Cross-granularity representation knowledge tracking system

Abstract

The invention provides a cross-granularity representation knowledge tracking system, which belongs to the technical field of knowledge and comprises a multi-granularity knowledge point network construction module, a knowledge point cross-granularity representation module and an exercise cross-granularity representation module. According to the method, the actual knowledge point granularity is combined, the effect of the granularity on knowledge point representation is increased during modeling of knowledge point representation, and a multi-granularity knowledge point network is constructed; according to the method, an attention mechanism is applied in a multi-granularity knowledge point network, the influence degree of neighbor nodes with different granularities on a center node is focused, different attention scores are distributed to the knowledge points according to the granularities of the knowledge points, and finally cross-granularity representation of the knowledge points is obtained by aggregating the neighbor nodes with the different attention scores. According to the method, knowledge points contained in exercises and cross-granularity representation of the knowledge points are combined, and when the exercises are modeled, the influence of granularity on exercise representation is increased.

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 correctness of answers to exercises. Deep Knowledge Tracing (DKT) uses recurrent neural networks (RNN) or long short-term memory networks (LSTM) to track the learner's knowledge state and represents it through hidden state vectors. However, DKT does not consider the direct representation of knowledge points, nor does it explicitly model the relationship between knowledge points. Dynamic Key-Value Memory Networks for Knowledge Tracing (DKVMN) stores concepts through a key matrix and stores the learner's mastery of these concepts through a value matrix. DKVMN can accurately point out the learner's specific knowledge state on each concept, but it only uses static matrices to store knowledge representation and does not consider other information about knowledge points. Subsequent related work has improved on the basis of DKT, taking into account the knowledge points examined in the exercises, and introducing new model architectures to improve the representation of knowledge points and exercises. In order to further improve the modeling effect of knowledge points and exercises, subsequent research generally only includes information about the knowledge points themselves in the modeling of knowledge points. The above methods are based on exercises and knowledge points, and model knowledge point representation from different angles to 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 do not consider the exercise representation under the influence of knowledge points of different granularity.

[0003] The prior art solution most similar 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, in which each key corresponds to a knowledge point and the value represents the learner's mastery of the knowledge point. Each time the learner answers a question, the value of the corresponding knowledge point in the memory network is updated according to 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 points.

[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 status. However, exercise interaction data can only indicate whether the learner answered a question correctly or incorrectly, and the information it contains is relatively limited. In the actual learning process, knowledge points also have rich 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 status. For example, the two knowledge points in mathematics, "plane geometry" and "triangle", have different granularities, and there will be differences in representation, and knowledge points of different granularities will affect each other when representing. 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 knowledge tracking system for cross-granularity representation, so as 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 by c i ,1≤i≤N, the knowledge point set is recorded as C={c 1 ,c 2 ,...,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 the linear combination and activation unit to aggregate the embedding of knowledge points of different granularities to obtain the knowledge point cross-granularity representation of the knowledge point;

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

[0016] The cross-granularity representation knowledge tracking system provided by the present invention has the following beneficial effects compared with 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 representations through knowledge point content or knowledge point relationships. 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 to map the knowledge point information entropy to the knowledge point granularity space. Finally, a multi-granularity knowledge point network composed of knowledge points of different granularities is obtained.

[0018] (2) When tracking the learner's knowledge status, the present invention focuses on the impact of knowledge point granularity on the relationship between adjacent knowledge points, and models a cross-granularity mechanism for mutual representation between knowledge points of different granularities. The attention mechanism is applied in the multi-granularity knowledge point network, focusing on the degree of influence of neighbor nodes of different granularities on the central node, and assigning different attention scores to the knowledge point according to the granularity. Finally, the cross-granularity representation of the knowledge point is obtained by aggregating neighbor 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 exercises and knowledge point content, ignoring the impact of knowledge points of different granularities contained in the exercises on 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, the following briefly introduces 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 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] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are 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 "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "include one..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[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 by c i ,1≤i≤N, the knowledge point set is recorded as C={c 1 ,c 2 ,...,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 ,cj ); otherwise 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.

[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 is 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. 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, 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 With the knowledge point feature matrix X∈R N×d Multiply through the softmax function as follows:

[0042]

[0043] Through the feed-forward layer Convert to knowledge point c i Particle 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 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.

[0049] In a multi-granularity knowledge point network, the representation of a node is directly affected by its neighbor nodes, and the degree of influence of neighbor nodes of different granularities is also different, which 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 neighbor nodes of different granularities on the central knowledge point, and assigning different attention scores to them according to the granularity of the knowledge point, and finally obtaining the cross-granularity representation of the knowledge point by aggregating neighbor nodes with different attention scores.

[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 select 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 is obtained. 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 mastered by learners originate from the multi-granularity knowledge point network. Therefore, when learners answer exercises, the knowledge points contained in the exercises will activate the multi-granularity knowledge point network. The representation of the exercises is directly affected by the contained knowledge points, which causes the cross-granularity representation of the activated knowledge points and their neighboring nodes to further act on the exercise representation, and finally affect the exercise representation. In order to describe the exercises more accurately, the present invention first activates the multi-granularity knowledge point network, and then models the cross-granularity representation of the exercises by fusing the cross-granularity representation 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-granular representations of the activated knowledge point and its neighbors are fused. The knowledge point contained in the exercise is affected by each incoming neighbor, so the activated knowledge point c in the multi-granular 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 node; ⊕ 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 examination 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 weights of knowledge points of different granularities in the exercises, that is, to represent cross-granularity reasoning exercises. t ∈R 1 ×N and F calculation problems to represent Q across granularity 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 ⊕q 1 ,...,q t ,a 1 ,...,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 a wrong 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 the experiments based on 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 under different data sets. AUC is the area enclosed by the receiver operating characteristic curve and the coordinate axis. This indicator is generally used to characterize the prediction effect of the model. The higher the AUC value, the better the prediction performance of the model.

[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 beneficial effects compared with 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. Secondly, information entropy is used as the measurement basis of knowledge point granularity to map the knowledge point information entropy to the knowledge point granularity space. Finally, a multi-granularity knowledge point network composed of knowledge points of different granularities is obtained.

[0086] (2) When tracking the learner's knowledge status, the present invention focuses on the impact of knowledge point granularity on the relationship between adjacent knowledge points, and models a cross-granularity mechanism for mutual representation between knowledge points of different granularities. The attention mechanism is applied in the multi-granularity knowledge point network, focusing on the degree of influence of neighbor nodes of different granularities on the central node, and assigning different attention scores to the knowledge point according to the granularity. Finally, the cross-granularity representation of the knowledge point is obtained by aggregating neighbor 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 exercises and knowledge point content, ignoring the impact of knowledge points of different granularities contained in the exercises on 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 the scope of the present disclosure cannot be limited thereto. 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 here, those skilled in the art will easily think of the implementation scheme of the present disclosure. This application is intended to cover any modification, 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 technical field not recorded in the present disclosure. The description and examples are 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 may 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 only 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 protection scope of the present invention.

Claims

1. A knowledge tracking system with cross-granularity representation, characterized in that: 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 by 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 the linear combination and activation unit to aggregate the embedding of knowledge points of different granularities to obtain the knowledge point cross-granularity representation of the knowledge point; The exercise cross-granularity representation module is used to activate the multi-granularity knowledge point network and model the exercise cross-granularity representation by fusing the cross-granularity representations of the activated knowledge point and its 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; 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 is characterized in that: The weight matrix updating 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 for: 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 With the knowledge point feature matrix X∈R N×d The multiplication is processed through 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 for: 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 of the exercise is specifically used for: 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 examination weight W of the exercise q for the knowledge points it contains through the softmax function. t ∈R 1 ×N : W t =softmax(q′×Z Τ ); Using W t ∈R 1×N and F calculation problems to represent Q across granularity 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 comprises: 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 the 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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