AI-based personalized error analysis and practice generation system

Abstract

This invention provides a personalized error analysis and practice generation system based on AI algorithms, belonging to the fields of AI, personalized error analysis, and practice generation technologies. The system includes: an error feature extraction and knowledge graph construction module, a learning situation diagnosis and weak point location module, a personalized practice generation and difficulty adjustment module, and a learning effect feedback and model optimization module. This invention achieves a breakthrough optimization of traditional error analysis and practice generation models through the integrated application of multiple AI algorithms and module collaboration.

Description

Technical Field

[0001] This invention relates to the fields of AI, personalized error analysis, and practice generation, and in particular to a personalized error analysis and practice generation system based on AI algorithms. Background Technology

[0002] In traditional learning processes, error analysis and practice arrangement often rely on human experience, which has significant limitations. On the one hand, error handling remains at the level of simple categorization, only identifying surface errors (such as "calculation errors" or "conceptual errors"), failing to delve into deeper issues such as the connections between knowledge points and skill deficiencies behind the errors. For example, a wrong answer to a math equation might involve both a weakness in factorization and insufficient calculation accuracy; traditional methods struggle to quantify such multi-dimensional connections. On the other hand, practice generation lacks precise adaptability, often employing a "sea of ​​questions" approach or arranging questions at a uniform pace. This fails to provide targeted training for learners' individual weaknesses or match their current skill level, resulting in a large amount of ineffective practice and wasted learning time. Furthermore, traditional models lack dynamic feedback mechanisms; error analysis and practice arrangement are not adjusted in real time according to learning progress, making it difficult to form a virtuous cycle of "analysis-training-optimization."

[0003] With the development of artificial intelligence technology, algorithms such as natural language processing, time series modeling, and feature fusion have provided possibilities for solving the above problems. However, in existing technologies, there is a lot of application of single algorithms (such as using only language models to extract text features), lacking deep collaboration of multiple algorithms, and failing to make full use of multi-source data such as text, time series, and question attributes of incorrect questions; at the same time, the correlation between algorithm output and subsequent learning diagnosis and practice generation is weak, making it difficult to achieve a closed loop from incorrect question data to personalized learning plans. Summary of the Invention

[0004] This invention provides a personalized error analysis and practice generation system based on AI algorithms. Through the integrated application and module collaboration of multiple AI algorithms, it achieves a breakthrough optimization of the traditional error analysis and practice generation mode.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A personalized error analysis and practice generation system based on AI algorithms includes:

[0007] The module for extracting incorrect question features and constructing a knowledge graph is used to receive raw incorrect question data, extract semantic features of incorrect question stems through a large language model, extract temporal features of answer time series through GRU, extract structural features of incorrect question attributes and answer behavior through surface fitting, and then fuse semantic features, temporal features and structural features through self-organizing mapping to obtain a fused feature matrix. At the same time, it calculates the co-occurrence strength between knowledge points based on semantic features to construct a knowledge association matrix.

[0008] The learning situation diagnosis and weak point location module is used to receive the fusion feature matrix and knowledge association matrix, combine the knowledge point tags corresponding to the wrong questions to calculate the error rate of each knowledge point, calculate the weight of weak knowledge points based on the error rate and knowledge association matrix, and obtain the ability defect vector by performing PCA dimensionality reduction on the fusion feature matrix and combining the weight of weak knowledge points.

[0009] The personalized practice generation and difficulty adjustment module receives the weights of weak knowledge points and the vector of ability deficiencies, combines them with the knowledge point association vectors and ability adaptation vectors preset in the question bank, calculates the difficulty coefficient of the questions, and selects suitable questions to generate a personalized practice set.

[0010] The learning effect feedback and model optimization module is used to receive personalized practice sets and corresponding practice results, evaluate the practice effect based on the practice results and the difficulty coefficient of the questions, and output parameter adjustment instructions if the effect does not meet the preset target, and adjust the parameters of each algorithm in the error feature extraction and knowledge graph construction module in reverse to form a complete data closed loop.

[0011] In this specification, in the module for extracting incorrect question features and constructing a knowledge graph, when the large language model extracts semantic features, it first obtains the original semantic vector of the question stem through a pre-trained language model, and then combines the subject knowledge point labels to fine-tune the weight matrix and bias vector to convert the original semantic vector into a semantic feature vector associated with the knowledge points.

[0012] In this specification, in the module for extracting incorrect question features and constructing a knowledge graph, when GRU extracts temporal features, it concatenates the answer time series with the semantic feature vector output by the large language model as input. The update gate controls the retention ratio of historical hidden states, and the reset gate controls the forgetting ratio of historical hidden states. Finally, it outputs a temporal feature vector that reflects the answer behavior pattern. The intensity value of this temporal feature vector is used as the dependent variable for surface fitting.

[0013] In this specification, in the module for extracting incorrect question features and constructing a knowledge graph, when extracting structural features by surface fitting, the complexity of incorrect questions and the importance of knowledge points obtained based on semantic feature vectors are used as independent variables, and the intensity value of temporal feature vectors is used as the dependent variable. A bivariate quadratic surface function is constructed and the coefficients are solved. The structural features are obtained by calculating the residual between the actual intensity value and the fitted value. The structural features, together with the semantic feature vector and the temporal feature vector, are used as inputs to the self-organizing map.

[0014] In this specification, in the module for extracting incorrect question features and constructing a knowledge graph, when fusing features through self-organizing mapping, semantic feature vectors, temporal feature vectors, and structural features are concatenated into a high-dimensional feature vector. The best matching neuron is found through a neuron grid, and the weight vector of that neuron is used as the corresponding row vector in the fusion feature matrix. Furthermore, the neuron weights are continuously optimized through iterative learning to improve the fusion accuracy.

[0015] In this specification, when the learning situation diagnosis and weak point location module calculates the weight of weak knowledge points, it adopts a weighted fusion method, which combines the direct impact of the error rate with the indirect impact of the error rate of the associated knowledge points in the knowledge association matrix. The weighting coefficient is determined through cross-validation, so that the calculation results are consistent with the degree of weakness marked by manual annotation to a preset threshold.

[0016] In this specification, when the personalized practice generation and difficulty adjustment module calculates the difficulty coefficient of the questions, it performs a weighted fusion based on the matching degree between the weight of weak knowledge points and the correlation vector of knowledge points in the questions, and the matching degree between the vector of ability deficiencies and the vector of ability adaptation in the questions. The weighting coefficient is optimized through historical practice data to ensure that the expected accuracy of the generated questions is within a preset range.

[0017] In this specification, when the learning effect feedback and model optimization module evaluates the practice effect, it calculates the evaluation value by matching the practice accuracy with the difficulty coefficient of the questions. When the evaluation value is lower than the preset target value for several consecutive times, it initiates the synchronous adjustment of the large language model's fine-tuning weights, GRU gating parameters, and self-organizing map neuron weights.

[0018] In this specification, in the data closed loop, after receiving the parameter adjustment instruction, the error feature extraction and knowledge graph construction module prioritizes adjusting the algorithm parameters that have the greatest impact on the identification of the current weak knowledge points. The adjustment range is positively correlated with the difference between the practice effect evaluation value and the preset target value.

[0019] In this specification, the co-occurrence strength between knowledge points in the knowledge association matrix is ​​calculated based on the average value of the product of the association strengths of corresponding knowledge points in the semantic feature vectors across all incorrect questions. This co-occurrence strength is dynamically updated as new incorrect question data is added, and the update frequency is consistent with the practice feedback cycle.

[0020] In summary, the present invention has at least the following beneficial effects:

[0021] This invention, through the deep application of AI technology, transforms incorrect answers from "simple error records" into "personalized learning guidelines," significantly improving the depth of error analysis, the accuracy of practice scheduling, and the dynamic adaptability of the learning process, thus providing technical support for efficient learning. Specific technical effects are as follows:

[0022] The analysis of incorrect question features is more in-depth: With the synergy of large language models, GRU, surface fitting and self-organizing maps, it can extract incorrect question features from multiple dimensions such as semantic connotation, answering behavior and question attribute association. It can not only identify "which type of question is wrong", but also clarify "why it is wrong" (such as quick wrong answer caused by blind spot in knowledge points, hesitant wrong answer caused by insufficient ability, etc.), which breaks through the superficial limitations of traditional manual analysis.

[0023] More accurate learning diagnosis: Based on the fusion of features and knowledge association matrix, the weight of weak knowledge points and ability deficiencies can be quantified. It considers both the direct error rate and the linkage effect between knowledge points (such as the impact of a weak knowledge point A on answering questions on knowledge point B). The diagnostic results are upgraded from "qualitative description" to "quantifiable indicators", providing clear targets for subsequent training.

[0024] More tailored practice exercises: The difficulty and content of exercises are dynamically adjusted based on the learning progress diagnosis results to ensure that the questions accurately cover weak knowledge points and related areas, and that the difficulty matches the learner's current ability. This avoids ineffective repetition of overly easy questions and prevents frustration from overly difficult questions, truly achieving "targeted training" and improving learning efficiency.

[0025] The learning process forms a closed loop: through the feedback optimization module, the practice effect can be iteratively optimized to improve the front-end feature extraction and diagnostic algorithms, enabling the system to dynamically adjust the analysis accuracy and practice strategy according to the learner's ability. This solves the static problem of the traditional model of "one-time analysis and fixed training" and realizes continuous adaptation and personalized learning support. Attached Figure Description

[0026] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a schematic diagram of the composition of the AI-based personalized error analysis and practice generation system involved in this invention.

[0028] Figure 2This is a flowchart illustrating the personalized error analysis and practice generation system based on AI algorithms involved in this invention.

[0029] Figure 3 This is a schematic diagram of a radar map showing the distribution of capability defects involved in this invention.

[0030] Figure 4 This is a schematic diagram of the heat map showing the weakness of the knowledge points involved in this invention.

[0031] Figure 5 This is a schematic diagram of the learning trend curve involved in this invention. Detailed Implementation

[0032] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of the invention. Therefore, the drawings and descriptions are considered to be exemplary in nature and not restrictive. To simplify the disclosure of embodiments of the invention, components and arrangements of specific examples are described below. Of course, these are merely examples and are not intended to limit the embodiments of the invention. Furthermore, reference numerals and / or reference letters may be repeated in different examples of embodiments of the invention. Such repetition is for simplification and clarity and does not in itself indicate a relationship between the various implementations and / or arrangements discussed.

[0033] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0034] like Figure 1 and Figure 2 As shown, this embodiment provides a personalized error analysis and practice generation system based on AI algorithms, including:

[0035] The module for extracting incorrect question features and constructing a knowledge graph is used to receive raw incorrect question data, extract semantic features of incorrect question stems through a large language model, extract temporal features of answer time series through gated recurrent units (GRU), extract structural features of incorrect question attributes and answer behavior through surface fitting, and then fuse semantic features, temporal features and structural features through self-organizing mapping to obtain a fused feature matrix. At the same time, it calculates the co-occurrence strength between knowledge points based on semantic features to construct a knowledge association matrix.

[0036] The learning progress diagnosis and weak point location module is used to receive the fusion feature matrix and knowledge association matrix, combine the knowledge point tags corresponding to the wrong questions to calculate the error rate of each knowledge point, calculate the weight of weak knowledge points based on the error rate and knowledge association matrix, and perform principal component analysis (PCA) on the fusion feature matrix. After PCA dimensionality reduction, the module combines the weight of weak knowledge points to obtain the ability defect vector.

[0037] The personalized practice generation and difficulty adjustment module receives the weights of weak knowledge points and the vector of ability deficiencies, combines them with the knowledge point association vectors and ability adaptation vectors preset in the question bank, calculates the difficulty coefficient of the questions, and selects suitable questions to generate a personalized practice set.

[0038] The learning effect feedback and model optimization module is used to receive personalized practice sets and corresponding practice results, evaluate the practice effect based on the practice results and the difficulty coefficient of the questions, and output parameter adjustment instructions if the effect does not meet the preset target, and adjust the parameters of each algorithm in the error feature extraction and knowledge graph construction module in reverse to form a complete data closed loop.

[0039] In some embodiments, when constructing the knowledge association matrix, the error feature extraction and knowledge graph construction module will calculate the semantic feature vector of newly added error questions in real time. After accumulating a preset number (e.g., 20) of new error questions, it will automatically update the co-occurrence strength of the corresponding knowledge points in the knowledge association matrix to ensure that the matrix can reflect the latest knowledge point association trends.

[0040] In some embodiments, when the learning situation diagnosis and weak point location module performs PCA dimensionality reduction on the fused feature matrix, it dynamically adjusts the number of principal components according to the subject to which the wrong questions belong. For example, the mathematics subject retains 8 principal components of ability, and the Chinese reading subject retains 6 principal components of ability.

[0041] In some embodiments, when the personalized practice generation and difficulty adjustment module selects suitable questions, in addition to the difficulty coefficient, it also considers the question type characteristics of the wrong questions to ensure that the proportion of each question type in the generated personalized practice set matches the question type distribution of the user's wrong questions, and the number of questions of the same question type does not exceed 30% of the total number of questions in the practice set, so as to avoid the question type being too monotonous.

[0042] In some embodiments, the fine-tuning process of the large language model is carried out in stages. The first stage uses general subject knowledge point tags for basic fine-tuning, and the second stage introduces textbook knowledge point tags of the user's grade for targeted fine-tuning. During the fine-tuning process, the matching accuracy between semantic feature vectors and knowledge point tags is monitored in real time, and fine-tuning is stopped when the accuracy reaches 90% or more.

[0043] In some embodiments, when the GRU extracts time-series features, it preprocesses the answer time series, removes obviously abnormal time points (such as values ​​that exceed 5 times the average time of similar questions), and supplements the missing time data by interpolation, so that the length of the preprocessed time series is uniformly set to a preset time step (such as 10 time steps), thereby improving the stability of the time-series features.

[0044] In some embodiments, after the learning situation diagnosis and weak point location module calculates the weight of the weak knowledge points, it generates a hierarchical relationship diagram of the weak knowledge points. Centered on the core weak knowledge points, it radiates outwards to related knowledge points with a high to low degree of relevance, and marks the weak weight value of each knowledge point, so that users can intuitively understand the relationship network of the weak points.

[0045] In some embodiments, the preset accuracy range of the personalized practice generation and difficulty adjustment module can be adjusted by the user. The default range is 60% to 80%. When the user selects the "Intensive Training" mode, the range is automatically adjusted to 40% to 60% (increased difficulty); when the user selects the "Consolidate Basics" mode, the range is adjusted to 70% to 90% (decreased difficulty).

[0046] In some embodiments, when the learning effect feedback and model optimization module adjusts the algorithm parameters, it adopts the gradient descent method. The adjustment range decreases dynamically with the number of iterations. The initial adjustment range is a preset maximum value. When the improvement of the evaluation value is less than 5% after two consecutive adjustments, the adjustment range is halved until the evaluation value reaches the preset target value.

[0047] In some embodiments, after receiving the parameter adjustment instruction, the error feature extraction and knowledge graph construction module records the feature extraction effect before and after each parameter adjustment. When a certain type of parameter adjustment fails to bring about an improvement in effect three times in a row, the adjustment of that type of parameter is automatically paused, and other types of parameter adjustments are tried first.

[0048] In some embodiments, the system further includes a visualization module for receiving the weights of weak knowledge points and the vector of ability deficiencies from the learning progress diagnosis and weakness identification module, as well as the practice set information from the personalized practice generation and difficulty adjustment module, and displaying the distribution of ability deficiencies in the form of a radar chart (e.g., Figure 3 As shown, the ability deficiency coefficient ranges from 0 to 1, with higher values ​​indicating more pronounced deficiencies. The degree of weakness in knowledge points is displayed in the form of a heatmap (e.g., ...). Figure 4 As shown, the darker the color, the higher the level of weakness in the knowledge point (0-1), allowing users to intuitively obtain the diagnostic results.

[0049] In some embodiments, the coefficients of the bivariate quadratic surface function fitted by the surface are updated periodically. After every 50 new wrong questions are accumulated, the coefficient vector is re-solved by the least squares method so that the surface function can dynamically adapt to the changes in the user's answering behavior. Wrong questions whose residual characteristic values ​​exceed a preset threshold (such as mean + 2 times standard deviation) will be marked as "abnormal wrong questions" and included in the key analysis separately.

[0050] In some embodiments, the size of the neuron grid of the self-organizing map can be dynamically adjusted. Initially, it is a 20×20 grid. When the sample size difference between different clustering regions in the fused feature matrix exceeds 3 times, the dense region is automatically split into a 4×4 sub-grid, and the sparse region is merged with neurons to improve the fineness of feature fusion.

[0051] In some embodiments, the weighting coefficient α of the weak knowledge points adopts a dynamic adjustment mechanism. In the initial stage of the user (the first 30 wrong questions), α is 0.8 (focusing on the direct error rate). As the number of wrong questions accumulates (more than 50), α gradually decreases to 0.6 (balancing the influence of correlation), so that the diagnostic results are more in line with the actual learning status as the amount of data increases.

[0052] In some embodiments, the difficulty coefficient of the personalized practice set adopts a gradient distribution. From the first question to the last question in the practice set, the difficulty coefficient increases (or decreases) in a gradient of 0.05-0.1 to avoid sudden changes in difficulty. The gradient direction is adjusted according to the ability deficiency vector. If the "basic ability" deficiency is significant, the gradient increases; if the "advanced ability" deficiency is significant, the gradient decreases.

[0053] In some embodiments, the learning performance evaluation value is not only based on the accuracy rate, but also incorporates the answering time indicator: for questions with matching difficulty coefficients, if the answering time is within ±30% of the average time of similar questions, the evaluation value weight is increased by an additional factor (e.g., 1.2 times), and the weight is appropriately reduced (e.g., 0.8 times) for questions that are completed too quickly or too late, so that the evaluation is more in line with the actual ability.

[0054] In some embodiments, the pre-trained language model of the large language model adopts a subject-specific version (such as MathBERT for mathematics and PhysBERT for physics). When extracting semantic features, it will prioritize the identification of subject-specific terms (such as "factorization" and "Lorentz force") and assign higher attention weights to these terms to improve the accuracy of professional semantic understanding.

[0055] In some embodiments, the hidden layer dimension of the GRU can be dynamically adjusted according to the number of incorrect questions. When there are fewer than 100 incorrect questions, a 64-dimensional hidden layer is used; when there are 100 to 300 incorrect questions, a 128-dimensional hidden layer is used; and when there are more than 300 incorrect questions, a 256-dimensional hidden layer is used, thus achieving a balance between computational efficiency and feature extraction accuracy.

[0056] In some embodiments, the hierarchical relationship diagram of weak knowledge points supports interactive operation. When a user clicks on any knowledge point node, the system will automatically display typical wrong questions, related exercises and ability requirements for that knowledge point, realizing the linkage jump of "diagnosis results - wrong question tracing - exercise recommendation".

[0057] In some embodiments, the visualization module also generates a "learning trend curve," with time as the horizontal axis and the average weight of weak knowledge points and the average coefficient of ability deficiency as the vertical axis, to intuitively display the user's improvement trend in weak points within a 1-week or 1-month period (e.g., ...). Figure 5 As shown, the lower the value, the better the improvement.

[0058] In some embodiments, the question feature vectors (knowledge point association vectors, ability adaptation vectors) of the question bank adopt a semi-automatic update mechanism: newly entered questions are first automatically generated by the AI ​​model to generate initial feature vectors, and then manually verified and corrected by subject teachers (the correction ratio is not less than 20%) to ensure that the question features are consistent with the actual examination objectives.

[0059] The technical concept of this invention is as follows:

[0060] I. System Overall Design Concept and Core Values

[0061] The personalized error analysis and practice generation system aims to deeply analyze learners' error data using artificial intelligence algorithms, breaking through the limitations of traditional "practice makes perfect" approaches and achieving a personalized learning loop of "precise diagnosis - targeted training - dynamic optimization." The system's core value lies in: constructing a learner's knowledge graph and ability model based on multi-dimensional error characteristics; generating practice content tailored to individual weaknesses through algorithmic collaboration; and continuously optimizing analysis accuracy through iterative feedback. This design not only significantly improves learning efficiency (reducing ineffective practice by more than 50%) but also helps teachers and learners accurately pinpoint the root causes of problems, achieving quantifiable improvements "from incorrect answers to score increases."

[0062] The AI-based personalized error analysis and practice generation system operates on a core logic of "error data-driven approach - multi-dimensional feature fusion - precise diagnosis - personalized practice - closed-loop optimization," comprising four closely interconnected modules. The first module (error feature extraction and knowledge graph construction) is the foundation of the entire system, integrating four algorithms: surface fitting, Large Language Model (LLM), GRU neural network, and Self-Organizing Map (SOM), achieving in-depth error analysis through multi-level feature interaction. The second module (learning status diagnosis and weakness identification) quantifies learning status based on the feature results of the first module. The third module (personalized practice generation) dynamically generates suitable content based on diagnostic results. The fourth module (feedback optimization) iteratively optimizes the front-end algorithm through back-step optimization of practice results. These four modules form a complete closed loop: "data input → feature extraction → diagnostic analysis → content generation → effect feedback → model optimization."

[0063] II. Module 1: Error Feature Extraction and Knowledge Graph Construction (Deep Integration of Four Major Algorithms)

[0064] Module core objectives

[0065] This module transforms raw incorrect answer data into multi-dimensional feature vectors that computers can understand, while simultaneously constructing a network of connections between knowledge points. This provides a dual basis for subsequent diagnosis: "micro-features + macro-associations." This module acts as the system's "data translator," addressing three key questions: How to extract the semantic meaning of incorrect answers? How to capture the behavioral characteristics of the answering process? How to integrate multi-source information to form a unified representation?

[0066] Module location and input

[0067] The first module is the system's "perception center," responsible for transforming raw incorrect question data into quantifiable feature vectors and constructing relationships between knowledge points. The input is the learner's original set of incorrect questions. Each of the incorrect questions Includes the question stem text (e.g., solving a quadratic equation in one variable) "), Answering time sequence (Record the thinking time for each step in the answering process, in seconds), error marking. (1 indicates error, 0 indicates correct) as well as basic attributes marked by manual annotation (such as knowledge point tags and complexity level).

[0068] First Sub-Algorithm: Semantic Feature Extraction from Large Language Models (LLM) – Deciphering the "Semantic Code" of Errors

[0069] Core function: Extract semantic information such as knowledge point connections and question type characteristics from incorrect question texts.

[0070] Application Scenario: The text of each incorrect question (such as the math problem "Solve the inequality 3x + 5 > 8") contains key information such as the connection between knowledge points and the characteristics of the question type. Traditional keyword matching methods have difficulty understanding the deep connection between "application problems of quadratic equations" and "factorization", while LLM can achieve accurate analysis through contextual semantic understanding.

[0071] Technical details:

[0072] Model Construction: A pre-trained language model (such as BERT) is used as the basic architecture, and the input is the segmented question text sequence. ( For the j=1,2…Lth word), output dimension The original semantic vector To adapt to the knowledge point system of a specific learning stage, new fully connected layer parameters have been added. , where k is the total number of knowledge points in this learning stage (e.g., about 80 core knowledge points in junior high school mathematics), or the total number of knowledge points in a subject (e.g., "quadratic equation in one variable" and "factorization" in mathematics). This is the semantic mapping weight matrix. This is the bias vector.

[0073] Training process: Collect 100,000+ labeled wrong questions (each question is associated with 1 to 3 knowledge point tags), and fine-tune the model using the cross-entropy loss function of formula (1). During training, mini-batch gradient descent (batch_size=32) is used, the learning rate is initialized to 0.0001, and decays by 10% every 5 epochs until the accuracy of the validation set no longer improves (usually 20-30 epochs are required).

[0074] Tag the knowledge points of the questions you got wrong ( The knowledge point number (representing the i-th question) is used as the supervision signal, and the parameters are optimized using the cross-entropy loss function:

[0075] (1)

[0076] During training, gradient descent is used to update the parameters: ,in Set a learning rate (e.g., 0.001) to ensure the model can accurately identify the knowledge points corresponding to incorrect questions.

[0077] Model Application: After fine-tuning, the model outputs the semantic feature vector of the i-th question. Each element in the vector represents the strength of the association between the question and the corresponding knowledge point (the larger the value, the stronger the association):

[0078] (2)

[0079] Application effect: Output semantic features It can accurately quantify the correlation between incorrect answers and various knowledge points. For example, a wrong answer about "solving a quadratic equation using factorization" has... The values ​​for the dimensions "factorization" and "quadratic equations" are significantly higher than those for other knowledge points.

[0080] Second sub-algorithm: GRU temporal feature extraction – capturing the "behavioral fingerprint" of responses.

[0081] Core function: Capture time-series characteristics during the answering process (such as the duration of hesitation and traces of repeated modifications) to reflect the learner's thought process.

[0082] Application Scenarios: Learners' answering processes (such as thinking time and number of revisions) contain important signals of their abilities. For example, for the same wrong question, "answering incorrectly instantly" may reflect a blind spot in knowledge, while "answering incorrectly after a long period of hesitation" may reflect a lack of thorough understanding. GRU can effectively capture these behavioral characteristics by processing time series data.

[0083] Technical details:

[0084] Model construction: Input is the time series of answers. (Taking the first 10 key time points, in seconds) and LLM semantic features The concatenated vector (dimension 10+k). GRU hidden layer dimensions. =128, by updating and resetting the gates to control the flow of information (Equation 3-6), the gradient vanishing problem of traditional RNNs is solved. A gated recurrent unit (GRU) is used to process time-series data; the input includes not only the answer time sequence. It also incorporates the semantic features of LLM output. (Achieving cross-modal fusion of "text semantics + answering behavior"). Model parameters include updating gate weights. Reset gate weight Hidden layer weights and input feature weights (L is the time step, k is the semantic feature dimension).

[0085] Training innovation: Integrating LLM semantic features into temporal modeling (instead of using only time data) enables the model to distinguish between "easy questions taking too long" and "difficult questions taking a reasonable amount of time". For example, for questions whose semantic features indicate "basic calculation questions", if the answering time is significantly longer than similar questions, GRU will output a higher abnormal behavior score.

[0086] Model training: using error tags for incorrect questions (1 indicates error, 0 indicates correct) serves as the monitoring signal, and the parameters are optimized using the binary cross-entropy loss function:

[0087] (3)

[0088] in This represents the hidden state at the last time step of question i (representing the overall strength of the temporal features). During training, all parameters of the GRU are updated using the backpropagation algorithm, enabling the model to predict the answer result (incorrect / correct) based on the answer time series.

[0089] Model application: Time series analysis of each incorrect question Process the data to output a time-series feature vector. The specific calculation process is as follows (taking the s-th time step as an example):

[0090] Update gate (controls the proportion of historical information retained): ;

[0091] Reset gate (controls the proportion of historical information forgotten): ;

[0092] Candidate hidden layer (generating new information): ;

[0093] Final hidden state: ;

[0094] Take the hidden state of the last step as the temporal feature: (4)

[0095] Application effect: Output time series characteristics It can effectively distinguish different error types. Experiments show that this feature can achieve an accuracy rate of 82% in identifying "knowledge gaps" and "careless mistakes," which is significantly higher than the traditional time statistics method (65%).

[0096] Third sub-algorithm: Surface fitting feature extraction – mining nonlinear relationships between "attribute-behavior"

[0097] Core function: Discover the nonlinear relationship between "question attributes and answering behavior" through surface fitting, and extract the residuals as structural features.

[0098] Application scenario: There is a non-linear relationship between question complexity, knowledge point importance, and answering behavior. For example, if a question with low complexity but high importance (such as the application of basic formulas) takes too long to answer, it often reflects a lack of solid foundation. This relationship is difficult to capture using a linear model.

[0099] Technical details:

[0100] Model building: based on problem complexity (Scores are based on a 1-10 scale, with 3 teachers independently assigning an average score; higher scores indicate greater difficulty) and the importance of the knowledge point. ( The maximum value (i.e., the score of the knowledge point with the strongest association among the semantic features) is taken as the independent variable, and the GRU time-series strength is... ( , i.e., the time sequence feature vector Using the norm (reflecting the degree of fluctuation in the answering process) as the dependent variable, a bivariate quadratic surface is constructed. .

[0101] Training process: The coefficients A are solved using the least squares method (Equation 5) to ensure the surface best fits the sample data. For example, in a middle school math dataset, the solution is obtained... (The coefficient of the squared complexity term is positive), indicating that the impact of complexity on the fluctuation of the answer is increasing. (The interaction coefficient is negative) This indicates that as the complexity of highly important questions increases, the fluctuation in answer volume slows down (learners are more cautious).

[0102] Solving for the coefficient vector of the surface function using the least squares method The goal is to minimize the fitting error:

[0103] (5)

[0104] In the specific solution process, the data is organized into matrix form. (Where X is the independent variable matrix and Z is the dependent variable vector), through The coefficients are calculated to obtain a surface model that reflects the relationship between "complexity-importance-answer fluctuation".

[0105] Model application: Calculate the residuals between the actual and fitted values ​​as structural features. The larger the residual, the more significantly the answering behavior deviates from the conventional pattern (e.g., taking too long on a simple question).

[0106] (6)

[0107] Application value: Residual characteristics It can identify abnormal answer patterns. For example, a question... (Low complexity) (High importance) questions, if actually If the residual is much larger than the fitted value (positive and large), it indicates that the learner has not firmly grasped the basic and important knowledge points.

[0108] Fourth sub-algorithm: Self-organizing map (SOM) feature fusion – constructing a "feature map"

[0109] Core function: It integrates LLM semantic features, GRU temporal features, and surface fitting residual features into a unified low-dimensional feature vector while retaining key information.

[0110] Application scenarios: LLM semantic features (k-dimensional), GRU temporal features (128-dimensional), and surface fitting residuals (1-dimensional) have large dimensional differences, and direct concatenation will lead to feature redundancy. SOM maps high-dimensional features to a two-dimensional grid through unsupervised clustering, achieving dimensionality reduction while retaining key patterns.

[0111] Technical details:

[0112] Model Construction: SOM by A two-dimensional grid composed of neurons, each neuron corresponding to a weight vector. (Dimensions consistent with input features). Input is a concatenation of features extracted in the first three steps: (The semicolon indicates vector concatenation). For example, using... The neuron grid contains 400 neurons, and the weight vector of each neuron has a dimension of k+128+1.

[0113] Training process: Initial weights are randomly sampled from the input feature distribution, and optimization is performed through 1000 iterations. The first 500 iterations use a larger neighborhood (radius 10) and a learning rate (0.1) to quickly capture global patterns; the next 500 iterations reduce the neighborhood (radius 3) and learning rate (0.01) to fine-tune the local structure. After training, semantically similar and behaviorally similar incorrect answers are mapped to neighboring neurons.

[0114] Initialization: Randomly select feature vectors from some incorrect questions as the initial weights of the neurons. ;

[0115] Iterative learning: for each feature vector Find the neuron that is most similar to it (Best Matching Unit, BMU):

[0116] (7)

[0117] Weight Update: Adjust the weights of the BMU and neighboring neurons to make them closer to the input vector.

[0118] (8)

[0119] in For the number of iterations Decreasing learning rate (e.g., from 0.1 to 0.01). The neighborhood radius (controls the update range) ensures that similar features are mapped to neighboring neurons, such as... , Let the initial radius be , This is the attenuation coefficient.

[0120] Model Application: Utilizing the feature vectors of incorrect answers Mapped to the SOM grid, the output BMU weight vector is used as the fusion feature. :

[0121] (9)

[0122] This feature preserves semantic, temporal, and structural information while reducing dimensionality through clustering, making it easier for subsequent modules to process.

[0123] First module output parsing

[0124] 1. Fusion Feature Matrix Each row corresponds to a 130-dimensional comprehensive feature (after SOM dimensionality reduction) of a single incorrect question, preserving semantic, temporal, and structural information while eliminating redundancy through clustering. This matrix is ​​the core input for subsequent learning progress diagnosis.

[0125] 2. Knowledge Association Matrix M: Matrix, elements The co-occurrence strength of knowledge points a and b is calculated based on LLM semantic features:

[0126] (10)

[0127] For example, in junior high school mathematics (Strong correlation) (Weak association) provides a quantitative basis for analyzing the impact of knowledge transfer.

[0128] Module Three: Learning Situation Diagnosis and Weakness Identification – Building a Learner's "Competency Profile"

[0129] Module core objectives

[0130] Based on the feature data from the first module, learners' weaknesses are quantified from two levels: "knowledge point mastery" and "ability dimension," addressing the problem of traditional diagnosis being "more qualitative descriptions and fewer quantitative indicators." Diagnostic results must simultaneously meet the following criteria: accuracy (consistency with teacher assessment >85%), interpretability (clearly identifying the reasons for weaknesses), and operability (directly guiding practice generation).

[0131] Core Algorithm: Weighted Fusion Diagnostic Model

[0132] Technical details:

[0133] Model building:

[0134] Error rate The percentage of incorrect answers for knowledge point a out of the total number of questions answered for that knowledge point ( ) (A larger value indicates more errors in that knowledge point).

[0135] Weak weights Quantitative indicators that combine error rate and associated impact ( (A larger value indicates a weaker structure).

[0136] Fusion coefficient The balancing error rate directly affects ( ) and related knowledge points indirectly affect (1- The weight of ).

[0137] Model training: Optimization through cross-validation The goal is to make the calculated weak weights The actual weakness compared to manual annotation As close as possible:

[0138] (11)

[0139] For example, if knowledge point a is closely related to knowledge point b ( If b has a high error rate, then the weak weight of a will also be increased, reflecting the "linkage effect of knowledge points".

[0140] Model Application:

[0141] 1. Calculate the weight of weak knowledge points:

[0142] (12)

[0143] In formula (12), Optimization using 5-fold cross-validation (typically with a value of 0.6-0.7) balances the direct error rate and associated effects. For example, if the learner's error rate on "quadratic equations" is... Furthermore, the error rate of its strongly related knowledge point "factorization" is low. ,but (Higher than the direct error rate), more accurately reflecting the actual degree of weakness.

[0144] 2. Analytical capability deficiency: The fusion feature matrix of the first module... PCA dimensionality reduction is performed to obtain the principal component matrix. (m represents the capability dimension, such as "computational ability" or "logical reasoning ability"), and then the capability defect vector is calculated by combining the weak weights. :

[0145] (13)

[0146] in Let D be the g-th column vector of U, and each element of D represents the degree of deficiency in the corresponding capability dimension (the larger the value, the weaker the capability).

[0147] The fused feature matrix is ​​analyzed using PCA. Dimensionality reduction yields 5-8 principal components of ability (such as "calculation accuracy", "logical reasoning speed", and "spatial imagination"). The higher-valued dimensions in the ability deficiency vector D correspond to the learner's most needed ability to improve. For example, if the "calculation accuracy" dimension of D has a value of 0.8 (out of 1), it indicates that this ability is a major weakness.

[0148] IV. Module Three: Personalized Exercise Generation – Achieving “Targeted Training”

[0149] Module core objectives

[0150] Based on the diagnostic results of the second module, the most suitable practice content for learners is selected and generated from the question bank, ensuring that each question "targets weaknesses and matches the ability level". The practice generation must meet three principles: relevance (80% of the questions cover weak knowledge points), adaptability (difficulty matches ability), and diversity (avoiding repetitive question types).

[0151] Dynamic Difficulty Generation Model Details

[0152] Question bank feature engineering: Each question Pre-calculated knowledge point association vectors (The strength of association with each knowledge point, such as the high value of the question "solving equations by factoring" in the dimensions of "factoring" and "quadratic equations") and the ability fit vector. (For example, geometry problems have high values ​​in the "spatial imagination" dimension). To calculate the t-th problem... Corresponding knowledge point association vector and capability adaptation vector This requires combining text analysis of the question, prior definitions of knowledge points / abilities, and the quantification of association strength by the algorithm model. The entire process needs to integrate a large language model (text feature extraction), cosine similarity (association strength calculation), and self-organizing maps (feature optimization) to ensure that the vector accurately reflects the essential association between the question and the knowledge points / abilities. The specific calculation steps and logic are as follows:

[0153] I. Preliminary Preparations: Defining Basic Data and Model Input

[0154] Before calculation, two core prior data points need to be defined as "reference benchmarks" for vector computation:

[0155] 1. Knowledge point base and feature vectors

[0156] Pre-determine k core knowledge points (such as "solution of quadratic equations" and "Newton's laws of motion"), and generate a feature vector for each knowledge point. (a=1,2,...,k; d is the feature dimension). Feature vectors can be obtained by encoding the text describing knowledge points (such as textbook definitions and typical examples) through a large language model, and are used to represent the core semantics of knowledge points.

[0157] 2. Ability Dimension and Feature Vector

[0158] Pre-determine m capability dimensions (such as "logical reasoning", "data computation", "spatial imagination", etc.), and generate feature vectors for each capability dimension. (c=1,2,...,m). The feature vector is obtained by encoding the definition text of the ability dimension (such as "logical reasoning: the ability to deduce conclusions from known conditions") through a large language model, and is used to represent the core attributes of the ability.

[0159] II. Knowledge Point Association Vector Calculation: From Text Matching to Intensity Quantization

[0160] The core is quantitative questions. The strength of association with each knowledge point needs to be determined through three steps: "feature extraction of question text → matching with knowledge point features → strength optimization".

[0161] Step 1: Feature extraction from the question text (based on a large language model)

[0162] topic The text content (such as the question stem, question, and options) is the core basis for linking knowledge points. Using a large language model (such as BERT) to encode the text yields the question's feature vector:

[0163] ;

[0164] in, Represents the encoding function of a large language model (which converts text into a d3-dimensional semantic vector). Representational topics The core semantics (such as the concepts, operations, and scenarios involved).

[0165] Step 2: Initial association strength calculation (based on cosine similarity)

[0166] Through the feature vector of the question With knowledge point feature vectors The similarity is used to initially determine the strength of the association. Cosine similarity (which measures the consistency of vector direction; a larger value indicates a stronger association) is employed.

[0167] ;

[0168] in, For the title The initial association strength with the a-th knowledge point ( ), Represents the dot product of vectors. This represents the L2 norm of a vector.

[0169] Step 3: Strength Optimization (Based on Self-Organizing Map (SOM))

[0170] The initial association strength may have "semantic bias" (e.g., the "equation" mentioned in the question text may be mismatched with the "function" knowledge point), which needs to be optimized by self-organizing map (SOM) - using the inherent association between knowledge points (e.g., "quadratic equation" and "factorization" are often associated) to adjust the strength.

[0171] The SOM predetermines k neurons (corresponding to k knowledge points), and each neuron has a weight vector. (Initial value set to) During training, For input, find the match The most similar neuron ("winning neuron") is selected, and its weights, along with those of its neighboring neurons, are updated to better align with the semantics of the question. Finally, the strength of the knowledge point association corresponding to the winning neuron is used as the optimization result.

[0172] ;

[0173] in, The similarity between the neuron weights optimized by SOM and the question features (obtained through SOM iterative training, ranging from [0,1]) is used to correct the initial association strength, making the weights of strongly associated knowledge points higher.

[0174] III. Capability Adaptation Vector Calculation: From Target to Intensity Quantification

[0175] The core is to quantify the intensity of the questions' assessment of each ability dimension. This requires combining three steps: "analysis of the question's assessment target → matching with ability dimensions → intensity calibration," and... Connections (the connections between knowledge points will affect the requirements for assessing abilities).

[0176] Step 1: Analysis of the Question's Objective (Based on a Large Language Model)

[0177] The abilities assessed in the questions are implicitly embedded in the question logic (e.g., "deriving formulas" corresponds to "logical reasoning," and "calculation results" corresponds to "data calculation"). A large language model is used to "label the assessment targets" in the question text, generating assessment feature vectors.

[0178] ;

[0179] in, It is a large language model that has been fine-tuned with "ability assessment annotation" data (specifically identifying the ability requirements of the questions). The core competencies and tendencies that the questions assess are characterized by.

[0180] Step 2: Initial assessment intensity calculation (based on the ability requirements of related knowledge points)

[0181] There is an inherent correlation between knowledge points and ability dimensions (e.g., the knowledge point of "geometric proof" requires the abilities of "spatial imagination" and "logical reasoning"). Define a knowledge point-ability correlation matrix. ,in This represents the dependence strength of the a-th knowledge point on the c-th ability (through manual annotation or data statistics, such as "geometric proof" on "spatial imagination"). =0.8).

[0182] based on (Strength of relevance between knowledge points) and R, the intensity of assessment of preliminary calculation ability:

[0183] ;

[0184] In other words, the intensity of the question's assessment of the b-th ability is the weighted sum of the dependence of all related knowledge points on that ability (the weights are the correlation strengths of the knowledge points). ).

[0185] pass With ability dimension feature vector Cosine similarity quantifies the direct correlation between questions and abilities:

[0186] ;

[0187] in, The larger the value, the more likely the problem is to be solved. The stronger the direct correlation with the c-th ability dimension (e.g., the higher the similarity between geometric proof problems and the ability of "spatial imagination").

[0188] Step 3: Basic strength calculation and strength calibration (judgment based on question characteristics and large language model)

[0189] Basic strength integration: combining "the direct correlation between questions and abilities" (through ability benchmark vectors) And the indirect connection brought about by the association of knowledge points (through) ), to obtain the basic strength ;

[0190] ;

[0191] Balance "direct examination of questions" ) and "indirect examination based on the connection between knowledge points" (1- The coefficients (optimized through historical data, usually) =0.6);

[0192] Preliminary results This might overlook the differences in difficulty between the questions themselves (e.g., simple and difficult questions on the same knowledge point assess different levels of ability). A large language model is needed to analyze the additional ability requirements imposed by the question difficulty and to calibrate the intensity of those requirements.

[0193] ;

[0194] in:

[0195] It is a large language model for the question Difficulty rating (0 is the easiest, 1 is the hardest);

[0196] It is the "difficulty sensitivity" of the c-th ability dimension (e.g., "logical reasoning" is more sensitive to difficulty). =0.8);

[0197] It is the calibration coefficient (the degree to which the difficulty of control affects the strength, such as...) =0.3, to avoid over-correction).

[0198] Correction logic: The higher the difficulty ( Large) and highly sensitive to ability ( (Large), final strength The higher the difficulty level (which aligns with the reality that "difficult problems test abilities more deeply").

[0199] IV. Core Relationships: and Interaction logic

[0200] yes The foundation—the connection between knowledge points—directly determines which abilities the questions need to test (e.g., connecting the knowledge point of "solid geometry" necessarily requires the ability of "spatial imagination"); and It will also have a counter-effect Optimization (if the question places a very high emphasis on "calculation ability," it may strengthen its connection with "numerical calculation" knowledge points). This interaction is achieved through formulas... right The contribution, and the practical application of "if

[0201] Abnormally high, can be adjusted retrospectively. The weights of the corresponding knowledge points are implemented to ensure that the two are logically consistent.

[0202] and The calculation starts with the "semantic meaning of the question text," extracts features through a large language model, quantifies the initial associations using cosine similarity, optimizes the associations of knowledge points using self-organizing maps, and optimizes the intensity of ability assessment using difficulty calibration, ultimately forming a vector that accurately reflects the attributes of the question. These two calculations are not independent but are mutually constrained through the inherent connection between "knowledge points → abilities," ensuring that the results align with the actual assessment objectives of the question.

[0203] Model building:

[0204] Difficulty level The difficulty of question t (the larger the value, the more difficult) is determined by two parts: the degree of matching of knowledge points. (The stronger the connection between weak knowledge points, the more difficult the questions should be); Ability matching degree: (The more significant the skill deficiency, the more difficult the questions should be.)

[0205] Fusion coefficient Balance the matching degree of knowledge points ( ) and ability matching degree (1- The weight of ).

[0206] Model training: Optimization using historical practice data The goal is to match the difficulty of the generated questions with the learners' abilities (with an accuracy rate close to 0.7, neither too easy nor too difficult):

[0207] (14)

[0208] in Historically difficult The accuracy rate of the questions is determined by an exponential function, which ensures that the closer the accuracy rate is to 0.7, the higher the score.

[0209] Model Application: Calculate the difficulty coefficient of each question and select questions with a difficulty range of [0.4, 0.6] to form a practice set.

[0210] (15)

[0211] in The perturbation term is randomized to avoid the practice set being too homogeneous.

[0212] Output personalized practice sets It includes questions that match learners' weaknesses and skill deficiencies.

[0213] Difficulty coefficient calibration: in formula (15) Optimized using historical data (typically with a value of 0.5-0.6), the system balances knowledge points and ability factors. For example, for learners who are "weak in factorization and have poor calculation skills," the weight of "factorization relevance" and "calculation load" will be increased when generating questions.

[0214] Practice set construction strategy: Select questions with a difficulty level of 0.4-0.6 (to ensure an accuracy rate of around 70%, in line with the "zone of proximal development" theory), while controlling the coverage ratio of knowledge points (60% for weak knowledge points, 30% for related knowledge points, and 10% for basic knowledge points), and the question type repetition rate is <20%.

[0215] V. Module Four: Feedback Optimization – The Core Mechanism of System “Self-Evolution”

[0216] Module core objectives

[0217] The effectiveness of the system's diagnosis and generation is evaluated by assessing the completion of practice, and the front-end algorithm parameters are optimized in reverse so that the system can dynamically adjust as the learner's level improves, thus solving the problem that "static models are difficult to adapt to changes in the learning process".

[0218] Closed-loop optimization details

[0219] The effectiveness evaluation index S: In formula (16), a higher S value indicates a better match between practice and ability (ideal value > 0.7). For example, if a learner answers a high-difficulty question correctly ( The score is Making mistakes on easy questions ( The score is Both are positive contributions.

[0220] (16)

[0221] S scores higher when answering difficult questions correctly or easy questions incorrectly.

[0222] Parameter update strategy: when (such as target value) When the value is 0.6, initiate parameter updates and adjust the algorithm parameters of the first module in reverse:

[0223] LLM weight adjustment: Enhance the sensitivity to identify weak knowledge points (such as increasing the weight of word vectors related to "factorization"). ;

[0224] GRU gating parameter adjustment: Pay more attention to abnormal fluctuations in answer time (such as extending the time series analysis window for high-importance questions). ;

[0225] SOM weight adjustment: refine the neuron resolution of weak knowledge areas (e.g., increase the number of neurons in the "algebraic calculation area" by 20%). ;

[0226] in Set the learning rate (e.g., 0.0001) to ensure that the parameter adjustment direction is consistent with the increase of S.

[0227] VI. Detailed Explanation of Algorithm Interaction and Collaboration Relationships

[0228] Interaction between LLM and GRU: Semantic Features Extracted by LLM As one of the inputs to GRU (Formula 3-5), the temporal features not only include answering behavior, but also incorporate semantic information of the questions (such as the difference in answering time patterns between questions of the type "quadratic equation" and questions of the type "geometric proof").

[0229] Interaction between GRU and surface fitting: Temporal feature strength of GRU output As the dependent variable in surface fitting (Formula 5), ​​the surface model can capture the pattern of "how question attributes (complexity, importance) affect answering behavior (time fluctuation)", residual characteristics This reflects an abnormal answering pattern.

[0230] Interaction of multiple features with SOM: LLM semantic features, GRU temporal features, and surface fitting residual features are fused into a unified feature through SOM. (Formula 9) achieves cross-dimensional information integration of "semantics-behavior-structure" to provide a comprehensive basis for subsequent diagnosis.

[0231] The interaction between the first and second modules: The knowledge association matrix M of the first module directly affects the calculation of the weak weights of the second module (Formula 12), so that the analysis of weak points not only depends on the direct error rate, but also considers the linkage effect between knowledge points (such as the weakness of "factorization" may lead to the error of "solving quadratic equations in one variable").

[0232] Full-link closed-loop interaction: The evaluation value S of the fourth module is used to optimize all algorithm parameters of the first module, so that the system can dynamically adjust the feature extraction method as the learner's level changes (e.g., as learning deepens, the accuracy of LLM in recognizing knowledge points continuously improves).

[0233] Algorithm Collaboration Case Study: The Entire Process from a Single Incorrect Problem to Personalized Practice

[0234] The learner answered incorrectly, "Solve using factorization." Taking this as an example, we will demonstrate the collaborative process of the various algorithms in the system:

[0235] 1. LLM processing: Extracting semantic features Among them, the high dimension values ​​of "factorization" (0.85) and "quadratic equation in one variable" (0.72) indicate that the question mainly relates to these two knowledge points.

[0236] 2. GRU processing: Input answer time series (total time 90 seconds, far exceeding the average of 40 seconds for similar questions) and Output time series features The "Error after prolonged hesitation" pattern is displayed (characteristic value 0.78).

[0237] 3. Surface fitting: The complexity of this problem is... Importance of knowledge points GRU strength The fitted value was calculated. residual (0.15 higher than the average) indicates an abnormal answer.

[0238] 4. SOM Fusion: The three features are concatenated and mapped to the "algebraic computation - outlier time" region of the SOM, thus fusing the features. Marked as typical features of the area.

[0239] 5. Diagnostic Module: Based on the knowledge association matrix M (the correlation between "factorization" and "quadratic equation" is 0.78), the following is calculated: (Weak weights), capability deficiencies .

[0240] 6. Practice generation: Based on W and D, generate 5 questions with a difficulty of 0.5, of which 3 are "basic factorization questions" (strengthening weak points) and 2 are "applying factorization to solving equations" (related transfer).

[0241] 7. Feedback Optimization: If the practice accuracy is 60% (S=0.65<0.7), then fine-tune the LLM's recognition weight for "factorization" and increase the GRU's time sensitivity to this type of question.

[0242] Through this end-to-end collaboration, the system achieves precise transformation from a single incorrect question to a personalized learning solution, enabling the output of each algorithm to be used efficiently, and ultimately achieving a closed-loop optimization of "learning through mistakes".

[0243] The core role of AI technology in this solution is to transform raw incorrect question data into interpretable features, diagnostic results, and personalized content, specifically manifested as follows:

[0244] 1. Enables in-depth analysis of multi-dimensional data (text, time series, question attributes) that are difficult for humans to process;

[0245] 2. Achieve cross-modal association of "semantics-behavior-knowledge" through algorithmic fusion;

[0246] 3. Based on the dynamic nature of the feedback learning process, the system accuracy is continuously improved through closed-loop optimization.

[0247] These technologies significantly differ from traditional error analysis methods (such as manual categorization and experience-based recommendations) in terms of efficiency and accuracy, and are the core driving force for achieving "personalization".

[0248] I. Module 1: Error Feature Extraction and Knowledge Graph Construction (Core AI Algorithm Cluster)

[0249] 1. Semantic Feature Extraction from Large Language Models (LLM)

[0250] AI technology belonging to the field of Natural Language Processing (NLP) performs semantic understanding of the question text based on pre-trained language models (such as BERT and MathBERT), and achieves accurate association between wrong questions and knowledge points by fine-tuning and adapting to the knowledge point system of specific disciplines (Formula 1-2).

[0251] Core AI capabilities: contextual semantic understanding, domain transfer learning, and text feature vector generation.

[0252] 2. GRU Temporal Feature Extraction

[0253] Deep learning technology, which belongs to the recurrent neural network (RNN) branch, captures dynamic features (such as hesitation duration and modification pattern) in the time series of answering questions through gating mechanisms, and integrates semantic features to achieve cross-modal modeling (Equation 3-6).

[0254] Core AI capabilities: time series data modeling, long-term and short-term dependency capture, and behavioral pattern recognition.

[0255] 3. Self-Organizing Map (SOM) Feature Fusion

[0256] This belongs to unsupervised learning neural network technology, which uses a two-dimensional neuron grid to cluster and reduce the dimensionality of high-dimensional features (semantics, temporal sequence, structure) to achieve adaptive fusion of multi-source information (Equation 7-9).

[0257] Core AI capabilities: feature dimensionality reduction, unsupervised clustering, and nonlinear mapping.

[0258] 4. Knowledge Association Matrix Construction

[0259] The co-occurrence relationship of knowledge points is calculated based on the AI ​​feature extraction results (LLM semantic vector) (Formula 10). This is an AI association mining technology in knowledge graph construction, which can automatically discover the linkage relationship of knowledge points that is difficult for humans to detect (such as the strong association between "factorization" and "quadratic equation").

[0260] II. Second Module: Learning Situation Diagnosis and Weakness Identification (AI-Driven Diagnostic Model)

[0261] This is a machine learning technique that integrates multi-source information. It integrates error rate, knowledge point correlation, and ability dimension features through a weighted fusion algorithm (Formulas 11-13) to achieve quantitative diagnosis of weaknesses.

[0262] Core AI capabilities: multi-feature weighted fusion, PCA dimensionality reduction decomposition, and statistical learning of learner behavior patterns.

[0263] Module 3: Personalized Practice Generation (AI Dynamic Decision-Making System)

[0264] This technology combines adaptive recommendation systems with reinforcement learning. It dynamically calculates the difficulty of questions based on the weights of weaknesses and the vectors of ability deficiencies (Formulas 14-15), thereby achieving precise adaptation of practice content.

[0265] Core AI capabilities: dynamic difficulty adjustment, personalized recommendations, and feedback-based decision optimization.

[0266] Module 4: Feedback Optimization (AI Adaptive Iterative Mechanism)

[0267] This machine learning optimization technique, which belongs to closed-loop control, updates the algorithm parameters (LLM, GRU, SOM weights) of the first module in reverse by using the effect evaluation value (Formula 16 and parameter adjustment strategy), enabling the system to have the ability to adaptively evolve according to the learner's state.

[0268] Core AI capabilities: online learning, adaptive parameter adjustment, and closed-loop feedback optimization.

[0269] Examples are given below:

[0270] I. Comparison of "Accuracy of Knowledge Point Association Recognition" (Traditional Solution 65% vs. This Solution 82%)

[0271] Traditional Solution Implementation

[0272] A middle school math teacher used a "keyword matching method" to analyze incorrect problems: in a problem about "solving quadratic equations using factorization," the teacher treated "factorization" as the only relevant knowledge point, ignoring its strong connection to "solving quadratic equations." Subsequent practice only included five basic factorization problems, resulting in students still failing to grasp "the application of factorization in equations," with a secondary error rate of 45% for this type of question.

[0273] This solution embodiment

[0274] The system extracts semantic features using a large language model, calculating that the incorrect question has a correlation strength of 0.85 with "factorization" and 0.72 with "solving quadratic equations" (the knowledge association matrix shows a correlation of 0.78 between the two). Of the 10 generated exercises, 6 are comprehensive questions combining "factorization and equation solving," and 4 are basic questions. A week later, during a retest, the second-order error rate for this type of question dropped to 18%, and the accuracy rate of knowledge point association recognition improved to 82% (consistent with the teacher's manual annotations).

[0275] 2. Comparison of "Error Type Identification Accuracy" (Traditional Solution 65% vs. This Solution 82%)

[0276] Traditional Solution Implementation

[0277] A student answered incorrectly when calculating 3x + 5 = 20 due to a mistake in using the transposition symbol. The traditional system only counted "calculation errors" without distinguishing between "knowledge gaps" and "careless mistakes." Subsequent 20 similar calculation problems were then provided, but the student became fatigued from repeated practice, and the accuracy rate remained around 60%.

[0278] This solution embodiment

[0279] The system analyzed the answer time sequence using GRU: the answer time for this question was 12 seconds (the average for similar questions is 10 seconds), with no obvious hesitation. Combined with LLM semantic features (basic calculation questions), it was judged as a "careless mistake" (error type identification accuracy rate 82%). Only 5 questions were pushed, and each question was marked with a "Pay attention to the transposition symbol" prompt. After completing the test, the student's accuracy rate increased to 90%, and the practice time was reduced by 70%.

[0280] III. Comparison of "Accuracy of Weak Point Location" (Traditional Solution 60% vs. This Solution 85%)

[0281] Traditional Solution Implementation

[0282] A student answered three consecutive "quadratic equation word problems" incorrectly. The traditional approach only considered the 80% error rate for quadratic equations and identified this as a weak point. The actual reason was insufficient "problem-solving skills" (incorrect equation formulation). Even after targeted practice, the accuracy rate remained only 40%.

[0283] This solution embodiment

[0284] The system, through surface fitting, identified that the complexity of incorrect questions was moderate (x=5), but the strength of the GRU time-series feature (z=0.8) was much higher than the fitted value (f=0.4), with a residual of 0.4 (an outlier). Combining this with SOM fusion features, the weakness was identified as "application problem analysis → extraction of equivalent relationships" (not simply solving equations). After providing eight tiered practice questions on "question simplification → equivalent relationship annotation," the accuracy rate improved to 85%, achieving 85% consistency with the teacher's manual diagnosis.

[0285] IV. Comparison of "Improved Practice Efficiency" (Traditional approach with no quantification vs. this approach which reduces ineffective practice by 50%)

[0286] Traditional Solution Implementation

[0287] A student completed 100 math problems (covering all knowledge points) during final exam review, 60 of which were repetitive exercises on knowledge points already mastered (ineffective practice). Due to the excessive time spent (3 hours), the student did not complete the practice on weak knowledge points, and the final score for these knowledge points was still lower than the class average.

[0288] This solution embodiment

[0289] The system uses weak weight vectors ( =0.72, =0.1) Generates 50 questions: 40 covering weak and related knowledge points, and 10 basic questions. Students complete it in 1.5 hours, and the amount of practice on weak knowledge points increases by 30%. The final exam score for the corresponding knowledge points increases by 15 points, and the proportion of ineffective practice decreases from 60% to 30% (a reduction of 50%).

[0290] The embodiments described above are for illustrative purposes only and are not intended to limit the invention. Therefore, any changes in numerical values ​​or substitutions of equivalent elements should still fall within the scope of this invention.

[0291] The above detailed description will enable those skilled in the art to understand that the present invention can indeed achieve the aforementioned objectives and has complied with the provisions of the Patent Law.

[0292] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention. The above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

[0293] It should be noted that the above description of the process is for illustrative purposes only and does not limit the scope of this specification. Those skilled in the art can make various modifications and changes to the process under the guidance of this specification. However, these modifications and changes remain within the scope of this specification.

[0294] The basic concepts have been described above. Obviously, for those skilled in the art who have read this application, the above disclosure is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this application. Such modifications, improvements, and corrections are suggested in this application, and therefore, such modifications, improvements, and corrections still fall within the spirit and scope of the exemplary embodiments of this application.

[0295] Furthermore, this application uses specific terms to describe its embodiments. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of this application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different positions in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of this application can be appropriately combined.

[0296] Similarly, it should be noted that, in order to simplify the description of the present application and thus aid in the understanding of one or more embodiments of the invention, the foregoing description of the embodiments of the present application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this approach of the present application should not be construed as reflecting an intention that the claimed subject matter requires more features than expressly recited in each claim. Rather, the subject of the invention should possess fewer features than in any single embodiment described above.

Claims

1. A personalized error analysis and practice generation system based on AI algorithms, characterized in that: include: The module for extracting incorrect question features and constructing a knowledge graph is used to receive raw incorrect question data, extract semantic features of incorrect question stems through a large language model, extract temporal features of answer time series through gated loop units, extract structural features of incorrect question attributes and answer behavior through surface fitting, and then fuse semantic features, temporal features and structural features through self-organizing mapping to obtain a fused feature matrix. At the same time, it calculates the co-occurrence strength between knowledge points based on semantic features to construct a knowledge association matrix. The learning situation diagnosis and weak point location module is used to receive the fusion feature matrix and knowledge association matrix, combine the knowledge point tags corresponding to the wrong questions to calculate the error rate of each knowledge point, calculate the weight of weak knowledge points based on the error rate and knowledge association matrix, and obtain the ability defect vector by performing principal component analysis to reduce the dimensionality of the fusion feature matrix and combining the weight of weak knowledge points. The personalized practice generation and difficulty adjustment module receives the weights of weak knowledge points and the vector of ability deficiencies, combines them with the knowledge point association vectors and ability adaptation vectors preset in the question bank, calculates the difficulty coefficient of the questions, and selects suitable questions to generate a personalized practice set. The learning effect feedback and model optimization module is used to receive personalized practice sets and corresponding practice results, evaluate the practice effect based on the practice results and the difficulty coefficient of the questions, and output parameter adjustment instructions if the effect does not meet the preset target, and adjust the parameters of each algorithm in the error feature extraction and knowledge graph construction module in reverse to form a complete data closed loop.

2. The personalized error analysis and practice generation system based on AI algorithm according to claim 1, characterized in that, In the module for extracting incorrect question features and constructing a knowledge graph, when the large language model extracts semantic features, it first obtains the original semantic vector of the question stem through a pre-trained language model, and then combines the subject knowledge point labels to fine-tune the weight matrix and bias vector to convert the original semantic vector into a semantic feature vector associated with the knowledge points.

3. The personalized error analysis and practice generation system based on AI algorithm according to claim 1, characterized in that, In the module for extracting incorrect question features and constructing a knowledge graph, when the gated loop unit extracts temporal features, it concatenates the answer time series with the semantic feature vector output by the large language model as input. By updating the retention ratio of the historical hidden state through the gate control and resetting the forgetting ratio of the historical hidden state through the gate control, the final output is a temporal feature vector that reflects the answer behavior pattern. The intensity value of this temporal feature vector is used as the dependent variable for surface fitting.

4. The personalized error analysis and practice generation system based on AI algorithm according to claim 1, characterized in that, In the module for extracting incorrect question features and constructing a knowledge graph, when extracting structural features through surface fitting, the complexity of incorrect questions and the importance of knowledge points obtained based on semantic feature vectors are used as independent variables, and the intensity value of temporal feature vectors is used as the dependent variable. A bivariate quadratic surface function is constructed and the coefficients are solved. The structural features are obtained by calculating the residual between the actual intensity value and the fitted value. The structural features, along with the semantic feature vector and the temporal feature vector, are used as inputs to the self-organizing map.

5. The personalized error analysis and practice generation system based on AI algorithm according to claim 1, characterized in that, In the module for extracting incorrect question features and constructing a knowledge graph, when fusing features using self-organizing mapping, semantic feature vectors, temporal feature vectors, and structural features are concatenated into a high-dimensional feature vector. The best matching neuron is found through a neuron grid, and the weight vector of that neuron is used as the corresponding row vector in the fusion feature matrix. Furthermore, the neuron weights are continuously optimized through iterative learning to improve the fusion accuracy.

6. The personalized error analysis and practice generation system based on AI algorithm according to claim 1, characterized in that, When calculating the weight of weak knowledge points, the learning diagnosis and weak point location module adopts a weighted fusion method, which combines the direct impact of the error rate with the indirect impact of the error rate of related knowledge points in the knowledge association matrix. The weighting coefficient is determined through cross-validation, so that the calculation results are consistent with the degree of weakness marked by manual annotation to a preset threshold.

7. The personalized error analysis and practice generation system based on AI algorithm according to claim 1, characterized in that, When calculating the difficulty coefficient of a question, the personalized practice generation and difficulty adjustment module performs a weighted fusion based on the matching degree between the weight of weak knowledge points and the correlation vector of question knowledge points, and the matching degree between the vector of ability deficiencies and the vector of question ability adaptation. The weighting coefficient is optimized through historical practice data to ensure that the expected accuracy of the generated questions is within a preset range.

8. The personalized error analysis and practice generation system based on AI algorithm according to claim 1, characterized in that, When evaluating the learning effect feedback and model optimization module, the evaluation value is calculated by matching the accuracy of the practice with the difficulty coefficient of the questions. When the evaluation value is lower than the preset target value for several consecutive times, the module initiates synchronous adjustment of the weights of the large language model, the gating parameters of the gated recurrent unit, and the weights of the self-organizing map neurons.

9. The personalized error analysis and practice generation system based on AI algorithm according to claim 1, characterized in that, In the data closed loop, after receiving the parameter adjustment instruction, the error feature extraction and knowledge graph construction module prioritizes adjusting the algorithm parameters that have the greatest impact on the identification of the current weak knowledge points. The adjustment range is positively correlated with the difference between the practice effect evaluation value and the preset target value.

10. The personalized error analysis and practice generation system based on AI algorithm according to claim 1, characterized in that, The co-occurrence strength among knowledge points in the knowledge association matrix is ​​calculated based on the average value of the product of the association strengths of corresponding knowledge points in the semantic feature vectors across all incorrect questions. This co-occurrence strength is dynamically updated as new incorrect question data is added, and the update frequency is consistent with the practice feedback cycle.

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