An interactive knowledge tracing method based on graph neural network

Abstract

This invention discloses an interactive knowledge tracking method based on graph networks, relating to the field of artificial intelligence. The method includes the following steps: constructing a graph relating questions and knowledge points; for each question and knowledge point in a student's learning sequence, a graph neural network is used to aggregate the features of its higher-order neighbors, and a long short-term memory network is used to extract the features of the represented historical learning sequence, thereby obtaining a low-dimensional vector representation of the student's knowledge mastery status at the current moment. An attention mechanism is used to select historical information related to the question to be predicted, and these information are interacted pairwise to obtain the probability of correctly predicting the target question. This method can effectively improve the accuracy of knowledge tracking prediction and enhance the feasibility of adaptive learning.

Description

Technical Field

[0001] This invention relates to knowledge tracking tasks in the field of intelligent education, and more particularly to an interactive knowledge tracking method based on graph neural networks. Background Technology

[0002] Knowledge tracking is a crucial task in online intelligent education. It involves tracking changes in students' knowledge status, enabling intelligent education systems to understand student learning progress, plan appropriate learning paths, and personalize subsequent learning content recommendations. During interactions with the intelligent education system, students record a large amount of learning data. Various knowledge tracking methods are used to extract student learning characteristics, accurately capture changes in their knowledge status, and further predict the probability of a student answering a new question correctly at the next moment. Considering the large number of questions, sparse student interactions, and long learning sequences, designing efficient knowledge tracking methods presents challenges. Introducing domain prior knowledge helps alleviate the problem of sparse interactions, and modeling long sequences using attention mechanisms also helps improve the efficiency of the methods.

[0003] In existing technologies, some methods fail to consider the complex relationships between questions and knowledge points, facing the challenge of sparse question interactions. Other methods consider the relationships between questions but neglect the relationships between questions and knowledge points. Some use deep recurrent neural networks to replace previous rule-based knowledge tracing methods for sequential feature extraction from student learning history. However, this model only makes predictions at the coarse-grained knowledge point level, limiting its accuracy. Furthermore, it faces the challenge of sparse interactions when dealing with a large number of questions. Some methods construct graphs of knowledge point relationships and utilize graph networks to extract relevant features, leveraging prior knowledge in the domain; however, they also cannot achieve fine-grained question-level predictions.

[0004] Analysis of relevant domestic and international patents and related research leads to the following conclusions: Most current deep knowledge tracing methods directly focus on the learning patterns of knowledge points, neglecting fine-grained prediction at the question level. Furthermore, methods that directly predict the probability of answering questions correctly often face the challenge of sparse interactions. Additionally, there are currently no knowledge tracing methods capable of handling long-sequence inputs, all of which limit the prediction accuracy of existing knowledge tracing methods.

[0005] Therefore, those skilled in the art are dedicated to developing an interactive knowledge tracing method based on graph networks, aiming to obtain the probability of answering the final question correctly and achieve highly accurate knowledge tracing. Summary of the Invention

[0006] In view of the above-mentioned deficiencies of the prior art, the present invention aims to solve the technical problems faced by existing knowledge tracing methods, such as lack of fine-grained prediction, sparse interaction, and difficulty in extracting features from long sequences.

[0007] To achieve the above objectives, this invention provides an interactive knowledge tracing method based on graph neural networks, comprising the following steps:

[0008] Step 1: Construct a graph G(S, Q, E) showing the relationship between questions and knowledge points, where S is a knowledge point node, Q is a question node, and E is the edge connecting a question node and a knowledge point node, indicating that a question belongs to a certain knowledge point. Based on the information in the graph G, use a graph neural network to calculate the vector representation of each question in the student's learning sequence.

[0009] Step 2: Vector representation of the student learning sequence obtained in Step 1 Use a Long Short-Term Memory (LSTM) network f to extract the hidden state h of the network. t As a vector representation of students' knowledge mastery status;

[0010] Step 3: Characterizing the problem to be predicted at the next time step The cosine similarity between the vector and the historical information vector is calculated. The historical information includes the knowledge mastery state vector representation h. i and problem representation Where 1 ≤ i ≤ t. Calculate the cosine similarity and select the K most relevant historical information items as the historical information set, denoted as N. h ;

[0011] Step 4: Characterize the problem to be predicted at the next time step. The vector representations of multiple knowledge points associated with this problem are taken as the target information set, denoted as N. q ;

[0012] Step 5: Process the historical information set N h and the target information set N q The vector representation in the model uses the inner product operation to perform pairwise interactions, resulting in multi-level predictions of mastery levels.

[0013] Step 6: Learn weight 'a' for all information interactions through an attention mechanism. i，j ;

[0014] Step 7: Perform a weighted summation of the predicted mastery levels at multiple levels to obtain the probability p of the student correctly answering the question to be predicted. t+1 ;

[0015] Step 8: Train the graph neural network and long short-term memory network end-to-end using a real student historical learning dataset, and minimize the cross-entropy loss function of the predicted probability and the student's real answer label through gradient descent.

[0016] Further, step 1 includes:

[0017] Step 1.1: For node i in the relation graph G, randomly initialize the vector representation of node i, denoted as e. i ;

[0018] Furthermore, step 1 also includes:

[0019] Step 1.2: For each node i in the relation graph G, its neighbors are the set N of neighbor nodes with direct edges. i For the node i and the set of neighboring nodes N i The vector representations of nodes within the node i are subjected to mean pooling, and the vector representation e of node i is updated. i

[0020]

[0021] Where l represents the aggregation number, w l b l These are the trainable network parameters, and σ is a non-linear activation function, specifically the sigmoid function.

[0022] Furthermore, step 1 also includes:

[0023] Step 1.3: Repeat step 1.2 multiple times, aggregating the information of higher-order neighbors for each node, denoted as...

[0024] Further, step 2 includes:

[0025] For each time t, the hidden state h of the Long Short-Term Memory network is... t As a vector representation of students' knowledge mastery status; the vector representation of students' knowledge mastery status is updated in the following way:

[0026]

[0027]

[0028]

[0029]

[0030] h t =o ttanh(c t )

[0031] Among them W i W f W o W c b i b f b c b o These are all trainable network parameters; c t It refers to the state of a network unit, which on the one hand retains some historical information, and on the other hand receives information input at the current moment; the memory of historical information is controlled by the forgetting gate f. t Control, the input of current information is controlled by input gating i t Control; o t It is an output gating mechanism that controls the conversion of the cell states of the Long Short-Term Memory (LSTM) network into the network output information h. t σ is the Sigmoid activation function, i.e., σ(x) = 1 / (1+e^x). -x The output range of this function is between 0 and 1.

[0032] Furthermore, in step 3,

[0033]

[0034] Among them, h i It is a vector representation of the knowledge mastery state at a historical moment. It represents the problem to be predicted at time t+1; by using vector cosine similarity, select the K most relevant historical information about the problem to be predicted at the current time.

[0035] Furthermore, in step 5, the pairwise interactions are as follows:

[0036]

[0037] Vector set N q It includes the representation of the problem to be predicted. And the vector representations of its multiple related knowledge points; N h It is the set of similar historical information selected in step 6.

[0038] Furthermore, in step 6,

[0039] a i，j =softmaxi, j (W[f i f j ]+b)

[0040]

[0041] Where W and b are trainable network parameters, and softmax is the normalization function.

[0042] Furthermore, in step 7,

[0043]

[0044] Furthermore, in step 8, the student's actual answer label refers to correct / incorrect answer;

[0045] The cross-entropy loss function is

[0046] minL=-∑ t (a t+1 logp t+1 +(1-a t+1 log(1-p) t+1 )).

[0047] The graph neural network used in this invention, in principle, aggregates neighbor features for each node. Multiple aggregations yield higher-order neighbor features for each node, enriching the vector representations of problems and knowledge points and mitigating the impact of sparse data interactions. However, even with long short-term memory networks, the challenge of long-term dependencies remains when sequences are very long. Therefore, an attention mechanism is used to select historically relevant information, strengthening the influence of behaviors over longer time intervals and alleviating this challenge. Furthermore, an inner product interaction method is used to fuse historical information with the current problem and related knowledge point representations, making predictions at both the knowledge point and problem levels, thus increasing prediction accuracy.

[0048] Compared with the prior art, the present invention has the following beneficial technical effects:

[0049] 1. This invention uses graph neural networks to aggregate neighbor features of problems and knowledge points, which can capture high-order correlations and mitigate the impact of coefficient interactions.

[0050] 2. This invention designs a historical information selection method based on an attention mechanism, which can obtain the historical information most relevant to the current moment for prediction in long sequence feature extraction.

[0051] 3. This invention designs an information interaction method based on inner product, which can make predictions at both the coarse-grained knowledge point level and the fine-grained problem level, thereby achieving higher prediction accuracy.

[0052] 4. Practice has proven that the knowledge tracing method proposed in this invention has excellent prediction accuracy. Furthermore, the graph network method, historical information selection method, and information interaction method designed in this invention can be easily used to improve existing knowledge tracing methods based on sequence features.

[0053] The following will further explain the concept, specific structure, and technical effects of the present invention with reference to the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0054] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0055] The following description, with reference to the accompanying drawings, illustrates a preferred embodiment of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different embodiments, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0056] In one embodiment of the present invention, the interactive knowledge tracing method based on graph neural networks is applied to the environment of an intelligent education system. This environment contains a certain number of knowledge points and questions, with the questions and knowledge points having a priori relationships within the domain. Students interact with the intelligent education system by answering questions, and the system provides feedback on whether the answers are correct or incorrect. Based on the student's answer sequence and feedback, the system uses the knowledge tracing method to predict the student's level of knowledge mastery and further optimize the student's learning path. The specific steps are as follows:

[0057] 1. Given a set of questions Q and a set of knowledge points S, construct a graph G(S,Q,E) representing the relationship between questions and knowledge points based on prior expert knowledge. E represents the edges connecting question nodes and knowledge point nodes, indicating that a question belongs to a certain knowledge point. Use a graph convolutional network to represent the nodes in the graph using vectors. The specific steps are as follows:

[0058] (1) For node i in graph G, randomly initialize its vector representation, denoted as e. i .

[0059] (2) For each node i in graph G, its neighbors are the set of nodes N with which it has a direct connection. i Perform mean pooling on the vector representations of the node and its neighbors, and update the vector representation of the node.

[0060]

[0061] Where l represents the number of aggregations, when l = 1 w l b l These are the network parameters, which can be obtained through gradient backpropagation training. σ is the non-linear activation function; the sigmoid function is chosen.

[0062] (3) By repeating step (2) multiple times, information about higher-order neighbors can be aggregated for each node, denoted as . 2. The vector representation of the student learning sequence obtained in step 1 is used to extract sequence features using a Long Short-Term Memory (LSTM) network. At each time t, the hidden state h of the network... t This serves as a vector representation of students' knowledge mastery status. The update method is... The f(*) function is a Long Short-Term Memory (LSTM) network that takes the representation of the problem to be predicted and the hidden state of the network at the previous time step as input, and updates the hidden state of the network at the current time step. The specific implementation is as follows:

[0063]

[0064]

[0065]

[0066]

[0067] h t =o t tanh(c t )

[0068] Among them W i W f W o W c b i b f b c b o These are all trainable network parameters; c t This refers to the state of a network unit, which retains some historical information while simultaneously receiving current information input. The retention of historical information is controlled by a forgetting gate f. t Control, the input of current information is controlled by input gating i t Control. t It is an output gating mechanism that controls the conversion of the cell states of the Long Short-Term Memory (LSTM) network into the network output information h. t σ is the Sigmoid activation function, i.e., σ(x) = 1 / (1+e^x). -x The output range of this function is between 0 and 1.

[0069] 3. Characterization of the problem to be predicted at the next time step The cosine similarity between the knowledge-possessing state vector representation and the problem representation at each historical moment is calculated. The cosine similarity between two vectors is defined as follows: Then, select the K most relevant historical information items as the auxiliary information set, denoted as N. h The formal definition is as follows:

[0070]

[0071] 4. Vector representation of the problem to be predicted at the next time step The vector representations of multiple knowledge points associated with this problem are taken as the target information set, denoted as N. q .

[0072] 5. For the historical information set Nh and the target information set N... q The vector representation in the algorithm utilizes pairwise vector inner product operations to obtain multi-level predictions of mastery levels. The interaction method is as follows:

[0073]

[0074] 6. Learn weights a for all information interactions through an attention mechanism. i，j .

[0075] a i，j =softmax i，j (W[f i f j ]+b)

[0076]

[0077] Where W and b are the trainable network parameters. softmax is a commonly used normalization function.

[0078] 7. The predicted levels of mastery at multiple levels are weighted and summed to obtain the probability p of a student correctly answering the question to be predicted. t+1 .

[0079]

[0080] 8. After the model is built, it is trained using a real student historical learning dataset, including optimizing the initialized node vector table on the graph and multiple trainable parameters in the network. Gradient descent is used to minimize the cross-entropy loss function between the predicted probability and the student's actual answer label (correct / incorrect).

[0081]

[0082] 9. Once the model training converges, the trained network parameters, given the question set Q and the knowledge point set S, can be used to predict the probability of a student answering a question correctly using the algorithm described above, i.e., p. t+1 This allows us to infer the students' level of knowledge acquisition.

[0083] In knowledge tracing tasks within the field of intelligent education, this method fully leverages prior knowledge in the domain to construct a relationship graph between questions and knowledge points. It utilizes graph neural networks to aggregate high-order neighbor features on the graph, resulting in vector representations richer in semantic information. This mitigates the impact of sparse interactions to some extent and enables fine-grained question-level prediction. Considering the long learning sequences of students, this method proposes historical information selection and information interaction schemes, effectively utilizing historical information over extended time intervals. The method was compared with previous schemes on three datasets containing real-world data. Using the commonly used metric AUC (area under curvey), the AUC values ​​obtained by this invention were 0.7896, 0.7754, and 0.7523, respectively. The best AUC values ​​of previous schemes were 0.7684, 0.7652, and 0.7281, respectively. The classification accuracy of this invention significantly outperforms previous schemes. Furthermore, the improvements proposed in this method can be transferred to other existing knowledge tracing methods to improve their performance. In summary, this method leverages graph neural networks to aggregate high-order neighbor features based on the complex relationship between questions and knowledge points, mitigating the impact of sparse interactions. Simultaneously, it incorporates historical auxiliary information through an attention mechanism, enabling pairwise interactions to make predictions at both the knowledge point and question levels. Finally, the prediction results from both levels are fused to obtain the final probability of a correct answer, achieving highly accurate knowledge tracking.

[0084] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. An interactive knowledge tracing method based on graph neural networks, characterized in that, The method comprises the following steps: Step 1, construct a relationship graph G(S, Q, E) of questions and knowledge points, S is a knowledge point node, Q is a question node, E is the edge between the question node and the knowledge point node, indicating that the question belongs to a certain knowledge point; based on the information in the relationship graph G, use a graph neural network to calculate the vector representation of each question in the student learning sequence ; The step 1 comprises: Step 1.

1. For a node in the relational graph G , randomly initialize the vector representation of the node , denoted as ; Step 1.

2. For each of the nodes in the graph G whose neighbors are the set of neighbor nodes having direct edges , update the vector representation of the node and the set of neighbor nodes by performing mean-pooling operation on the vector representations of the nodes within ​ wherein denotes the number of aggregations, is a trainable network parameter, is a non-linear activation function, which is a sigmoid function, sigmoid ; Step 2, vector representation of the student learning sequence based on the vector representation obtained in step 1 using a long short-term memory network f to extract the hidden state of the network as a vector representation of the student knowledge mastery state; Step 3, for the next time to be predicted problem representation , and the history information vector calculates the cosine similarity, the history information includes the knowledge mastery state vector representation and the problem representation , wherein , the cosine similarity is calculated, and the most relevant K history information is selected as the history information set, denoted as ; Step 4, the next time to be predicted problem representation The vector representation of the multiple knowledge points associated with the problem as a target information set, denoted as ; Step 5, interacting with vector representation in the history information set and the target information set using vector inner product operation to obtain multi-level mastery prediction values; Step 6, learn weights for all information interactions through attention mechanism ; Step 7, weighted summing the multi-level mastery level prediction values to obtain the probability of the student correctly answering the problem to be predicted ; Step 8, using a real student history learning data set to train the graph neural network and the long short-term memory network end to end, minimizing the cross-entropy loss function of the predicted probability and the student real answer label through gradient descent. 2.The graph neural network-based interactive knowledge tracing method of claim 1, wherein, The step 1 further comprises: Step 1.

3. Repeat the step 1.2 several times, aggregating information of higher order neighbors for each node, denoted as .

3. The interactive knowledge tracing method based on graph neural networks of claim 2, wherein, The step 2 comprises: For each time instant the hidden state of the long short-term memory network as a vector representation of the student's knowledge mastery state; the vector representation of the student's knowledge mastery state is updated in a manner wherein are trainable network parameters; is a network unit state, on one hand, reserves part of historical information, and on the other hand, receives information input at the current time; wherein the memory of the historical information is controlled by a forget gate , and the input of the information at the current time is controlled by an input gate ; is an output gate, which controls the transformation of the unit state of the long short-term memory network into network output information ; is a Sigmoid activation function, that is , the output value range of the function is between 0 and 1.

4. The interactive knowledge tracing method based on graph neural networks of claim 2, wherein, In the step 3, wherein, is a historical time knowledge mastery state vector representation, is a time to be predicted problem representation; through vector cosine similarity, select the most relevant historical information to the current time to be predicted problem.

5. The interactive knowledge tracing method based on graph neural networks according to claim 4, wherein, In the step 5, the interaction mode is as follows: Vector set is a vector representation of the problem to be predicted and its associated plurality of knowledge points; is the set of similar historical information selected in step 6.

6. The interactive knowledge tracing method based on graph neural networks according to claim 5, wherein, In the step 6, wherein are trainable network parameters, and softmax is a normalization function.

7. The graph neural network-based interactive knowledge tracing method of claim 6, wherein, In the step 7, 。 8. The interactive knowledge tracing method based on graph neural networks of claim 7, wherein, In the step 8, the student real answer label refers to correct answer / wrong answer; The cross-entropy loss function is 。

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