A job correction and learning diagnosis method based on error cause label

Abstract

This invention discloses a homework correction and learning diagnosis method based on error cause labels. In the structured modeling of questions, this invention simultaneously binds each scoring point to a set of error cause instances and a set of knowledge point nodes in a many-to-many relationship. A serial hybrid error cause matching engine, comprising three sub-modules—rule matching, model matching, and post-rule validation—matches error cause labels to the problem-solving steps, achieving strict alignment with teaching rules. Based on students' historical error cause sequences, the error cause transition probability matrix P(i,j) is estimated using Laplace smoothing, formally modeling the transmission law between error causes. In the recommendation stage, the expected error rate e of candidate questions is estimated, and only questions with α≤e≤β are selected as recommendation results, achieving adaptive difficulty. This invention significantly improves the accuracy of error cause matching and consistency with teaching rules, expands the dimensions of learning diagnosis, and makes the difficulty of personalized recommendations quantifiable and controllable.

Description

Technical Field

[0001] This invention relates to the fields of educational informatization and artificial intelligence, specifically to a method for homework correction and learning diagnosis based on error cause labels, applicable to intelligent homework correction, learning diagnosis, and personalized practice recommendation scenarios in primary and secondary schools and higher education institutions across various subjects. Background Technology

[0002] With the development of educational information technology, automatic homework grading and learning diagnosis systems have been widely introduced into classroom teaching and home learning scenarios. Existing solutions can be broadly categorized as follows:

[0003] The first type is an automated grading scheme for objective questions. It compares student answers with standard answers at the character or structural level to determine whether they are correct or incorrect and assigns a score. This type of scheme has a high accuracy rate for objective questions, but it cannot handle process-based questions or reveal the reasons behind errors.

[0004] The second category is solutions based on Large Language Models (LLM) for error analysis of student responses. These solutions typically construct a context containing question information, standard answers, and problem-solving strategies, and then input this context into the LLM, combined with hint engineering. The LLM then outputs the error analysis results for the student's responses in one go. This type of solution has advantages in the natural language expression of error descriptions, but it has three main drawbacks: First, the LLM-generated results lack a controllable labeling structure, making it difficult to establish a stable interface with downstream learning diagnosis and recommendation systems; second, the interpretability of error generation depends on the model itself, lacking a correction mechanism when the results conflict with teaching rules; and third, error generation requires high computational power for reasoning, making it unsuitable for large-scale concurrent scenarios.

[0005] The third type is based on knowledge graphs and knowledge tracing models (such as BKT, DKT, and DKVMN) to model students' learning progress and provide recommendations for weak knowledge points. This type of solution only diagnoses at the level of "knowledge point mastery," failing to differentiate whether a student's error on the same question stems from different reasons such as a lack of knowledge, misunderstanding of concepts, inappropriate thinking methods, incorrect problem-solving strategies, careless calculations, or improper expression. Therefore, it is difficult to provide targeted feedback and intervention.

[0006] The fourth category is a scheme that matches error causes based on an error cause classification system combined with an error pool or error sample database. Although this type of scheme introduces the concept of error cause classification, it usually has the following shortcomings: First, error cause classification exists only in the form of a static classification tree, with each error cause being independent of the others, and it cannot depict the transmission pattern of error causes across knowledge points and question types; second, error cause matching is performed at the question level, and it cannot locate the specific problem-solving steps; third, personalized recommendations often use "knowledge point similarity + difficulty level" or simply "error cause relevance" as the basis for recommendations, lacking prior estimation of the student's expected error rate on the question, which can easily lead to recommendations that are too difficult or too easy.

[0007] In summary, existing solutions still have significant gaps in the following four specific technical dimensions:

[0008] (a) At the level of question structure modeling, a stable many-to-many binding structure is not formed between scoring points, error cause instances, and knowledge graph nodes, making it difficult to synchronize error cause matching and knowledge point diagnosis;

[0009] (b) At the error matching engine level, there is a lack of implementation methods that unify rule-based precise matching, model-based generalized matching, and rule-based post-validation within the same serial architecture. This results in poor generalization of single rule solutions, poor interpretability of single model solutions, and potential conflicts with teaching rules.

[0010] (c) At the level of learning situation modeling, there is a lack of formal modeling of the transmission rules between error causes, and it is impossible to identify the correlation pattern of "students making error cause j again after making error cause i";

[0011] (d) In terms of personalized recommendation, there is a lack of a mechanism to use "expected error rate" as a constraint for selecting recommended topics, and there is a lack of quantifiable criteria for adaptive recommendation difficulty.

[0012] To address the aforementioned gaps, this invention provides a method for homework correction and learning diagnosis based on error cause labels, thereby resolving the aforementioned technical problems. Summary of the Invention

[0013] The purpose of this invention is to address the four technical gaps in the existing technology by providing a homework correction and learning diagnosis method based on error cause labels, so as to achieve fine-grained automatic correction of homework, formal modeling of the transfer patterns of students' error causes, and controllable difficulty of personalized practice recommendations.

[0014] To achieve the above objectives, the present invention adopts the following technical solution:

[0015] A method for homework correction and learning diagnosis based on error cause labeling includes the following steps:

[0016] Step S1: Construct an error cause tag library and a subject knowledge graph; the error cause tag library consists of several error cause instances, each error cause instance including an error cause instance number, error cause description text, and error cause attributes; the subject knowledge graph consists of several knowledge point nodes and the relationships between nodes;

[0017] Step S2: Perform structured modeling on the questions to be graded to generate structured question data; in the structured question data, the questions are divided into several scoring points, and each scoring point is simultaneously bound to: (i) a set of error cause instances in the error cause tag library; (ii) a set of knowledge point nodes in the subject knowledge graph; and the relationship between scoring point-error cause instances and scoring point-knowledge point nodes is a many-to-many relationship;

[0018] Step S3: Obtain student answer data, convert it into structured electronic answers, and use the positions of the scoring points mentioned in Step S2 as initial segmentation boundary candidates. Fine-tune the initial segmentation boundary candidates using a deep learning step boundary detection model to obtain the student's answer step sequence.

[0019] Step S4: Using a serial hybrid error cause matching engine that includes a rule matching submodule, a model matching submodule, and a rule post-validation submodule, error cause label matching is performed for each problem-solving step. The matching process includes:

[0020] (a) Symbolically compare the problem-solving steps with the standard steps for the corresponding scoring points to generate step difference items;

[0021] (b) Input the step difference item into the rule matching submodule. The rule matching submodule performs precise matching according to the preset difference pattern-error cause mapping rule. If the rule is hit and the rule matching confidence is greater than the first threshold T1, the error cause instance of the rule matching is directly used as the error cause label of this step, and the process ends.

[0022] (c) If the rule matching fails or the rule matching confidence is not greater than the first threshold T1, then proceed to the model matching submodule; the model matching submodule uses a trained error cause classification neural network model to predict the error causes of the step difference items, and outputs candidate error cause instances and their confidence levels;

[0023] (d) Input the candidate error cause instances output by the model matching submodule into the rule post-validation submodule. The rule post-validation submodule validates the candidate error cause instances according to a preset set of error cause validity constraint rules. If a candidate error cause instance conflicts with the prohibition condition of a certain validation rule, the candidate error cause instance is invalidated, and the error cause instance is corrected according to the correction condition of the validation rule before being output. If there is no conflict, the candidate error cause instances from model matching are directly used.

[0024] Step S5: Generate question-level grading results based on step-level error cause tags. The question-level grading results include at least the question score, a summary of error cause tags, the location of key error steps, a list of associated weak knowledge points, and explanatory error cause feedback text.

[0025] Step S6: Estimate the error transition probability matrix P based on the student's historical error sequence. The error transition probability matrix P is an N×N matrix, where N is the number of error instances. Elements P(i,j) are estimated using the formula P(i,j) = (C(i→j) + λ) / (C(i) + λ × N), where C(i→j) represents the frequency of error j immediately following error i in the student's historical error sequence, C(i) represents the total frequency of error i, and λ is the Laplace smoothing coefficient, with a default value of λ = 1. The error transition probability matrix P is used to characterize the transmission patterns between errors in scenarios involving different knowledge points and question types.

[0026] Step S7: Based on the error cause transition probability matrix P, the current error cause label set, and the student's historical error cause frequency, determine the diagnostic result containing at least one error cause transmission chain and at least one high-frequency error cause. The diagnostic result is output in the form of visualization or structured data.

[0027] Step S8: Select candidate questions from the candidate question bank that satisfy α ≤ e ≤ β as the recommendation result output, where e is the expected error rate estimated in advance for each candidate question, and α and β are system-level configurable parameters with default values ​​of α = 0.3 and β = 0.5.

[0028] Further, in step S8, the estimation formula for the expected error rate e of the candidate question is: e = 1 − ∏(m∈M) σ(θ − b_m + γ_m × η). Where M is the set of error instances [that the student has not overcome] in the preset set of error instance sets at the scoring point corresponding to the candidate question; b_m is the question difficulty parameter corresponding to error instance m; θ is the student's current ability value (taken from item response theory (IRT) estimation or ability value estimated based on the Bayesian knowledge tracing (BKT) model); γ_m is the stability coefficient of error instance m for the student; η is the time decay factor; σ(·) is the Sigmoid function; ∏ represents the product of all error instances in M.

[0029] Furthermore, in step S4, the input of the error cause classification neural network model is the concatenation vector of the symbolic vector of the step difference item and the encoding vector of the candidate set of error cause instances corresponding to the question scoring point, and the output is the probability distribution on the candidate error cause instances; during the training phase, the error cause labels manually annotated by the teacher are used as supervision signals; during model inference, the candidate error cause instances are selected from the preset set of error cause instances corresponding to the scoring point, thereby forming a natural constraint on the model output space.

[0030] Furthermore, the method also includes step S9: teacher feedback closed loop; the request for teacher feedback is initiated only when any of the following conditions are met: (i) the final confidence of the error cause matching engine is lower than the set threshold T2; (ii) the error cause transition probability matrix P changes by more than a preset magnitude within the most recent time window; (iii) the stability coefficient of the same error cause instance on the student exceeds the preset threshold and no improvement trend is observed; the teacher feedback is incorporated into the training sample library of the error cause classification neural network model and the rule post-validation rule set for iterative optimization.

[0031] It should be noted that although the error cause transition probability matrix P described in this invention is formally isomorphic to a first-order Markov chain, it differs fundamentally from a general Markov chain in the following two aspects: First, the state space of a general Markov chain is usually composed of user behavior or system state, while the state space described in this invention is composed of error cause instances, and each error cause instance forms a many-to-many binding with the subject knowledge graph. This makes P not only represent the probability transition between states but also implicitly contain the semantic transmission between knowledge points behind the error cause. Second, the output of a general Markov chain is usually used for single-step prediction, while this invention uses P to further define the transmission chain strength S(i→j→k) = P(i,j) × P(j,k) and uses the transmission chain as the basis for teaching intervention decisions. In addition, compared with the existing knowledge tracing DKT / DKVMN model, the error cause profiling described in this invention outputs the transition rules and error cause transmission chains between error causes, while the latter outputs the mastery probability of knowledge points. The two are fundamentally different in the objects being modeled, and the output of this invention can be used simultaneously for dual-layer diagnosis at the error cause layer and the knowledge point layer.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] First, by simultaneously binding the error cause instance set and the knowledge graph node set to the scoring point in a many-to-many structure, this invention enables error cause matching and knowledge point diagnosis to form a stable interface at the question structure level, avoiding the loss of diagnostic information caused by incomplete interfaces in the existing "modeling separately and then fusing" scheme.

[0034] Second, through a serial hybrid error cause matching engine of "rule matching + model matching + rule post-validation," this invention retains the high interpretability of the rule-based scheme while introducing the generalization ability of the model-based scheme. The rule post-validation submodule ensures the consistency between the model output and the teaching rules, overcoming the problem of existing schemes based on large language models being "difficult to strictly align with the teaching rules" in error cause generation. Experiments show that this hybrid matching engine improves the error cause matching recall rate by about 18% compared to the single rule scheme; and improves the error cause matching accuracy by about 9% compared to the single neural network model scheme, while eliminating the output that conflicts between the model and the teaching rules.

[0035] Third, by formally modeling the transmission pattern between error causes using the error cause transfer probability matrix P(i,j), this invention can identify the error cause transmission chain of students in cross-knowledge point and cross-question type scenarios, thus breaking through the traditional paradigm of the single dimension of "knowledge point mastery" in the dimension of learning assessment; on the experimental dataset of mathematics, the diagnostic report based on the error cause transmission chain has a prediction accuracy rate of about 13.3 percentage points higher for the effect of teachers' next round of teaching intervention than the diagnostic report based solely on knowledge point mastery.

[0036] Fourth, by introducing the filtering constraint of [expected error rate α ≤ e ≤ β] during the content recommendation selection stage, this invention provides a quantifiable criterion for the adaptive difficulty of personalized practice recommendations, avoiding recommendations that are too difficult or too easy. Experiments on a junior high school math word problem dataset show that, with the setting of [α, β] = [0.3, 0.5], the proportion of students whose actual error rate on the recommended questions falls within the range exceeds 76%, and the recurrence rate of students making the same mistakes within 7 study days decreases by approximately 31% compared to the recommendation scheme without this constraint.

[0037] Fifth, through a condition-triggered teacher feedback loop, this invention significantly reduces the feedback burden on teachers. While ensuring the quality of model iteration, it reduces the proportion of error annotations requiring teacher intervention from the total number of annotations to approximately 8%-15% of key annotations. Attached Figure Description

[0038] Figure 1 is a schematic diagram of the overall process of the homework correction and learning diagnosis method based on error cause labeling according to an embodiment of the present invention;

[0039] Figure 2 is a schematic diagram of the many-to-many binding structure of scoring points, error cause instances, and knowledge graph nodes in the structured modeling of questions according to an embodiment of the present invention;

[0040] Figure 3 is a schematic diagram of the workflow of the serial hybrid error matching engine (rule matching + model matching + rule post-validation) according to an embodiment of the present invention;

[0041] Figure 4 is a schematic diagram of the error cause transition probability matrix P(i,j) and the error cause propagation chain derived therefrom according to an embodiment of the present invention;

[0042] Figure 5 is a schematic diagram of the error cause-oriented recommendation process based on expected error rate constraints according to an embodiment of the present invention;

[0043] Figure 6 is a schematic diagram of the condition-triggered teacher feedback closed loop according to an embodiment of the present invention;

[0044] Figure 7 is a schematic diagram of the hardware and module architecture of the system described in an embodiment of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. Key variables and terminology definitions

[0046] To facilitate understanding of this invention, the key variables and terms used in the specification and claims are defined as follows:

[0047] Error Cause Instance: A complete record in the error cause tag library, uniquely identified by the error cause instance number (e.g., E201, E402, etc.). Each error cause instance contains the error cause instance number, error cause description text, and error cause attributes (optional attributes include the nature of the error cause, the applicable question type, and the set of related knowledge point nodes, etc.).

[0048] Error Cause Label: This refers to the labeling of errors made by a student in a specific step of their problem-solving process, using the error cause instance number as the carrier. In other words, the "error cause label" is the annotation result of errors found during the student's answer process, and the "error cause instance" is the specific entry in the label library referenced by that annotation. In this manual, all scenarios involving the annotation of errors in the student's answer steps will uniformly use the "error cause label"; all references to specific entries in the label library will uniformly use the "error cause instance".

[0049] Derived error factors: Defined as a derived form of error factor instance X, denoted as DX. When an upstream scoring point has been labeled with an error factor instance X, items in the downstream scoring point that should have been labeled as operational error factors (such as E303 coefficient simplification error) are rewritten as derived error factors DX (representing "operation under the premise of error") by the rule post-validation submodule. Derived error factors exist as independent entries in the error factor tag library, and their error factor instance numbers are composed of the prefix "D-" plus the original error factor instance number. In the statistics of the error factor transition probability matrix P, derived error factors DX and their original error factors X can be counted together (to reduce data sparsity) or counted independently (to retain finer error factor propagation granularity). The specific merging method is a system-level configurable option, and the default is to use merged counting.

[0050] Stability coefficient γ_m: Used to characterize the recurrence of a student's error instance m. It is defined as the proportion of times error m is actually marked in the student's most recent k answers to questions involving error m, with a value range of [0, 1]; the default window length k = 10. When γ_m is closer to 1, it indicates a higher probability that the student will repeatedly make the same error; when γ_m is close to 0, it indicates that the student has essentially stopped making the same error.

[0051] The time decay factor η is used to characterize the current activity level of error m over time. It is defined as an exponential decay form: η = exp(−τ × Δt / k), where Δt is the time interval (in study days) between the student's most recent occurrence of error m and the current moment, and τ is the time decay constant, with a default value of 0.1. When Δt is small (the error has just occurred), η is close to 1; as Δt increases, η gradually decays, indicating that the influence of the error weakens over time.

[0052] First threshold T1: The rule matching submodule directly uses the lowest confidence threshold of the rule results, with a default T1 = 0.85.

[0053] Teacher feedback trigger threshold T2: When the final confidence of the error cause matching engine is lower than this threshold, the teacher feedback request is initiated. The default T2 = 0.7.

[0054] Error propagation chain strength threshold ε: The lower limit of strength required to identify a significant error propagation chain, with a default value of ε = 0.01. Example 1: Implementation process of the core method

[0055] This embodiment uses a middle school mathematics application problem involving a system of two linear equations in two variables as an example to illustrate in detail the implementation process of the method described in this invention.

[0056] Problem: A store purchased 100 items of two types of goods, A and B, for a total cost of 1200 yuan. Each item of goods A costs 10 yuan, and each item of goods B costs 15 yuan. How many items of each type of goods were purchased?

[0057] Step S1 Implementation Process: The error cause tag library and subject knowledge graph used in this embodiment are constructed as follows. The error cause tag library consists of several error cause instances E001, E002, ..., and each error cause instance is stored according to the structure described in

[0047] . The error cause nature optional attribute categories in the error cause instance attributes include at least several categories from "knowledge mastery", "thinking method", "problem-solving skills", "expression norms", and "learning attitude", but the number and naming of the categories do not constitute necessary features of the technical solution of this invention. The subject knowledge graph consists of knowledge point nodes K001, K002, ... and their hierarchical / preceding relationships.

[0058] Step S2 Implementation Process: The question is structured and modeled. An example of the structured data is shown in the table below, illustrating the many-to-many binding between scoring points, the set of error cause instances, and the set of knowledge graph nodes. Scoring points, scoring point descriptions, preset error cause examples, set of related knowledge graph nodes. SP1 Define unknowns E101 (no variable defined), E102 (unclear meaning of the defined variable), E103 (missing unit of the defined variable). K201 (variables and unknowns), K205 (modeling for application problems). SP2 Equation system: E201 (missing constraints), E202 (reversed equation direction), E203 (misinterpretation of quantitative relationships), K301 (two linear equations in two variables), K302 (construction of the equation system), K205 SP3 Solve the system of equations: E301 (Incorrect direction of elimination), E302 (Incorrect transposition sign), E303 (Incorrect coefficient simplification), K401 (Substitution elimination), K402 (Addition and subtraction elimination), K403 (Integer arithmetic operations). SP4 Verification and Response: E401 (Reasonableness of solution not verified), E402 (Missing response), E403 (Missing unit), K501 (Practical significance of solution), K502 (Standardized mathematical expression).

[0059] As shown in the table above, each scoring point is bound to multiple error cause instances, and each error cause instance can be bound to one or more knowledge graph nodes; conversely, the same knowledge graph node (such as K205) can be bound to error cause instances on multiple scoring points simultaneously, thus forming a many-to-many structure. This structure enables error cause matching and knowledge point diagnosis to form a stable interface at the question structure level.

[0060] Step S3 Implementation Process: Students upload photos of their assignments taken with a tablet. The system uses a combination of OCR, HWR, and formula recognition to obtain the electronic answers. When segmenting the problem-solving steps, the positions of scoring points SP1~SP4 in the structured data of the question are used as initial candidate segmentation boundaries. These initial candidate boundaries are then fine-tuned using a deep learning step boundary detection model. The step segmentation results for a student's answer are as follows: Step 1: "Solution: Let x be the number of units of product A and y be the number of units of product B" → Align to SP1; Step 2: "10x + 15y = 1200" → Align to SP2; Step 3: "Solve for x = 60, y = 40" → Align to SP3; SP4 is missing (the student did not provide any verification or response).

[0061] Step S4 Implementation Process: Start the serial hybrid error matching engine for each step.

[0062] (a) Initiating error matching in step two, symbolic comparison revealed that the student's answer contained only one equation, missing the constraint equation "x + y = 100".

[0063] (b) The rule matching submodule queries the difference pattern-error cause mapping rule base and hits rule R023: "When setting up the equation, the total constraint implied by the problem was missed → E201 (constraint condition missing)". The rule matching confidence is 0.95, which is greater than the first threshold T1 = 0.85. Therefore, E201 is directly used as the error cause label in step two, and the process ends.

[0064] (c) Initiate error cause matching for step three, with the difference term being "operations performed under incorrect premises". The rule matching submodule did not find an exact matching rule, so it proceeds to the model matching submodule. The model matching submodule performs error cause prediction on the difference term and outputs candidate error causes E303 (coefficient simplification error) with a confidence level of 0.62 and E302 (transposition sign error) with a confidence level of 0.58.

[0065] (d) Candidate error factors E303 and E302 enter the rule post-validation submodule. The rule post-validation submodule queries the error factor validity constraint rule set and matches the validation rule V008: "If the upstream scoring point of this step has been marked with error factor E201 (missing constraint), then the operational error factors of the downstream step (such as E303 and E302) should be marked as derived error factor D-201 (operation under incorrect premise), rather than independent operational error factors." Therefore, E303 and E302 output by the model matching are determined by the validation submodule to conflict with the rule, are invalidated, and corrected to derived error factor D-201.

[0066] (e) Initiate error cause matching for the missing SP4. The rule matching submodule directly hits rule R045: "Answer to the problem is completely missing → E402 (Answer missing)", with a confidence level of 0.99, and uses it as the error cause label for this step.

[0067] Besides rule V008 (which is a type of rule that corrects the corresponding error cause in the downstream scoring point to a derived error cause when the upstream scoring point has already been labeled with a specific error cause instance), the above set of error cause validity constraint rules typically also includes the following two types of rules: (i) Rules for mutually exclusive errors that do not occur simultaneously. Example: If the model matching submodule outputs both E101 (no set element) and E102 (unclear set element meaning) for the SP1 score point, since the two are semantically mutually exclusive (without a set element, there is no "set element meaning" problem), the post-validation rule V003 is hit, retaining the one with higher confidence and deleting the other; (iii) The rule that the knowledge points associated with the error cause must be included in the knowledge point set bound to the scoring point. Example: If the model matching submodule outputs error cause E303 (coefficient simplification error) for the SP2 scoring point, but the associated knowledge point of E303 is K403 (integer arithmetic operations), while the knowledge point set bound to the SP2 scoring point is {K301, K302, K205}, which does not include K403, the post-validation rule V012 determines that the associated knowledge points of this error cause do not match and invalidates the error cause. This rule ensures that the error causes output by the model are consistent with the knowledge point bindings of the question scoring points, avoiding the model making predictions on error cause instances unrelated to the scoring point.

[0068] Step S5 Implementation Process: The final set of error cause labels for this question is {E201, D-201, E402}, with a score of 4 points (out of 10); the explanatory error cause feedback text is generated from the error cause instance description template.

[0069] Step S6 Implementation Process: The system writes the current error causes E201 and E402 into the student's historical error cause sequence; the derived error cause D-201 is counted by default as described in

[0049] in this embodiment, that is, it is included in the count as the occurrence event of E201. Assume that the frequency statistics of the student's historical error cause sequence in the past 8 weeks are as follows: Error i C(i) Error j C(i→j) E201 (Missing Constraint) 12 E402 (Missing Response) 7 E201 12 D-201 (Derivation operation error) 9 E201 12 Others Total 12 E402 10 E201 5 Given the number of error cases N = 80 and the smoothing coefficient λ = 1, substituting these values ​​into the estimation formula in step S6 yields: P(E201 → E402) = (7 + 1) / (12 + 1 × 80) = 8 / 92 ≈ 0.087; P(E201 → D-201) = (9 + 1) / (12 + 80) = 10 / 92 ≈ 0.109.

[0070] Given the large total number of error cases and the sparse historical data for a single student, the absolute value of P(i,j) may seem low. However, by comparing its relative rank with all error cases occurring after E201 for that student, E402 can be identified as one of the most frequent error cases after E201. Therefore, this invention typically uses the relative rank of P or a defined conduction chain strength threshold ε for determination, rather than directly using an absolute value threshold.

[0071] Furthermore, for the candidate conduction pathway E201 → D-201 → E402, the pathway strength is S = 0.109 × P(D-201 → E402). If P(D-201 → E402) ≈ 0.12, then S ≈ 0.013, which is greater than the student's pathway strength threshold ε = 0.01. Therefore, this pathway is considered significant and included in the diagnostic results.

[0072] Step S7 Implementation Process: The learning and diagnosis module outputs diagnostic results based on this, and the core conclusion is: • This student frequently made the error E201 (missing constraint). • Significant error propagation chain: E201 → D-201 → E402, meaning that "missing constraints" will further lead to subsequent calculation errors and the final missing answer; • Recommended learning path: Prioritize correcting E201 → Simultaneously focus on the expression norms and habits of E402.

[0073] Step S8 Implementation Process: The error-cause-oriented recommendation engine selects candidate questions from the question bank in the following manner. Assuming there are 50 questions related to K205 (application problem modeling) in the candidate question bank, the expected error rate e_k is estimated for each question Q_k. Taking a question with difficulty parameter b_m = 0.6, stability coefficient γ_m = 0.4, student ability value θ = 0.5, and time decay factor η = 1.0 as an example: σ(θ − b_m + γ_m × η) = σ(0.5 − 0.6 + 0.4 × 1.0) = σ(0.3) ≈ 0.574; Assuming the candidate question involves only one target error factor (i.e., |M| = 1), then e ≈ 1 − 0.574 = 0.426; Since e ≈ 0.426 falls within [α, β] = [0.3, 0.5], this candidate topic is selected for the recommendation results.

[0074] Regarding the above-mentioned expected error rate formula, this embodiment further illustrates the processing logic for three boundary cases: Scenario 1: M = ∅. When the set of error instances that the student has not overcome is empty in the preset error instance set corresponding to the scoring point of the candidate question, according to mathematical convention, the empty product equals 1, therefore e = 1 − 1 = 0. The system determines that the question is a question that the student has already mastered and directly removes it from the candidate queue, without entering the expected error rate screening.

[0075] Scenario 2: e > β. When the expected error rate of a candidate question exceeds the upper bound of the interval, the question is judged as "too difficult at the current stage" and will not be included in the recommended results. However, the system retains the question in the "prospective question pool" and will re-evaluate it after the student overcomes some of the error factors in M. At that time, |M| will decrease, and e will usually decrease. The question may be included in the recommended results in a future round of evaluation.

[0076] Case 3: e < α. When the expected error rate of a candidate question is lower than the lower bound of the interval, the question is judged as "too easy" and directly removed from the recommendation queue to avoid invalid practice.

[0077] Through the above boundary processing logic, this invention ensures that the recommendation results retain only questions that are challenging yet achievable for the student's current learning status.

[0078] After performing the same estimation on all candidate questions, only questions with e ∈ [0.3, 0.5] are retained as the final recommendation result, thereby avoiding pushing questions that are too difficult or too easy.

[0079] Step S9 Implementation Process: Teacher Feedback Trigger Judgment. In this error annotation process, the rule matching confidence level in Step 2 is 0.95, the rule post-validation in Step 3 has been corrected, and the rule matching confidence level in Step 4 is 0.99. All of these are not lower than the teacher feedback trigger threshold T2 = 0.7, and the error cause transition probability matrix P has not changed by more than 5% in the most recent time window. There are also no cases where the error cause stability exceeds the threshold and has not been improved. Therefore, no teacher feedback request is triggered this time. The system will directly present the error annotation and diagnosis results to the students. Example of a neural network model architecture for error cause classification

[0080] In this embodiment, the error cause classification neural network model can adopt a multi-classification model based on a Transformer encoder. Its structure is as follows: the input layer receives the concatenation of the symbolic vector (dimension d1) of the step difference term and the encoding of the candidate error cause instance set (dimension d2); after feature extraction by a 4-layer Transformer encoder (8 attention heads per layer, hidden layer dimension 512), the fully connected classification layer outputs the probability distribution on the candidate error cause instance set; the model is trained using cross-entropy loss with an initial learning rate of 1e-4, employing the Adam optimizer, and undergoing approximately 30 training epochs. Those skilled in the art should understand that the specific architecture of the neural network model does not constitute a limitation of the error cause classification model in this invention; other structures such as LSTM, CNN, Graph Attention Network (GAT), or knowledge-enhanced pre-trained language models can also be used, as long as their output space is naturally constrained to the preset error cause instance set corresponding to the scoring point. Example 2: Comparative Experiment with Existing Technologies

[0081] To illustrate the beneficial effects of the present invention compared to the prior art, this embodiment conducted a comparative experiment on a self-built junior high school mathematics application problem dataset (a total of 12,500 problems and 3,200 students' answer records).

[0082] Experimental setup: Dataset partitioning: 70% training set (8,750 questions), 15% validation set (1,875 questions), and 15% test set (1,875 questions); partitioning is done by question ID to ensure that the same question does not appear in both the training and test sets.

[0083] R-Only solution: The rule set has 380 rules, which were compiled by the teaching and research team based on common error patterns in junior high school mathematics, and implemented using regular expressions + template matching.

[0084] The NN-Only approach employs a 4-layer Transformer encoder (8 attention heads per layer, 512-dimensional hidden layers) + a fully connected classification head. The model output space is the complete set of error cause label libraries. It is trained using cross-entropy loss and is consistent with the neural network architecture used in the matching submodule of this invention to ensure comparability.

[0085] LLM-Prompt Solution: This solution uses a publicly available, general-purpose large language model and zero-sample prompts. The prompts follow the industry-standard four-element structure of "question + standard answer + student response + please output the reason for the error". The temperature parameter is set to the default value.

[0086] The Hybrid solution of this invention is implemented as a serial hybrid error matching engine as described in this specification, wherein the neural network architecture of the model matching submodule is completely consistent with the NN-Only solution to ensure comparability.

[0087] Hardware environment: The server is configured with a single NVIDIA A100 40GB GPU, batch size = 32; the LLM-Prompt scheme is a single-request sequential inference.

[0088] The experimental results are as follows: Evaluation metrics: R-Only, NN-Only, LLM-Prompt. This invention is a hybrid... Error matching accuracy: 82.1% 84.6% 86.5% 92.3% Misleading cause-match recall rates: 65.4%, 81.2%, 83.7%, 83.9%. Conflict rates with teaching rules: 1.2%, 11.8%, 9.7%, 0.6% Average reasoning time (ms / question): 120, 260, 1850, 310

[0089] As shown in the table above, the Hybrid scheme described in this invention significantly outperforms the single rule, single neural network, and single LLM schemes in both the error cause matching accuracy and consistency with teaching rules; it maintains a comparable level to NN-Only and LLM-Prompt in terms of recall; and although its inference time is higher than R-Only and NN-Only, it is significantly lower than the LLM-Prompt scheme, demonstrating the feasibility of large-scale concurrent deployment.

[0090] Regarding the effectiveness of error propagation modeling, this embodiment further compares the predictive accuracy of the diagnostic results based on the error transfer probability matrix P with those based solely on the knowledge point mastery level for the teacher's next round of teaching intervention: the former reached 71.5%, while the latter was 58.2%, with the former improving by approximately 13.3 percentage points. In terms of expected error rate constraint recommendation, with [α, β] = [0.3, 0.5] set, the proportion of the actual error rate of the pushed questions falling within the interval was 76.4%, and the recurrence rate of the same error cause within 7 learning days was reduced by approximately 30.8% compared to the scheme without constraints.

[0091] Limitations of the Experiments: In the above comparative experiments, the three baseline schemes—R-Only, NN-Only, and LLM-Prompt—were reproduced by the implementers of this invention according to their representative implementations, rather than being directly implemented by the original authors of each scheme. The specific performance of the LLM-Prompt scheme may fluctuate significantly due to factors such as the selected large language model version and the level of detail in the prompt project. Therefore, the above experimental data are only used to illustrate the technical effects of the schemes described in the embodiments of this invention relative to the representative baseline schemes on a self-built dataset. In actual deployment, the data may differ due to differences in dataset distribution, hyperparameter selection, and implementation details of the comparison baselines. Those skilled in the art should understand that the technical contribution of this invention lies in the three core mechanisms: a structured serial hybrid error cause matching engine, formal modeling of the error cause transition probability matrix, and expected error rate constraint recommendation, rather than relying on the specific experimental data mentioned above. Example 3: Hardware Implementation in Other Disciplines and Systems

[0092] For questions such as classical Chinese translation and composition in Chinese language subjects, a corresponding error cause label library and difference pattern-error cause mapping rule set can be constructed based on their linguistic features; the input of the model matching submodule in the error cause matching engine can be changed to the concatenation of difference vectors based on syntactic analysis and similarity vectors based on semantic embedding; the remaining steps are consistent with the method described in this invention.

[0093] The system for implementing the method of this invention consists of a student terminal, a teacher terminal, a grading server, an error cause label library, a knowledge graph library, a question bank, a profile library, and a management backend. The grading server deploys core modules including an OCR / HWR recognition engine, a serial hybrid error cause matching engine, an error cause transition probability matrix estimation engine, an expected error rate estimation engine, and a recommendation engine.

[0094] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for homework correction and learning diagnosis based on error cause labeling, characterized in that... The method includes: (1) Construct an error cause tag library and a subject knowledge graph; the error cause tag library consists of several error cause instances, each error cause instance including an error cause instance number, error cause description text, and error cause attributes; the subject knowledge graph consists of several knowledge point nodes and the relationships between nodes; (2) The questions to be graded are structured and modeled to generate structured question data; in the structured question data, the questions are divided into several scoring points, and each scoring point is simultaneously bound to a set of error cause instances in the error cause tag library and to a set of knowledge point nodes in the subject knowledge graph; the scoring point-error cause instance association and the scoring point-knowledge point node association are both many-to-many associations; (3) Obtain student answer data and convert it into electronic answers. Use the position of the scoring point in step (2) as the initial segmentation boundary candidate. Fine-tune the initial segmentation boundary candidate through a deep learning step boundary detection model to obtain the step sequence of student answers. (4) A serial hybrid error cause matching engine, comprising a rule matching submodule, a model matching submodule, and a rule post-validation submodule, performs error cause label matching for each problem-solving step. The matching process includes: (a) symbolically comparing the problem-solving step with the standard steps of the corresponding scoring point to generate a step difference item; (b) the rule matching submodule performs precise matching based on the difference pattern-error cause mapping rule. If the rule is hit and the rule matching confidence is greater than the first threshold T1, the error cause instance of the rule matching is directly used as the error cause label for that step; (c) otherwise, the step difference item is input into the model matching submodule, and the trained error cause classification neural network model outputs candidate error cause instances; (d) the candidate error cause instances are validated by the rule post-validation submodule according to the preset error cause validity constraint rule set. If they conflict with the prohibition conditions of the validation rules, they are invalidated and corrected before being output. (5) Estimate the error transition probability matrix P based on the student's historical error sequence. The error transition probability matrix P is an N×N dimensional matrix, where N is the number of error instances. The element P(i,j) is estimated according to the formula P(i,j) = (C(i→j) + λ) / (C(i) + λ × N), where C(i→j) represents the frequency of error j immediately following error i in the student's historical error sequence, C(i) represents the total frequency of error i, and λ is the Laplace smoothing coefficient. (6) Based on the error cause transition probability matrix P, the current error cause label set, and the student's historical error cause frequency, determine the diagnostic result containing at least one error cause transmission chain and at least one high-frequency error cause; (7) Select candidate questions that satisfy α ≤ e ≤ β from the candidate question bank as the recommendation result output, where e is the expected error rate estimated in advance for each candidate question, and α and β are system-level configurable parameters.

2. The method according to claim 1, characterized in that... In step (1), the error attribute of the error example in the error attribute library includes at least the error nature attribute. The value of the error nature attribute includes several of the following: related to the student's knowledge mastery, related to the student's thinking method, related to the student's problem-solving skills, related to the student's expression norms, and related to the student's learning attitude. The error example is simultaneously bound to one or more knowledge point nodes in the subject knowledge graph. In step (2), the scoring point-error example association and the scoring point-knowledge point node association have at least one of the following characteristics: the number of error examples bound to the same scoring point is greater than one; the same error example is simultaneously bound to different scoring points of different questions; the same knowledge point node is simultaneously bound to different error examples on different scoring points.

3. The method according to claim 1, characterized in that... In step (3), when fine-tuning the initial segmentation boundary candidates, the deep learning step boundary detection model comprehensively considers the step separator, line spacing features and contextual semantic coherence, outputs the probability that each candidate boundary is a real step boundary, and determines the final step boundary position according to the set threshold.

4. The method according to claim 1, characterized in that... In step (4), the input of the error cause classification neural network model is the concatenation vector of the symbolic vector of the step difference item and the vector of the candidate set encoding of the error cause instance of the corresponding scoring point of the step, and the output is the probability distribution on the candidate error cause instance; when the model reasones, the candidate error cause instance is selected from the preset error cause instance set corresponding to the scoring point; the error cause validity constraint rule set adopted by the rule post-verification submodule includes any one or more of the following: (i) No two mutually exclusive error cause instances appear in the same question and the same scoring point. If they appear at the same time, the one with higher confidence is retained; (ii) When the upstream scoring point has been labeled with a specific error cause instance, the specific error cause instance corresponding to the downstream scoring point is corrected to a derived error cause. The derived error cause is a derived form of the specific error cause instance; (iii) The associated knowledge points of the error cause instance output by the model matching must be included in the knowledge point node set bound to the scoring point. Otherwise, the error cause instance is invalidated.

5. The method according to claim 1, characterized in that... Based on the error transfer probability matrix P, the error transmission chain strength S(i→j→k) = P(i,j) × P(j,k) is defined. When S is greater than the preset threshold ε, it is determined that there is a significant error transmission chain between error i, j, and k, and the significant error transmission chain is included in the diagnosis result in step (6).

6. The method according to claim 1, characterized in that... In step (7), the estimation formula for the expected error rate e is: e = 1 − ∏(m∈M) σ(θ − b_m + γ_m × η), where M is the set of error instances that the student has not overcome in the preset error instance set at the scoring point corresponding to the candidate question, b_m is the question difficulty parameter corresponding to error instance m, θ is the student's current ability value, γ_m is the stability coefficient of error instance m on the student, η is the time decay factor, and σ(·) is the Sigmoid function; when M is an empty set, e takes the value of 0, and the candidate question is removed from the candidate queue; the default values ​​of α and β are α = 0.3 and β = 0.

5.

7. The method according to claim 1, characterized in that... The method further includes the steps of constructing a student learning profile based on the student's historical error label data and a teacher feedback step; the student learning profile includes at least several of the following dimensions: error frequency profile, knowledge point mastery profile, error stability profile, and error improvement profile; wherein the error stability profile characterizes the degree of recurrence of each error instance by the student based on the stability coefficient γ_m, and the error improvement profile characterizes the correction trend of the student over time for each error instance; the teacher feedback is initiated only when any of the following conditions are met: (i) the final confidence of the error matching engine for the current step is lower than the threshold T2; (ii) the change amplitude of the elements in the error transition probability matrix P within the most recent time window exceeds the set threshold; (iii) the stability coefficient γ_m of the same error instance for the student exceeds the preset threshold and no improvement trend is observed; the teacher feedback is incorporated into the update samples of the error classification neural network model and the rule post-validation rule set.

8. A homework correction and learning diagnosis system based on error cause labeling, characterized in that... The system includes: a fault cause tag library and subject knowledge graph storage module for storing fault cause instances and knowledge graph nodes; a question structure modeling module for generating question structure data in accordance with the method described in claim 1; a serial hybrid fault cause matching engine module, which internally consists of a rule matching submodule, a model matching submodule, and a rule post-verification submodule connected in series; a fault cause transition probability matrix estimation module for estimating the fault cause transition probability matrix P in step (5) of claim 1; a diagnosis result generation module; and a recommendation result selection module for selecting recommendation results from the candidate question bank in step (7) of claim 1.

9. An electronic device, characterized in that... The method includes a processor and a memory communicatively connected to the processor; the memory stores a computer program, and the processor executes the computer program to implement the steps of the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that... When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

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