Multi-granularity learning path recommendation and optimization method based on large language model

Abstract

The invention discloses a multi-granularity learning path recommendation and optimization method based on a large language model. The method comprises the following steps: preprocessing a learning data set; constructing a multi-granularity knowledge structure; constructing a multi-level incidence matrix; constructing a double-layer concept lattice; constructing a knowledge unit and a skill multi-granularity dependency graph; generating a multi-granularity learning path; and recommending and optimizing the path. A three-level hierarchical knowledge structure of a large unit, a knowledge unit and a fine-grained skill is constructed through a large language model, and coarse-grained knowledge unit overall planning and fine-grained skill collaborative recommendation are realized. Compared with the prior art that multiple granularities are defined only according to the number of knowledge nodes of learning resources and clear hierarchical collaboration is lacked, the method ensures that the learning path conforms to an internal logic system of subject knowledge, enables the recommended path to directly guide the practical operation practice of learners through accurate mapping of fine-grained skills and specific topics, and improves the learning efficiency. The problem that a knowledge system and practical operation are separated in the prior art is solved, and the practicability and the performability of the path are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of intelligent education technology, specifically involving a multi-granularity learning path recommendation and optimization method based on a large language model. Background Technology

[0002] With the rapid development of intelligent education and online learning, personalized learning path recommendation has become a key technology for solving problems such as learning confusion and cognitive overload, and improving learning efficiency. Related technological research and applications have received widespread attention. For example, the invention patent with publication number CN118941421A proposes a multi-granularity learning path recommendation method. This method, based on a two-layer planning perspective of structural and content layers, integrates domain knowledge graphs, learner models, and learning resource models. It constructs a mathematical model through a linear weighting method and optimizes the solution using an improved ant colony algorithm. This achieves the integration and ordering optimization of multi-granularity learning resources, providing learners with learning paths that meet structured knowledge constraints, and has made significant progress in multi-granularity resource adaptation and path planning.

[0003] However, existing learning path recommendation technologies, including the methods mentioned above, still have the following limitations: First, the multi-granularity of existing technologies mainly reflects the differences in the granularity of learning resources, such as the number of knowledge nodes. They fail to form a hierarchical knowledge structure that integrates macro-level planning, meso-level connections, and micro-level implementation, focusing only on the granularity adaptation of learning resources. This makes it difficult to achieve the coordinated advancement of coarse-grained knowledge system leadership and fine-grained skill implementation, resulting in a disconnect between the systematic nature and practicality of the path. Second, existing methods require manual sorting of domain knowledge nodes and dependencies, and labeling the multi-dimensional attributes of learners and learning resources. This is not only costly but also difficult to adapt to differences in teaching standards across different disciplines and regions. Furthermore, their reliance on pre-defined rules to define constraints and dependencies results in weak parsing capabilities for unstructured teaching texts and limited generalization. Third, the optimization goals of existing technologies are focused on reducing the repetition rate of knowledge nodes in the structural layer and improving the adaptability of learners and resources in the content layer. By integrating the dual objective function through linear weighting, the dynamic balance between the cost and the benefits of learning is not considered. It is difficult to provide differentiated and efficient paths according to the learner's skill mastery progress, and the adaptability is insufficient for learners with weak foundations or advanced learners. Summary of the Invention

[0004] The technical problem to be solved by this invention is to overcome the shortcomings of the prior art and provide a multi-granularity learning path recommendation and optimization method based on a large language model that is clearer in terms of multi-granularity hierarchical collaboration, more in line with the learning cost-benefit logic of path optimization, and more practical.

[0005] The technical solution adopted to solve the above technical problems is: a multi-granularity learning path recommendation and optimization method based on a large language model, including the following steps:

[0006] Step 1. Preprocess the learning dataset

[0007] Collect subject learning data, including past exam questions, accompanying mock questions, and teaching standard documents. Preprocess the subject learning data, including labeling the fine-grained skill points corresponding to the questions, dividing them into coarse-grained knowledge units, mining the dependencies between knowledge units and skills, and classifying the difficulty of the questions.

[0008] Step 2. Construct a multi-granularity knowledge structure

[0009] The teaching standard document based on the large language model analysis extracts teaching knowledge points into a three-layer knowledge structure of large units, knowledge units, and fine-grained skills;

[0010] Step 3. Construct a multi-level association matrix

[0011] Construct an association matrix R1 between large units and knowledge units, an association matrix R2 between knowledge units and problems, and an association matrix R3 between fine-grained skills and problems. The elements of matrix R1 indicate whether a large unit contains a specific knowledge unit, the elements of matrix R2 indicate whether a specific knowledge unit is used to solve a specific problem, and the elements of matrix R3 indicate whether a specific skill is used to solve a specific problem.

[0012] Step 4. Construct a two-level concept lattice

[0013] Based on the theory of formal concept analysis, we construct concept lattices for skills and problems and for knowledge units and problems, respectively. With the set of skills and the set of knowledge units as the connotation and the set of problems as the extension, concept nodes are generated to form a hierarchical structure, resulting in a two-level concept lattice.

[0014] Step 5. Construct a multi-granularity dependency graph of knowledge units and skills.

[0015] The input and output values ​​of each concept node are calculated, redundant nodes are pruned, and a simplified two-level concept lattice structure is obtained. Based on the hierarchical structure of the simplified two-level concept lattice and the pre-dependencies between the knowledge units and skills mined out, a multi-granularity dependency graph is constructed.

[0016] Step 6. Generate multi-granularity learning paths

[0017] The simplified two-level concept lattice is fused with a multi-granularity dependency graph to generate a directed acyclic graph containing concept nodes and the progressive relationships between nodes. Multi-granularity learning paths are obtained through the directed acyclic graph.

[0018] Step 7. Path Recommendation and Optimization

[0019] Iterate through all multi-granularity learning paths, calculate the recommendation index for each path, and select and recommend the optimal learning path based on the learner's basic level and learning goals.

[0020] As a preferred technical solution, in step (5), the method for calculating the cost and reward value of each concept node is as follows:

[0021]

[0022] In the formula, The cost of a concept node. A set of skills contained within a concept node. For the first The cognitive level coefficient of each skill For the first The process requirement coefficient for each skill For the first The inherent difficulty coefficient of each skill The normalization constant is The reward value for the concept node. No. The weight of each skill's knowledge segment For the first The frequency coefficient of each skill's assessment For the first The core competency bonus coefficient for each skill.

[0023] As a preferred technical solution, in step 5, the method for constructing a multi-granularity dependency graph based on the hierarchical structure of the simplified concept lattice and the pre-dependencies between the mined knowledge units and skills is as follows: traverse the hierarchical structure of the simplified concept lattice, check the relationships between each concept node, and if the nodes... It is a node The child nodes, and master the nodes. It is about mastering the nodes The necessary condition is to establish from arrive Given directed edges, obtain a skill dependency graph. and knowledge unit dependency graph ,in, For the collection of all skills, Let the set of edges represent skill dependencies; For the set of all knowledge units, Let be the set of edges representing the dependencies between knowledge units.

[0024] As a preferred technical solution, in step 6, the method for generating a directed acyclic graph containing concept nodes and the progressive relationships between nodes is as follows: mapping the concept nodes in the simplified two-level concept lattice to knowledge unit nodes in the directed acyclic graph. and skill nodes First, based on the knowledge unit dependency relationship Construct edges between nodes in a directed acyclic graph of knowledge units. Generate a directed acyclic graph of knowledge units. It generates knowledge unit learning paths, and then, based on the planning of these knowledge unit learning paths and skill dependencies... Constructing edges between nodes in a directed acyclic graph of skills Generate a directed acyclic graph , where each node Representing a knowledge state, which includes a set of skills, each edge... Indicates from the state of knowledge To the state of knowledge The leap.

[0025] As a preferred technical solution, the method for calculating the recommendation index of each path in step 7 is as follows: calculate the recommendation index of each pair of adjacent nodes in each path. The conversion sensitivity is calculated, and the geometric mean of all conversion sensitivities in the path is used as the recommendation index for the path; the conversion sensitivity of each pair of adjacent nodes... Conversion sensitivity The beneficial effects of this invention are as follows:

[0026] This invention constructs a three-tiered hierarchical knowledge structure—comprising large units, knowledge units, and fine-grained skills—through a large language model. This enables collaborative recommendation that integrates the overall planning of coarse-grained knowledge units with the practical implementation of fine-grained skills. Compared to existing technologies that define multi-granularity solely based on the number of knowledge nodes in learning resources and lack clear hierarchical collaboration, this invention ensures that the learning path conforms to the inherent logical system of subject knowledge. Furthermore, through precise mapping between fine-grained skills and specific questions, the recommended path directly guides learners' practical exercises. This solves the problem of the disconnect between the knowledge system and practical application in existing technologies, significantly improving the practicality and feasibility of the path.

[0027] This invention uses a large language model as its core to automatically parse unstructured teaching standard documents, eliminating the need for manual analysis of knowledge node dependencies and annotation of multi-dimensional attributes of learning resources. This significantly reduces the manual cost and data preparation threshold for knowledge structure construction. Furthermore, this invention is adaptable to different subjects such as mathematics, Chinese, and English, different teaching standards, and different educational stages such as primary, middle, and high school. It overcomes the shortcomings of existing technologies that rely on manually preset rules and have limited generalization capabilities, thus broadening the applicability of the technology.

[0028] This invention introduces a binary evaluation index of input and output value. By quantifying the cognitive cost and learning benefits of skills, it calculates conversion sensitivity to optimize learning paths. Based on learners' initial skill levels, it dynamically recommends efficient paths with low input and high returns, accurately matching the needs of learners with different skill levels. Learners with weak foundations prioritize mastering cost-effective core skills, while advanced learners focus on high-return enhancement skills, achieving a dynamic balance between learning costs and benefits and improving the personalization and efficiency of path recommendations.

[0029] This invention constructs a two-level concept lattice based on formal concept analysis. It automatically uncovers prerequisite dependencies between skills by parsing teaching documents using a large language model, and integrates these dependencies to generate a directed acyclic graph, ensuring that the recommended path conforms to the cognitive pattern of starting with basic skills and progressing to advanced ones. The discovery of skill dependencies is more automated and more aligned with the logic of the knowledge itself, effectively avoiding skill gaps or logical conflicts in the path. Simultaneously, through the association matrix between knowledge units and questions, and between skills and questions, it achieves precise alignment between the learning path and specific exercises, allowing learners to gradually solidify their skills according to the path, further improving learning effectiveness.

[0030] Based on formal concept analysis, this invention employs a hierarchical construction strategy of macroscopic coarse-grained concept lattices and local fine-grained concept lattices, combined with a cluster search algorithm to select the optimal path, thus avoiding the combinatorial explosion problem caused by constructing all concept lattices or large-scale searches. Compared to the improved ant colony algorithm used in existing technologies, this invention has simpler computational logic, a more focused search space, and significantly improves solution efficiency while ensuring path quality, making it more suitable for practical applications in scenarios with large-scale skill and question banks. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the multi-granularity learning path recommendation and optimization method based on a large language model, as described in this invention.

[0032] Figure 2 This is a schematic diagram of the structure of a partial two-level concept lattice in an embodiment of the present invention.

[0033] Figure 3 This is a dependency graph between some knowledge units in an embodiment of the present invention.

[0034] Figure 4 This is a partial directed acyclic graph in an embodiment of the present invention. Detailed Implementation

[0035] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0036] Example

[0037] Taking mathematics as an example, based on the "Hunan Province Junior High School Academic Proficiency Examination Standards (2019 Edition)" (hereinafter referred to as the "Examination Standards"), such as... Figure 1 This embodiment of a multi-granularity learning path recommendation and optimization method based on a large language model includes the following steps:

[0038] Step 1. Preprocess the learning dataset

[0039] Subject learning data is collected, including past exam questions, corresponding mock questions, and teaching standard documents. The subject learning data is preprocessed, including labeling the fine-grained skill points corresponding to the questions, dividing them into coarse-grained knowledge units, and classifying the difficulty of the questions. In this embodiment, past exam questions, mock questions, and the "Examination Standard" text of the Hunan Province Junior High School Academic Proficiency Examination in Mathematics are collected and preprocessed.

[0040] Step 2. Construct a multi-granularity knowledge structure

[0041] Based on the analysis of teaching standard documents using a large language model, teaching knowledge points are extracted into a three-layer knowledge structure consisting of large units, knowledge units, and fine-grained skills.

[0042] This embodiment utilizes the gemini3 large language model to parse the "Examination Standards" text:

[0043] Major Unit Division: According to the "Examination Content and Requirements" in the "Examination Standards", junior high school mathematics is divided into 7 major units, including: Numbers and Algebra, Functions, Geometry and Graphics, Variations of Graphics, Statistics and Probability, Proof and Reasoning, and Integration and Practice;

[0044] Knowledge Unit Division: Under each major unit, there are 22 further subdivided knowledge units. For example, under the major unit of "Numbers and Algebra", it is divided into "Rational Number Unit", "Real Number Unit", "Algebraic Expression Unit", "Equation and Inequality Unit", etc.

[0045] Fine-grained skills: Utilizing a large language model, each knowledge unit is broken down into specific test-point skills, resulting in a total of 150 fine-grained skills. For example, the "Rational Numbers Unit" includes: 1. The meaning of rational numbers; 2. Opposite numbers and absolute values; 3. Rational number operations, etc. The "Functions Unit" includes: 47. The graph and properties of quadratic functions; 48. The vertex and axis of symmetry of quadratic functions, etc.

[0046] Step 3. Construct a multi-level association matrix

[0047] Construct an association matrix R1 between large units and knowledge units, an association matrix R2 between knowledge units and problems, and an association matrix R3 between fine-grained skills and problems. The elements of matrix R1 indicate whether a large unit contains a specific knowledge unit, the elements of matrix R2 indicate whether a specific knowledge unit is used to solve a specific problem, and the elements of matrix R3 indicate whether a specific skill is used to solve a specific problem.

[0048] In this embodiment, the association matrix R1 between large units and knowledge units is 7 rows and 22 columns, and the association matrix R2 between knowledge units and questions is 22 rows and N columns, where N is the number of questions, establishing a mapping between units and questions. The association matrix R3 between fine-grained skills and questions is 150 rows and N columns, establishing a precise mapping between fine-grained skills and questions; for example, questions... When dealing with "opposite numbers" and "absolute values", then in the matrix... The position corresponding to skill ID 2 is 1.

[0049] Step 4. Construct a two-level concept lattice

[0050] Based on the theory of formal concept analysis, we construct concept lattices for skills and problems and for knowledge units and problems, respectively. With the set of skills and the set of knowledge units as the connotation and the set of problems as the extension, concept nodes are generated and a hierarchical structure is formed to obtain a two-level concept lattice.

[0051] In the skill and problem concept lattice, each concept node contains a set of skills in its connotation and a set of problems in its extension, satisfying the following conditions: each problem is related to the skill set of that node; each skill is related to at least one problem in the problem set of that node.

[0052] The hierarchical structure is such that if the skill set of concept node C1 is a subset of concept node C2, then concept node C1 is a child node of concept node C2, forming a parent-child relationship.

[0053] In the knowledge unit and problem concept lattice, each concept node contains a set of knowledge units in its connotation and a set of problems in its extension, satisfying the following conditions: each problem is related to the knowledge unit set of that node; each knowledge unit is related to at least one problem in the problem set of that node;

[0054] The hierarchical structure is such that if the set of knowledge units of concept node C1 is a subset of concept node C2, then concept node C1 is a child node of concept node C2, forming a parent-child relationship.

[0055] First, based on the knowledge units and problem concept lattice, a macro-learning sequence is planned to form a macro-path, providing a top-level framework for the learning path and ensuring that learners can systematically master the knowledge units. In this embodiment, the macro-path is from "Numbers and Algebra" to "Functions" and then to "Graphics and Geometry".

[0056] Under the constraints of the macro-path, and based on the skill and problem concept lattice, the learning path within each knowledge unit is refined. In this embodiment, within the "Numbers and Algebra" knowledge unit, the learning sequence is further refined into fine-grained skills such as "rational number operations," "real number operations," and "algebraic expression operations," avoiding combinatorial explosion caused by full-scale construction. Figure 2 As shown, the left side of the figure represents a partial knowledge unit concept lattice, based on a matrix. The structure is as follows: 'a' represents a function unit, 'b' represents an inverse proportional function, 'c' represents a linear function, 'd' represents a quadratic function, and '1', '2', '3', and '4' represent the problems solved by coarse-grained knowledge units. The right side of the figure shows a partial skill concept grid, based on a matrix. The concept lattice is constructed and constrained by knowledge units, that is, it is constructed only within the skills corresponding to the knowledge units. Knowledge unit c contains skills s1, s2, and s3, and knowledge unit d contains skills s4, s5, and s6. Here, s1 represents the meaning and expression of a linear function, s2 represents the graph and properties of a linear function, s3 represents the application of a linear function, s4 represents the meaning and expression of a quadratic function, s5 represents a quadratic function and a quadratic equation in one variable, s6 represents the graph and properties of a quadratic function, and q1, q2, q3, q4, and q5 represent the problems solved by the fine-grained skills.

[0057] Step 5. Construct knowledge units and multi-granularity dependency graphs for skills based on skill indicators and dependencies.

[0058] Step 5.1. Calculate the cost and reward value for each concept node according to the following formula.

[0059]

[0060] In the formula, The cost of a concept node. A set of skills contained within a concept node. For the first The cognitive level coefficients for each skill are as follows: understanding = 1.0, comprehension = 1.2, mastery = 1.5, and application = 2.0. For the first The process requirement coefficients for each skill are as follows: None = 1.0, Experience = 1.1, Exploration = 1.3; For the first The difficulty coefficients for each skill are as follows: Easy = 0.8, Medium = 1.0, Difficult = 1.2, and Extremely Difficult = 1.5. This is a normalization constant, in this embodiment , The reward value for the concept node. No. The knowledge module weights for each skill are as follows: Mathematics and Algebra = 5.0, Geometry = 3.5, and Statistics = 1.5. For the first The frequency coefficients for each skill are as follows: low frequency = 0.5, medium frequency = 1.0, and high frequency = 1.5. For the first The core competency bonus coefficients for each skill are as follows: Basic = 1.0, Core = 3.0;

[0061] Example: For the skill "Graphs and Properties of Quadratic Functions" (ID:47), the Examination Standard requires "Mastery" (1.5), involves "Exploration" (1.3), and is a challenging final point (1.5), so the required effort is... .

[0062] Example: For the skill "Graph and properties of quadratic functions" (ID:47), it belongs to Number and Algebra (5.0), a high-frequency test point (1.5), and belongs to the core competency test point (3.0).

[0063] but .

[0064] Step 5.2. Prune redundant nodes to obtain a simplified two-level conceptual lattice structure, where redundant nodes are nodes that can be logically covered by other nodes;

[0065] Step 5.3. Traverse the simplified hierarchical structure of the two-level concept lattice, and based on the discovered dependencies, examine the relationships between each node. If the nodes... It is a node The child nodes, and master It is to master The necessary condition is to establish from arrive Given directed edges, obtain a skill dependency graph. and knowledge unit dependency graph , For the collection of all skills, It is a set of edges representing skill dependencies; For the set of all knowledge units, It is a set of edges representing the dependencies between knowledge units. For example... Figure 3 , is a dependency graph between some knowledge units, where a represents a function unit, b represents an inverse proportional function, c represents a linear function, and d represents a quadratic function. The dependency graph reveals the learning order: a -> b, a -> c, c -> d.

[0066] Step 6. Generate multi-granularity learning paths

[0067] By fusing a simplified two-level concept lattice with a multi-granularity dependency graph, a directed acyclic graph (DAG) containing concept nodes and their progressive relationships is generated. Specifically, the concept nodes in the simplified two-level concept lattice are mapped to knowledge unit nodes in the DAG. and skill nodes First, based on the knowledge unit dependency relationship Construct edges between nodes in a directed acyclic graph of knowledge units. Generate a directed acyclic graph of knowledge units. It generates knowledge unit learning paths, and then, based on the planning of these knowledge unit learning paths and skill dependencies... Constructing edges between nodes in a directed acyclic graph of skills Generate a directed acyclic graph , where each node Representing a knowledge state, which includes a set of skills, each edge... Indicates from the state of knowledge To the state of knowledge The leap. For example... Figure 4 This is a partially directed acyclic graph obtained by combining a coarse-grained concept lattice with a knowledge unit dependency graph. All generative learning paths in the graph strictly follow the dependencies between knowledge units. Figure 3 To maintain consistency, there is no situation where c (linear function) is not learned before d (quadratic function).

[0068] Step 7. Path Recommendation and Optimization

[0069] Step 7.1. Traverse the directed acyclic graph to generate multiple candidate paths, and calculate the number of adjacent nodes in each path. The transition sensitivity is calculated by taking the geometric mean of all transition sensitivities along the path as the path's recommendation index, where each pair of adjacent nodes... Conversion sensitivity ;

[0070] Step 7.2. Based on the learner's basic level and learning goals, select and recommend the optimal learning path. For learners with weak foundations, prioritize paths with low input and high return; for learners with good foundations, recommend more challenging paths.

[0071] For example, for a student with a weak foundation (currently with a 30% mastery rate), the system prioritizes highly responsive paths, i.e., basic modules with low input and high return, such as "rational numbers," "polynomial operations," and "basic linear functions." For skill ID:2 (opposite numbers), Pay=9.6, Re=35.0, the cost-effectiveness is extremely high, and it is prioritized. For skill ID:47 (comprehensive quadratic functions), Pay=29.25, Re=105.0, although the return is high, the input is huge. The system will place it at the end of the path, recommending it only after the student has mastered the prerequisite lower-level skills such as "equations" and "coordinate systems."

Claims

1. A method for recommending and optimizing multi-granularity learning paths based on a large language model, characterized in that, Includes the following steps: Step 1. Preprocess the learning dataset Collect subject learning data, including past exam questions, accompanying mock questions, and teaching standard documents. Preprocess the subject learning data, including labeling the fine-grained skill points corresponding to the questions, dividing them into coarse-grained knowledge units, mining the dependencies between knowledge units and skills, and classifying the difficulty of the questions. Step 2. Construct a multi-granularity knowledge structure The teaching standard document based on the large language model analysis extracts teaching knowledge points into a three-layer knowledge structure of large units, knowledge units, and fine-grained skills; Step 3. Construct a multi-level correlation matrix Construct an association matrix R1 between large units and knowledge units, an association matrix R2 between knowledge units and problems, and an association matrix R3 between fine-grained skills and problems. The elements of matrix R1 indicate whether a large unit contains a specific knowledge unit, the elements of matrix R2 indicate whether a specific knowledge unit is used to solve a specific problem, and the elements of matrix R3 indicate whether a specific skill is used to solve a specific problem. Step 4. Construct a two-level concept lattice Based on the theory of formal concept analysis, we construct concept lattices for skills and problems and for knowledge units and problems, respectively. With the set of skills and the set of knowledge units as the connotation and the set of problems as the extension, concept nodes are generated to form a hierarchical structure, resulting in a two-level concept lattice. Step 5. Construct a multi-granularity dependency graph of knowledge units and skills. The input and output values ​​of each concept node are calculated, redundant nodes are pruned, and a simplified two-level concept lattice structure is obtained. Based on the hierarchical structure of the simplified two-level concept lattice and the pre-dependencies between the knowledge units and skills mined out, a multi-granularity dependency graph is constructed. Step 6. Generate multi-granularity learning paths The simplified two-level concept lattice is fused with a multi-granularity dependency graph to generate a directed acyclic graph containing concept nodes and the progressive relationships between nodes. Multi-granularity learning paths are obtained through the directed acyclic graph. Step 7. Path Recommendation and Optimization Iterate through all multi-granularity learning paths, calculate the recommendation index for each path, and select and recommend the optimal learning path based on the learner's basic level and learning goals.

2. The method for recommending and optimizing multi-granularity learning paths based on a large language model according to claim 1, characterized in that, In step (5), the method for calculating the cost and reward value of each concept node is as follows: In the formula, The cost of a concept node. A set of skills contained within a concept node. For the first The cognitive level coefficient of each skill For the first The process requirement coefficient for each skill For the first The inherent difficulty coefficient of each skill The normalization constant is The reward value for the concept node. No. The weight of each skill's knowledge segment For the first The frequency coefficient of each skill's assessment For the first The core competency bonus coefficient for each skill.

3. The method for recommending and optimizing multi-granularity learning paths based on a large language model according to claim 1, characterized in that, In step 5, the method for constructing a multi-granularity dependency graph based on the hierarchical structure of the simplified concept lattice and the pre-dependencies between the mined knowledge units and skills is as follows: traverse the hierarchical structure of the simplified concept lattice, check the relationships between each concept node, and if the nodes... It is a node The child nodes, and master the nodes. It is about mastering the nodes The necessary condition is to establish from arrive Given directed edges, obtain a skill dependency graph. and knowledge unit dependency graph ,in, A collection of all skills. Let be the set of edges representing skill dependencies; For the set of all knowledge units, Let be the set of edges representing the dependencies between knowledge units.

4. The method for recommending and optimizing multi-granularity learning paths based on a large language model according to claim 3, characterized in that, In step 6, the method for generating a directed acyclic graph containing concept nodes and the progressive relationships between nodes is as follows: mapping the concept nodes in the simplified two-level concept lattice to knowledge unit nodes in the directed acyclic graph. and skill nodes First, based on the knowledge unit dependency relationship Construct edges between nodes in a directed acyclic graph of knowledge units. Generate a directed acyclic graph of knowledge units. It generates knowledge unit learning paths, and then, based on the planning of these knowledge unit learning paths and skill dependencies... Constructing edges between nodes in a directed acyclic graph of skills Generate a directed acyclic graph , where each node Representing a knowledge state, which includes a set of skills, each edge... Indicates from the state of knowledge To the state of knowledge The leap.

5. The method for recommending and optimizing multi-granularity learning paths based on a large language model according to claim 4, characterized in that, The method for calculating the recommendation index for each path in step 7 is as follows: calculate the recommendation index for each pair of adjacent nodes in each path. The conversion sensitivity is calculated, and the geometric mean of all conversion sensitivities in the path is used as the recommendation index for the path; the conversion sensitivity of each pair of adjacent nodes... Conversion sensitivity .

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