Personalized knowledge tracking method and system based on graph neural network and question difficulty

Abstract

The invention discloses a personalized knowledge tracking method and system based on a graph neural network and question difficulty, and relates to the technical field of wisdom education, and the method comprises the steps: obtaining a data set of a field to be subjected to knowledge tracking; modeling is carried out on the difficulty of problems and knowledge concepts in the data set, and difficulty information is extracted; taking the difficulty as a node in the meta-path, and fusing the difficulty into a heterogeneous graph neural network model; constructing a difficulty-adaptive knowledge tracking model based on the fused heterogeneous graph neural network model; performing knowledge state updating on the knowledge tracking model; and final knowledge tracking is realized. According to the method, the heterogeneous graph is introduced, the difficulty feature of practice is fully utilized, the limitation on feature mining is overcome, and the accuracy of knowledge tracking is improved. By considering the perception of the individual students on the exercise difficulty and the learning income obtained from the exercises with different difficulties, more refined initial knowledge state modeling is realized, and the learning progress of the students can be reflected more accurately.

Description

Technical Field

[0001] The present invention relates to the field of smart education technology, and more specifically to a personalized knowledge tracking method and system based on graph neural network and question difficulty. Background Art

[0002] Knowledge tracking is an important application of smart education, which aims to ① model and analyze students' learning behaviors; ② accurately track the changes in students' knowledge status; and ③ predict students' performance in future exercises. Due to the development of deep learning, its efficient training and better performance have almost completely replaced earlier statistical learning and even traditional machine learning methods. So far, the research on deep knowledge tracking has formed a complete research system from model design, modeling optimization, training techniques to data set analysis. However, there are still some major defects and loopholes that can be further optimized.

[0003] Some early deep learning methods used simple neural network layers to complete knowledge tracking tasks, such as DKT, DKVMN, etc. Based on this, some methods tried to consider some explicit behavioral features by adding educational theory, forgetting theory, etc., such as DKT+, LPKT, HawkesKT, etc. However, these methods face the same difficulties as sequence modeling. The simple networks such as RNN used by them are difficult to accurately track students' knowledge changes. The self-attention mechanism was proposed and played a key role in the Transformer model. The attention mechanism can handle variable-length sequences well, reduce dependence on external information, and is better at capturing the internal correlation of data or features. Some methods such as SAKT and AKT use the sequence modeling idea of ​​the attention mechanism.

[0004] Compared with sequence information, graph structures provide a more comprehensive and detailed representation of data. In the context of knowledge tracking, the relationship between learners, exercises, and knowledge concepts can be easily described by graphs, which facilitates the extraction of features from exercises and concepts. Therefore, there has been a surge in methods of graph-based KT models. The GKT method proposed by Nakagawa et al. initially used graph convolutional networks (GCNs) to model students' proficiency in knowledge concepts. PEBG pre-trains exercise embeddings and integrates different side information to achieve rich representations, which is a new training strategy for improving the effectiveness of graph representation learning. DGEKT introduces an integrated approach to knowledge tracking that uses hypergraphs and directed graphs to extract knowledge to improve learning. Xu et al. proposed using implicit interactions between questions generated by student-question-skill interactions to enhance question embeddings for knowledge tracking.

[0005] In recent years, many graph-based knowledge tracking models have made significant progress, but there are still some unresolved issues:

[0006] (1) It is not possible to distinguish the learning benefits obtained due to different difficulty levels of questions. First, learners have different proficiency levels, and they perceive the difficulty of the same exercise differently, so the degree of knowledge improvement after completing the exercise is also different. In addition, when learners participate in multiple exercises of varying difficulty, the learning benefits inferred from their answers will also be different. Therefore, when updating students' knowledge mastery, personalized attention to learners and exercises is crucial to accurately measure the extent of learning progress. Most existing graph-based knowledge tracking models do not fully consider individual differences among students and the diversity of exercise difficulty. When updating students' knowledge status, the lack of personalized attention to students and exercises leads to inaccurate assessment of learning benefits.

[0007] (2) In the graph structure used for knowledge tracing tasks, the high-level information between concept nodes and question nodes is not sufficiently considered. Recent studies (Schlichtkrull et al.) mainly use graph convolutional networks (GCNs) and similar isomorphism-based graph neural networks (GNNs), which ignore the importance of high-order information when only focusing on the communication between each node and its immediate neighbors. This limitation makes it difficult for the model to capture and preserve the key high-order features in the graph structure.

[0008] (3) Little attention has been paid to incorporating difficulty features of exercises and concepts in graph representation learning to achieve personalized differentiation of learning outcomes. It is worth noting that some knowledge tracing datasets lack explicit difficulty information of exercises, and even if it exists, this information is not fully utilized in most knowledge tracing frameworks. This deficiency hinders the accurate assessment of the difficulty level of exercises and concepts in graph representation learning, resulting in the loss of difficulty features and posing challenges for the personalized construction of students' knowledge states.

[0009] (4) Early deep learning methods, such as RNN, have problems with gradient vanishing and gradient exploding when processing long sequence data, making it difficult for the model to effectively capture the long-term changes in students’ knowledge status over time. Although the self-attention mechanism effectively alleviates this problem through the Transformer model, the complexity and computational cost also increase, leading to the difficulty of modeling long sequences.

[0010] Therefore, how to propose a personalized knowledge tracking method and system based on graph neural networks and question difficulty, by introducing heterogeneous graphs, making full use of the difficulty characteristics of exercises, considering individual students' perception of exercise difficulty and the learning benefits obtained from exercises of different difficulty levels, and achieving more refined initial knowledge state modeling, which helps to more accurately reflect students' learning progress is a problem that technical personnel in this field urgently need to solve. Summary of the invention

[0011] In view of this, the present invention provides a personalized knowledge tracking method and system based on graph neural network and question difficulty. By introducing heterogeneous graphs, making full use of the difficulty characteristics of exercises, considering individual students' perception of exercise difficulty and the learning benefits obtained from exercises of different difficulty levels, a more refined initial knowledge state modeling is achieved, which helps to more accurately reflect students' learning progress. In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0012] A personalized knowledge tracking method based on graph neural network and question difficulty, including:

[0013] Obtain the dataset of the domain to be tracked;

[0014] Model the difficulty of questions and knowledge concepts in the dataset and extract difficulty information;

[0015] Integrate difficulty into the heterogeneous graph neural network model as a node in the meta-path;

[0016] Build a difficulty-adaptive knowledge tracking model based on the fused heterogeneous graph neural network model;

[0017] updating the knowledge status of the knowledge tracking model;

[0018] The final knowledge tracing is achieved through the updated knowledge tracing model.

[0019] Optionally, the data set includes: user / student ID, exercise ID, concept ID, answer status, exercise response time, number of attempts, question type, exercise sequence, concept sequence, answer sequence and exercise difficulty sequence.

[0020] Optionally, modeling the difficulty of the questions and knowledge concepts in the data set and extracting difficulty information includes:

[0021] represents the difficulty coefficient corresponding to each exercise, that is, the error rate, which represents the number of times it is wrong in the entire data set divided by the total number of attempts. Its range is [0, 1]. The larger the error rate, the higher the difficulty coefficient. i For practice.

[0022] Optionally, it also includes the knowledge tracking task definition:

[0023] Set m exercises and k knowledge concepts, respectively represented as E = {e 1 ,…,e m} and C={c 1 ,…,c k};

[0024] Let the set c(e i) indicates practice e i All the concepts involved, let r t ∈{0,1} represents the correctness of the answer at time t, let d(e t )∈{0,1} represents the exercise e t The average difficulty coefficient of the learning sequence in the past T-1 period is expressed as X = [x 1 ,x 2 ,…,x T-1 ], where x t =(e t ,c(e t ),r t ,d(e t )) represents the interaction situation at the tth moment;

[0025] The knowledge tracking task is described as: given an exercise sequence X, predict the future time T for a certain exercise e T The probability of answering correctly is: P(r T =1|X).

[0026] Optionally, the difficulty-adaptive knowledge tracking model constructed based on the fused heterogeneous graph neural network model includes: a heterogeneous graph representation learning module, a difficulty perception module and a learning benefit module, in which different meta-paths are constructed to integrate difficulty features and refine the representation of exercise nodes and concept nodes; the information of heterogeneous graph learning and the information of exercise interaction are processed by the difficulty perception module to obtain the difficulty perception of the question; and the learner's difficulty perception is converted into his growth benefit by the learning benefit module.

[0027] Optionally, the heterogeneous graph representation learning module includes:

[0028] The feature vectors of various node categories are mapped into a common vector space by applying a type-specific linear transformation to the feature vector of each node type;

[0029] After completing the node feature mapping, the semantic information is aggregated from the meta-path to the target node, and the different attributes of the nodes in each meta-path instance are converted into a coherent and compressed vector representation;

[0030] After converting the meta-path instances into vector representations, the graph attention mechanism is used to combine the meta-path instances related to the target node;

[0031] For each meta-path, the meta-path is aggregated by calculating the average value of all node vectors converted in the meta-path, and then the attention mechanism is used to aggregate and update the information between different meta-paths;

[0032] Linear transformations are combined with nonlinear activation functions to project node embeddings into the required vector space, ensuring the specified dimensionality of the output.

[0033] Optionally, the difficulty perception module includes:

[0034] Among them, W 1 and β 1 is a learnable parameter, δ t To practice embedding vectors, h t-1 is the current state of knowledge, It is the intermediate result of the calculation process and is used to calculate the difficulty perception;

[0035] in, is a gated unit used to calculate difficulty perception, W 2 and β 2 is a learnable parameter, σ is the sigmoid activation function;

[0036] Among them, d t Feel the vector for difficulty.

[0037] Optionally, the learning benefit module includes:

[0038] For the current exercise, combine the previous knowledge state with the current exercise to obtain a knowledge state related to the current exercise, so that the current knowledge state h t-1 Combined question sequence;

[0039] Perform matrix multiplication of the previous knowledge state and the representation of the current exercise to obtain a knowledge state related to the current exercise;

[0040] Regulate the learning gains achieved through learning gating;

[0041] The actual learning gain is obtained by multiplying the previously calculated knowledge state with the output of the learning gate, and a linear transformation is applied to constrain the result to the range (0, 1).

[0042] Optionally, updating the knowledge status of the knowledge tracking model includes:

[0043] Among them, Γ is the gate control unit, W 5 and β 5 is a learnable parameter, δ t To practice embedding vectors, a t For question q t The answer sequence:

[0044] h t=(1-Γ)·ω t +Γ·h t-1 ; Among them, h t is the knowledge state after the next time step, ω t For the ultimate learning benefit;

[0045] μ t =σ(W 6 ·h t +β 6 ), where μ t is the final knowledge state, W 6 and β 6 are learnable parameters.

[0046] Optionally, a personalized knowledge tracking system based on graph neural network and question difficulty, including:

[0047] Acquisition module: used to obtain the data set of the field to be tracked;

[0048] Modeling module: used to model the difficulty of questions and knowledge concepts in the data set and extract difficulty information;

[0049] Fusion module: used to integrate difficulty as a node in the meta-path into the heterogeneous graph neural network model;

[0050] Model building module: used to build a difficulty-adaptive knowledge tracking model based on the fused heterogeneous graph neural network model;

[0051] Update module: used to update the knowledge status of the knowledge tracking model;

[0052] Knowledge tracking module: used to achieve final knowledge tracking through the updated knowledge tracking model.

[0053] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a personalized knowledge tracking method and system based on graph neural network and question difficulty, which has the following beneficial effects:

[0054] The present invention proposes a personalized knowledge tracking method based on graph neural network and question difficulty, including: obtaining a data set of the field to be tracked; modeling the difficulty of the questions and knowledge concepts in the data set and extracting difficulty information; taking difficulty as a node in the meta-path and integrating it into the heterogeneous graph neural network model; constructing a difficulty-adaptive knowledge tracking model based on the fused heterogeneous graph neural network model; updating the knowledge state of the knowledge tracking model; and realizing the final knowledge tracking through the updated knowledge tracking model. By introducing heterogeneous graphs, the GDPKT model can make full use of the difficulty characteristics of exercises, overcome the limitations of traditional homogeneous graph models in feature mining, and improve the accuracy of knowledge tracking. Taking into account the individual student's perception of the difficulty of exercises and the learning benefits obtained from exercises of different difficulty levels, a more refined initial knowledge state modeling is achieved, which helps to more accurately reflect the student's learning progress. Comparative analysis on three real-world benchmark data sets shows that GDPKT has significant advantages over the most advanced knowledge tracking methods, can effectively predict students' future practice performance, and provides strong support for personalized learning. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0056] Figure 1 A schematic flow chart of a personalized knowledge tracking method based on graph neural network and question difficulty provided by the present invention.

[0057] Figure 2 A schematic diagram of the principle of a personalized knowledge tracking method based on graph neural network and question difficulty provided by the present invention.

[0058] Figure 3 A structural framework diagram of a personalized knowledge tracking system based on graph neural network and question difficulty provided by the present invention. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only 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.

[0060] The embodiment of the present invention discloses a personalized knowledge tracking method based on graph neural network and question difficulty, such as Figure 1 As shown, including:

[0061] Obtain the dataset of the domain to be tracked;

[0062] Model the difficulty of questions and knowledge concepts in the dataset and extract difficulty information;

[0063] Integrate difficulty into the heterogeneous graph neural network model as a node in the meta-path;

[0064] Build a difficulty-adaptive knowledge tracking model based on the fused heterogeneous graph neural network model;

[0065] updating the knowledge status of the knowledge tracking model;

[0066] The final knowledge tracing is achieved through the updated knowledge tracing model.

[0067] In a specific implementation, (1) Self-attention mechanism: The self-attention mechanism achieves effective processing of variable-length sequences by calculating the attention weight of each element in the input sequence to other elements. This mechanism reduces the model's dependence on external information and improves the ability to capture the internal correlation of the data. (2) Graph Neural Networks (GNNs): Graph Neural Networks are a type of neural network model that can process graph-structured data. They update the representation of nodes through information transmission and aggregation between nodes, thereby capturing the characteristic information in the graph structure. The application of GNNs in the field of knowledge tracking helps to integrate the relationship between learners, exercises, and knowledge concepts. (3) Prompt Learning: Prompt Learning is a method that guides the model to understand and perform specific tasks by adding specific prompts to the model input. This method does not require direct modification of model parameters and can avoid retraining the entire model. It is particularly suitable for situations where data is scarce. In the field of knowledge tracking, prompt learning is expected to solve the problem of high cost of traditional pre-training. (4) Masked Task: Masked Task is a commonly used pre-training task that trains the model by randomly masking some elements in the input sequence and requiring the model to predict these masked elements. This kind of task helps the model learn deep representations and contextual information of the data. In knowledge tracing, wrapping the downstream prediction task into a mask task similar to the pre-training process helps achieve overall training consistency.

[0068] In a specific implementation, a personalized knowledge tracking method based on graph neural network and question difficulty, such as Figure 2 As shown, the specific steps are as follows:

[0069] A knowledge tracking model based on heterogeneous graph neural networks and adaptive to difficulty, the GDPKT model, is proposed. The heterogeneous graph neural network is personalized combined with the difficulty level of the questions.

[0070] Model the difficulty of questions and knowledge concepts in the dataset to extract their respective difficulty information;

[0071] In the graph representation learning process, the difficulty is isolated as the nodes participating in computing the meta-path;

[0072] Model students' perception of problem difficulty and the benefits gained from learning at different difficulty levels to achieve personalized tracking of students' knowledge status.

[0073] Step 1: Dataset description and input composition

[0074] For the Knowledge Tracking research area, the following data items are included:

[0075] (1) User / student ID: a number that uniquely identifies the subject;

[0076] (2) Exercise ID: a number. Each exercise ID can uniquely identify an exercise question.

[0077] (3) Concept ID: a number. Each concept ID can uniquely identify a knowledge concept (knowledge point).

[0078] (4) Answer status: The number 1 or 0 indicates the answer status record corresponding to each exercise;

[0079] (5) Additional records (side information): including response time, number of attempts, type of questions, and other factors of the exercise. The specific content may vary depending on the different data sets.

[0080] Among the above data items, (2), (3), and (4) are essential for completing the knowledge tracking task. Among them, there is a corresponding relationship between exercises and concepts, and a specific exercise question may involve one or more knowledge concepts. In addition, due to system records, user preferences, etc., the exercise sequence of different users may be different. In combination with the relevant steps involved in this embodiment, the input data used is listed below:

[0081] (1) Exercise sequence: Each sequence consists of a series of exercise IDs, arranged in the order in which the exercises were completed. Each exercise in the sequence comes from the exercise record of the same user / student;

[0082] (2) Concept sequence: corresponds to the exercise sequence and consists of the concept ID set corresponding to each exercise;

[0083] (3) Answer sequence: record whether the answer to each exercise is correct or not, 1 for correct answer and 0 for incorrect answer;

[0084] (4) Exercise difficulty sequence: This data is generated based on the data set and represents the difficulty coefficient (error rate) corresponding to each exercise, that is, the number of times it was done wrong in the entire data set divided by the total number of attempts. Its range is [0, 1], and the larger the value, the higher the difficulty coefficient. i For example, the difficulty coefficient is calculated as follows:

[0085]

[0086] Step 2: Knowledge tracing task definition

[0087] The purpose of knowledge tracking is to predict the performance of a student on a future exercise, i.e., whether the answer is correct or not, or the probability of answering correctly, given all the past exercise interaction records of a student (often expressed as exercise behavior or exercise sequence). Assume that in the smart education system, there are m exercises and k knowledge concepts, which are represented by E = {e 1 ,…,e m} and C={c 1 ,…,c k}. Let the set c(e i ) indicates practice e i All the concepts involved. Let r t ∈{0,1} represents the correctness of the answer at time t. Considering the difficulty information, let d(e t )∈{0,1} represents the exercise e t The average difficulty coefficient of the student in the past T-1 period is expressed as X = [x 1 ,x 2 ,…,x T-1 ], where x t =(e t ,c(e t ),r t ,d(e t )) represents the student’s interaction at time t. Based on the above settings, the knowledge tracking task can be described as: given an exercise sequence X, predict the student’s interaction with an exercise e at the next time T. T The probability of answering correctly is:

[0088] P(r T =1|X).

[0089] Step 3: Model structure

[0090] like Figure 2As shown in the figure, the GDPKT model consists of three main modules: heterogeneous graph representation learning, obtaining students' perception of the difficulty of the questions, and obtaining students' learning benefits. In heterogeneous graph representation learning, different meta-paths are constructed to integrate difficulty features, thereby refining the representation of exercise nodes and concept nodes. In addition, difficulty perception and students' learning benefits are used to optimize the construction of students' knowledge status. Through difficulty perception, the information of heterogeneous graph learning and the information of students' practice interaction are processed to obtain students' perception of the difficulty of the questions. Through students' learning benefits, learners' perception of difficulty is converted into their growth benefits to improve students' mastery of knowledge.

[0091] 1) Heterogeneous Graph Embedding

[0092] In previous knowledge tracing studies, heterogeneous graphs have been difficult to effectively capture difficulty features. Therefore, this embodiment incorporates difficulty as a node in the meta-path into the heterogeneous graph learning representation. Difficulty is a key factor that significantly affects the prediction of students' answer accuracy. Therefore, it is crucial to incorporate difficulty into subsequent knowledge state generation. First, it improves prediction accuracy. By explicitly introducing difficulty nodes into the heterogeneous graph model, the model demonstrates a stronger ability to identify the complex interdependencies between difficulty, student performance, and concept mastery. This direct correlation helps the model to more accurately predict students' performance on exercises at different difficulty levels, thereby improving overall prediction accuracy. In addition, it also enhances the interpretability of the model. Traditional knowledge tracing models may find it difficult to directly explain why some students perform poorly on specific exercises. However, by incorporating difficulty nodes, the model can clearly show how difficulty affects students' answers. This enhanced interpretability helps educators better understand students' learning status, enabling them to develop more targeted teaching strategies.

[0093] The goal of heterogeneous graph embedding is to obtain a d-dimensional embedding vector to represent complex features that can cover different types of nodes (such as questions, concepts, and other entities).

[0094] Specifically, in order to perform representation learning on such heterogeneous graphs, the first step is to map the feature vectors of various node categories into a common vector space. This is achieved by applying a type-specific linear transformation to the feature vectors of each node type, thereby mapping them into a common latent factor space.

[0095]

[0096] Among them, W A is the weight matrix, is the initial feature vector of the node.

[0097] Specifically, after completing the node feature mapping, the semantic information is aggregated from the meta-path to the target node. The different attributes of the nodes in each meta-path instance are converted into a coherent and compressed vector representation. M (v,u) is defined as a specific meta-path instance, which is used to connect the target node with its associated neighbor nodes. Its precise expression is that in the meta-path M, the target node v is connected to its neighbor u. Represents the neighbors of node v.

[0098]

[0099] Among them, f θ Represents a function that converts this metapath instance into a vector.

[0100] Specifically, after converting the meta-path instances into vector representations, the graph attention mechanism is utilized to effectively combine the meta-path instances related to the target node.

[0101]

[0102] in, is the parameterized attention vector of the meta-path, used to calculate the “attention score”. is the attention score obtained under the meta-path M (about the target node v and its neighbor u).

[0103]

[0104] in, is the “attention coefficient” calculated by the softmax method (for the target node v in the meta-path), s is the same as u, It also represents the neighbors of node v. The numerator is the attention score of a neighbor node u of node v. Perform an exponential operation, and the denominator is the exponential operation of the attention scores of all neighboring nodes (including u) of node v, and sum them up.

[0105]

[0106] in, is the feature vector of the target node v obtained in the meta-path M, and σ is the sigmoid activation function.

[0107] By adopting the "Multi-Head Attention Mechanism", the robustness of the training process can be enhanced while reducing the high variability that may be caused by the complexity and diversity of the graph itself. Once the information of nodes and edges is aggregated within a single meta-path, the semantic content revealed by all these meta-paths needs to be integrated.

[0108] Specifically, the aggregation strategy between meta-paths also adopts the attention-based method. First, for each meta-path, the meta-path is aggregated by calculating the average value of all node vectors transformed in the meta-path (these vectors are unique to the meta-path).

[0109]

[0110] Among them, W' A and b A is a "learnable parameter", tanh is a "tanh function", A represents the type of node, V A Represents a node of type A. The vector after the meta-path is aggregated.

[0111] Then the attention mechanism is used to aggregate and update the information between different meta-paths:

[0112]

[0113] in, is the attention score, is the “parameterized attention vector” of class A nodes.

[0114]

[0115] in, After the internal aggregation of the meta-path, the meta-path M i The "attention coefficient", P A Represents the set of all meta-paths whose target node type is A.

[0116]

[0117] in, is the feature vector obtained after calculation by the attention mechanism.

[0118] Specifically, an additional linear transformation is finally integrated and matched with a nonlinear activation function to project the node embedding into the required vector space to ensure the specified dimension of the output.

[0119]

[0120] Among them, g v is the final feature vector of the target node v, W o are learnable parameters.

[0121] For the loss function of heterogeneous graph representation learning, this embodiment is defined as follows:

[0122]

[0123] 2) Difficulty Perception

[0124] After completing each exercise, students' knowledge states undergo corresponding changes, which reflect the complexity of individual understanding and the different educational benefits obtained from the problem-solving process. Given the diversity of learning backgrounds among students, there are significant differences in the perception of the difficulty level of the same exercise and the training results achieved. Therefore, when constructing a model of students' personalized learning trajectories, the impact of exercise difficulty on the "exercise embedding vector" must be considered. In addition, when constructing preliminary features of students' knowledge states, the understanding they gain after completing the exercise should also be considered. Students' perception of problem difficulty varies. In order to model the personalized experience of the same exercise in different students, the difference between the "exercise embedding vector" and the "student's current knowledge state" can be quantified to represent it. If the student's current knowledge state cannot meet the requirements of the exercise, then the student is likely to think that the exercise is difficult.

[0125]

[0126] Among them, W 1 and β 1 is a “learnable parameter”, δ t To practice embedding vectors, h t-1 is the student’s current knowledge status, It is the intermediate result of the calculation process and is used to calculate students' perception of difficulty.

[0127]

[0128] in, is a gated unit used to calculate the student's difficulty perception, W 2 and β 2 are “learnable parameters”.

[0129]

[0130] Among them, d t Vector for students' difficulty perception.

[0131] Difficulty perception aims to capture individual learners' perception of different levels of difficulty, which is crucial for the subsequent work of personalized knowledge state modeling based on students' feedback on their answers to questions of different difficulty levels. By understanding students' different perceptions of problem difficulty, their knowledge level and comprehension ability can be more accurately assessed, thereby providing them with more personalized learning resources and guidance. This personalized knowledge state modeling helps teachers or learning systems better understand the needs of each student and adjust teaching strategies or recommend appropriate learning materials accordingly. Therefore, this section not only emphasizes students' subjective feelings when facing questions of different difficulty levels, but also points out the importance of such feelings in personalized learning, providing a basis for subsequent knowledge state modeling and learning path planning.

[0132] 3) Learning benefits

[0133] Different students can gain different learning gains from answering the same exercise. The learning gains students gain from solving exercises are closely related to their subjective feelings about the difficulty of the questions before answering them, their previous knowledge mastery, and their answering performance. If a student is relatively weak in knowledge mastery, but finds an exercise challenging and successfully solves it, then they are likely to have gained significant learning gains from this exercise. Therefore, in order to accurately model the updating process of learning gains, these three factors must be fully considered.

[0134] Specifically, in order to focus on the current exercise, the previous knowledge state is first combined with the current exercise to obtain a knowledge state related to the current exercise (so that h t-1 Combined with the question sequence). This step is an important part of the modeling process, which can help more accurately understand the changes in students' knowledge status when facing different exercises. In this way, students' learning progress and gains can be better captured, so as to provide them with more personalized learning guidance and support.

[0135] In order to focus on the current exercise, the previous knowledge state is first matrix-multiplied with the representation of the current exercise to obtain a knowledge state related to the current exercise.

[0136]

[0137] in, is the intermediate result in the calculation process of “temporary knowledge state”, q t is the problem sequence,

[0138] The purpose of this step is to link the student's previous knowledge state with the current exercise in order to more accurately assess the student's knowledge level and possible learning gains when solving the exercise. In this way, a knowledge state representation that is closely related to the current exercise can be constructed, which reflects the student's knowledge preparation when facing the exercise.

[0139] Similar to the modeling step of difficulty perception, recognizing that not all learning can be converted into effective gains, a "learning gate" is designed to regulate the learning gains obtained by students:

[0140]

[0141] in, is a gate control unit used to calculate the final learning benefit. is the “temporary learning benefit”, W 3 , W 4 , β 3 , β 4 is a “learnable parameter”, a t For question q t The answer sequence.

[0142] The core of the “learning gating” mechanism is that it can evaluate the effectiveness of learning activities based on a series of factors and adjust the actual learning gains of students accordingly. These factors may include students’ learning attitude, concentration, quality of exercises and relevance to previous knowledge.

[0143] Furthermore, the actual learning gain is obtained by multiplying the previously calculated relevant knowledge state with the output of the learning gate. Considering that the output range of the tanh activation function is (-1,1), and the learning gain should be positive in nature, a linear transformation needs to be applied to constrain the result to the range of (0,1).

[0144] Among them, ω t For the ultimate learning benefit.

[0145] 4) Knowledge status update

[0146] After answering a specific exercise, different students’ knowledge states are updated to different degrees. If a student can successfully solve a challenging exercise, their understanding of the relevant basic concepts should be enhanced accordingly. The update of students’ knowledge states mainly considers three factors: their previous knowledge state, their answering performance, and the embedded representation of the exercise. In addition, a learning indicator is used to balance the learners’ previous knowledge state and their current learning gains, so as to update their knowledge state and obtain the current state. The learning indicator plays a vital role in this updating process. It evaluates the students’ current learning effect based on their answering performance and the difficulty of the exercise, and adjusts the extent of their knowledge state update accordingly. In this way, it can ensure that the students’ knowledge state update reflects both their previous learning foundation and their learning progress on the current exercise.

[0147]

[0148] Where Γ is the gate unit, W 5 and β 5 is a learnable parameter, δ t Embedding vectors for practice.

[0149] h t =(1-Γ)·ω t +Γ·h t-1 , where h t is the student’s knowledge state after the next “time step”.

[0150] Finally, the hidden layer representation of the student's knowledge state is further processed to generate an output state, which represents the student's current knowledge state.

[0151] μ t =σ(W 6 ·h t +β 6 );

[0152] Among them, μ t is the student’s final knowledge state, W 6 and β 6 are learnable parameters.

[0153] Specifically, in order to predict the answer, the previous output state (representing the student's current knowledge state) is concatenated with the representation of the current question. In order to optimize the performance of the model, the model parameters are adjusted through the gradient descent optimization method, with the goal of minimizing the cross entropy loss. This loss function is used to quantify the difference between the correct probability of the answer predicted by the model and the actual student answer label.

[0154]

[0155] in, The predicted answer sequence will be compared with the actual answer sequence in the next step to calculate the accuracy. t-1 It is the student’s knowledge status at the previous “time step”.

[0156]

[0157] The formula for the final loss function is as follows:

[0158]

[0159] In the specific implementation, parameters also need to be configured:

[0160] In order to achieve the knowledge tracking goal in the best possible way and balance the prediction performance and training cost, this embodiment adopts the following (hyper) parameter configuration during the deployment process:

[0161] ① Embedding layer dimension: 256; ② (Attention) hidden layer dimension: 256; ③ Maximum sequence length limit: 50; ④ Parameter tuning strategy: 5-fold cross validation ⑤ Training set / test set ratio: 4:1; ⑦ Number of meta-path types: 6; ⑦ Gradient descent mini-batch size: 64; ⑧ Learning rate: 5e-4.

[0162] In a specific implementation method, the above advantages and the rationality of this solution are verified through a series of technical means such as comparative experiments, exploratory experiments, and ablation experiments.

[0163] (I) Comparative experiment

[0164] The purpose of this experiment is to compare the performance of this embodiment with the latest MPSG knowledge tracking method. All experimental projects are deployed on three public education datasets, namely ASSIST09, ASSIST17, and EdNet. The selected comparison methods include four typical knowledge tracking models: DKT (2015), DKT+ (2018), DKVMN (2017) and AKT (2020), as well as four latest pre-trained knowledge tracking models: GKT (2019), PEBG (2021), DGEKT (2024) and MPSG (2024). Given that knowledge tracking is essentially a binary classification (prediction) task, the area under the curve (AUC) is used as the evaluation criterion, and its validity range is [0, 1]. When its value is greater than 0.5, the model can be considered valid. The closer to 1, the better the model. Table 1 gives the results of the comparative experiment.

[0165] Table 1 Comparative experiment

[0166]

[0167] In the table, the bold numbers are the best AUC performance achieved on the dataset, and the underlined numbers represent the suboptimal performance. Specifically, by comparing two key evaluation indicators - AUC (area under the curve) and ACC (accuracy), it is found that the GDPKT model shows significant advantages on all tested datasets. On the ASSISST09 dataset, GDPKT surpassed the previous baseline model, especially achieving an AUC of 0.8. Before GDPKT, PEBG had the highest AUC value of 0.7704, while DGEKT showed the highest ACC value of 0.7385. The progress of GDPKT highlights its versatility, stability and superior generalization ability on different datasets. Its AUC value is 0.00149 higher than PEBG, and its ACC value is 0.00162 higher than DGEKT, further consolidating its position as the current best method. For the EdNet dataset, although the ACC value of GDPKT is comparable to other top performing models such as AKT and DGEKT, its AUC value is still ahead, reaching 0.7485, indicating its high accuracy in predicting students' knowledge mastery status.

[0168] Experimental results show that the GDPKT model outperforms traditional and advanced baseline frameworks in predicting students' knowledge mastery status and evaluating learning outcomes. Its excellent AUC and ACC values ​​indicate that the model can effectively understand and predict students' knowledge status, which is helpful for the development of educational assessment and personalized learning systems.

[0169] (II) Embedding Representation Ablation Experiment

[0170] In this example, after pre-training the training data, three methods of constructing the practice embedding representation used in subsequent KT training are obtained: using only practice embedding (GDP-onlyQ), using only concept embedding (GDP-onlyC), and combining practice and concept embedding as practice embedding (GDP-Q&C). This series of experiments formally compares the performance of these three representation combination methods, and the results are shown in Table 2.

[0171] Table 2 Experiments with different embedding representation lengths

[0172]

[0173] From the table above, we can see that the GDPKT model that only contains question features obtains the best results. The method that integrates both question and concept information obtains suboptimal performance, while the model that only integrates concept node embedding representation performs the worst. Taking the AUC of the ASSISST17 dataset as an example, GDP-onlyQ is 4.24% and 3.36% higher than GDP-onlyC and GDP-Q&C, respectively. This shows that in heterogeneous graph learning representation, the relationship between skills and difficulties is not as effective as the relationship between difficulties and problems, which is more obvious.

[0174] (III) Graph Structure Ablation Comparison Experiment

[0175] In the graph representation learning part, different graph structures will affect the effect of embedding representation, and thus have a greater impact on the final experimental results, so it is necessary to conduct an ablation experiment to find the optimal combination. Compared with the GDPKT framework finally determined in this embodiment, three comparison frameworks were selected for experiments.

[0176] GDP-GCN adopts a homogeneous graph convolutional network (GCN) model for graph representation learning. The basic concept of GCN is to simultaneously utilize node attributes and structural details of the graph during the training phase. More specifically, GDP-GCN updates the representation of each node by calculating the weighted sum of all neighboring node features.

[0177] GDP-GAT is a variant of GDP-GCN, where the graph representation learning component is replaced by the Graph Attention Network (GAT) model. GAT is a graph neural network that uses the attention mechanism to assign weights to the influence of neighboring nodes when updating node representations.

[0178] GDP-noDi uses a similar heterogeneous graph structure as GDPKT, but makes significant changes in the construction of meta-paths. Specifically, GDP-noDi excludes difficulty nodes from these meta-paths and instead relies only on students, exercises (or questions), and concept nodes to establish connections and relationships within the graph. This change aims to explore the impact of removing the difficulty dimension on graph representation and the subsequent role of this impact on knowledge tracking performance. The results are shown in Table 3.

[0179] Table 3. Comparison of structure and ablation experiment

[0180]

[0181] According to the statistical results in Table 3, GDPKT achieves the best AUC performance on the three datasets, reaching 82.65%, 78.53% and 74.85% on ASSIST09, ASSIST17 and EdNet respectively. In contrast, GDP-noDi's AUC performance on ASSIST09 and ASSIST17 is slightly inferior, at 81.20% and 77.86% respectively. The above results show that homogeneous graphs like GCN and GAT cannot extract high-order information between nodes as efficiently as heterogeneous graphs. Therefore, they are not suitable for difficult personalized knowledge tracking tasks. In addition, for difficulty-oriented personalized prediction tasks, failure to incorporate difficulty features into graph representation learning will greatly weaken the effectiveness of prediction.

[0182] (IV) Comparative experiment on KT ablation of downstream tasks

[0183] In the embodiment, two classic knowledge tracking (KT) models are selected to construct knowledge state representation and compared with GDPKT. The two variants are GDP-DKT and GDP-AKT, which respectively adopt the knowledge state construction methods of DKT and AKT. Both DKT and AKT are mature and efficient frameworks in the field of knowledge tracking, so they are suitable as candidates for verifying the superior performance of GDPKT. The experimental results are shown in Table 4.

[0184] Table 4. Comparative experiments on KT ablation of downstream tasks

[0185]

[0186] Among the three data sets, GDPKT achieved the highest accuracy. Taking EdNet as an example, the AUCs of GDPKT, GDP-DKT, and GDP-AKT are 74.85%, 71.72%, and 68.55%, respectively. By comparison, it can be found that the AUC values ​​of GDP-DKT and GDP-AKT are almost the same as those of DKT and AKT in Table 1. These results show that difficulty perception and learning benefits are indispensable for GDPKT. When the models of DKT and AKT are applied to downstream knowledge tracking tasks, although the performance is improved, it is not significant, and the importance of heterogeneous graph representations designed specifically for difficulty features is also lost. The graph representation learning part of this embodiment is specially designed for the improvement of subsequent downstream knowledge tracking tasks.

[0187] Compared with the traditional graph representation learning strategy adopted by the current knowledge tracking model, the embedded representation of knowledge concepts and skills in the present invention is realized by utilizing heterogeneous graph neural networks. This method isolates the nodes representing the difficulty level and then integrates them into the meta-path calculation to facilitate subsequent personalized differentiation; it combines the difficulty perception module and the learning benefit module to construct the knowledge state of different students in a personalized way; it proposes a new knowledge state update method, which is conducive to modeling the personalized growth of students due to different question difficulties; in the designed knowledge tracking task, the meta-path update aggregation of the graph representation learning part pays more attention to the difficulty information.

[0188] In a specific implementation, a personalized knowledge tracking system based on graph neural network and question difficulty, such as Figure 3 As shown, including:

[0189] Acquisition module: used to obtain the data set of the field to be tracked;

[0190] Modeling module: used to model the difficulty of questions and knowledge concepts in the data set and extract difficulty information;

[0191] Fusion module: used to integrate difficulty as a node in the meta-path into the heterogeneous graph neural network model;

[0192] Model building module: used to build a difficulty-adaptive knowledge tracking model based on the fused heterogeneous graph neural network model;

[0193] Update module: used to update the knowledge status of the knowledge tracking model;

[0194] Knowledge tracking module: used to achieve final knowledge tracking through the updated knowledge tracking model.

[0195] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0196] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A personalized knowledge tracking method based on graph neural network and question difficulty, characterized in that: include: Obtain the dataset of the domain to be tracked; Model the difficulty of questions and knowledge concepts in the dataset and extract difficulty information; Integrate difficulty into the heterogeneous graph neural network model as a node in the meta-path; Build a difficulty-adaptive knowledge tracking model based on the fused heterogeneous graph neural network model; updating the knowledge status of the knowledge tracking model; The final knowledge tracing is achieved through the updated knowledge tracing model.

2. According to claim 1, a personalized knowledge tracking method based on graph neural network and question difficulty is characterized in that: The data set includes: user / student ID, exercise ID, concept ID, answer status, exercise response time, number of attempts, question type, exercise sequence, concept sequence, answer sequence and exercise difficulty sequence.

3. According to claim 1, a personalized knowledge tracking method based on graph neural network and question difficulty is characterized in that: The difficulty of the questions and knowledge concepts in the data set is modeled and the difficulty information is extracted, including: represents the difficulty coefficient corresponding to each exercise, that is, the error rate, which represents the number of times it is wrong in the entire data set divided by the total number of attempts. Its range is [0, 1]. The larger the error rate, the higher the difficulty coefficient. i For practice.

4. According to claim 1, a personalized knowledge tracking method based on graph neural network and question difficulty is characterized in that: It also includes knowledge tracking task definition: Set m exercises and k knowledge concepts, represented by E = {e1,…,e m } and C={c1,…,c k }; Let the set c(e i ) indicates practice e i All the concepts involved, let r t ∈{0,1} represents the correctness of the answer at time t, let d(e t )∈{0,1} represents the exercise e t The average difficulty coefficient of the learning sequence in the past T-1 period is represented as X = [x1, x2, ..., x T-1 ], where x t =(e t ,c(e t ),r t ,d(e t )) represents the interaction situation at the tth moment; The knowledge tracking task is described as: given an exercise sequence X, predict the future time T for a certain exercise e T The probability of answering correctly is: P(r T =1|X).

5. The personalized knowledge tracking method based on graph neural network and question difficulty according to claim 1 is characterized in that: The difficulty-adaptive knowledge tracking model based on the fused heterogeneous graph neural network model includes: a heterogeneous graph representation learning module, a difficulty perception module and a learning benefit module. Different meta-paths are constructed in the heterogeneous graph representation learning module to integrate difficulty features and refine the representation of exercise nodes and concept nodes; the information of heterogeneous graph learning and the information in exercise interaction are processed by the difficulty perception module to obtain the difficulty perception of the questions; and the learner's difficulty perception is converted into his growth benefit through the learning benefit module.

6. A personalized knowledge tracking method based on graph neural network and question difficulty according to claim 5, characterized in that: The heterogeneous graph representation learning module includes: The feature vectors of various node categories are mapped into a common vector space by applying a type-specific linear transformation to the feature vector of each node type; After completing the node feature mapping, the semantic information is aggregated from the meta-path to the target node, and the different attributes of the nodes in each meta-path instance are converted into a coherent and compressed vector representation; After converting the meta-path instances into vector representations, the graph attention mechanism is used to combine the meta-path instances related to the target node; For each meta-path, the meta-path is aggregated by calculating the average value of all node vectors converted in the meta-path, and then the attention mechanism is used to aggregate and update the information between different meta-paths; Linear transformations are combined with nonlinear activation functions to project node embeddings into the required vector space, ensuring the specified dimensionality of the output.

7. The personalized knowledge tracking method based on graph neural network and question difficulty according to claim 5 is characterized in that: The difficulty perception module includes: Among them, W1 and β1 are learnable parameters, δ t To practice embedding vectors, h t-1 is the current state of knowledge, It is the intermediate result of the calculation process and is used to calculate the difficulty perception; in, is a gated unit used to calculate difficulty perception, W2 and β2 are learnable parameters, and σ is the sigmoid activation function; Among them, d t Feel the vector for difficulty.

8. The personalized knowledge tracking method based on graph neural network and question difficulty according to claim 5 is characterized in that: The learning benefit module includes: For the current exercise, combine the previous knowledge state with the current exercise to obtain a knowledge state related to the current exercise, so that the current knowledge state h t-1 Combined question sequence; Perform matrix multiplication of the previous knowledge state and the representation of the current exercise to obtain a knowledge state related to the current exercise; Regulate the learning gains achieved through learning gating; The actual learning gain is obtained by multiplying the previously calculated knowledge state with the output of the learning gate, and a linear transformation is applied to constrain the result to the range (0, 1).

9. The personalized knowledge tracking method based on graph neural network and question difficulty according to claim 1 is characterized in that: Updating the knowledge status of the knowledge tracking model includes: Among them, Γ is the gate unit, W5 and β5 are learnable parameters, δ t To practice embedding vectors, a t For question q t The answer sequence: h t =(1-Γ)·ω t +Γ·h t-1 ; Among them, h t is the knowledge state after the next time step, ω t For the ultimate learning benefit; μ t =σ(W6·h t +β6); where μ t is the final knowledge state, W6 and β6 are learnable parameters.

10. A personalized knowledge tracking system based on graph neural network and question difficulty, characterized in that: include: Acquisition module: used to obtain the data set of the field to be tracked; Modeling module: used to model the difficulty of questions and knowledge concepts in the data set and extract difficulty information; Fusion module: used to integrate difficulty as a node in the meta-path into the heterogeneous graph neural network model; Model building module: used to build a difficulty-adaptive knowledge tracking model based on the fused heterogeneous graph neural network model; Update module: used to update the knowledge status of the knowledge tracking model; Knowledge tracking module: used to achieve final knowledge tracking through the updated knowledge tracking model.

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