A Deep Learning-Based Method and System for Automatic Labeling of Knowledge Points in Mathematical Exam Questions

Abstract

This invention provides a method and system for automatic annotation of mathematical test questions' knowledge points based on deep learning. The method includes: constructing a knowledge graph of knowledge points to obtain structured test question data; performing structure encoding based on a tree encoder to obtain formula structure encoding vectors, combining this with a formula semantic mapping table to generate semantic enhancement vectors and perform fusion to generate a test question token sequence representation; independently encoding and aggregating the test question token sequence representation according to semantic regions to generate a global test question semantic representation, obtaining preliminary knowledge point prediction results through classification, performing reasoning and constraint optimization based on the knowledge graph to generate a set of predicted knowledge point labels; and performing attention attribution and confidence grading based on the predicted knowledge point label set, extracting corresponding annotation basis fragments, and generating knowledge point annotation results. This invention can significantly improve the efficiency of knowledge point annotation.

Description

Technical Field

[0001] This invention relates to the field of knowledge point annotation technology, and in particular to a method and system for automatic annotation of knowledge points in mathematical test questions based on deep learning. Background Technology

[0002] Knowledge point annotation is the core foundation for building intelligent question banks, realizing personalized learning recommendations, and automatic test paper generation. As a core subject in K-12 education, mathematics has a network-like knowledge point system, and a single test question often involves the comprehensive application of multiple knowledge points. Accurate annotation is a necessary prerequisite for teachers to conduct learning analysis and for students to identify and fill knowledge gaps.

[0003] With the rapid development of online education platforms, K-12 math question banks have reached hundreds of thousands to millions of questions. Traditional manual annotation methods are inefficient, costly, and difficult to guarantee consistent annotation standards, failing to meet the needs of large-scale question bank construction and maintenance. Furthermore, math questions contain numerous formulas, symbols, and graphs; these elements, which carry key knowledge points, are difficult to directly parse using conventional natural language processing methods. Therefore, automatic annotation of knowledge points in math questions has become a pressing issue requiring breakthroughs in the field of educational intelligence.

[0004] Existing automatic annotation schemes are mainly divided into two categories: one is rule-based matching methods, which identify formula patterns through keyword dictionaries and regular expressions, and supplement them with TF-IDF weighted mapping of knowledge points, but the rule coverage is limited and the generalization ability is insufficient; the other is traditional machine learning methods, which transform the task into multi-label text classification, and rely on TF-IDF, Word2Vec and other methods to extract text features and annotate them through classifiers, but the semantic representation ability of mathematical formulas and symbols is weak, and the overall annotation accuracy is difficult to meet the actual teaching needs. Summary of the Invention

[0005] Based on this, the purpose of this invention is to provide a method and system for automatic annotation of mathematical test knowledge points based on deep learning, so as to solve the problems of limited rule coverage, insufficient generalization ability, and weak semantic representation ability of mathematical formulas and symbols in the existing technology, which makes it difficult to meet the actual teaching needs in terms of overall annotation accuracy.

[0006] The first aspect of the present invention proposes: A method for automatically labeling mathematical test questions with knowledge points based on deep learning, wherein the method includes: The raw data of math test questions is preprocessed to identify and segment multiple semantic regions of the test questions and label them with semantic role tags in order to detect the position index of mathematical formulas in the test questions. At the same time, a knowledge graph of knowledge points is constructed to obtain structured test question data. The structured test data is parsed to generate an abstract syntax tree. The structure is encoded using a tree encoder to obtain a formula structure encoding vector. A semantic enhancement vector is generated by combining the formula semantic mapping table and then fused to generate a test token sequence representation. The test question token sequence is independently encoded and region aggregated according to semantic regions to generate a global test question semantic representation. Preliminary knowledge point prediction results are obtained through classification. The knowledge point knowledge graph is then combined with reasoning and constraint optimization to generate a set of knowledge point prediction labels. Based on the knowledge point predicted label set, attention attribution and confidence level are performed, corresponding labeling basis fragments are extracted, and knowledge point labeling results are generated.

[0007] The beneficial effects of this invention are as follows: This solution preprocesses the original data of mathematics test questions in basic education, identifies and segments multiple semantic regions and labels them with semantic roles. While retaining the original position index of the formula, it separates mathematical formulas from ordinary text and simultaneously constructs a knowledge graph of knowledge points to obtain structured test question data, breaking through the limitation of the limited coverage of traditional rule-based methods. By parsing mathematical formulas to generate abstract syntax trees, and through tree structure encoding and semantic mapping enhancement fusion, it generates a sequence representation of test question tokens, effectively strengthening the semantic representation ability of mathematical formulas and symbols and making up for the weak semantic representation of traditional solutions. Combining semantic region independent encoding aggregation and gating adaptive fusion to generate a global semantic representation of test questions, supplemented by progressive multi-label classification and knowledge graph graph convolutional reasoning optimization, it significantly improves the model's generalization ability and knowledge point prediction accuracy. Finally, by extracting annotation basis fragments through attention attribution and confidence grading, it outputs interpretable knowledge point annotation results, which can fully meet the high-precision annotation needs of test questions in actual teaching scenarios.

[0008] Furthermore, the steps of parsing the structured test data to generate an abstract syntax tree, performing structure encoding based on a tree encoder to obtain a formula structure encoding vector, and combining the formula semantic mapping table to generate a semantic enhancement vector and complete the fusion include: A preset formula parser is used to parse the LaTeX format formula text in the test questions into an abstract syntax tree, and organizes mathematical structures such as fractions, radicals, subscripts and superscripts, summation integrals, and matrices into a tree structure with parent-child and sibling relationships. Based on the abstract syntax tree, a preset tree encoder is used to transmit information along the parent-child and sibling edges of the syntax tree, encode the structural hierarchy of the formula, and output a fixed-dimensional formula structure encoding vector corresponding to each formula. A mapping table between mathematical formula patterns and mathematical semantics is constructed. A learnable embedding layer is used to map the semantic labels corresponding to the formulas into semantic enhancement vectors. The formula structure encoding vector and the semantic enhancement vector are additively fused or gatedly fused to obtain the enhanced formula encoding vector.

[0009] Furthermore, the step of generating a sequence of test question tokens by achieving bidirectional semantic interaction between ordinary text and formulas through a cross-attention mechanism includes: The token representation vector of the ordinary text in the test question is used as the Query, and all the enhanced formula encoding vectors are used as the Key and Value. The attention weight of the formula to the text is calculated to obtain the enhanced text representation. The enhanced formula encoding vector is used as the Query, and the token representation vectors of all ordinary texts are used as the Key and Value. The attention weight of the text to the formula is calculated to obtain the enhanced formula representation with formula awareness of text context. The enhanced text representation and the enhanced formula representation are concatenated according to the position index of the formula in the original text, and then mapped back to the original dimension through a linear projection layer to obtain the test token sequence representation.

[0010] Furthermore, the step of independently encoding and aggregating the question token sequence representation according to semantic regions to generate a global question semantic representation includes: The question stem area, option area, answer area, and analysis area are divided into regions. The question token sequence representation is split into corresponding semantic regions, and each region obtains an independent region token sequence representation through an encoding network. Insert a target token at the beginning of the token sequence in each region, and use the output vector of the target token as the region aggregation representation of the corresponding region. The aggregated representation of the question stem region is used as the Query, and the aggregated representation of all regions is used as the Key and Value. The attention weight of the question stem to other regions is calculated, and the importance weight of each region is learned through a gating adaptive fusion mechanism. The weighted sum is then used to obtain the global question semantic representation vector.

[0011] Furthermore, the step of obtaining preliminary knowledge point prediction results through classification includes: Based on the preset knowledge domain hierarchy, coarse-grained multi-label classification is performed on the global test question semantic representation. The set of knowledge domains to which the test questions belong is predicted, and the coarse-grained classification loss is calculated using binary cross-entropy loss. Based on the prediction results of coarse-grained classification, a knowledge point subspace under the corresponding knowledge domain is selected, and fine-grained multi-label classification of knowledge points is performed within the knowledge point subspace. The fine-grained classification loss is calculated using the binary cross-entropy loss. The classification loss is calculated only for the knowledge point subspace corresponding to the coarse-grained categories that are predicted to be positive, thus narrowing down the candidate label space and outputting preliminary knowledge point prediction results.

[0012] Furthermore, the step of combining the knowledge point knowledge graph for reasoning and constraint optimization to generate a set of predicted knowledge point labels includes: The preliminary knowledge point prediction results are used as the input node features of the graph convolutional network, and message passing is performed on the knowledge point knowledge graph to aggregate the feature information of neighboring nodes. After neighbor aggregation by the graph convolutional network, the output enhanced features are passed through the sigmoid function to obtain the knowledge point prediction probability, while setting the constraint loss. The coarse-grained classification loss, fine-grained classification loss, and constraint loss are weighted and summed to obtain the total loss function, which is then used for model optimization to output a set of predicted labels for knowledge points.

[0013] Furthermore, the steps of performing attention attribution and confidence grading based on the knowledge point predicted label set, extracting corresponding labeling basis fragments, and generating knowledge point labeling results include: Extract the weight vectors corresponding to the target knowledge point dimension from the fully connected layer of the classifier, perform a dot product with the token-level representation vector to obtain the contribution score of each token to the target knowledge point, and select the consecutive tokens with the highest scores as the text fragments for annotation. Set a dual confidence threshold for each predicted knowledge point. Knowledge points with a predicted probability higher than the first threshold are marked as automatically accepted, those with a probability between the first and second thresholds are marked as pending manual review, and those with a probability lower than the second threshold are not output. The output includes a structured annotation result containing the question ID, knowledge point name, hierarchical path, confidence score, confidence level, annotation basis text fragment, and source region.

[0014] The second aspect of the present invention proposes: An automatic annotation system for mathematical test questions based on deep learning, wherein the system includes: The processing module is used to preprocess the raw data of math test questions, identify and segment multiple semantic regions of the test questions and label them with semantic role tags, detect the position index of mathematical formulas in the test questions, and construct a knowledge graph of knowledge points to obtain structured test question data. The encoding module is used to parse the structured test data to generate an abstract syntax tree, perform structural encoding based on a tree encoder to obtain a formula structure encoding vector, combine the formula semantic mapping table to generate a semantic enhancement vector and complete the fusion to generate a test token sequence representation. The reasoning module is used to independently encode and aggregate the test question token sequence representation according to semantic regions, generate a global test question semantic representation, obtain preliminary knowledge point prediction results through classification, and combine the knowledge point knowledge graph to perform reasoning and constraint optimization to generate a set of knowledge point prediction labels. The output module is used to perform attention attribution and confidence grading based on the knowledge point predicted label set, extract the corresponding labeling basis fragments, and generate knowledge point labeling results.

[0015] Furthermore, the steps of parsing the structured test data to generate an abstract syntax tree, performing structure encoding based on a tree encoder to obtain a formula structure encoding vector, and combining the formula semantic mapping table to generate a semantic enhancement vector and complete the fusion include: A preset formula parser is used to parse the LaTeX format formula text in the test questions into an abstract syntax tree, and organizes mathematical structures such as fractions, radicals, subscripts and superscripts, summation integrals, and matrices into a tree structure with parent-child and sibling relationships. Based on the abstract syntax tree, a preset tree encoder is used to transmit information along the parent-child and sibling edges of the syntax tree, encode the structural hierarchy of the formula, and output a fixed-dimensional formula structure encoding vector corresponding to each formula. A mapping table between mathematical formula patterns and mathematical semantics is constructed. A learnable embedding layer is used to map the semantic labels corresponding to the formulas into semantic enhancement vectors. The formula structure encoding vector and the semantic enhancement vector are additively fused or gatedly fused to obtain the enhanced formula encoding vector.

[0016] Furthermore, the step of generating a sequence of test question tokens by achieving bidirectional semantic interaction between ordinary text and formulas through a cross-attention mechanism includes: The token representation vector of the ordinary text in the test question is used as the Query, and all the enhanced formula encoding vectors are used as the Key and Value. The attention weight of the formula to the text is calculated to obtain the enhanced text representation. The enhanced formula encoding vector is used as the Query, and the token representation vectors of all ordinary texts are used as the Key and Value. The attention weight of the text to the formula is calculated to obtain the enhanced formula representation with formula awareness of text context. The enhanced text representation and the enhanced formula representation are concatenated according to the position index of the formula in the original text, and then mapped back to the original dimension through a linear projection layer to obtain the test token sequence representation.

[0017] Furthermore, the step of independently encoding and aggregating the question token sequence representation according to semantic regions to generate a global question semantic representation includes: The question stem area, option area, answer area, and analysis area are divided into regions. The question token sequence representation is split into corresponding semantic regions, and each region obtains an independent region token sequence representation through an encoding network. Insert a target token at the beginning of the token sequence in each region, and use the output vector of the target token as the region aggregation representation of the corresponding region. The aggregated representation of the question stem region is used as the Query, and the aggregated representation of all regions is used as the Key and Value. The attention weight of the question stem to other regions is calculated, and the importance weight of each region is learned through a gating adaptive fusion mechanism. The weighted sum is then used to obtain the global question semantic representation vector.

[0018] Furthermore, the step of obtaining preliminary knowledge point prediction results through classification includes: Based on the preset knowledge domain hierarchy, coarse-grained multi-label classification is performed on the global test question semantic representation. The set of knowledge domains to which the test questions belong is predicted, and the coarse-grained classification loss is calculated using binary cross-entropy loss. Based on the prediction results of coarse-grained classification, a knowledge point subspace under the corresponding knowledge domain is selected, and fine-grained multi-label classification of knowledge points is performed within the knowledge point subspace. The fine-grained classification loss is calculated using the binary cross-entropy loss. The classification loss is calculated only for the knowledge point subspace corresponding to the coarse-grained categories that are predicted to be positive, thus narrowing down the candidate label space and outputting preliminary knowledge point prediction results.

[0019] Furthermore, the step of combining the knowledge point knowledge graph for reasoning and constraint optimization to generate a set of predicted knowledge point labels includes: The preliminary knowledge point prediction results are used as the input node features of the graph convolutional network, and message passing is performed on the knowledge point knowledge graph to aggregate the feature information of neighboring nodes. After neighbor aggregation by the graph convolutional network, the output enhanced features are passed through the sigmoid function to obtain the knowledge point prediction probability, while setting the constraint loss. The coarse-grained classification loss, fine-grained classification loss, and constraint loss are weighted and summed to obtain the total loss function, which is then used for model optimization to output a set of predicted labels for knowledge points.

[0020] Furthermore, the steps of performing attention attribution and confidence grading based on the knowledge point predicted label set, extracting corresponding labeling basis fragments, and generating knowledge point labeling results include: Extract the weight vectors corresponding to the target knowledge point dimension from the fully connected layer of the classifier, perform a dot product with the token-level representation vector to obtain the contribution score of each token to the target knowledge point, and select the consecutive tokens with the highest scores as the text fragments for annotation. Set a dual confidence threshold for each predicted knowledge point. Knowledge points with a predicted probability higher than the first threshold are marked as automatically accepted, those with a probability between the first and second thresholds are marked as pending manual review, and those with a probability lower than the second threshold are not output. The output includes a structured annotation result containing the question ID, knowledge point name, hierarchical path, confidence score, confidence level, annotation basis text fragment, and source region.

[0021] The third aspect of the present invention proposes: A computer includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the deep learning-based automatic annotation method for mathematical test knowledge points as described above.

[0022] The fourth aspect of the present invention proposes: A readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the deep learning-based automatic annotation method for mathematical test knowledge points as described above.

[0023] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0024] Figure 1 A flowchart of the automatic annotation method for mathematical test knowledge points based on deep learning provided in the first embodiment of the present invention; Figure 2 The structural block diagram of the deep learning-based automatic annotation system for mathematical test knowledge points provided in the third embodiment of the present invention is shown.

[0025] The following detailed description, in conjunction with the accompanying drawings, will further illustrate the present invention. Detailed Implementation

[0026] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Several embodiments of the invention are illustrated in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.

[0027] It should be noted that when a component is said to be fixed to another component, it can be directly on the other component or there may be an intervening component. When a component is said to be connected to another component, it can be directly connected to the other component or there may be an intervening component. The terms vertical, horizontal, left, right, and similar expressions used in this document are for illustrative purposes only.

[0028] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The terminology used herein includes, and / or encompasses, any and all combinations of one or more of the associated listed items.

[0029] Please see Figure 1 The image shows the automatic annotation method for mathematical test questions based on deep learning provided in the first embodiment of the present invention. The automatic annotation method for mathematical test questions based on deep learning provided in this embodiment can extract annotation basis fragments through attention attribution and confidence level, and output interpretable knowledge point annotation results, which can fully meet the high-precision annotation needs of test questions in actual teaching scenarios.

[0030] Specifically, this embodiment provides: A method for automatically labeling mathematical test questions with knowledge points based on deep learning, wherein the method includes: Step S10: Preprocess the original data of math test questions, identify and segment multiple semantic regions of the test questions and label them with semantic role tags to detect the position index of mathematical formulas in the test questions, and at the same time construct a knowledge graph of knowledge points to obtain structured test question data. Step S20: Parse the structured test data to generate an abstract syntax tree, perform structure encoding based on a tree encoder to obtain a formula structure encoding vector, combine the formula semantic mapping table to generate a semantic enhancement vector and complete the fusion to generate a test token sequence representation; Step S30: Independently encode and aggregate the test question token sequence representation according to semantic regions to generate a global test question semantic representation, obtain preliminary knowledge point prediction results by classification, and combine the knowledge point knowledge graph to perform reasoning and constraint optimization to generate a set of knowledge point prediction tags; Step S40: Based on the knowledge point prediction label set, perform attention attribution and confidence level classification, extract the corresponding labeling basis fragments, and generate knowledge point labeling results.

[0031] Second Embodiment Furthermore, the steps of parsing the structured test data to generate an abstract syntax tree, performing structure encoding based on a tree encoder to obtain a formula structure encoding vector, and combining the formula semantic mapping table to generate a semantic enhancement vector and complete the fusion include: A preset formula parser is used to parse the LaTeX format formula text in the test questions into an abstract syntax tree, and organizes mathematical structures such as fractions, radicals, subscripts and superscripts, summation integrals, and matrices into a tree structure with parent-child and sibling relationships. Based on the abstract syntax tree, a preset tree encoder is used to transmit information along the parent-child and sibling edges of the syntax tree, encode the structural hierarchy of the formula, and output a fixed-dimensional formula structure encoding vector corresponding to each formula. A mapping table between mathematical formula patterns and mathematical semantics is constructed. A learnable embedding layer is used to map the semantic labels corresponding to the formulas into semantic enhancement vectors. The formula structure encoding vector and the semantic enhancement vector are additively fused or gatedly fused to obtain the enhanced formula encoding vector.

[0032] Furthermore, the step of generating a sequence of test question tokens by achieving bidirectional semantic interaction between ordinary text and formulas through a cross-attention mechanism includes: The token representation vector of the ordinary text in the test question is used as the Query, and all the enhanced formula encoding vectors are used as the Key and Value. The attention weight of the formula to the text is calculated to obtain the enhanced text representation. The enhanced formula encoding vector is used as the Query, and the token representation vectors of all ordinary texts are used as the Key and Value. The attention weight of the text to the formula is calculated to obtain the enhanced formula representation with formula awareness of text context. The enhanced text representation and the enhanced formula representation are concatenated according to the position index of the formula in the original text, and then mapped back to the original dimension through a linear projection layer to obtain the test token sequence representation.

[0033] Furthermore, the step of independently encoding and aggregating the question token sequence representation according to semantic regions to generate a global question semantic representation includes: The question stem area, option area, answer area, and analysis area are divided into regions. The question token sequence representation is split into corresponding semantic regions, and each region obtains an independent region token sequence representation through an encoding network. Insert a target token at the beginning of the token sequence in each region, and use the output vector of the target token as the region aggregation representation of the corresponding region. The aggregated representation of the question stem region is used as the Query, and the aggregated representation of all regions is used as the Key and Value. The attention weight of the question stem to other regions is calculated, and the importance weight of each region is learned through a gating adaptive fusion mechanism. The weighted sum is then used to obtain the global question semantic representation vector.

[0034] Furthermore, the step of obtaining preliminary knowledge point prediction results through classification includes: Based on the preset knowledge domain hierarchy, coarse-grained multi-label classification is performed on the global test question semantic representation. The set of knowledge domains to which the test questions belong is predicted, and the coarse-grained classification loss is calculated using binary cross-entropy loss. Based on the prediction results of coarse-grained classification, a knowledge point subspace under the corresponding knowledge domain is selected, and fine-grained multi-label classification of knowledge points is performed within the knowledge point subspace. The fine-grained classification loss is calculated using the binary cross-entropy loss. The classification loss is calculated only for the knowledge point subspace corresponding to the coarse-grained categories that are predicted to be positive, thus narrowing down the candidate label space and outputting preliminary knowledge point prediction results.

[0035] Furthermore, the step of combining the knowledge point knowledge graph for reasoning and constraint optimization to generate a set of predicted knowledge point labels includes: The preliminary knowledge point prediction results are used as the input node features of the graph convolutional network, and message passing is performed on the knowledge point knowledge graph to aggregate the feature information of neighboring nodes. After neighbor aggregation by the graph convolutional network, the output enhanced features are passed through the sigmoid function to obtain the knowledge point prediction probability, while setting the constraint loss. The coarse-grained classification loss, fine-grained classification loss, and constraint loss are weighted and summed to obtain the total loss function, which is then used for model optimization to output a set of predicted labels for knowledge points.

[0036] Furthermore, the steps of performing attention attribution and confidence grading based on the knowledge point predicted label set, extracting corresponding labeling basis fragments, and generating knowledge point labeling results include: Extract the weight vectors corresponding to the target knowledge point dimension from the fully connected layer of the classifier, perform a dot product with the token-level representation vector to obtain the contribution score of each token to the target knowledge point, and select the consecutive tokens with the highest scores as the text fragments for annotation. Set a dual confidence threshold for each predicted knowledge point. Knowledge points with a predicted probability higher than the first threshold are marked as automatically accepted, those with a probability between the first and second thresholds are marked as pending manual review, and those with a probability lower than the second threshold are not output. The output includes a structured annotation result containing the question ID, knowledge point name, hierarchical path, confidence score, confidence level, annotation basis text fragment, and source region.

[0037] In this embodiment, it should also be noted that the automatic annotation method for mathematical test knowledge points based on deep learning provided by the present invention is specifically implemented by the following: 1. Data Preprocessing Stage (1) Collect and organize test data of mathematics subjects in basic education, covering the three stages of primary school, junior high school and senior high school, including various question types such as multiple choice, fill-in-the-blank, problem solving and proof. Clean the original test data, remove irrelevant characters and noise information (such as non-standard whitespace characters, special Unicode control characters, etc.), and uniformly convert it into an intermediate representation format of plain text plus structured markup.

[0038] (2) Based on a combination of rule-based and sequence labeling models, different semantic regions of the test questions are identified and segmented. First, the test questions are initially divided into regions based on rules (such as

options

[0039] (3) Based on regular expressions and LaTeX syntax rules, detect the mathematical formulas embedded in the test text. LaTeX formulas usually appear in the form of $...$ (inline formula), $$...$$ (outline formula), etc. After detection, separate the formula part from the ordinary text part, and retain the position index of the formula in the original text so that the formula encoding result can be embedded in the correct position later. For formulas in non-LaTeX format (such as MathML, formulas in image form), first convert them to LaTeX intermediate representation using a format conversion tool.

[0040] (4) Based on the new mathematics curriculum standards (compulsory education and senior high school stages) and combined with the detailed rules for dividing knowledge points in actual teaching, a hierarchical knowledge point system tree is constructed. The root node of the tree is mathematics, the second level is the grade level (primary / junior high / senior high school), the third level is the knowledge domain (number and algebra, geometry, statistics and probability, integration and practice, etc.), the fourth level is the knowledge module, and the fifth level and below are specific knowledge point units. Each knowledge point node contains its hierarchical path, parent node, child node list and other structural information, covering all K12 mathematics knowledge points, and the total number of knowledge point nodes is in the thousands.

[0041] (5) Construct a knowledge graph based on the relationships between knowledge points. The edge types in the knowledge graph include: containment (parent knowledge point contains child knowledge point), prerequisite (learning knowledge point A is a prerequisite for learning knowledge point B), successor (B is a successor knowledge point of A), and strong correlation (A and B often appear together in the test questions), etc. The knowledge graph is used for subsequent GCN-assisted reasoning.

[0042] (6) Select high-quality knowledge point annotation data that has been reviewed by human experts from the existing question bank as the seed training set. Each question is annotated with one or more knowledge points (usually 1-5), and the semantic regions associated with the knowledge points are marked. For long-tail knowledge points with sparse annotation data, three enhancement strategies are adopted to expand the sample: a) Synonym replacement in mathematics discipline, using a thesaurus of mathematical theorem (such as trigonometric functions corresponding to trigonometric ratios, conic sections corresponding to quadratic curves, etc.) to replace non-critical mathematical terms in the question text with synonyms; b) Equivalent transformation of formulas, performing mathematically equivalent transformations on the mathematical formulas in the questions (such as adding, subtracting, multiplying, or dividing the same quantity on both sides of the equation, rewriting explicit equations into implicit equations, etc.), while keeping the knowledge point annotations unchanged; c) Semantic region reorganization of questions, recombining the question stems, options, and analysis areas of different questions according to reasonable rules to generate new training samples.

[0043] 2. Formula-aware coding stage This paper addresses the problem of losing mathematical structure information caused by treating formulas as plain text strings in traditional methods, which result in the large number of LaTeX format mathematical formulas in math exam questions.

[0044] (1) The formula text is parsed into an Abstract Syntax Tree (AST) using an ANTLR-based LaTeX formula parser. This AST organizes the mathematical structures in the formula, specifically including fractions (numerator and denominator), radicals (radical), superscripts and subscripts (superscript and subscript), summation integrals (lower limit and upper limit), matrices, etc., into a tree structure with clear parent-child and sibling relationships. The leaf nodes of the tree are atomic units such as numbers, variable symbols, and operators, while the internal nodes are mathematical operations or structure types.

[0045] (2) Based on the constructed formula AST, Tree-LSTM or Structure-AwareTransformer is used to encode the formulas. Unlike serializing formulas into a text sequence, the tree encoder can transmit information along the parent-child and sibling edges of the AST, enabling the model to perceive the structural hierarchy of the formula. For example, for the expression \frac{a+b}{c}, the encoder can distinguish that a+b is a component of the numerator, while c is the denominator. The two have different mathematical roles and different importance in knowledge point inference. After encoding, each formula outputs a fixed-dimensional vector representation.

[0046] (3) Construct a mapping table between common mathematical formula patterns and mathematical semantics (e.g., x 2 +y 2 =r 2 The equation of the corresponding circle, Δ=b 2 -4ac corresponds to the discriminant of a quadratic equation, y=kx+b corresponds to the analytical expression of a linear function, and sin(α+β)=sinαcosβ+cosαsinβ corresponds to the sine formula for the sum of two angles, etc. The mapping table is constructed as follows: formula-semantic description pairs are automatically extracted from the test question analysis texts in the question bank and textbooks. After manual review and noise reduction, a high-quality mapping table is formed. Based on the formula encoding, a learnable embedding layer maps the semantic labels of the formulas to semantic enhancement vectors. These vectors are then additively fused or gatedly fused with the formula structure encoding vectors to further enhance the semantic expressive power of the formulas.

[0047] (4) A cross-attention mechanism is used to achieve bidirectional semantic interaction between ordinary text and formulas in the test questions. The representation vector of the i-th position in the test question (which may be an ordinary text token or a formula token) is used as the Query, and all formula representation vectors in the test question are used as the Key and Value to calculate the attention weight of the formula to the text; conversely, the formula representation is used as the Query, and all text representations are used as the Key and Value to calculate the attention weight of the text to the formula. After the bidirectional attention calculation is completed, the text representation and the formula representation are concatenated and mapped back to the original dimension through a linear projection layer to obtain the fused test question token sequence representation.

[0048] 3. Multi-region semantic modeling and knowledge point classification stage The formula-aware encoded question representation is input into a hierarchical perception multi-label classifier, which outputs a set of knowledge point labels related to the question. The entire process includes three steps: region encoding, hierarchical classification, and knowledge graph-assisted reasoning.

[0049] The first step is region-independent encoding and fusion. The questions are encoded separately according to their identified semantic regions (question stem, answer choices, and explanation), using a perceptual coding process. Each region receives an independent token sequence encoding representation. A special [REGION] marker is inserted at the beginning of each region's token sequence; the output vector of this marker serves as the region's aggregated representation. Then, the aggregated representation h of the question stem region is used... q As a query, the aggregated representation of all regions serves as the key and value. Multi-head attention is used to calculate the attention weights of the question stem on other regions. Then, a gating adaptive fusion mechanism automatically learns the importance weights α for each region. i =softmax(w T ·tanh(W·h i +b)) yields the final global question semantic representation vector H. global =Σα i ·h i .

[0050] The second step is hierarchical knowledge point classification. First, coarse-grained multi-label classification is performed at the knowledge domain level (third layer), predicting the set of knowledge domains to which the test questions belong, using binary cross-entropy loss (BCELoss). Then, based on the prediction results, fine-grained knowledge point classification (fifth layer and below) is performed in the corresponding knowledge point subspace of that domain, also using BCELoss, but the loss is calculated only in the knowledge point subspace corresponding to the coarse-grained categories predicted as positive. This coarse-to-fine strategy effectively narrows the candidate label space and reduces the classification difficulty.

[0051] The third step involves knowledge graph-assisted reasoning using a graph convolutional network (GCN). The initial knowledge point score vectors predicted in the second step are used as input node features to the GCN, where 2-3 layers of message passing are performed on the pre-constructed knowledge graph. After neighbor aggregation, the feature vector of each knowledge point node incorporates information from its neighboring knowledge points (related knowledge points). Specifically, layer consistency is ensured through inclusion edges, logical rationality of the subject is ensured through pre-revision / successor edges, and mutual reinforcement is achieved through strongly related edges. Finally, the enhanced features output by the GCN are processed using a sigmoid function to obtain the final knowledge point prediction probability. A layer consistency constraint loss is also set: for any knowledge point pair (p,c) where p is an ancestor node of c, L(p,c)=max(0,score(c)-score(p)), ensuring that the predicted score of the child node does not exceed the predicted score of the ancestor node. The total loss function is a weighted sum of the three loss functions.

[0052] 4. Training and Reasoning Stage (1) Pre-training: Domain Adaptive Pre-training (DAPT) was performed on a large-scale unlabeled mathematical test corpus (millions of questions). The Masked Language Model (MLM) task was used to adapt the model to the text distribution in the mathematical domain, including unique language patterns such as mathematical formula symbols, mathematical terms, and logical reasoning expressions.

[0053] (2) Fine-tuning: Fine-tun the domain-adapted model on the labeled dataset, train the knowledge point labeling task, and optimize the coarse-grained classification loss, fine-grained classification loss and hierarchical consistency constraint loss.

[0054] (3) Distillation: Knowledge distillation technology is used to transfer the knowledge of the trained large model (Teacher) to the lightweight model (Student, such as TinyBERT or ALBERT-Tiny). The distillation loss includes soft label distillation loss and intermediate layer feature alignment loss. The lightweight model can significantly reduce inference latency and resource consumption while ensuring annotation accuracy, meeting the real-time annotation requirements of a million-level question bank.

[0055] (4) Reasoning: After data preprocessing and formula-aware encoding, the newly arrived test text is output by the trained model to predict the knowledge point labels and the corresponding prediction probabilities.

[0056] 5. Interpretable Output Stage For each predicted knowledge point, provide interpretable evidence and confidence assessment to make the annotation results transparent and traceable.

[0057] (1) Use attention weight attribution technique to locate the annotation basis. Extract the weight vector corresponding to the dimension of the target knowledge point from the weight of the fully connected layer of the classifier, and perform a dot product calculation with the token-level representation vector output by the multi-region semantic modeling module to obtain the contribution score of each token to the target knowledge point. Select several consecutive tokens with the highest scores as the annotation basis text fragments for the knowledge point. The basis fragments can come from any semantic region of the question (the stem, options, answer, and explanation are all acceptable).

[0058] (2) Output the model prediction probability as a confidence score for each predicted knowledge point. Set two thresholds θ. high and θ low (θ) high >θ low ): Predicted probability ≥ θ high Knowledge points are automatically accepted and marked as high confidence; θ low ≤Predicted probability<θ high The knowledge points marked as pending manual review will proceed to the manual review process; the predicted probability is <θ. lowKnowledge points that are not specified are not output. This dual-threshold mechanism achieves a balance between annotation efficiency and annotation quality.

[0059] (3) The final output annotation results include the following structural information: question ID, list of annotated knowledge points (each knowledge point includes: knowledge point name, hierarchical path, confidence score, confidence level, annotation basis text fragment, and basis fragment source area), which is convenient for downstream question bank management system and learning analysis system to call directly.

[0060] Please see Figure 2 The third embodiment of the present invention provides: An automatic annotation system for mathematical test questions based on deep learning, wherein the system includes: The processing module is used to preprocess the raw data of math test questions, identify and segment multiple semantic regions of the test questions and label them with semantic role tags, detect the position index of mathematical formulas in the test questions, and construct a knowledge graph of knowledge points to obtain structured test question data. The encoding module is used to parse the structured test data to generate an abstract syntax tree, perform structural encoding based on a tree encoder to obtain a formula structure encoding vector, combine the formula semantic mapping table to generate a semantic enhancement vector and complete the fusion to generate a test token sequence representation. The reasoning module is used to independently encode and aggregate the test question token sequence representation according to semantic regions, generate a global test question semantic representation, obtain preliminary knowledge point prediction results through classification, and combine the knowledge point knowledge graph to perform reasoning and constraint optimization to generate a set of knowledge point prediction labels. The output module is used to perform attention attribution and confidence grading based on the knowledge point predicted label set, extract the corresponding labeling basis fragments, and generate knowledge point labeling results.

[0061] Furthermore, the steps of parsing the structured test data to generate an abstract syntax tree, performing structure encoding based on a tree encoder to obtain a formula structure encoding vector, and combining the formula semantic mapping table to generate a semantic enhancement vector and complete the fusion include: A preset formula parser is used to parse the LaTeX format formula text in the test questions into an abstract syntax tree, and organizes mathematical structures such as fractions, radicals, subscripts and superscripts, summation integrals, and matrices into a tree structure with parent-child and sibling relationships. Based on the abstract syntax tree, a preset tree encoder is used to transmit information along the parent-child and sibling edges of the syntax tree, encode the structural hierarchy of the formula, and output a fixed-dimensional formula structure encoding vector corresponding to each formula. A mapping table between mathematical formula patterns and mathematical semantics is constructed. A learnable embedding layer is used to map the semantic labels corresponding to the formulas into semantic enhancement vectors. The formula structure encoding vector and the semantic enhancement vector are additively fused or gatedly fused to obtain the enhanced formula encoding vector.

[0062] Furthermore, the step of generating a sequence of test question tokens by achieving bidirectional semantic interaction between ordinary text and formulas through a cross-attention mechanism includes: The token representation vector of the ordinary text in the test question is used as the Query, and all the enhanced formula encoding vectors are used as the Key and Value. The attention weight of the formula to the text is calculated to obtain the enhanced text representation. The enhanced formula encoding vector is used as the Query, and the token representation vectors of all ordinary texts are used as the Key and Value. The attention weight of the text to the formula is calculated to obtain the enhanced formula representation with formula awareness of text context. The enhanced text representation and the enhanced formula representation are concatenated according to the position index of the formula in the original text, and then mapped back to the original dimension through a linear projection layer to obtain the test token sequence representation.

[0063] Furthermore, the step of independently encoding and aggregating the question token sequence representation according to semantic regions to generate a global question semantic representation includes: The question stem area, option area, answer area, and analysis area are divided into regions. The question token sequence representation is split into corresponding semantic regions, and each region obtains an independent region token sequence representation through an encoding network. Insert a target token at the beginning of the token sequence in each region, and use the output vector of the target token as the region aggregation representation of the corresponding region. The aggregated representation of the question stem region is used as the Query, and the aggregated representation of all regions is used as the Key and Value. The attention weight of the question stem to other regions is calculated, and the importance weight of each region is learned through a gating adaptive fusion mechanism. The weighted sum is then used to obtain the global question semantic representation vector.

[0064] Furthermore, the step of obtaining preliminary knowledge point prediction results through classification includes: Based on the preset knowledge domain hierarchy, coarse-grained multi-label classification is performed on the global test question semantic representation. The set of knowledge domains to which the test questions belong is predicted, and the coarse-grained classification loss is calculated using binary cross-entropy loss. Based on the prediction results of coarse-grained classification, a knowledge point subspace under the corresponding knowledge domain is selected, and fine-grained multi-label classification of knowledge points is performed within the knowledge point subspace. The fine-grained classification loss is calculated using the binary cross-entropy loss. The classification loss is calculated only for the knowledge point subspace corresponding to the coarse-grained categories that are predicted to be positive, thus narrowing down the candidate label space and outputting preliminary knowledge point prediction results.

[0065] Furthermore, the step of combining the knowledge point knowledge graph for reasoning and constraint optimization to generate a set of predicted knowledge point labels includes: The preliminary knowledge point prediction results are used as the input node features of the graph convolutional network, and message passing is performed on the knowledge point knowledge graph to aggregate the feature information of neighboring nodes. After neighbor aggregation by the graph convolutional network, the output enhanced features are passed through the sigmoid function to obtain the knowledge point prediction probability, while setting the constraint loss. The coarse-grained classification loss, fine-grained classification loss, and constraint loss are weighted and summed to obtain the total loss function, which is then used for model optimization to output a set of predicted labels for knowledge points.

[0066] Furthermore, the steps of performing attention attribution and confidence grading based on the knowledge point predicted label set, extracting corresponding labeling basis fragments, and generating knowledge point labeling results include: Extract the weight vectors corresponding to the target knowledge point dimension from the fully connected layer of the classifier, perform a dot product with the token-level representation vector to obtain the contribution score of each token to the target knowledge point, and select the consecutive tokens with the highest scores as the text fragments for annotation. Set a dual confidence threshold for each predicted knowledge point. Knowledge points with a predicted probability higher than the first threshold are marked as automatically accepted, those with a probability between the first and second thresholds are marked as pending manual review, and those with a probability lower than the second threshold are not output. The output includes a structured annotation result containing the question ID, knowledge point name, hierarchical path, confidence score, confidence level, annotation basis text fragment, and source region.

[0067] The fourth embodiment of the present invention provides a computer, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the deep learning-based automatic annotation method for mathematical test knowledge points as described above.

[0068] The fifth embodiment of the present invention provides a readable storage medium on which a computer program is stored, wherein when the program is executed by a processor, it implements the deep learning-based automatic annotation method for mathematical test knowledge points as described above.

[0069] In summary, the above embodiments of the present invention can extract annotation basis fragments through attention attribution and confidence grading, and output interpretable knowledge point annotation results, which can fully meet the high-precision annotation requirements of test questions in actual teaching scenarios.

[0070] It should be noted that the above modules can be functional modules or program modules, and can be implemented through software or hardware. For modules implemented through hardware, the above modules can reside in the same processor; or the above modules can be located in different processors in any combination.

[0071] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, a computer-readable medium can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0072] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0073] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0074] In the description of this specification, references to the terms "an embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0075] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for automatically labeling knowledge points in mathematical test questions based on deep learning, characterized in that, The method includes: The raw data of math test questions is preprocessed to identify and segment multiple semantic regions of the test questions and label them with semantic role tags in order to detect the position index of mathematical formulas in the test questions. At the same time, a knowledge graph of knowledge points is constructed to obtain structured test question data. The structured test data is parsed to generate an abstract syntax tree. The structure is encoded using a tree encoder to obtain a formula structure encoding vector. The semantic enhancement vector is generated by combining the formula semantic mapping table and then fused to generate a test token sequence representation. The test question token sequence is independently encoded and region aggregated according to semantic regions to generate a global test question semantic representation. Preliminary knowledge point prediction results are obtained through classification. The knowledge point knowledge graph is then combined with reasoning and constraint optimization to generate a set of knowledge point prediction labels. Based on the predicted knowledge point label set, attention attribution and confidence level are performed, corresponding labeling basis fragments are extracted, and knowledge point labeling results are generated.

2. The method for automatically labeling mathematical test knowledge points based on deep learning according to claim 1, characterized in that, The steps of parsing the structured test data to generate an abstract syntax tree, performing structure encoding based on a tree encoder to obtain a formula structure encoding vector, and combining the formula semantic mapping table to generate a semantic enhancement vector and complete the fusion include: A preset formula parser is used to parse the LaTeX format formula text in the test questions into an abstract syntax tree, and organizes mathematical structures such as fractions, radicals, subscripts and superscripts, summation integrals, and matrices into a tree structure with parent-child and sibling relationships. Based on the abstract syntax tree, a preset tree encoder is used to transmit information along the parent-child and sibling edges of the syntax tree, encode the structural hierarchy of the formula, and output a fixed-dimensional formula structure encoding vector corresponding to each formula. A mapping table between mathematical formula patterns and mathematical semantics is constructed. A learnable embedding layer is used to map the semantic labels corresponding to the formulas into semantic enhancement vectors. The formula structure encoding vector and the semantic enhancement vector are additively fused or gatedly fused to obtain the enhanced formula encoding vector.

3. The method for automatically labeling mathematical test knowledge points based on deep learning according to claim 2, characterized in that, The steps for generating a sequence of test question tokens by achieving bidirectional semantic interaction between ordinary text and formulas through a cross-attention mechanism include: The token representation vector of the ordinary text in the test question is used as the Query, and all the enhanced formula encoding vectors are used as the Key and Value. The attention weight of the formula to the text is calculated to obtain the enhanced text representation. The enhanced formula encoding vector is used as the Query, and the token representation vectors of all ordinary texts are used as the Key and Value. The attention weight of the text to the formula is calculated to obtain the enhanced formula representation with formula awareness of text context. The enhanced text representation and the enhanced formula representation are concatenated according to the position index of the formula in the original text, and then mapped back to the original dimension through a linear projection layer to obtain the test token sequence representation.

4. The method for automatically labeling mathematical test knowledge points based on deep learning according to claim 1, characterized in that, The step of independently encoding and aggregating the test question token sequence representation according to semantic regions to generate a global test question semantic representation includes: The question stem area, option area, answer area, and analysis area are divided into regions. The question token sequence representation is split into corresponding semantic regions, and each region obtains an independent region token sequence representation through an encoding network. Insert a target token at the beginning of the token sequence in each region, and use the output vector of the target token as the region aggregation representation of the corresponding region. The aggregated representation of the question stem region is used as the Query, and the aggregated representation of all regions is used as the Key and Value. The attention weight of the question stem to other regions is calculated, and the importance weight of each region is learned through a gating adaptive fusion mechanism. The weighted sum is then used to obtain the global question semantic representation vector.

5. The method for automatically labeling mathematical test knowledge points based on deep learning according to claim 4, characterized in that, The steps for obtaining preliminary knowledge point prediction results through classification include: Based on the preset knowledge domain hierarchy, coarse-grained multi-label classification is performed on the global test question semantic representation. The set of knowledge domains to which the test questions belong is predicted, and the coarse-grained classification loss is calculated using binary cross-entropy loss. Based on the prediction results of coarse-grained classification, a knowledge point subspace under the corresponding knowledge domain is selected, and fine-grained multi-label classification of knowledge points is performed within the knowledge point subspace. The fine-grained classification loss is calculated using the binary cross-entropy loss. The classification loss is calculated only for the knowledge point subspace corresponding to the coarse-grained categories that are predicted to be positive, thus narrowing down the candidate label space and outputting preliminary knowledge point prediction results.

6. The method for automatically labeling mathematical test knowledge points based on deep learning according to claim 5, characterized in that, The step of combining the knowledge graph of knowledge points for reasoning and constraint optimization to generate a set of predicted labels for knowledge points includes: The preliminary knowledge point prediction results are used as the input node features of the graph convolutional network, and message passing is performed on the knowledge point knowledge graph to aggregate the feature information of neighboring nodes. After neighbor aggregation by the graph convolutional network, the output enhanced features are passed through the sigmoid function to obtain the knowledge point prediction probability, while setting the constraint loss. The coarse-grained classification loss, fine-grained classification loss, and constraint loss are weighted and summed to obtain the total loss function, which is then used for model optimization to output a set of predicted labels for knowledge points.

7. The method for automatically labeling mathematical test knowledge points based on deep learning according to claim 6, characterized in that, The steps of performing attention attribution and confidence grading based on the knowledge point predicted label set, extracting corresponding labeling basis fragments, and generating knowledge point labeling results include: Extract the weight vectors corresponding to the target knowledge point dimension from the fully connected layer of the classifier, perform a dot product with the token-level representation vector to obtain the contribution score of each token to the target knowledge point, and select the consecutive tokens with the highest scores as the text fragments for annotation. Set a dual confidence threshold for each predicted knowledge point. Knowledge points with a predicted probability higher than the first threshold are marked as automatically accepted, those with a probability between the first and second thresholds are marked as pending manual review, and those with a probability lower than the second threshold are not output. The output includes a structured annotation result containing the question ID, knowledge point name, hierarchical path, confidence score, confidence level, annotation basis text fragment, and source region.

8. A deep learning-based automatic annotation system for mathematical test knowledge points, characterized in that, The system includes: The processing module is used to preprocess the raw data of math test questions, identify and segment multiple semantic regions of the test questions and label them with semantic role tags, detect the position index of mathematical formulas in the test questions, and construct a knowledge graph of knowledge points to obtain structured test question data. The encoding module is used to parse the structured test data to generate an abstract syntax tree, perform structural encoding based on a tree encoder to obtain a formula structure encoding vector, combine the formula semantic mapping table to generate a semantic enhancement vector and complete the fusion to generate a test token sequence representation. The reasoning module is used to independently encode and aggregate the test question token sequence representation according to semantic regions, generate a global test question semantic representation, obtain preliminary knowledge point prediction results through classification, and combine the knowledge point knowledge graph to perform reasoning and constraint optimization to generate a set of knowledge point prediction labels. The output module is used to perform attention attribution and confidence grading based on the knowledge point predicted label set, extract the corresponding labeling basis fragments, and generate knowledge point labeling results.

9. A computer comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method for automatically labeling mathematical test knowledge points based on deep learning as described in any one of claims 1 to 7.

10. A readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the deep learning-based automatic annotation method for mathematical test knowledge points as described in any one of claims 1 to 7.

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