An intelligent exercise recommendation system and method based on multi-dimensional target optimization

Abstract

The application discloses an intelligent exercise recommendation system and method based on multi-dimensional target optimization and belongs to the technical field of artificial intelligence. The method first extracts six-dimensional difficulty features from a question text and completes automatic labeling, and then, in combination with historical answering records of students, uses a graph attention network to mine causal coupling relationships among various ability dimensions, and identifies the root cause of the short board that truly restricts the score. On the basis, the six-dimensional recommendation weights are dynamically adjusted by using deep reinforcement learning, and personalized questions with high training value are continuously output to different students. The method has completed engineering deployment verification in learning machines, education APPs, AI intelligent learning platforms and other scenes.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, specifically to an intelligent exercise recommendation system and method based on multi-dimensional objective optimization. Background Technology

[0002] With the rapid development of smart education technology, AI-powered exercise recommendation has become a core function of intelligent learning terminals. Current mainstream intelligent exercise recommendation systems and publicly available patented solutions generally adopt a two-dimensional recommendation model of "knowledge point + difficulty," with related technologies including personalized knowledge point-based push systems and IRT single-dimensional ability assessment models. However, these technologies suffer from the following unresolved technical shortcomings in practical applications: First, the granularity of ability assessment is coarse, only evaluating knowledge mastery through answer accuracy, failing to distinguish the essential differences in students' ability weaknesses. Second, the recommendation dimensions are singular, unable to provide targeted training for specific student ability dimensions (such as reading comprehension, skill application, logical reasoning, etc.). Third, ability correlation modeling is lacking, failing to identify root causes such as "weak reading comprehension leading to poor skill application." Fourth, recommendation rules are rigid, unable to adjust strategies based on students' dynamic learning status, and unable to dynamically adjust recommendation weights according to multiple ability dimensions. Fifth, in the existing education system, teachers generally adopt a "one-size-fits-all" uniform homework model when assigning homework to the whole class, failing to provide customized, one-on-one, targeted homework assignments based on each student's different strengths and weaknesses in multiple dimensions, resulting in slow improvement and low teaching efficiency; excessive homework also leads to a heavy workload for students. Summary of the Invention

[0003] To address the aforementioned issues, this invention provides an intelligent exercise recommendation system and method based on multi-dimensional objective optimization. By constructing a six-dimensional ability intelligent exercise recommendation system, the system includes: a student six-dimensional ability assessment module, an automatic six-dimensional difficulty labeling module for questions, a root cause ability deficiency identification module, a multi-objective optimization recommendation module, a personalized recommended question set generation module, and a teacher-side collaborative assignment distribution module.

[0004] To achieve the above objectives, the present invention provides the following technical solution: an intelligent exercise recommendation system and method based on multi-dimensional objective optimization, specifically including the following steps: S1. Input the original question text data, and output the six-dimensional difficulty vector of the questions through the education big data model Qwen-7B and the regression model XGBoost, and construct the six-dimensional difficulty automatic labeling model of the questions.

[0005] S2. Based on the six-dimensional difficulty vector of the questions and the collection of student answer records, the six-dimensional ability vector of students is evaluated and output through the Bayesian joint inference algorithm, and the comprehensive ability score of students is calculated, thus constructing a six-dimensional ability assessment module for students.

[0006] S3. Collect anonymized student answer records, train the GAT coupled network by inputting the data, output a preset dimension coupling weight matrix, define the coupling weight matrix to obtain the subject coupling weight matrix; calculate the influence score based on the student's six-dimensional ability vector and the subject coupling weight matrix, output the six-dimensional influence score and determine the root cause dimension to obtain the root cause defect dimension and priority weight, thus completing the GAT-based root cause ability defect identification algorithm.

[0007] S4. Based on Deep Reinforcement Learning (DQN) and the student's six-dimensional ability vector, construct the DQN state space and action space, obtain the six-dimensional recommendation weights through dynamic adjustment, and construct a multi-objective optimization intelligent recommendation algorithm module.

[0008] S5. Based on student ability vectors, dynamically adjusted six-dimensional recommendation weights, and a candidate question bank, a personalized recommendation question set is output by constructing a recommendation objective function and a multi-objective optimization recommendation algorithm, thus completing a multi-dimensional objective optimization intelligent exercise recommendation system method.

[0009] S6. Based on the six-dimensional difficulty vector of the questions and the six-dimensional ability vector of the students, the system calculates the six-dimensional difference vector of each question for each student by uploading the class homework question set through the teacher's terminal. According to the preset distribution strategy, it performs many-to-many matching to generate a personalized homework distribution plan for the whole class. After the teacher confirms it, the homework is distributed to students through three channels: direct distribution through the learning terminal, PDF sending to the mobile phone, or printing through an external printer. This completes the group-level personalized homework distribution and realizes a complete closed loop of distribution-answering-ability update.

[0010] Preferably, step S1 specifically includes the following steps: S1.1 Based on the original question text, structured question data is output through text cleaning and structured information extraction; S1.2 Based on structured question data, a 32-dimensional structured feature vector is output by extracting 32-dimensional features. S1.3 Based on structured question data, 96-dimensional semantic features are extracted by fine-tuning the Qwen-7B educational big data model, and a 96-dimensional semantic feature vector is output. S1.4. Based on the 32-dimensional structured feature vector and the 96-dimensional semantic feature vector, a 128-dimensional question feature vector is obtained by concatenating them. By calling 6 independent XGBoost regression models and setting the model parameters, a six-dimensional difficulty vector of the question is output.

[0011] Preferably, step S2 specifically includes the following steps: S2.1 Based on the information of primary / junior high school / senior high school, the six-dimensional ability prior distribution parameters of primary / junior high school / senior high school are output by presetting prior parameters; S2.2 Based on student answer records and the six-dimensional difficulty vector of the questions, anomaly detection is performed after associating student answer records with the six-dimensional difficulty of the questions, and a weighted answer dataset is output. S2.3. Define a comprehensive ability function based on the six-dimensional difficulty vector of the question; S2.4 Based on the six-dimensional ability prior distribution parameters, the weighted answer dataset, and the comprehensive ability function, the posterior probability distribution is constructed using Bayes' theorem, the maximum a posteriori estimate is solved using the gradient descent method, and dynamic updates are performed to output the student's six-dimensional ability vector and calculate the student's comprehensive ability score. The formula for calculating the student's comprehensive ability score is: in, For students In the Ability scores for each ability dimension Indexed for capability dimensions.

[0012] Specifically, in S2.3, a comprehensive ability function is defined based on the six-dimensional difficulty vector of the question. The expression is: in, The weighting of each ability dimension is determined for different question types; For students In the Ability scores for each ability dimension Indexed for capability dimensions.

[0013] Preferably, step S3 specifically includes the following steps: S3.1 Collect anonymized student answer records, construct a six-dimensional ability change sequence as a training dataset, input a 2-layer GAT network for network training, output a 6×6 coupling weight matrix and define the coupling weight matrix to obtain the subject coupling weight matrix; S3.2. Based on the student's six-dimensional ability vector and subject coupling weight matrix, calculate the degree centrality and ability gap, then calculate the influence score and output the six-dimensional influence score; based on the six-dimensional influence score, determine the root cause dimension, obtain the root cause defect dimension and priority weight, and complete the root cause ability defect identification algorithm based on GAT.

[0014] Preferably, step S4 specifically includes the following steps: S4.1 Based on the student's six-dimensional ability vector, the accuracy rate of answering questions after a preset number of attempts, the six-dimensional coverage of the recommended selected question set, and the current recommendation mode encoding, a 19-dimensional continuous feature vector is formed by concatenating them, and the state vector is output and a DQN state space is constructed. S4.2. Define the DQN action space based on the state vector; S4.3 Based on the improvement of students' six-dimensional abilities and the weight of the current recommendation mode, a reward function is designed to output the DQN reward value; S4.4 Based on the DQN state space, DQN action space and reward function, the recommendation weight is updated after weight adjustment, and the dynamically adjusted six-dimensional recommendation weight is output to complete the multi-objective optimization intelligent recommendation algorithm. Preferably, in step S5, the expression for the objective function is: In the formula, To pre-determine the weights of the six-dimensional matching score, Assuming predefined dimensional coverage score weights, To pre-determine the scoring weights for different question types, To pre-determine the penalty score weight for repetition, The six-dimensional matching score is used to determine the degree of matching. Score the dimensional coverage. To score points for the diversity of question types, The score is a penalty for repetition.

[0015] This invention also provides an intelligent exercise recommendation system and method based on multi-dimensional objective optimization, specifically including: (1) The six-dimensional difficulty automatic labeling module is used to input the original question text data into S1 and output the six-dimensional difficulty vector of the question through the education big model Qwen-7B and the XGBoost regression model; (2) Student six-dimensional ability assessment module, which is used by S2 to assess and output the student's six-dimensional ability vector based on the six-dimensional difficulty vector of the question and the collected student answer record data through the Bayesian joint inference algorithm; (3) Root cause ability deficiency identification module, used by S3 to collect desensitized student answer record data, obtain subject coupling weight matrix through graph attention network GAT training, calculate influence score based on student six-dimensional ability vector and subject coupling weight matrix and determine root cause dimension, and obtain root cause deficiency dimension and priority weight. (4) Multi-objective optimization recommendation module, which is used by S4 to construct the DQN state space and action space based on deep reinforcement learning DQN and the student's six-dimensional ability vector, and obtain the six-dimensional recommendation weights through dynamic adjustment; (5) Personalized recommendation question set generation module, which is used by S5 to output personalized recommendation question sets by constructing a recommendation objective function and a multi-objective optimization recommendation algorithm based on the student's six-dimensional ability vector, dynamically adjusted six-dimensional recommendation weights and candidate question bank; (6) The teacher-side collaborative homework distribution module is used to receive the class homework question set uploaded by the teacher-side, call the six-dimensional difficulty automatic labeling module of the question to complete the six-dimensional difficulty identification, combine the six-dimensional ability vector of all students in the class to perform many-to-many difference matching, and after the teacher reviews and confirms, distribute the homework through three channels and send back the answer results to form a closed loop.

[0016] Compared with existing technologies, this invention provides an intelligent exercise recommendation system and method based on multi-dimensional objective optimization, which has the following beneficial effects: (1) This invention solves the problem of coarse granularity in the existing two-dimensional recommendation model by constructing a six-dimensional ability vector space and evaluating students’ subject abilities in a precise and multi-dimensional way; it uses graph attention network to mine the causal relationship between the six-dimensional abilities, find the core weakness dimension with the greatest impact, and solve the problem of not being able to identify the root cause of ability defects. (2) This invention achieves dynamic automatic adjustment of recommendation weights through deep reinforcement learning, adapts to different learning objectives and dynamic learning states, and solves the problems of rigidity and poor adaptability of existing recommendation rules; and constructs an AI automatic labeling model that integrates the semantic features of large models, and realizes the automation, standardization and scaling of question labeling, solving the problems of low efficiency and poor consistency of existing question labeling. (3) This invention constructs a six-dimensional difference partition star rating and filtering recommendation system to quantify the training value of each question in any set of homework / test questions, assign 1 to 5 stars as priority hierarchical labels, and recommend high-value questions in a targeted manner. At the same time, it generates a full-paper dimension health check report to guide students to accurately allocate their study time, reduce ineffective learning burden from the technical root, achieve the core educational goal of "reducing burden and increasing efficiency", and solve the core pain point of existing AI exercise recommendation systems that are only for active push scenarios and completely lack the ability to process existing homework and test questions.

[0017] (4) This invention uses a collaborative homework distribution module on the teacher's end. Based on the automatic identification of the six-dimensional difficulty of the S1 question and the many-to-many difference matching of the six-dimensional ability vector of all students in the class in S2, the complete distribution calculation response time is no more than 3 seconds in a standard scenario with a class size of 50 students and 10 to 30 homework questions. Compared with the teacher's manual assignment to each student, the efficiency is significantly improved. Compared with the uniform homework assignment, the proportion of invalid homework (questions with very low training value for the student) in the whole class is reduced from about 35% to less than 5%, which truly achieves "reducing the burden without reducing efficiency" and provides feasible technical support for the national "double reduction" policy. Attached Figure Description

[0018] Figure 1 This is a flowchart of an intelligent exercise recommendation system and method based on multi-dimensional objective optimization according to the present invention; Figure 2 This is the logic diagram for determining the five-star training value partition in this invention; Figure 3 This is a diagram illustrating the closed-loop data flow for collaborative assignment distribution on the teacher's end in this invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] To verify the rationality of selecting six dimensions, this invention conducted a controlled ablation experiment on a dataset consisting of 12,000 manually annotated exercises and 1 million anonymized student answer records for all partitioning schemes from 3 to 9 dimensions. The experimental results showed that schemes with 5 dimensions or less exhibited significant underfitting, with an ability assessment error 24.4% higher than 6 dimensions and a root cause false negative rate of 28%. Schemes with 7 dimensions or more suffered from the curse of dimensionality, resulting in a significant increase in the number of edges in the GAT topology and a decrease in cold-start convergence. The root cause identification accuracy actually dropped from 92% to 88% (7 dimensions) or even below 82% (8 dimensions and above), while computational time and user cognitive load also significantly worsened. Based on the above experimental data, 6 dimensions achieved Pareto optimality in terms of assessment accuracy, computational efficiency, and user interpretability, representing the best overall performance of the engineering parameter solution in this invention. The six dimensions (C1-C6) of this invention were not subjectively set but were determined through cross-validation and convergence of three independent objective paths.

[0021] The definitions of C1-C6 in this invention are explained as follows: C1 indicates precision in calculation / precision in expression; for science subjects: accuracy in multi-step calculations, nested application of formulas, unit conversion, and error control; for humanities subjects: standardization of text expression, logical coherence, and precision in the use of professional terminology. The complete scoring criteria for a score of 0-5 are as follows: 0 points: Science: Completely lacks computational ability and cannot complete basic calculations; Humanities: Unable to write single sentences and lacks basic expression skills; 1 point: Science: Can only complete one basic calculation step with an error rate >80%; Humanities: Can only complete single sentence writing with a spelling and grammatical error rate >80%; 2 points: Science: Can complete up to three calculation steps with an error rate of 50%~80%; Humanities: Can complete short paragraph writing with a spelling and grammatical error rate of 50%~80%; 3 points: Science: Can complete up to five calculation steps with an error rate of 20%~50% and no core errors. Humanities: Can complete a full paragraph with a spelling and grammatical error rate of 20%~50%, and no core semantic errors; 4 points: Science: Can complete complex calculations within 8 steps with an error rate of <20%, and apply formulas correctly; Humanities: Can complete a full chapter with a spelling and grammatical error rate of <20%, use professional terminology correctly, and have logical coherence; 5 points: Science: Can complete calculations of more than 10 steps with extremely high complexity, with zero errors, and the accuracy reaches the full score standard of the exam; Humanities: Can complete professional text creation with zero spelling and zero grammatical errors, and express themselves accurately and rigorously, meeting the full score standard of the subject exam.

[0022] C2 stands for reading comprehension / condition extraction; applicable to both arts and sciences, it refers to the ability to extract explicit information, uncover implicit conditions, and interpret unfamiliar concepts from the question text, charts, and new contexts. The complete scoring criteria from 0 to 5 points are as follows: 0 points: Completely unable to understand the question stem and unable to extract any useful information; 1 point: Only able to identify the most basic explicit concepts in the question stem, unable to extract the core information needed to solve the problem; 2 points: Able to extract all explicit information in the question stem, unable to identify any implicit conditions; 3 points: Able to extract all explicit information, identify 1-2 basic implicit conditions, and understand the logic of the question stem for common question types; 4 points: Able to quickly uncover 3 or more implicit conditions in the question stem, and be able to interpret the core logic of new scenarios and interdisciplinary question types; 5 points: Able to accurately identify all explicit and implicit information in complex question types, and be able to quickly deconstruct the core connotation of unfamiliar concepts without missing any information.

[0023] C3 indicates the number of questions / speed; applicable to both science and humanities subjects. The allotted time is based on the standard time allocation for the corresponding question type in the official exams for each grade level. For science subjects, the focus is on the efficiency of handling the number of problem-solving steps and the amount of calculation, based on the time allocated for a single question in mathematics. For humanities subjects, the focus is on the efficiency of completing reading and writing tasks, based on the time allocated for a single question in Chinese / English. The complete scoring criteria from 0 to 5 points are as follows: 0 points: Unable to complete any basic questions within the allotted time; 1 point: Able to complete basic questions within twice the allotted time; 2 points: Able to complete medium-difficulty questions within 1.5 times the allotted time; 3 points: Able to complete medium-difficulty questions within the standard allotted time without exceeding the time limit; 4 points: Able to efficiently complete high-difficulty questions within the allotted time, allowing sufficient time for review; 5 points: Able to complete all difficulty levels within 50% of the allotted time, achieving top-level efficiency.

[0024] C4 stands for broadening thinking; it is applicable to both arts and sciences, including innovative thinking, interdisciplinary integration ability, knowledge transfer ability, and critical thinking ability. The complete scoring criteria from 0 to 5 points are as follows: 0 points: No ability to transfer knowledge, can only memorize fixed formulas / statements, unable to cope with any changes in question types; 1 point: Can only cope with fixed question types that are exactly the same as the example questions, unable to solve questions with slight changes in question type; 2 points: Can cope with simple variations of basic question types (the variation does not exceed superficial substitutions such as changing numbers or units), unable to handle questions that integrate cross-knowledge points; 3 points: Can complete questions that integrate cross-knowledge points within the same module, possessing basic knowledge transfer ability; 4 points: Can complete questions that integrate cross-modules and cross-disciplinary topics, possessing strong innovative problem-solving ideas and knowledge transfer ability; 5 points: Can cope with open-ended and exploratory innovative question types, possessing extremely strong cross-domain knowledge integration and critical thinking ability.

[0025] C5 represents the application of skills; applicable to both arts and sciences, specifically the ability to identify and select the optimal problem-solving method, including the ability to select the best method, optimize calculations, apply templates, and use advanced problem-solving techniques. The complete scoring criteria from 0 to 5 points are as follows: 0 points: No knowledge of any problem-solving techniques, only able to use the most basic step-by-step derivation method; 1 point: Has knowledge of basic problem-solving techniques, but cannot apply them correctly in problem-solving; 2 points: Can apply basic problem-solving techniques with prompts, but cannot independently identify the applicable scenarios for the techniques; 3 points: Can independently identify the applicable scenarios for techniques in common question types, and correctly apply basic problem-solving methods to optimize the problem-solving process; 4 points: Can quickly identify the optimal solution path for complex question types, and flexibly apply a combination of multiple techniques to simplify the problem-solving process; 5 points: Can independently select and combine multiple optimization techniques in extremely difficult question types, achieving top-level problem-solving efficiency.

[0026] C6 represents steps / logic; applicable to both arts and sciences, specifically the completeness of problem-solving steps, the rigor of deductive logic, and the ability to adapt to scoring criteria. The complete scoring criteria for 0-5 points are as follows: 0 points: No logical reasoning ability whatsoever, and the solution process lacks complete steps; 1 point: The solution steps are chaotic, with serious logical gaps and no effective reasoning process; 2 points: The solution steps are incomplete, with obvious loopholes in the core logic, and cannot cover the scoring points; 3 points: The solution steps are complete, the core logic is rigorous, and it can cover the main scoring points without any key logical errors; 4 points: The solution steps are standardized and complete, the reasoning logic is interconnected, 100% covers the scoring points, and there are no logical loopholes; 5 points: The solution steps are rigorous and standardized, conform to the subject-specific reasoning standards, and have no flaws.

[0027] Example 1: An intelligent exercise recommendation system and method based on multidimensional objective optimization Please see Figures 1-3 A smart exercise recommendation system and method based on multi-dimensional objective optimization includes the following steps: S1. Input the original question text data, and output the six-dimensional difficulty vector of the question through the six-dimensional difficulty automatic labeling model; The six-dimensional difficulty automatic labeling model for the questions includes: the large education model Qwen-7B and the regression model XGBoost; The original question text includes, but is not limited to, homework, test paper, and question bank questions; Specifically, the following steps are included: S1.1 Based on the original question text, structured question data is output through text cleaning and structured information extraction; This invention constructs a training set using 12,000 annotated exercises from all K-12 subjects. Each question is cross-annotated with six-dimensional difficulty scores by three or more front-line teachers with five or more years of teaching experience. Annotation consistency is calculated using the Cohen Kappa coefficient, with a Kappa value ≥ 0.92 among multiple annotators. The dataset covers all grade levels, all question types, and all knowledge points. The original question text dataset is cleaned and structured information is extracted to output structured question data. S1.2 Based on structured question data, a 32-dimensional structured feature vector is output by extracting 32-dimensional features. The 32-dimensional structured features include: length of the question stem text, number of solution steps, number of formulas, number of charts, number of new concepts, number of interdisciplinary tags, and standard completion time for the question. S1.3 Based on structured question data, 96-dimensional semantic features are extracted by fine-tuning the Qwen-7B educational big data model, and a 96-dimensional semantic feature vector is output. The fine-tuning operation specifically involves: using the Qwen-7B base model and performing supervised fine-tuning using the LoRA method; The 96-dimensional semantic features are clearly defined: core features include "implicit condition density" and "cognitive load," where "implicit condition density" is the ratio of the number of implicit conditions in the question stem to the length of the question stem text, quantified as a continuous value from 0 to 1; "cognitive load" is calculated based on the complexity of the question stem text, the number of new concepts, and the cross-module relevance, quantified as a continuous value from 0 to 1; all semantic features are interpretable structured numerical values ​​output by the large model, rather than hidden layer vectors, and each feature in the 6 dimensions corresponds to a 16-dimensional binning code, totaling 96 dimensions.

[0028] In this embodiment, 128 dimensions are used directly as model input. However, actual tests show that about 30 of these dimensions contribute almost nothing. After pruning, the convergence speed is faster. Therefore, the 96 dimensions retained in this invention, namely "implicit condition density" (the ratio of the number of implicit conditions in the question stem to the text length) and "cognitive load" (the weighted value of complexity, number of new concepts, and cross-module correlation), are the two features that contribute the most to the six-dimensional difficulty prediction.

[0029] S1.4. Based on the 32-dimensional structured feature vector and the 96-dimensional semantic feature vector, a 128-dimensional question feature vector is obtained by concatenating them. By calling 6 independent XGBoost regression models and setting the model parameters, a six-dimensional difficulty vector of the question is output. In this embodiment, the XGBoost regression model has 120 trees, a maximum depth of 8, a learning rate of 0.1, and is trained using 5-fold cross-validation. XGBoost regression model training and deployment environment: The model training environment is 8×A100 GPUs, and the inference deployment adopts quantized INT8 format. Under normal network conditions, the average inference time for single question feature extraction and annotation is about 42.7ms. When facing high concurrency access during peak sales or exam seasons, which leads to computing power strain, the system can still control the peak latency to about 55ms through degradation strategies.

[0030] XGBoost regression model performance: The average MAE of the six-dimensional difficulty annotation is stable in the range of 0.26~0.32, and the consistency with expert annotation can reach 92.7%~94.1%. The annotation time of a single question is much lower than the several minutes of manual annotation, and the annotation efficiency is more than 1000 times higher than manual annotation. The expression for outputting the six-dimensional difficulty vector of the problem is: In the formula, Number the questions. For the title The difficulty score for the C1 ability dimension, For the title The difficulty score in the C2 ability dimension, For the title The difficulty score in the C3 ability dimension, For the title The difficulty score in the C4 ability dimension, For the title The difficulty score in the C5 ability dimension, For the title Difficulty score in the C6 ability dimension; Data feedback calibration mechanism: Based on real-time student answer data, when the actual pass rate of a question deviates from the model's predicted pass rate by more than 15%, the difficulty of the question is automatically recalibrated and the model is incrementally fine-tuned.

[0031] The formula for calculating the prediction pass rate of the XGBoost regression model is as follows: in, This represents the total number of students in the corresponding grade level. Let be the likelihood function for the accuracy of answering the questions.

[0032] S2. Based on the six-dimensional difficulty vector of the questions and the collected student answer records, the six-dimensional ability vector of students is evaluated and output and the comprehensive ability score of students is calculated through the Bayesian joint inference algorithm, thus constructing a six-dimensional ability evaluation module for students. This invention employs a multi-question joint Bayesian inference algorithm in a six-dimensional vector space to achieve accurate assessment of students' six-dimensional ability vectors. Unlike the one-dimensional inference of traditional independent IRT, the core design has been optimized in multiple layers based on engineering test experience.

[0033] S2.1 Based on the information of primary / junior high school / senior high school, the six-dimensional ability prior distribution parameters of primary / junior high school / senior high school are output by presetting prior parameters; This embodiment, based on experimental measurements and prior distributions of abilities set according to differences in students' learning stages, assumes that each dimension independently follows a normal distribution. After multiple rounds of experimental calibration, the prior parameters for each learning stage are determined as follows: For the primary school stage... μ =2.5、 σ =0.8; when it is the junior high school stage, μ =3.0、 σ =1.0; when it is the high school stage, μ =3.5、 σ =1.2; where μ is the first prior parameter and σ is the second prior parameter; this parameter setting can effectively reduce the capability assessment error in cold start scenarios and improve the model convergence speed.

[0034] S2.2 Based on student answer records and the six-dimensional difficulty vector of the questions, anomaly detection is performed after associating student answer records with the six-dimensional difficulty of the questions, and a weighted answer dataset is output. The anomaly detection specifically involves reducing the weight of a data point to 0.5 when the deviation between the answer score and the prediction is greater than 0.4, and triggering a manual review entry after three consecutive anomalies. S2.3. Define a comprehensive ability function based on the six-dimensional difficulty vector of the question; This invention constructs a six-dimensional comprehensive ability function based on the "barrel principle," using the matching weakness between the student's single-dimensional ability and the corresponding difficulty of the questions as the core constraint. It combines question type weights to achieve comprehensive matching quantification. The expression for the comprehensive ability function is: in, The weights for each ability dimension are assigned to different question types, with the sum of the weights being 1. For students In the The ability scores for each ability dimension, with a range of values ​​being... , For the title In the The difficulty score for each ability dimension, with a value range of [value missing]. In practical applications, adjustments can be made according to the characteristics of the discipline. After adjustments, normalization should be performed again to avoid weight imbalance. S2.4 Based on the six-dimensional ability prior distribution parameters, the weighted answer dataset, and the comprehensive ability function, the posterior probability distribution is constructed using Bayes' theorem, the maximum a posteriori estimate is solved using the gradient descent method, and dynamic updates are performed to output the student's six-dimensional ability vector and calculate the student's comprehensive ability score. The method of this invention constructs a posterior probability distribution based on Bayes' theorem, uses maximum a posteriori estimation (MAP) to solve for the student's optimal six-dimensional ability vector, and combines exponential smoothing to realize dynamic updating of the ability vector. The number of iterations in the gradient descent solution process is set to 100 by default.

[0035] The expression for outputting the student's six-dimensional ability vector is: in, Number the students. For students The ability score in the C1th ability dimension For students The ability score in the C2th ability dimension For students The ability score in the C3 ability dimension For students The ability score in the C4th ability dimension For students The ability score in the C5th ability dimension For students The ability score in the C6th ability dimension.

[0036] The formula for calculating the student's comprehensive ability score is: S2.5. Based on students' comprehensive ability scores, determine the level and corresponding color through mapping rules; The mapping rules for students' comprehensive ability scores in this invention are shown in Table 1: Table 1: Mapping Rules between Overall Score and LV Level The color mapping scheme is designed based on the pre-attentional feature processing theory in cognitive psychology (Treisman, 1985): color is a pre-attentional feature that the human visual system can automatically process, without occupying limited working memory capacity. This allows users to identify the difficulty level through color signals without interpreting LV values. Practical testing has verified that the recognition efficiency is more than 40% higher than that of pure numerical display. The color system is strongly bound to the LV level algorithm output and is used uniformly in visualizations across various scenarios, including question difficulty radar charts, student ability radar charts, recommended question sets, and personal ability dashboards. This ensures consistent visual language throughout the system and further reduces the cognitive adaptation cost for users when switching between different functional modules.

[0037] S3. Collect anonymized student answer records, input them into the GAT coupled network for training, output a 6×6 coupled weight matrix, define the coupled weight matrix to obtain the subject coupled weight matrix; calculate the influence score based on the student's six-dimensional ability vector and the subject coupled weight matrix, output the six-dimensional influence score and determine the root cause dimension to obtain the root cause defect dimension and priority weight, and complete the root cause ability defect identification algorithm based on GAT. S3.1 Collect anonymized student answer records, construct a six-dimensional ability change sequence as a training dataset, input a 2-layer GAT network for network training, output a 6×6 coupling weight matrix and define the coupling weight matrix to obtain the subject coupling weight matrix; The optimization function and parameters for training the GAT network coupled with the network are set as follows: mean squared error (MSE) is used as the loss function, Adam optimizer is used, learning rate is 0.001, and batch size is 256. Due to some labeling noise in the early batches, the model usually converges gradually after 45 to 51 epochs. After removing outliers, the mean squared error (MSE) of the validation set eventually stabilizes in the range of 0.021 to 0.026. According to the actual test, the model's coupling relationship prediction accuracy can reach 93.6% to 95.2%, which is about 35 percentage points higher than the root cause identification accuracy of manually defined matrices.

[0038] The training data for GAT came from 500,000 anonymized answer records from the K-12 stage, corresponding to a sample of over 10,000 students. During data preprocessing, we attempted to use single-response answers as sequence nodes, but experiments showed that a sequence of ability changes consisting of 10 consecutive answers had approximately 11 percentage points higher accuracy in root cause identification than a single answer. Therefore, we ultimately used 10 answers as the sequence length. All raw data underwent irreversible anonymization, ensuring that students' personal information could not be restored. The model used a two-layer Graph Attention Network (GAT) to train the anonymized answer records, mining the causal coupling coefficients between the six dimensions of abilities, and outputting a 6×6 coupling weight matrix.

[0039] The specific mechanism for defining and updating the coupling weight matrix in this invention is as follows: Coupling weight matrix It is a 6×6 matrix, matrix elements Representing dimensions When the score increases by 1 point, the dimension The basic rule for the synergy enhancement is: diagonal elements (Complete influence of itself); Off-diagonal elements The matrix is ​​asymmetric, reflecting the directionality of the influence of ability.

[0040] S3.2, Establish a dynamic update mechanism for the subject coupling weight matrix; To adapt to the dynamic changes in students' answer patterns, the system has set up a quarterly iterative update mechanism for the coupling matrix, enabling continuous model optimization. A matrix update is triggered at the end of each natural quarter, with the updated data based on over 100,000 newly added anonymized answer records for that quarter. Based on the new data, the GAT model is incrementally fine-tuned to generate a new version of the coupling matrix. The new version matrix must undergo A / B testing and meet two conditions before being fully deployed: root cause identification accuracy is no lower than the original version, and student ability improvement rate is no lower than the original version. If problems such as decreased recommendation performance or system anomalies occur after the new version matrix is ​​deployed, it can be rolled back to the previous stable version with one click, while retaining all operation logs to ensure system stability.

[0041] S3.3. Based on the student's six-dimensional ability vector and subject coupling weight matrix, calculate the degree centrality and ability gap, then calculate the influence score and output the six-dimensional influence score; based on the six-dimensional influence score, determine the root cause dimension, obtain the root cause defect dimension and priority weight, and complete the root cause ability defect identification algorithm based on GAT. This invention's system comprehensively evaluates the depth and scope of shortcomings across dimensions based on influence scores to determine the root cause defect dimension. The core calculation logic is as follows: first, out-degree centrality is used to characterize the total influence of one dimension on other dimensions, as shown in the formula: Then, the influence score is calculated by combining the capability gap. The higher the score, the more priority should be given to training in that dimension. The formula is as follows: The root cause dimension is determined by the dimension with the highest influence score, and its weight is doubled in subsequent recommendations. If the difference in influence scores between two or more dimensions is ≤0.2, they are determined to be parallel root cause dimensions. The weights of all parallel root cause dimensions are multiplied by 1.5, and then the entire dimension is normalized to avoid imbalance in weight distribution.

[0042] S4. Based on deep reinforcement learning (DQN) and the student's six-dimensional ability vector, after constructing the DQN state space, experience replay sampling optimization and designing a reward function are performed. Then, the DQN weights are dynamically adjusted to obtain the dynamically adjusted six-dimensional recommendation weights. A multi-objective optimization intelligent recommendation algorithm module is constructed. S4.1 Based on the student's six-dimensional ability vector, the accuracy rate of answering questions after a preset number of attempts, the six-dimensional coverage of the recommended selected question set, and the current recommendation mode encoding, a 19-dimensional continuous feature vector is formed by concatenating them, and the state vector is output and a DQN state space is constructed. In this embodiment, the DQN state space is constructed as follows: the student's current six-dimensional ability vector (6-dimensional), the accuracy rate of the last 5 answers (5-dimensional), the six-dimensional coverage of the selected question set in this recommendation (6-dimensional), and the current recommendation pattern encoding (2-dimensional), for a total of 19 continuous features; S4.2. Define the DQN action space based on the state vector; Defined as the discrete adjustment direction of the six-dimensional weight vector, each dimension supports an adjustment step size of ±0.05, with a total of 12 basic actions. After adjustment, the weights are automatically normalized to ensure that the sum of the weights is 1. To prevent DQN from outputting extreme weight distributions in the early stages of exploration (such as a sudden change in the weight of a certain dimension to 0), a clipping protection mechanism is embedded in the action space, which forces that the minimum value of a single-dimensional weight must not be lower than 0.05, thus avoiding the problem of severe imbalance in recommended content caused by the dimension weights returning to zero.

[0043] S4.3 Based on the improvement of students' six-dimensional abilities and the weight of the current recommendation mode, a reward function is designed to output the DQN reward value; This invention defines the reward as a weighted sum of the six-dimensional ability improvement of students after completing the recommended questions. The weights are consistent with the current recommendation model, and the greater the ability improvement, the higher the reward value. During the data sampling phase of the Replay Buffer, to avoid GPU memory (OOM) overflow, the system adopts a block tensor loading strategy. Excessively long historical answer sequences are truncated using a sliding window with a maximum length of N=20, retaining only the valid state data from the user's most recent 20 answers. This significantly reduces the GPU memory usage per batch of sampling without losing core features. Simultaneously, the system sets up an invalid state interception rule. Abnormal state data where a user has not answered for more than three consecutive times or whose answer duration is less than 2 seconds are directly removed from the Replay Buffer, preventing noisy data from interfering with model convergence.

[0044] Validated by 100,000 real student answer sequences, compared with the fixed weight scheme, this dynamic adjustment strategy can improve recommendation accuracy by 18% and student ability improvement rate by 12%.

[0045] S4.4 Based on the DQN state space, DQN action space and reward function, the recommendation weight is updated after weight adjustment, and the dynamically adjusted six-dimensional recommendation weight is output to complete the multi-objective optimization intelligent recommendation algorithm. S5. Based on student ability vectors, dynamically adjusted six-dimensional recommendation weights, and candidate question bank, a personalized recommendation question set is output by constructing a recommendation objective function and a multi-objective optimization recommendation algorithm, thus completing the method of multi-dimensional objective optimization intelligent exercise recommendation system. The system of this invention uses a greedy algorithm to solve for the globally optimal recommended question set. The question set size supports dynamic adjustment from 10 to 30 questions. The solution process is as follows: First, initialize the selected question set to empty and calculate the objective function score of all candidate questions. Then, select questions in descending order of score and add them to the selected set. After each new question is added, recalculate the number of questions and the proportion of question types in each dimension of the selected question set, and update the coverage score and diversity score simultaneously. Then, recalculate the total objective function score of the remaining candidate questions based on the updated scores. Stop when the preset question set size is reached and output the final recommended question set.

[0046] To address the potential local optima issue that may arise during the iteration of the greedy algorithm, the system incorporates a secondary verification logic. This logic reviews the dimensional coverage of the final generated recommended question set. If the number of questions in a particular dimension does not reach 60% of the target number, the system automatically supplements the corresponding dimension with highly matched questions from the candidate question bank, ensuring the complete dimensional coverage of the recommended question set.

[0047] The recommended expression for the objective function is: The default weight configuration is as follows: , , , The weights sum to 1, and can be slightly adjusted according to the learning scenario.

[0048] The four core sub-items of the objective function have all been adapted and optimized for practical engineering applications: Six-dimensional matching score The formula for measuring the match between the questions and the students' abilities is as follows: Among them, the ability-difficulty difference vector ; These are the dimension weights, which must sum to 1 and can be dynamically adjusted according to the recommendation mode. For single-dimensional matching functions, three optional modes are provided: standard Gaussian mode for daily learning scenarios, linear decay fault-tolerant mode for students with weak foundations, and challenge-first mode for pre-exam reinforcement. The hyperparameters of each mode can be adapted according to the learning stage, with the parameter increasing by 0.2 for primary school stages and decreasing by 0.2 for high school competition stages, ensuring that the matching logic meets the needs of different learning stages.

[0049] The dimensional weights support four preset recommendation modes, which can be switched according to user needs, including a weakness-filling mode, an elite-level mode, an exam-preparation mode, and a well-rounded development mode. Mode switching adopts an exponential smooth transition to avoid recommendation fluctuations caused by sudden weight changes. The transition coefficient α is preset to 0.3, as shown in Table 2. Table 2: Recommendation Mode and Weight Configuration Table Dimensional Coverage Score The formula for measuring the coverage of each ability dimension by the recommended question set is as follows: in The dimensions examined in the selected questions The number of questions; For dimension The target number of questions to be covered is automatically set based on the skill gap. The larger the skill gap, the greater the target number of questions, as shown in Table 3. Table 3: Number of target questions corresponding to competency gaps Question type diversity score The diversity score measures the uniformity of the question type distribution and its match with the target in the recommended question set. Information entropy is used for calculation, and during the greedy question selection process, the diversity score is calculated based on the match between the preset target question type ratio and the distribution of currently selected questions. In a typical scenario, the question types cover five categories: multiple choice, fill-in-the-blank, problem-solving, proof, and application. The score is normalized to the [0,1] interval; a larger value indicates a higher match between the question type distribution and the preset target, and better diversity.

[0050] Repetition penalty score This measures the similarity between recommended questions and questions the user has previously answered. Higher similarity results in a greater penalty. The calculation formula is as follows: in For the title The maximum cosine similarity between the recommended question and the user's most recent 50 completed questions is used. If the recommended question and the historical question have the same ID, the similarity is set to 1.0 to ensure that questions that have already been completed are not pushed to the user repeatedly.

[0051] The system of this invention uses a greedy algorithm to solve for the globally optimal recommended question set. The question set size supports dynamic adjustment from 10 to 30 questions. The solution process is as follows: First, initialize the selected question set to empty and calculate the objective function score of all candidate questions. Then, select questions in descending order of score and add them to the selected set. After each new question is added, recalculate the number of questions and the proportion of question types in each dimension of the selected question set, and update the coverage score and diversity score simultaneously. Then, recalculate the total objective function score of the remaining candidate questions based on the updated scores. Stop when the preset question set size is reached and output the final recommended question set.

[0052] S6. Based on the six-dimensional difficulty vector of the questions and the six-dimensional ability vector of the students, the system calculates the six-dimensional difference vector of each question for each student by uploading the class homework question set through the teacher's terminal, performs many-to-many matching according to the preset distribution strategy, generates a personalized homework distribution plan for the whole class, and after the teacher confirms it, it is distributed to students through three channels: direct distribution through the learning terminal, sending PDF to the mobile phone, or printing through an external printer. This completes the group-level personalized homework distribution and the multi-dimensional target optimization intelligent exercise recommendation system method.

[0053] Teachers can submit class homework sets by taking photos, uploading in Word / PDF format, or directly entering the data. The system then calls the S1's six-dimensional difficulty automatic labeling model to perform real-time identification of the six-dimensional difficulty vector for each question.

[0054] The system extracts the six-dimensional ability vector set of all N students in the class and the six-dimensional difficulty vector set of M questions, which have been compiled by the teacher. For each question q, the six-dimensional difference vector is calculated between each student s. It reuses the root cause defect dimension information output by S2 to perform N×M many-to-many difference matching calculation, with a time complexity of O(N×M). In the standard scenario (N≤60, M≤50), the response time does not exceed 3 seconds.

[0055] The system outputs a personalized homework distribution preview table for the whole class based on the preset distribution strategy: by default, questions with extremely low training value for the student (the difference in each of the six dimensions does not exceed -1.0) are filtered out, and high-value questions that hit the root cause defect dimension are forcibly retained, with the total number of questions being about 60% to 80% of the uploaded questions; teachers can manually fine-tune any student-question combination in the preview table.

[0056] After the teacher confirms the distribution plan, the system distributes the assignments through the following three channels: (1) Direct distribution channel to learning terminals, which pushes the assignments directly to the "My Assignments" queue for students who have bound their terminals; (2) PDF mobile terminal channel, which generates personalized PDF files for students without terminals and sends them to their mobile terminals; and (3) External printer channel, which outputs paginated print files for scenarios without network access. After the students complete their answers, the system sends the answer data back to the S2 Bayesian capability update module, triggering the real-time update of each student's six-dimensional capability vector, thus forming a complete technical closed loop of distribution-answering-capability update.

[0057] To verify the feasibility of this invention, this embodiment takes the scenario of a junior high school student named Xiaoming learning to improve his math skills as an example to fully demonstrate the implementation process of this invention. All numerical values ​​can be reproduced and verified.

[0058] Xiaoming is a second-year junior high school student using this system for the first time. He has no prior answer data, so his ability vector is initialized using junior high school prior parameters. The system sends out five diagnostic questions covering six dimensions of ability. After Xiaoming completes the questions, the system uses gradient descent to calculate the Bayesian posterior probability based on the answers. After 100 iterations and convergence, it obtains Xiaoming's six-dimensional ability vector: Student comprehensive ability score This corresponds to level LV3.

[0059] Load the coupling weight matrix of junior high school mathematics subject, and calculate the out-degree centrality, ability gap, and influence scores for each dimension: Out-degree centrality: Capacity gap : , Total gap = 2.2 + 2.4 + 2.5 + 2.5 + 2.4 + 2.4 = 14.4; Influence Score ( ): C1: C2: C3: C4: C5: C6: Based on the maximum influence score, the root cause defect dimension is determined to be C2 (reading comprehension / condition mining).

[0060] Xiaoming chose the midterm review and gap-filling mode, and configured the dimension weights according to the rules: Initial gap weights (gap weights in each dimension / total gap, normalized and summed to 1.0): The root cause dimension C2 weights are doubled and then renormalized to obtain the final weights: Original weights after doubling Final normalized weights The objective function weights are dynamically adjusted using DQN. , , , Number of questions covered for each objective dimension: 4 for C2, 3 for C3 / C4, and 2 for C1 / C5 / C6.

[0061] Step 4: Calculation and Recommendation of Candidate Topic Matching Taking candidate question Q103 as an example, its six-dimensional difficulty vector is: Computational ability - Difference vector: Adopting a challenge-first mode ( , , The single-dimensional matching function value is calculated strictly according to the piecewise formula: C1: C2: C3: C4: C5: C6: Final matching function value: Calculate the six-dimensional matching score: Diversity Score Explanation: In the greedy question selection process of this invention, the diversity score is calculated based on the preset question type ratio target. The recommended target question set size is 15 questions, with a preset question type distribution of 3 multiple-choice questions, 3 fill-in-the-blank questions, 6 problem-solving questions, 2 proof questions, and 1 application question; Q103 is a problem-solving question, and its inclusion and the degree of matching with the target distribution are used to calculate the diversity score. This meets the pre-set requirements for question type distribution.

[0062] Calculate the total score of the multi-objective function: The currently selected question set is empty, and the coverage is... Repeatability ,therefore: A greedy algorithm was used to solve a recommended set of 15 questions. Question Q103 was the top recommended question with the highest matching degree. The system simultaneously generated the following recommendation reason: This question focuses on the root cause dimension C2 (reading comprehension / condition mining). The difficulty matches your ability by 71.5%. It is estimated that after completion, it can directly improve your C2 ability by about 0.10 points, and also improve your C5 ability by about 0.05 points and your C6 ability by about 0.04 points.

[0063] Xiaoming completed question Q103 with an actual score of 0.6. According to the Bayesian posterior update rule, the updated six-dimensional ability vector is: The C2 dimension capability improved from 2.6 to 2.81, consistent with the predicted improvement trend. The learning gain coefficient and coupling propagation attenuation coefficient used in this embodiment were optimized based on measured data from junior high school. The mean absolute error (MAE) between the actual capability improvement and the predicted value is ≤0.15, which conforms to the prediction trend and error range, verifying the effectiveness of the proposed invention.

[0064] This embodiment uses a math weekly test paper (20 questions in total) uploaded by Xiao Li, a science student in the second year of high school, as an example to demonstrate the complete implementation process of the homework test paper training value rating function of this invention.

[0065] Preliminary system diagnosis: Xiao Li's six-dimensional capability vector is: AXiaoLi = (3.2, 3.3, 3.1, 2.6, 3.0, 3.2) Overall ability score S A,i = (3.2+3.3+3.1+2.6+3.0+3.2) / 6 = 18.4 / 6 ≈ 3.07, corresponding to LV4 level.

[0066] Load the high school mathematics subject coupling weight matrix and calculate the out-degree centrality, ability gap, and influence scores for each dimension: Out-degree centrality: Centrality = (0.85, 1.40, 0.75, 1.10, 1.00, 0.90) Capacity gap (5) a _i,Ck Gap = (1.8, 1.7, 1.9, 2.4, 2.0, 1.8), Total Gap = 11.6 Influence Score (Gap × Centrality): C1: 1.8 × 0.85 = 1.53 C2: 1.7 × 1.40 = 2.38 C3: 1.9 × 0.75 = 1.43 C4: 2.4 × 1.10 = 2.64 C5: 2.0 × 1.00 = 2.00 C6: 1.8 × 0.90 = 1.62 Based on the maximum influence score, the root cause defect dimension is determined to be C4 (broadening thinking), with an influence score of 2.64. The difference between C4 (2.38) and the second-ranked C2 (2.38) is 0.26, which is greater than 0.2. Therefore, it is determined to be the only root cause dimension.

[0067] Weighting of dimensions in the gap-filling mode: Xiao Li chose the "focus on weaknesses" approach for final exam review, and configured the dimension weights according to the rules: Initial gap weights (gap in each dimension / total gap, normalized and summed to 1.0): w 0 = (1.8 / 11.6, 1.7 / 11.6, 1.9 / 11.6, 2.4 / 11.6, 2.0 / 11.6, 1.8 / 11.6) ≈ (0.155, 0.147, 0.164, 0.207, 0.172, 0.155) After doubling the weights of the root cause dimension C4, it is renormalized: The sum of the original weights after doubling is: 0.155 + 0.147 + 0.164 + (0.207 × 2) + 0.172 + 0.155 = 1.207 The final normalized weights w ≈ (0.129, 0.121, 0.136, 0.343, 0.143, 0.129), and the sum of weights = 1.001 (rounding error). The objective function weights were dynamically adjusted using DQN: α1=0.52, α2=0.24, α3=0.14, α4=0.10; Number of questions covered by each target dimension: 4 questions for C4 (largest gap), 3 questions for C3 / C5, and 2 questions for C1 / C2 / C6.

[0068] The complete grading process for the three representative questions is as follows; Question T03 (Basic Set Operations, Multiple Choice) - 1 Star: Six-dimensional difficulty vector D _T03 = (1.8, 2.0, 1.5, 1.2, 1.5, 1.8) Difference vector ΔC = D _T03 A _小李 : ΔC = (1.8 3.2, 2.0 3.3, 1.5 3.1, 1.2 2.6, 1.5 3.0, 1.8 3.2) = ( 1.4, 1.3, 1.6, 1.4, 1.5, 1.4); Partition determination: All six dimensions satisfy ΔC_k ≤ 1.0, triggering condition A of the first partition capability redundancy zone, is judged as 1 star.

[0069] Question T11 (Cicada sections, the final question, problem-solving) – 2 stars: Six-dimensional difficulty vector D _T11 = (4.5, 4.5, 3.5, 5.0, 5.0, 4.5) (all values ​​are in the range [0,5]); Difference vector ΔC = D _T11 A_Xiao Li: ΔC = (4.5 3.2, 4.5 3.3, 3.5 3.1, 5.0 2.6, 5.0 3.0, 4.5 3.2) = (+1.3, +1.2, +0.4, +2.4, +2.0, +1.3) Partition determination: (1) Exclude 1 star: The difference in each dimension is greater than Version 1.0 does not trigger the capability redundancy zone.

[0070] (2) 2-star check: C4 dimension ΔC4 = +2.4 ≥ +2.0; C5 dimension ΔC5 = +2.0 ≥ +2.0. There are 2 dimensions that meet the conditions, triggering the second partition cognitive overload zone condition A (at least two dimensions have a difference ≥ +2.0), and is judged as 2 stars.

[0071] Question T08 (New Contextual Problem in Solid Geometry, Problem Solving) – 5 stars: Six-dimensional difficulty vector D _T08 = (3.2, 3.5, 3.1, 3.8, 3.2, 3.3); Difference vector ΔC = D _T08 A _小李 : ΔC = (3.2 3.2, 3.5 3.3, 3.1 3.1, 3.8 2.6, 3.2 Versions 3.0 and 3.3 3.2) = (+0.0, +0.2, +0.0, +1.2, +0.2, +0.1) Partition determination: (1) Exclude 1 star: The difference in each dimension is greater than 1.0.

[0072] (2) Exclude 2 stars: No dimension difference ≥ +2.0, root cause dimension C4 difference 1.2<2.5, does not trigger cognitive overload zone.

[0073] (3) 4-star condition: C4 dimension ΔC4 = +1.2, satisfying the moderate challenge condition of +0.5 < ΔC4 ≤ +1.5; the differences of the other 5 dimensions are all within [ Within the range of 1.0, +0.5, all conditions for a 4-star rating are met.

[0074] (4) 5-star superposition condition: C4 is the root cause defect dimension, ΔC4 = +1.2 satisfies the root cause hit interval requirement; for the problem, the weight of C4 dimension is 0.343 ≥ 0.20, the root cause hit condition is fully satisfied, triggering the fifth partition root cause target area, and is judged as 5 stars.

[0075] Continuous scoring verification (confirming the highest score for the entire T08 paper) The matching function uses a challenge-first Gaussian model with parameters δ=0.8 and σ=0.6 (2σ²=0.72): f(ΔC _k ) = exp( (ΔC _k 0.8)² / 0.72) f-values ​​for each dimension: C1(ΔC=0.0):exp( 0.64 / 0.72) = exp( 0.889) ≈ 0.411 C2(ΔC=0.2):exp( 0.36 / 0.72) = exp( 0.500) ≈ 0.607 C3(ΔC=0.0):exp( (0.64 / 0.72) ≈ 0.411 C4(ΔC=1.2):exp( 0.16 / 0.72) = exp( 0.222) ≈ 0.801 C5(ΔC=0.2):exp( (0.36 / 0.72) ≈ 0.607 C6(ΔC=0.1):exp( 0.49 / 0.72) = exp( 0.681) ≈ 0.506; Weighted matching score: Score_match = 0.129×0.411 + 0.121×0.607 + 0.136×0.411 + 0.343×0.801 + 0.143×0.607 + 0.129×0.506 = 0.053 + 0.073 + 0.056 + 0.275 + 0.087 + 0.065 ≈ 0.609; Root cause reward: Bonus = 0.15 (root cause hit, indicator function value is 1) Total capability improvement: ImpactSum ≈ 0.25 (including direct improvement from C4 + coupled improvement from C5 / C6, normalized) Final score: TrainValue_T08 = 0.55×0.609 + 0.25×0.15 + 0.20×0.25 ≈0.335 + 0.037 + 0.050 = 0.422, ranking first in the entire test, confirming the validity of the 5-star rating.

[0076] Summary of the physical examination report for the whole paper (20 questions): 2 questions with 5 stars (T08 and T13, both of which hit the C4 root cause dimension), 6 questions with 4 stars, 8 questions with 3 stars, 3 questions with 2 stars (including T11), and 1 question with 1 star (T03). The average challenge level of the entire paper's C4 dimension is ΔC4 = +0.80 (moderately matched), and the C1 dimension's ΔC1 = 0.45 (Slightly Easy); The system predicts that completing all 5-star + 4-star questions (a total of 8 questions) will improve overall ability by 78% compared to completing the entire paper, and take approximately 42% of the time required for the entire paper. The efficiency gain from precise training is 1.86 times.

[0077] This embodiment uses the example of a junior high school math teacher, Mr. Wang, assigning homework on "quadratic functions" to all 50 students in his class to demonstrate the implementation process of the collaborative homework distribution module on the teacher's side of this invention.

[0078] Initial system conditions: 38 students have bound their learning terminals, and their six-dimensional ability vectors are automatically synchronized to the teacher's terminal; 12 students do not have terminals, and the teacher manually enters their six-dimensional scores according to the C1-C6 grading standards. The six-dimensional ability vectors of 50 students are summarized. Representative student data: Student S1 (LV5, top student): C=(4.2,4.5,3.8,4.0,3.9,4.1); Student S2 (LV3, average student): C=(2.8,2.5,2.6,2.9,2.4,2.7); Student S3 (LV1, weak student): C=(1.5,1.2,1.8,1.6,1.4,1.7).

[0079] Teacher Wang uploaded 10 homework questions by photo. The system called the S1 six-dimensional difficulty automatic annotation model to calculate the six-dimensional difficulty vector for each question. Representative questions: Q1 (basic formula, multiple choice) D=(1.2,1.0,1.1,0.9,1.0,1.1), LV1; Q5 (parabola intersection, problem-solving) D=(3.0,3.5,3.2,2.8,2.5,2.9), LV4; Q9 (final maximum / minimum value, proof) D=(4.0,4.2,4.5,3.8,3.5,4.0), LV5.

[0080] The system performed 50×10 many-to-many difference matching, taking approximately 1.8 seconds. Representative matching results: Q1's difference with S1 across all dimensions was ≤-1.0, filtered (extremely low training value for top students); Q5's difference with S2 across dimension C2 was 1.0, hitting the root cause deficiency dimension of S2 (reading comprehension), judged as high training value, and prioritized for retention; Q9's difference with S3 across all dimensions was ≥2.0, exceeding the effective training range, and filtered. The system generated a pre-distribution overview table. S1 received 7 challenging questions focusing on C3 / C4, S2 received 7 C2 reinforcement questions including Q5, and S3 received 7 basic consolidation questions. After Teacher Wang's confirmation, a three-channel distribution was triggered with one click: 38 students with terminals received the questions directly to their learning machines, and 12 students generated PDFs which were sent to their parents' mobile phones, with a total time of approximately 6.5 seconds.

[0081] The next day's response feedback showed that the C2 dimension capability of S2 improved from 2.5 to 2.68, with an error of 0.01 points compared to the system's predicted improvement (approximately 0.19 points). Within the MAE ≤ 0.15 accuracy range, this verified the effectiveness of personalized distribution on the teacher side in targeting and improving the root cause dimension.

[0082] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An intelligent exercise recommendation system and method based on multi-dimensional objective optimization, characterized in that, Includes the following steps: S1. Input the original question text data, and output the six-dimensional difficulty vector of the questions through the education big data model Qwen-7B and the regression model XGBoost to build an automatic six-dimensional difficulty labeling model for questions; S2. Based on the six-dimensional difficulty vector of the questions and the collection of student answer records, the six-dimensional ability vector of students is evaluated and output through the Bayesian joint inference algorithm, and the comprehensive ability score of students is calculated, thus constructing a six-dimensional ability evaluation module for students. S3. Collect anonymized student answer records, train the GAT coupling network by inputting it, output a preset dimension coupling weight matrix, define the coupling weight matrix, and obtain the subject coupling weight matrix. Based on the student's six-dimensional ability vector and subject coupling weight matrix, the influence score is calculated, the six-dimensional influence score is output, and the root cause dimension is determined to obtain the root cause defect dimension and priority weight, thus completing the root cause ability defect identification algorithm based on GAT. S4. Based on Deep Reinforcement Learning (DQN) and the student's six-dimensional ability vector, construct the DQN state space and action space, obtain the six-dimensional recommendation weights through dynamic adjustment, and construct a multi-objective optimization intelligent recommendation algorithm module. S5. Based on the six-dimensional student ability vector, the dynamically adjusted six-dimensional recommendation weights, and the candidate question bank, a personalized recommendation question set is output by constructing a recommendation objective function and a multi-objective optimization recommendation algorithm. S6. Based on the six-dimensional difficulty vector of the questions and the six-dimensional ability vector of the students, the system calculates the six-dimensional difference vector of each question for each student by uploading the class homework question set through the teacher's terminal, performs many-to-many matching according to the preset distribution strategy, generates a personalized homework distribution plan for the whole class, and distributes it to students through three channels: direct distribution through learning terminals, PDF mobile phone sending, or printing through external printers. This completes the intelligent exercise recommendation system method of group-level personalized homework distribution and multi-dimensional goal optimization.

2. The intelligent exercise recommendation system and method based on multi-dimensional objective optimization according to claim 1, characterized in that, S1 specifically includes the following steps: S1.1 Based on the original question text, structured question data is output through text cleaning and structured information extraction; S1.2 Based on structured question data, a 32-dimensional structured feature vector is output by extracting 32-dimensional features. S1.3 Based on structured question data, 96-dimensional semantic features are extracted by fine-tuning the Qwen-7B educational big data model, and a 96-dimensional semantic feature vector is output. S1.

4. Based on the 32-dimensional structured feature vector and the 96-dimensional semantic feature vector, a 128-dimensional question feature vector is obtained by concatenating them. By calling 6 independent XGBoost regression models and setting the model parameters, a six-dimensional difficulty vector of the question is output.

3. The intelligent exercise recommendation system and method based on multi-dimensional objective optimization according to claim 1, characterized in that, S2 specifically includes the following steps: S2.1 Based on the information of primary / junior high school / senior high school, the six-dimensional ability prior distribution parameters of primary / junior high school / senior high school are output by presetting prior parameters; S2.2 Based on student answer records and the six-dimensional difficulty vector of the questions, anomaly detection is performed after associating student answer records with the six-dimensional difficulty of the questions, and a weighted answer dataset is output. S2.

3. Define a comprehensive ability function based on the six-dimensional difficulty vector of the question; S2.4 Based on the six-dimensional ability prior distribution parameters, the weighted answer dataset, and the comprehensive ability function, the posterior probability distribution is constructed using Bayes' theorem, the maximum a posteriori estimate is solved using the gradient descent method, and dynamic updates are performed to output the student's six-dimensional ability vector and calculate the student's comprehensive ability score. The formula for calculating the student's comprehensive ability score is: in, For students In the Ability scores for each ability dimension Indexed for capability dimensions.

4. The intelligent exercise recommendation system and method based on multi-dimensional objective optimization according to claim 3, characterized in that, In S2.3, a comprehensive ability function is defined based on the six-dimensional difficulty vector of the question. The expression is: in, The weighting of each ability dimension is determined for different question types; For students In the Ability scores for each ability dimension Indexed for capability dimensions.

5. The intelligent exercise recommendation system and method based on multi-dimensional objective optimization according to claim 1, characterized in that, S3 specifically includes the following steps: S3.1 Collect anonymized student answer records, construct a six-dimensional ability change sequence as a training dataset, input a 2-layer GAT network for network training, output a 6×6 coupling weight matrix and define the coupling weight matrix to obtain the subject coupling weight matrix; S3.

2. Based on the student's six-dimensional ability vector and subject coupling weight matrix, calculate the degree centrality and ability gap, then calculate the influence score and output the six-dimensional influence score; based on the six-dimensional influence score, determine the root cause dimension, obtain the root cause defect dimension and priority weight, and complete the root cause ability defect identification algorithm based on GAT.

6. The intelligent exercise recommendation system and method based on multi-dimensional objective optimization according to claim 1, characterized in that, S4 specifically includes the following steps: S4.1 Based on the student's six-dimensional ability vector, the accuracy rate of answering questions after a preset number of attempts, the six-dimensional coverage of the recommended selected question set, and the current recommendation mode encoding, a 19-dimensional continuous feature vector is formed by concatenating them, and the state vector is output and a DQN state space is constructed. S4.

2. Define the DQN action space based on the state vector; S4.3 Based on the improvement of students' six-dimensional abilities and the weight of the current recommendation mode, a reward function is designed to output the DQN reward value; S4.4 Based on the DQN state space, DQN action space and reward function, the recommendation weights are updated after weight adjustment, and the dynamically adjusted six-dimensional recommendation weights are output to complete the multi-objective optimization intelligent recommendation algorithm.

7. The intelligent exercise recommendation system and method based on multi-dimensional objective optimization according to claim 1, characterized in that, In step S5, the expression for the recommended objective function is: In the formula, To pre-determine the weights of the six-dimensional matching score, Assuming predefined dimensional coverage score weights, To pre-determine the scoring weights for different question types, To pre-determine the penalty score weight for repetition, The six-dimensional matching score is used to determine the degree of matching. Score the dimensional coverage. To score points for the diversity of question types, The score is a penalty for repetition.

8. The intelligent exercise recommendation system and method based on multi-dimensional objective optimization according to claim 1, characterized in that, S6 further includes: calculating the six-dimensional difference vector ΔC = D(q) - C(s) between each question and the student based on the six-dimensional difficulty vector D(q) output by S1 and the six-dimensional ability vector C(s) output by S2; and assigning a training priority label of 1 to 5 stars to each question according to the following five-category partitioning rules: 1 star represents the ability redundancy zone: the difference in all dimensions does not exceed -1.0, or the overall difficulty score of the question is more than 1.2 points lower than the student's overall ability score; 2 stars indicates cognitive overload: there are at least two dimensions with a difference of not less than +2.0, or the root cause defect dimension has a difference of not less than +2.5; 3-star as the base maintenance zone: all dimensional differences satisfy -1.0 to +0.5, and the root cause hit condition is not triggered; 4 stars represents a moderate challenge zone: there are 1 to 2 dimensions with differences ranging from +0.5 to +1.5, and the remaining dimensions with differences ranging from -1.0 to +0.5; 5 stars represent the root cause target area: In addition to meeting all the conditions for 4 stars, the difference in the root cause defect dimension is between +0.5 and +1.5, and the weight of the corresponding root cause dimension for this question type is not less than 0.20; Based on the above 1 to 5 star rating, the system filters 1-star questions, downgrades 2-star questions, prioritizes 4-star and 5-star questions, outputs a set of questions with high training value, and generates a comprehensive examination report.

9. The intelligent exercise recommendation system and method based on multi-dimensional objective optimization according to claim 3, characterized in that, In S2.4, the specific implementation of determining the LV level and corresponding color through mapping rules based on the student's comprehensive ability score is as follows: The system establishes a one-to-one mapping table between nine difficulty levels from LV0 to LV8 and a color system. Each LV level is strongly bound to a color and stored. The color system is used to visualize various application scenarios, including the question difficulty radar chart, the student ability radar chart, and the recommended question set display interface. The color mapping rules follow the principle of minimizing cognitive load: low difficulty levels LV0-LV2 use gray, white, and green to match users' psychological expectations for low-threshold content; medium difficulty levels LV3-LV5 use neutral colors such as blue, purple, and cyan to represent a moderately challenging range; and high difficulty levels LV6-LV8 use gold, orange, and black to indicate high cognitive load content. When the system displays the question radar chart and the student ability radar chart side by side, it uses color differences to intuitively present the gap between ability and difficulty, allowing users to complete the difficulty identification through visual signals without interpreting numerical values. This reduces the difficulty level identification time to less than 0.3 seconds, achieving an engineered reduction in cognitive load.

10. A multi-dimensional objective optimization-based intelligent exercise recommendation system, characterized in that, include: (1) The six-dimensional difficulty automatic labeling module is used to input the original question text data into S1 and output the six-dimensional difficulty vector of the question through the education big model Qwen-7B and the XGBoost regression model; (2) Student six-dimensional ability assessment module, which is used by S2 to assess and output the student's six-dimensional ability vector based on the six-dimensional difficulty vector of the question and the collected student answer record data through the Bayesian joint inference algorithm; (3) Root cause ability deficiency identification module, used by S3 to collect desensitized student answer record data, obtain subject coupling weight matrix through graph attention network GAT training, calculate influence score based on student six-dimensional ability vector and subject coupling weight matrix and determine root cause dimension, and obtain root cause deficiency dimension and priority weight. (4) Multi-objective optimization recommendation module, which is used by S4 to construct the DQN state space and action space based on deep reinforcement learning DQN and the student's six-dimensional ability vector, and obtain the six-dimensional recommendation weights through dynamic adjustment; (5) Personalized recommendation question set generation module, which is used by S5 to output personalized recommendation question sets by constructing a recommendation objective function and a multi-objective optimization recommendation algorithm based on the student's six-dimensional ability vector, dynamically adjusted six-dimensional recommendation weights and candidate question bank; (6) The teacher-side collaborative homework distribution module is used by S6 to receive the class homework question set uploaded by the teacher, call the question six-dimensional difficulty automatic labeling module to complete the six-dimensional difficulty identification of each question, combine the six-dimensional ability vector of the whole class of students output by the student six-dimensional ability assessment module, perform many-to-many six-dimensional difference matching calculation, output the whole class personalized homework distribution preview table according to the star filtering rules, and after the teacher reviews and confirms, perform multimodal distribution through the three channels of learning terminal, PDF and printer, and send the students' answer results back to the Bayesian ability update module to form a closed loop of distribution-answer-ability update.

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