A represents the adjacency matrix, represents the granularity matrix; The knowledge point similarity calculation unit is used to calculate the similarity between different knowledge points using a Gaussian kernel function to obtain a similarity matrix S; The adjacency matrix updating unit is used to set a threshold ε and update the adjacency matrix A according to the similarity matrix S and the threshold ε; The weight matrix updating unit is used to update the weight matrix W using the adjacency matrix A and the similarity matrix S; The knowledge point granularity calculation unit is used to map the information entropy of the knowledge point to the knowledge point granularity by using the mapping relationship between the knowledge point granularity and the information entropy, so as to construct a granularity matrix; The knowledge point cross-granularity representation module includes an attention coefficient calculation unit and a neighbor node feature aggregation unit, which are used to generate a knowledge point cross-granularity representation; the knowledge point cross-granularity representation is a knowledge point representation obtained by capturing the influence of the knowledge point granularity on the relationship between adjacent knowledge points; The attention coefficient calculation unit is used to calculate the attention score of any knowledge point relative to neighboring nodes of different granularities using a nonlinear activation function, and normalize the attention score to obtain the attention coefficient; The neighbor node feature aggregation unit is used to multiply the attention coefficient with the corresponding neighbor node feature, and then use linear combination and activation units to aggregate the embeddings of knowledge points of different granularities to obtain the cross-granularity representation of the knowledge points; The cross-granularity representation module of the exercises is used to activate the multi-granularity knowledge point network and model the cross-granularity representation of the exercises by fusing the cross-granularity representations of the activated knowledge points and their neighboring nodes.

2. The cross-granularity representation knowledge tracking system according to claim 1, characterized in that: The knowledge point similarity calculation unit is used to calculate the similarity between different knowledge points using a Gaussian kernel function to obtain a similarity matrix S, which is specifically: Among them, x i and x j They are knowledge points c i ,c j ∈C, σ is the width parameter of the function, S ij Represents the element in the i-th row and j-th column of the similarity matrix, and exp() represents the exponential function.

3. The cross-granularity representation knowledge tracking system according to claim 2, characterized in that: The adjacency matrix updating unit is used to set a threshold ε and update the adjacency matrix A according to the similarity matrix S and the threshold ε, specifically: Among them, the threshold ε is the median of the similarity; in S ij ≥ε, knowledge point c i ,c j ∈C, otherwise, the knowledge point c i ,c j There is no edge between A∈C; ij Represents the element in the i-th row and j-th column of the adjacency matrix.

4. The cross-granularity representation knowledge tracking system according to claim 3, characterized in that The weight matrix update unit is used to update the weight matrix W using the adjacency matrix A and the similarity matrix S. Specifically: W ij =A ij ·S ij ; Among them, W ij Represents the element in the i-th row and j-th column of the weight matrix.

5. The cross-granularity representation knowledge tracking system according to claim 4, characterized in that: The knowledge point granularity calculation unit is specifically used to: For knowledge point c i Normalize the edge weights to get the corresponding probability vector p ij : Calculation knowledge point c i The information entropy H(c i ): Set the embedding matrix B∈R 1×N H(c i ) is mapped into a distributed real-valued vector h i =B·H(c i ), And h i and the knowledge point feature matrix X∈R N×d The multiplication is processed by the softmax function: Through the feed-forward layer Convert to knowledge point c i Particle size g i ∈R 1×d : Among them, MLP() represents the feedforward layer, which is used to obtain the knowledge point granularity through nonlinear mapping; Calculate the granularity of all knowledge points and form a granularity matrix.

6. The cross-granularity representation knowledge tracking system according to claim 5, characterized in that: The attention coefficient calculation unit is specifically used to: Use nonlinear activation function to calculate any knowledge point c i Attention scores relative to neighboring nodes of different granularities: Among them, α∈R d×1 is the attention weight vector, || is the concatenation operation, · is the inner product operation, and σ(·) is the nonlinear activation function; Represents knowledge point c i The granularity value of the current neighbor node, Represents knowledge point c i The granularity value of the kth neighbor node; Normalize the attention score to get the attention coefficient a ik :

7. The cross-granularity representation knowledge tracking system according to claim 6, characterized in that: The neighbor node feature aggregation unit obtains the knowledge point c i Cross-granularity representation of knowledge points for: Among them, a ik represents the attention coefficient used to combine neighbor node representations of different granularities, X ik Represents knowledge point c i The corresponding eigenvalue of the kth neighbor node.

8. The cross-granularity representation knowledge tracking system according to claim 7, characterized in that: The cross-granularity representation module is specifically used to: The knowledge points contained in the exercises are set C q The knowledge point in G g The corresponding knowledge point set C is found, and the knowledge point set J activated by the multi-granularity knowledge point network is obtained; among them, |q| represents the knowledge point set C q The number of knowledge points contained in The activated knowledge point c in the multi-granularity knowledge point network i ∈J and its neighboring nodes c j Cross-granularity representation splicing: Among them, W o ′ and b o ′ are weight parameters and bias terms respectively; Represents knowledge point c i ∈J is the set of neighbor nodes, Represents knowledge point c i ∈J’s neighbor nodes; Represents the concatenation operation; Relu represents the Relu activation function; Represent the ID of exercise q as a one-hot encoding O(q)∈R 1×N , set an embedding matrix W q ∈R M×d , map the problem q into an embedding vector q′∈R 1×d : q′=O(q)×W q ; Use Z∈R m×n The matrix describes the many-to-many relationship between exercises and knowledge points. Each row in the matrix corresponds to an exercise, and each column in the matrix corresponds to a knowledge point. When an exercise tests a certain knowledge point, the value of the corresponding position in the matrix Z is 1, otherwise it is 0. Multiply q′ by the Z matrix and convert it into the weight W of the knowledge points contained in the exercise q through the softmax function t ∈R 1 ×N : W t =softmax(q′×Z Τ ); Using W t ∈R 1×N and F calculation exercises cross-granularity representation Q c : Q c =softmax(F·W t )。 9. The cross-granularity representation knowledge tracking system according to claim 1, characterized in that: The system further includes: a prediction module; The prediction module is used to predict the learner's future answer performance based on the cross-granularity representation of the exercises and historical answers.

10. The cross-granularity representation knowledge tracking system according to claim 1, characterized in that: The nonlinear activation function is: leaky relu function.

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