An adaptive learning path planning method based on a knowledge graph and multiple agents

Abstract

This invention presents an adaptive learning path planning method based on knowledge graphs and multi-agent systems. It utilizes the KG-MAS-Plan adaptive planning framework to accurately perceive the learner's cognitive state and learning intentions, formalizing personalized learner path planning. Subsequently, a planning agent generates candidate paths, and a review agent is introduced to perform dual verification of logical compliance and personalized adaptability. Based on the verification results, the learning path is planned. This invention effectively solves the problems of poor path logic, insufficient personalization, high risk of LLM illusion, and difficulty in dynamic adaptation in existing technologies. It can generate highly reliable, highly adaptable, and interpretable personalized learning paths, suitable for scenarios such as online education platforms and intelligent tutoring systems.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence education, specifically to an adaptive learning path planning method based on knowledge graphs and multi-agent systems. Background Technology

[0002] In recent years, Large Language Models (LLMs) have demonstrated outstanding reasoning and generative capabilities, offering new possibilities for more intelligent path planning. Meanwhile, knowledge graphs, as important tools for characterizing subject-specific knowledge structures and prerequisite dependencies, have been widely applied in educational recommendation and cognitive modeling.

[0003] Despite its promising future, current research faces a dual dilemma in generating high-quality personalized learning paths. On one hand, early static path generation methods, such as clustering-based techniques, often recommend redundant or irrelevant content because they ignore potential dependencies between learning objects. On the other hand, while some methods attempt to capture shifts in user preferences and changes in features through relational networks, item response theory, or Bayesian update mechanisms, they generally suffer from long evaluation cycles, causing path adjustments to lag behind actual learning progress. Finally, while emerging technologies like LLM hold promise for breaking this deadlock, they have revealed new fatal flaws in practical applications. Research shows that LLM is prone to factual and logical illusions when performing complex subject-specific reasoning, and its general knowledge struggles to automatically align with strict educational domain constraints such as curriculum standards. Therefore, it needs to be guided by structured knowledge and constrained reasoning.

[0004] To address this, this invention proposes an adaptive learning path planning method based on knowledge graphs and multi-agent systems. This framework uses a deep reasoning model as its core, injecting pre- and post-relationships and concept dependencies from the subject knowledge graph as constraints into the model's reasoning process through progressive LoRA fine-tuning. This suppresses potential illusions during model generation, making the results more reliable. Based on Bloom's Taxonomy of Educational Objectives, diagnostic experts are deployed to assess students' cognitive levels at each level—memory, comprehension, application, analysis, evaluation, and creation—based on knowledge mastery, problem-solving ability, and learning behavior patterns. These assessments are then integrated by higher-level experts to achieve accurate identification of cognitive states from multiple perspectives and levels. The multi-agent adaptive learning path planning framework, combined with cognitive diagnostic results, adjusts learners' learning paths in real time, achieving dynamic learning. Summary of the Invention

[0005] The purpose of this invention is to address the problems in the background art by providing an adaptive learning path planning method based on knowledge graphs and multi-agent systems.

[0006] The above-mentioned technical objective of the present invention is achieved through the following technical solution:

[0007] An adaptive learning path planning method based on knowledge graphs and multi-agent systems is characterized by accurately perceiving the learner's cognitive state and learning intention through the adaptive planning framework KG-MAS-Plan, and formalizing personalized learner path planning; then, the planning agent generates candidate paths, and a review agent is introduced to perform dual verification of logical compliance and personalized adaptability; based on the verification results, the learning path is planned.

[0008] The adaptive planning framework KG-MAS-Plan includes: a dual-drive infrastructure module, a multi-expert cognitive diagnosis module, and a multi-agent collaborative planning module.

[0009] The dual-drive infrastructure module includes: ① constructing a domain knowledge graph and performing serialization representation, wherein the domain knowledge graph contains knowledge point entities and logical dependencies between entities, and is serialized using a hierarchical YAML format; ② based on a deep reasoning large model, the knowledge graph and the model are integrated through progressive LoRA fine-tuning, wherein the fine-tuning process includes four stages: knowledge graph pre-training, multi-hop reasoning training, question answering adaptation optimization, and path planning educational guidance training.

[0010] The multi-expert cognitive diagnostic module includes: ① a diagnostic template based on Bloom's taxonomy; ② a multi-expert collaborative diagnostic architecture;

[0011] The multi-agent collaborative planning module includes: ① an intent analysis agent; ② a knowledge point retrieval agent; ③ a profile parsing agent; ④ a path planning agent; and ⑤ a path evaluation agent.

[0012] Preferably, the specific steps of the formalized personalized learner path planning problem are as follows: Let Indicates by A knowledge base composed of knowledge points, which are connected through a knowledge graph. Organization, among which It is a collection of relationships between knowledge points;

[0013] make Represents a learner, whose time is... The cognitive state is represented by a vector It means that among them Indicate learner Knowledge points The learner's level of mastery; At any moment Learning intentions It is usually expressed in the form of natural language text;

[0014] According to learners Current cognitive state and learning intention Generate an optimal learning path The function is as follows:

[0015]

[0016] Among them, learning path It is a sequence of knowledge points.

[0017] Preferably, the dual-drive infrastructure module constructs a subject knowledge graph covering core concepts in the algebra domain. This knowledge graph is based on formalized triples, where the entity set encompasses core concepts in the knowledge domain, and the relation set includes logical dependencies such as "prerequisite," "successor," "belongs to," and "related to." A hierarchical YAML format is used to serialize the graph. A guided instruction fine-tuning strategy is applied to the knowledge graph, and three types of self-supervised instruction tasks are constructed based on the algebraic graph: 1) Entity and relation prediction, forcing the model to infer prerequisite concepts from context or complete missing knowledge triples; 2) Graph to text, converting structured subgraphs into coherent natural language teaching guidance, enhancing the model's understanding of structured data; 3) Text to graph, training the model to extract core concepts and their logical dependencies from unstructured teaching texts and reverse-engineer a structured graph.

[0018] Preferably, in the progressive fine-tuning, the low-rank adaptation (LoRA) method in the Parametric Efficient Fine-Tuning (PEFT) technique is used to perform multi-stage progressive training on the base model DeepSeek-R1-Distill-Qwen-7B; the multi-stage training process steps are as follows:

[0019] 1) Knowledge Graph Pre-training: Based on instruction fine-tuning, in order to further internalize the global factual knowledge in the graph and implement a continuous pre-training strategy, the complete knowledge graph is serialized into a YAML format with hierarchical indentation; the model is optimized on the serialized KG corpus by minimizing the negative log-likelihood loss of the next label prediction, so as to enhance the ability to capture long-range structural dependencies and domain knowledge distribution.

[0020] 2) Multi-hop reasoning training: To address the issues of retrieval noise interference and lack of explicit reasoning paths, a teacher-student paradigm is adopted to construct high-quality reasoning supervision data; a noisy candidate subgraph is obtained using an untuned retrieval machine, and a strong teacher model DeepSeek-R1-32b is introduced as a generator; the question, retrieval context, and standard answer are simultaneously input into the teacher model, forcing it to plan the logical thought chain (CoT) of the correct answer in the noisy data, transforming the implicit answer mapping into an explicit reasoning trajectory;

[0021] 3) Question-answering adaptation optimization: Optimize the model's autonomous reasoning ability. The model input only includes the question and the retrieved YAML format knowledge graph, and the standard answer is hidden. The training objective is to reproduce the thought chain steps generated by the teacher's model.

[0022] 4) Path planning education guidance and training: Based on a comprehensive model of students' learning status, ability level and learning preferences, the model dynamically generates adaptive path suggestions and resource recommendations by analyzing students' historical learning data and current performance.

[0023] Preferably, the diagnostic template of Bloom's Taxonomy includes a bijective mechanism of "knowledge point - cognitive level," and the six dimensions of Bloom's Taxonomy are formalized into three computable assessment levels: basic abilities (memory, comprehension), core abilities (application, analysis), and higher-order abilities (evaluation, creation); for each knowledge point... The system constructs differentiated structured evaluation templates, transforming behavioral characteristics such as answering time, completeness of steps, and innovative expression into quantitative indicators;

[0024] set up For learners in the The accuracy rate at each cognitive level is determined by pre-setting a basic weight vector, taking into account the differences in the contribution of different levels to mastery. To mitigate assessment bias caused by the complete failure of specific question types, a penalty factor is introduced. Construct an adaptive weight adjustment mechanism:

[0025]

[0026] in The indicator function is used; after normalization, the final hierarchical weights are obtained. :

[0027] ;

[0028] Ultimately, the overall mastery level is derived from a weighted average:

[0029] .

[0030] Preferably, the multi-expert collaborative diagnostic architecture, based on the assessment hierarchy, deploys three functionally decoupled expert agents working in parallel to achieve comprehensive cognitive assessment:

[0031] Knowledge Mastery Diagnosis Expert: This expert agent corresponds to memory and comprehension. By analyzing the accuracy rate of basic question types, it constructs a baseline of learners' cognitive understanding of facts and concepts.

[0032] Problem-solving ability diagnostic expert: This expert agent corresponds to the application and analysis, analyzes the learner's strategy selection and the rigor of steps in complex situations, and assesses the knowledge transfer and logical reasoning ability.

[0033] Learning Behavior Pattern Diagnostic Expert: This expert agent corresponds to evaluation and creation, and is a reflection of the depth of system diagnosis. By monitoring the degree of cue dependence, answer correction trajectory and the innovativeness of open-ended questions, it reveals the level of metacognitive skills and critical thinking.

[0034] After all experts have completed the information refinement through interaction, a senior comprehensive expert will be responsible for the final summary and refinement of these three sets of collaboratively revised professional reports; based on the hierarchical relationship of Bloom's theory, the performance patterns of students in different cognitive dimensions will be analyzed; finally, a structured, personalized, multi-dimensional cognitive diagnostic report will be generated, clearly identifying the highest effective cognitive level achieved by the student in each knowledge point and its weak points.

[0035] To enhance the semantic depth of the diagnosis, a large language model is used to perform fine-grained analysis of the problem-solving process and output qualitative conclusions: not mastered, weakly mastered, well mastered, and excellent mastered; to achieve algorithm integration, these conclusions are mapped to numerical indicators.

[0036] The final knowledge point mastery level is calculated using a linear weighted fusion strategy:

[0037]

[0038] in, As a balance factor, .

[0039] Preferably, the intent analysis agent utilizes a large language model fine-tuned for the education domain and performs deep semantic parsing of the original query through a prompting engineering guidance model to accurately extract key semantic elements such as learning objectives and difficulty preferences, and maps them into a standardized structured intent representation; this process can be formally represented as:

[0040]

[0041] in, This indicates that the large language model, fine-tuned with data from the education sector, possesses the ability to recognize intent and generate structured data. Its model parameters; for The raw natural language statements entered by the user at any given moment; The structured intent representation of the model output;

[0042] Preferably, the knowledge point retrieval agent utilizes a high-performance embedding model, nomic-embed-text, to construct a user intent and knowledge graph. Semantic mapping; firstly, the discrete knowledge points in the graph are mapped to the structured intent. The vectors are projected onto a unified high-dimensional dense vector space, and then vector similarity is calculated in this semantic space to filter the candidate set.

[0043]

[0044] in, This represents a vectorization function for a knowledge graph based on nomic-embed-text, used to construct a semantic index space; It is an isomorphic intent encoding function. It is a retrieval algorithm based on vector similarity calculation;

[0045] Preferably, the profile analysis agent is responsible for real-time tracking and dynamic modeling of the user's cognitive state; based on the user's historical interaction logs, it utilizes the logical reasoning capabilities of a large model to identify knowledge gap distribution patterns and missing prerequisites, and achieves iterative evolution of the user profile through a state update function.

[0046]

[0047] in, Represents the user's current step The cognitive state vector, Representing the user's steps in the previous time period The cognitive state vector, Represents the time step The collection of user learning behavior logs; It is an update function driven by fine-tuning the LLM;

[0048] Preferably, the path planning agent, as the core decision-making unit of the system, functions to determine the path planning based on the input set of knowledge concepts. Learner's current status and knowledge graphs Output a unique learning path; employ a state-aware sequence generation mechanism to directly construct the target path based on the knowledge graph's topology and learner profile; the generation process, while satisfying knowledge dependency constraints, incorporates the learner's current cognitive state. As a condition for generating the model, a logically coherent learning sequence that conforms to the individual's cognitive level is generated.

[0049] This process is mathematically formalized as a direct mapping function from the state space to the path space:

[0050]

[0051] in, This represents a path generation function; by integrating the structural information of the knowledge graph with the learner's feature vector, this function directly outputs an optimal path that conforms to subject-specific logic and meets personalized learning needs. ;

[0052] Preferably, the path evaluation agent takes as input the inference chain and candidate learning paths generated by the path planning agent described above, and outputs the evaluation result (Approved or Rejected) and structured feedback for the path. Based on the policy evaluation concept in reinforcement learning, the path evaluation agent constructs a hierarchical constraint satisfaction mechanism to evaluate the generated paths. Dual verification of execution logic and adaptability;

[0053] Based on the verification results, the system performs binary decision-making; if a constraint violation is detected, the path review agent generates a structured feedback signal, driving the path planning agent to perform multiple rounds of policy iteration and replanning until an optimal path that satisfies all constraints is generated, thereby achieving robust closed-loop optimization.

[0054] Preferably, the dual verification includes:

[0055] (1) Logical consistency constraints:

[0056] Check path Does it strictly adhere to the dependencies in the knowledge graph G, for any knowledge point in the path? All prerequisite knowledge points must satisfy the following:

[0057]

[0058] in, For knowledge points The set of prerequisite dependencies in the graph; This represents the set of knowledge that the learner has currently mastered.

[0059] (2) Multidimensional adaptability constraints:

[0060] Based on satisfying the logical constraints, the agent further evaluates whether the path adequately responds to the user's learning intent. First, does the core knowledge point include the assessment path? Next, is the assessment path tailored to the weaknesses identified in the learner's cognitive diagnosis? We focused on key areas and, after comprehensively considering learning efficiency and cognitive load, avoided recommending overly long or difficult paths.

[0061] In summary, the beneficial effects of this invention are as follows:

[0062] 1. The KG-MAS-Plan framework employed in this invention uses a deep reasoning large-scale model as its core. Through progressive LoRA fine-tuning, it injects pre- and post-relationships and concept dependency structures from the subject knowledge graph as constraints into the large-scale model's reasoning process, suppressing potential illusions during model generation and making the results more reliable. Based on Bloom's Taxonomy of Educational Objectives, diagnostic experts are deployed to assess students' cognitive levels at each level—memory, comprehension, application, analysis, evaluation, and creation—based on knowledge mastery, problem-solving ability, and learning behavior patterns. These assessments are then integrated by higher-level experts to achieve accurate identification of cognitive states from multiple perspectives and levels. Based on a multi-agent adaptive learning path planning framework, combined with cognitive diagnostic results, the learner's learning path is adjusted in real time to achieve dynamic learning.

[0063] 2. The KG-MAS-Plan framework proposed in this invention does not rely on reinforcement learning for end-to-end policy learning. Instead, it employs agents based on large language models for symbolic reasoning. By decomposing complex tasks into sub-tasks such as intent understanding, knowledge retrieval, profile updating, and diagnostic analysis, these sub-tasks are processed in parallel by specialized agents and coordinated and validated through a knowledge graph—a form of "shared memory." This approach combines the semantic understanding advantages of large models with the logical constraints of knowledge graphs, avoiding the training difficulties of pure reinforcement learning methods while achieving higher interpretability. This opens up a new path for building efficient and transparent intelligent education systems. Attached Figure Description

[0064] Figure 1 This is a schematic diagram of the overall architecture of the KG-MAS-Plan framework in this invention;

[0065] Figure 2 This is an example of KG serialization into YAML format in this invention;

[0066] Figure 3 This is a flowchart of the cognitive diagnosis process in this invention;

[0067] Figure 4 This is the multi-agent collaborative process in this invention.

[0068] Figure 5 This describes the impact of different model parameters on CDA and PMS in Example 2. Detailed Implementation

[0069] The following specific embodiments are merely illustrative of the present invention and are not intended to limit the invention. After reading this specification, those skilled in the art can make modifications to these embodiments without contributing any inventive step, but such modifications are protected by patent law as long as they fall within the scope of the claims of the present invention.

[0070] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0071] Example 1:

[0072] An adaptive learning path planning method based on knowledge graphs and multi-agent systems is characterized by accurately perceiving the learner's needs and state through the adaptive planning framework KG-MAS-Plan, and formalizing and personalizing the learner's intentions and profile; subsequently, the planning agent generates candidate paths, and a review agent is introduced to perform dual verification of logical compliance and personalization adaptability; based on the verification results, the learning path is planned. The adaptive planning framework KG-MAS-Plan includes: a dual-drive infrastructure module, a multi-expert cognitive diagnosis module, and a multi-agent collaborative planning module.

[0073] The specific steps of the formal personalized learner path planning problem are as follows: Let Indicates by A knowledge base composed of knowledge points, which are connected through a knowledge graph. Organization, among which It is a collection of relationships between knowledge points;

[0074] make Represents a learner, whose time is... The cognitive state is represented by a vector It means that among them Indicate learner Knowledge points The learner's level of mastery; At any moment Learning intentions It is usually expressed in the form of natural language text;

[0075] According to learners Current cognitive state and learning intention Generate an optimal learning path The function is as follows:

[0076]

[0077] Among them, learning path It is a sequence of knowledge points.

[0078] The dual-drive infrastructure module includes: ① Constructing a domain knowledge graph and performing serialization representation, wherein the domain knowledge graph contains knowledge point entities and logical dependencies between entities, and is serialized using a hierarchical YAML format; constructing a subject knowledge graph covering core concepts in the algebra domain; the knowledge graph is based on formal triples, wherein the entity set covers the core concepts in the knowledge domain, and the relation set contains logical dependencies such as "prerequisite", "successor", "belongs to", and "related"; the graph is serialized using a hierarchical YAML format; and a guided instruction fine-tuning strategy is applied to the knowledge graph, and three types of self-supervised instruction tasks are constructed based on the algebra graph: 1) Entity and relation prediction, forcing the model to infer prerequisite concepts or fill in missing knowledge triples based on context; 2) Graph to text, converting structured subgraphs into coherent natural language teaching guidance, strengthening the model's understanding of structured data; 3) Text to graph, training the model to extract core concepts and their logical dependencies from unstructured teaching texts, and reverse-engineering a structured graph.

[0079] ② Based on a large deep reasoning model, the knowledge graph and the model are integrated through progressive LoRA fine-tuning. The fine-tuning process includes four stages: knowledge graph pre-training, multi-hop reasoning training, question-answering adaptation optimization, and path planning educational guidance training. In the progressive fine-tuning, the Low-Rank Adaptation (LoRA) method in Parametric Efficient Fine-Tuning (PEFT) technology is used to perform multi-stage progressive training on the base model DeepSeek-R1-Distill-Qwen-7B. The steps of the multi-stage training process are as follows:

[0080] 1) Knowledge Graph Pre-training: Based on instruction fine-tuning, in order to further internalize the global factual knowledge in the graph and implement a continuous pre-training strategy, the complete knowledge graph is serialized into a YAML format with hierarchical indentation; the model is optimized on the serialized KG corpus by minimizing the negative log-likelihood loss of the next label prediction, so as to enhance the ability to capture long-range structural dependencies and domain knowledge distribution.

[0081] 2) Multi-hop reasoning training: To address the issues of retrieval noise interference and lack of explicit reasoning paths, a teacher-student paradigm is adopted to construct high-quality reasoning supervision data; a noisy candidate subgraph is obtained using an untuned retrieval machine, and a strong teacher model DeepSeek-R1-32b is introduced as a generator; the question, retrieval context, and standard answer are simultaneously input into the teacher model, forcing it to plan the logical thought chain (CoT) of the correct answer in the noisy data, transforming the implicit answer mapping into an explicit reasoning trajectory;

[0082] 3) Question-answering adaptation optimization: Optimize the model's autonomous reasoning ability. The model input only includes the question and the retrieved YAML format knowledge graph, and the standard answer is hidden. The training objective is to reproduce the thought chain steps generated by the teacher's model.

[0083] 4) Path planning education guidance and training: Based on a comprehensive model of students' learning status, ability level and learning preferences, the model dynamically generates adaptive path suggestions and resource recommendations by analyzing students' historical learning data and current performance.

[0084] The multi-expert cognitive diagnostic module includes:

[0085] ① The diagnostic template of Bloom's Taxonomy; the diagnostic template of Bloom's Taxonomy includes a bijective mechanism of "knowledge point - cognitive level". The six dimensions of Bloom's Taxonomy are formalized into three computable assessment levels: basic abilities (memory, comprehension), core abilities (application, analysis), and higher-order abilities (evaluation, creation); for each knowledge point The system constructs differentiated structured evaluation templates, transforming behavioral characteristics such as answering time, completeness of steps, and innovative expression into quantitative indicators;

[0086] set up For learners in the The accuracy rate at each cognitive level is determined by pre-setting a basic weight vector, taking into account the differences in the contribution of different levels to mastery. To mitigate assessment bias caused by the complete failure of specific question types, a penalty factor is introduced. Construct an adaptive weight adjustment mechanism:

[0087]

[0088] in The indicator function is used; after normalization, the final hierarchical weights are obtained. :

[0089] ;

[0090] Ultimately, the overall mastery level is derived from a weighted average:

[0091] .

[0092] ② Multi-expert collaborative diagnostic architecture; the multi-expert collaborative diagnostic architecture, based on the evaluation level, deploys three functionally decoupled expert agents to work in parallel to achieve comprehensive cognitive evaluation:

[0093] Knowledge Mastery Diagnosis Expert: This expert agent corresponds to memory and comprehension. By analyzing the accuracy rate of basic question types, it constructs a baseline of learners' cognitive understanding of facts and concepts.

[0094] Problem-solving ability diagnostic expert: This expert agent corresponds to the application and analysis, analyzes the learner's strategy selection and the rigor of steps in complex situations, and assesses the knowledge transfer and logical reasoning ability.

[0095] Learning Behavior Pattern Diagnostic Expert: This expert agent corresponds to evaluation and creation, and is a reflection of the depth of system diagnosis. By monitoring the degree of cue dependence, answer correction trajectory and the innovativeness of open-ended questions, it reveals the level of metacognitive skills and critical thinking.

[0096] After all experts have completed the information refinement through interaction, a senior comprehensive expert will be responsible for the final summary and refinement of these three sets of collaboratively revised professional reports; based on the hierarchical relationship of Bloom's theory, the performance patterns of students in different cognitive dimensions will be analyzed; finally, a structured, personalized, multi-dimensional cognitive diagnostic report will be generated, clearly identifying the highest effective cognitive level achieved by the student in each knowledge point and its weak points.

[0097] To enhance the semantic depth of the diagnosis, a large language model is used to perform fine-grained analysis of the problem-solving process and output qualitative conclusions: not mastered, weakly mastered, well mastered, and excellent mastered; to achieve algorithm integration, these conclusions are mapped to numerical indicators.

[0098] The final knowledge point mastery level is calculated using a linear weighted fusion strategy:

[0099]

[0100] in, As a balance factor, .

[0101] The multi-agent collaborative planning module includes: ① an intent analysis agent; ② a knowledge point retrieval agent; ③ a profile parsing agent; ④ a path planning agent; and ⑤ a path evaluation agent.

[0102] 1) The intent analysis agent: Utilizing a large language model fine-tuned for the education domain, and guided by a prompting engineering model, performs deep semantic parsing of the original query to accurately extract key semantic elements such as learning objectives and difficulty preferences, and maps them into a standardized structured intent representation; this process can be formally represented as:

[0103]

[0104] in, This indicates that the large language model, fine-tuned with data from the education sector, possesses the ability to recognize intent and generate structured data. Its model parameters; for The raw natural language statements entered by the user at any given moment; The structured intent representation of the model output;

[0105] 2) The knowledge point retrieval agent: Utilizes the high-performance embedding model nomic-embel-text to construct a user intent and knowledge graph. Semantic mapping; firstly, the discrete knowledge points in the graph are mapped to the structured intent. The vectors are projected onto a unified high-dimensional dense vector space, and then vector similarity is calculated in this semantic space to filter the candidate set.

[0106]

[0107] in, This represents a vectorization function for a knowledge graph based on nomic-embed-text, used to construct a semantic index space; It is an isomorphic intent encoding function. It is a retrieval algorithm based on vector similarity calculation;

[0108] 3) The user profile analysis agent: responsible for real-time tracking and dynamic modeling of the user's cognitive state; based on the user's historical interaction logs, it uses the logical reasoning ability of a large model to identify the distribution patterns of knowledge gaps and the absence of prerequisite dependencies, and realizes the iterative evolution of the user profile through a state update function.

[0109]

[0110] in, Represents the user's current step The cognitive state vector, Representing the user's steps in the previous time period The cognitive state vector, Represents the time step The collection of user learning behavior logs; It is an update function driven by fine-tuning the LLM;

[0111] 4) The path planning agent: As the core decision-making unit of the system, its function is to make decisions based on the input set of knowledge concepts. Learner's current status and knowledge graphs Output a unique learning path; employ a state-aware sequence generation mechanism to directly construct the target path based on the knowledge graph's topology and learner profile; the generation process, while satisfying knowledge dependency constraints, incorporates the learner's current cognitive state. As a condition for generating the model, a logically coherent learning sequence that conforms to the individual's cognitive level is generated.

[0112] This process is mathematically formalized as a direct mapping function from the state space to the path space:

[0113]

[0114] in, This represents a path generation function; by integrating the structural information of the knowledge graph with the learner's feature vector, this function directly outputs an optimal path that conforms to subject-specific logic and meets personalized learning needs. ;

[0115] 5) The path evaluation agent: its input is the inference chain and candidate learning paths generated by the path planning agent described above, and its output is the evaluation result (Approved or Rejected) and structured feedback for the path; the path evaluation agent is based on the policy evaluation idea in reinforcement learning, and constructs a hierarchical constraint satisfaction mechanism to evaluate the generated paths. Dual verification of execution logic and adaptability;

[0116] Based on the verification results, the system performs binary decision-making; if a constraint violation is detected, the path review agent generates a structured feedback signal, driving the path planning agent to perform multiple rounds of policy iteration and replanning until an optimal path that satisfies all constraints is generated, thereby achieving robust closed-loop optimization.

[0117] The dual verification includes:

[0118] (1) Logical consistency constraints:

[0119] Check path Does it strictly adhere to the dependencies in the knowledge graph G, for any knowledge point in the path? All prerequisite knowledge points must satisfy the following:

[0120]

[0121] in, For knowledge points The set of prerequisite dependencies in the graph; This represents the set of knowledge that the learner has currently mastered.

[0122] (2) Multidimensional adaptability constraints:

[0123] Based on satisfying the logical constraints, the agent further evaluates whether the path adequately responds to the user's learning intent. First, does the core knowledge point include the assessment path? Next, is the assessment path tailored to the weaknesses identified in the learner's cognitive diagnosis? We focused on key areas and, after comprehensively considering learning efficiency and cognitive load, avoided recommending overly long or difficult paths.

[0124] Example 2:

[0125] In this embodiment, experiments are conducted on a real dataset to evaluate the performance of each method on the learning path planning task.

[0126] 1. Create a dataset

[0127] To comprehensively evaluate the effectiveness of this system in personalized learning path planning tasks, we constructed a multimodal education dataset that integrates structured knowledge graphs with real student behavior data.

[0128] The experimental data came from the “2012-13 School Data with Affect” dataset on the ASSISTments platform. This dataset records approximately 4.2 million interaction logs of American middle school students in the process of learning mathematics. Each record includes student ID, question ID, knowledge point tag, correctness of answer, answer time, number of times hints were used, and emotional state (such as confusion, focus, frustration, etc.) predicted by the emotion model, as shown in Table 1.

[0129] Table 1. 2012-13 School Data with Affect Dataset Composition

[0130]

[0131] To construct supervised learning data that can be used for path planning evaluation, records with missing key fields (such as correctness and knowledge points) are removed, and outlier filtering is performed on the response time (removing extreme values ​​of <5 seconds or >30 minutes). The original questions are mapped to fine-grained knowledge point nodes in the Math_KG graph to ensure the consistency of knowledge representation.

[0132] To verify the authenticity of the constructed dataset, three experts with over five years of experience teaching secondary school mathematics were invited to manually annotate the optimal learning path segment (i.e., the next set of knowledge points to be learned) for each student at a specific time point, based on students' historical behavioral sequences (such as consecutive errors, long delays, and frequent use of prompts) and their final mastery status. The annotation process employed a double-blind review process, with disagreements arbitrated by a third expert to ensure annotation quality.

[0133] After data cleaning and anonymization, a test set containing 1086 users was constructed, as shown in Table 2.

[0134] The new user test set consists of 486 users (used to evaluate cold start scenarios); the existing user test set consists of 600 users, further subdivided as follows:

[0135] 1) Users with weak foundation: 200 (meeting the following condition: number of weak knowledge points - number of mastered knowledge points ≥ 5);

[0136] 2) Balanced users: 200 (satisfying: |number of weak knowledge points -number of mastered knowledge points|≤2);

[0137] 3) Advanced users: 200 (meeting the following criteria: number of knowledge points mastered - number of weak knowledge points ≥ 5);

[0138] Table 2. Composition of the test set

[0139]

[0140] 2. Experiment

[0141] This system model:

[0142] Built upon the DeepSeek-R1 large language model, this model boasts significant advantages in Chinese understanding, inference efficiency, and localized deployment. All agents (path planning, cognitive diagnosis, and path evaluation) are based on DeepSeek-R1, with efficient parameter fine-tuning achieved through LoRA technology (rank=8, alpha=16, dropout=0.1). The backbone model parameters are frozen, and only the low-rank adaptation matrix is ​​trained.

[0143] The model was fine-tuned on a training set containing 10,000 labeled paths, using the AdamW optimizer (learning rate = 2e-5, weight decay = 0.01), a batch size of 32, and training for 5 epochs. The temperature parameter was set to 0.7 to balance generation diversity and stability. All experiments were performed on 4×NVIDIA V100 32GB GPUs, with 4-bit quantization used during inference to improve efficiency.

[0144] The system operates in a "fine-tuning + inference" mode, meaning that after the model is fine-tuned on the training set, path generation is performed on the test set, rather than using zero-shot hints.

[0145] Comparison Model:

[0146] ①DeepSeek-R1:7B: A large language model with 7 billion parameters that has not been specifically trained, serving as a zero-shot baseline.

[0147] ②Llama-3.1:8B: A large model with 8 billion parameters that possesses broader general knowledge, representing the current advanced general AI capabilities.

[0148] 3. Evaluation Indicators

[0149] The system performance is evaluated using two core metrics: (1) Cognitive diagnosis accuracy: This measures the accuracy of the model in predicting the user's mastery of knowledge points and calculates the proportion of correct predictions. (2) Path matching degree: This measures the consistency between the generated path and the ideal path designed by the expert and calculates the proportion of correctly predicted path samples.

[0150] This study uses three key dimensions—path order, node hit rate, and path compliance—to construct a comprehensive evaluation index. The specific formula for calculating path matching degree is as follows:

[0151]

[0152] in:

[0153] This represents the final path matching score.

[0154] The path order score measures whether the arrangement of knowledge points in the path conforms to the pre-dependencies in the knowledge graph. It can be calculated by checking the proportion of paths that violate dependency constraints.

[0155] The node hit score reflects the completeness of knowledge point coverage along the path. It can be weighted according to the matching type.

[0156]

[0157] in These represent the number of knowledge points that were exactly matched and the number that were approximately matched, respectively. This represents the total number of knowledge points that should be covered.

[0158] To evaluate the reasoning process, a 32B language model with a larger parameter scale is used as a meta-evaluator to perform deep semantic scoring on the reasoning links, knowledge connections, and logical rationality of the generated path.

[0159] The path order score has the highest weight, reflecting the educational principle of "gradual progression." The system selects the path with the best overall score, complete knowledge, and logical coherence as the output. Path matching is judged based on whether the overall score exceeds the threshold β=0.7. This value strikes a balance between accuracy and inclusiveness, ensuring recommendation quality while retaining a reasonable margin for error, supporting dynamic evaluation and continuous optimization.

[0160] This comprehensive evaluation system, through multi-dimensional weighted integration, comprehensively measures the performance of the generated path in three aspects: structural logic, knowledge completeness, and reasoning rationality, effectively improving the objectivity and credibility of the evaluation. The weight setting (6:2:2) reflects the dominant role of the path sequence logic in the quality of the learning path, while also taking into account the coverage of knowledge points and the interpretability of the generation process.

[0161] 3. Performance Comparison

[0162] Table 3 shows the performance comparison between the KG-MAS-Plan framework and various baseline models in terms of cognitive diagnosis accuracy and path matching accuracy. The results show that the KG-MAS-Plan framework achieved the best performance in both metrics. In terms of cognitive diagnosis accuracy, KG-MAS-Plan reached 0.821, outperforming all baselines, improving by 5.94% compared to the untrained DeepSeek-R1, and by 17.96% compared to the more knowledge-rich Llama-3.1. This indicates that through targeted training and multi-agent collaborative reasoning, KG-MAS-Plan can more accurately understand the user's state. In terms of path matching accuracy, KG-MAS-Plan reached 0.785, far exceeding Llama-3.1's 0.510 (an improvement of 53.92%). This demonstrates that the framework of this invention has significant advantages in generating personalized paths that conform to teaching logic. It is worth noting that Llama-3.1, with its richer knowledge base, performed poorly, indicating that general knowledge is not equivalent to reasoning ability for specialized tasks. This result validates the overall effectiveness of KG-MAS-Plan. KG-MAS-Plan significantly outperforms existing baseline models in both cognitive diagnosis accuracy and path matching, verifying its superiority in generating highly reliable and adaptive personalized learning paths.

[0163] Table 3 Performance Comparison of Different Models

[0164]

[0165] ② To verify the effectiveness of key components in the KG-MAS-Plan framework, we conducted ablation experiments. The results are shown in Table 4. The results show that removing any key module leads to performance degradation. Removing the knowledge graph (KG-MAS-Planw / oKG) has the greatest impact on path matching accuracy (a decrease of 0.065), indicating that KG is the cornerstone for ensuring the compliance of path logic. After removing the path review agent (KG-MAS-Planw / oReview), the path matching accuracy decreased by 0.035, indicating that this module effectively filters unreasonable paths and improves the reliability of the output. These results fully verify the necessity and effectiveness of the design of each module in the KG-MAS-Plan framework.

[0166] Table 4 Ablation Experiment Results

[0167]

[0168] ③ The system analyzes the impact of three key hyperparameters on model performance: LoRArank r, LLM generation temperature τ, and Top-p sampling probability p. The results are as follows: Figure 5 As shown.

[0169] LoRA rank r: This parameter determines the dimension of the low-rank matrix introduced during fine-tuning, directly affecting the model's learnable capacity. Experiments show that when r increases from 4 to 8, both cognitive diagnosis accuracy and path matching accuracy significantly improve, indicating that a larger r can capture more complex educational reasoning patterns. Performance peaks at r=8; further increasing to 16 results in a slight performance decrease, possibly due to slight overfitting caused by excessive model capacity. Therefore, r=8 is the optimal choice. Figure 5 As shown in (a).

[0170] Temperature τ: This parameter controls the randomness of the generation process. When τ=0, the model uses greedy decoding, resulting in overly deterministic outputs lacking diversity and low path matching accuracy. When τ=0.6, the model achieves the optimal balance between exploring new paths and maintaining logical consistency, with both metrics reaching their highest levels. When τ is further increased to 0.8 and 1.0, the output randomness becomes too strong, leading to logical jumps or knowledge gaps in the generated paths, resulting in a significant performance degradation, such as... Figure 5 As shown in (b).

[0171] Top-p p: This parameter controls the proportion of words considered during sampling. When p=0.1, only the words with the highest probability are retained, resulting in overly conservative generation that fails to cover diverse learning path patterns. When p=0.4, the model introduces moderate diversity while maintaining output stability, achieving optimal performance. When p=1.0, all words participate in sampling, leading to uncontrollable generated content and decreased path quality, such as... Figure 5 As shown in (c).

[0172] In summary, r=8, τ=0.6, and p=0.4 are the optimal configurations, verifying that setting the generation and fine-tuning parameters appropriately is crucial for improving system performance.

Claims

1. An adaptive learning path planning method based on knowledge graphs and multi-agent systems, characterized in that, The KG-MAS-Plan adaptive planning framework accurately perceives learners’ cognitive state and learning intentions, and formalizes personalized learner path planning. Subsequently, the planning agent generates candidate paths, and a review agent is introduced to perform dual verification of logical compliance and personalized adaptability. Based on the verification results, the learning path is planned. The adaptive planning framework KG-MAS-Plan includes: a dual-drive infrastructure module, a multi-expert cognitive diagnosis module, and a multi-agent collaborative planning module. The dual-drive infrastructure module includes: ① constructing a domain knowledge graph and performing serialization representation, wherein the domain knowledge graph contains knowledge point entities and logical dependencies between entities, and is serialized using a hierarchical YAML format; ② based on a deep reasoning large model, the knowledge graph and the model are integrated through progressive LoRA fine-tuning, wherein the fine-tuning process includes four stages: knowledge graph pre-training, multi-hop reasoning training, question answering adaptation optimization, and path planning educational guidance training. The multi-expert cognitive diagnostic module includes: ① a diagnostic template based on Bloom's taxonomy; ② a multi-expert collaborative diagnostic architecture; The multi-agent collaborative planning module includes: ① an intent analysis agent; ② a knowledge point retrieval agent; ③ a profile parsing agent; ④ a path planning agent; and ⑤ a path evaluation agent.

2. The adaptive learning path planning method based on knowledge graphs and multi-agent systems according to claim 1, characterized in that, The specific steps of the formal personalized learner path planning problem are as follows: Let Indicates by A knowledge base composed of knowledge points, which are connected through a knowledge graph. Organization, among which It is a collection of relationships between knowledge points; make Represents a learner, whose time is... The cognitive state is represented by a vector. It means that, among them Indicate learner Knowledge points The learner's level of mastery; At any moment Learning intentions It is usually expressed in the form of natural language text; According to learners Current cognitive state and learning intention Generate an optimal learning path The function is as follows: ； Among them, learning path It is a sequence of knowledge points.

3. The adaptive learning path planning method based on knowledge graphs and multi-agent systems according to claim 1, characterized in that, The dual-drive infrastructure module constructs a subject knowledge graph covering core concepts in the algebra domain. This knowledge graph is based on formalized triples, where the entity set encompasses the core concepts of the knowledge domain. A hierarchical YAML format is used to serialize the graph. A guided instruction fine-tuning strategy is applied to the knowledge graph, constructing three types of self-supervised instruction tasks based on the algebraic graph: 1) Entity and relation prediction, forcing the model to infer prerequisite concepts from context or complete missing knowledge triples; 2) Graph-to-text, converting structured subgraphs into coherent natural language teaching guidance, enhancing the model's understanding of structured data; 3) Text-to-graph, training the model to extract core concepts and their logical dependencies from unstructured teaching texts and reverse-engineer a structured graph.

4. The adaptive learning path planning method based on knowledge graphs and multi-agent systems according to claim 1, characterized in that, In the progressive fine-tuning, the low-rank adaptation (LoRA) method in the Parametric Efficient Fine-tuning (PEFT) technique is used to perform multi-stage progressive training on the base model. The multi-stage training process is as follows: 1) Knowledge Graph Pre-training: Based on instruction fine-tuning, in order to further internalize the global factual knowledge in the graph and implement a continuous pre-training strategy, the complete knowledge graph is serialized into a YAML format with hierarchical indentation; the model is optimized on the serialized KG corpus by minimizing the negative log-likelihood loss of the next label prediction, so as to enhance the ability to capture long-range structural dependencies and domain knowledge distribution. 2) Multi-hop reasoning training: To address the issues of retrieval noise interference and lack of explicit reasoning paths, a teacher-student paradigm is adopted to construct high-quality reasoning supervision data; a noisy candidate subgraph is obtained using an untuned retrieval tool, and a strong teacher model is introduced as a generator; the question, retrieval context, and standard answer are simultaneously input into the teacher model, forcing it to plan the logical thought chain (CoT) of the correct answer in the noisy data, transforming the implicit answer mapping into an explicit reasoning trajectory; 3) Question-answering adaptation optimization: Optimize the model's autonomous reasoning ability. The model input only includes the question and the retrieved YAML format knowledge graph, and the standard answer is hidden. The training objective is to reproduce the thought chain steps generated by the teacher's model. 4) Path planning education guidance and training: Based on a comprehensive model of students' learning status, ability level and learning preferences, the model dynamically generates adaptive path suggestions and resource recommendations by analyzing students' historical learning data and current performance.

5. The adaptive learning path planning method based on knowledge graphs and multi-agent systems according to claim 1, characterized in that, The diagnostic template of Bloom's Taxonomy includes a bijective mechanism of "knowledge point - cognitive level." The six dimensions of Bloom's Taxonomy are formalized into three computable assessment levels: basic abilities (memory, comprehension), core abilities (application, analysis), and higher-order abilities (evaluation, creation). For each knowledge point... The system constructs differentiated structured evaluation templates to transform behavioral characteristics into quantitative indicators; set up For learners in the The accuracy rate at each cognitive level is determined by pre-setting a basic weight vector, taking into account the differences in the contribution of different levels to mastery. To mitigate assessment bias caused by the complete failure of specific question types, a penalty factor is introduced. Construct an adaptive weight adjustment mechanism: ； in The indicator function is used; after normalization, the final hierarchical weights are obtained. : ； Ultimately, the overall mastery level was derived from a weighted average: 。 6. The adaptive learning path planning method based on knowledge graphs and multi-agent systems according to claim 1, characterized in that, The multi-expert collaborative diagnostic architecture, based on the assessment hierarchy, deploys three functionally decoupled expert agents working in parallel to achieve comprehensive cognitive assessment: Knowledge Mastery Diagnosis Expert: This expert agent corresponds to memory and comprehension. By analyzing the accuracy rate of basic question types, it constructs a baseline of learners' cognitive understanding of facts and concepts. Problem-solving ability diagnostic expert: This expert agent corresponds to the application and analysis, analyzes the learner's strategy selection and the rigor of steps in complex situations, and assesses the knowledge transfer and logical reasoning ability. Learning Behavior Pattern Diagnostic Expert: This expert agent corresponds to evaluation and creation, and is a reflection of the depth of system diagnosis. By monitoring the degree of cue dependence, answer correction trajectory and the innovativeness of open-ended questions, it reveals the level of metacognitive skills and critical thinking. After all experts have completed the information refinement through interaction, a senior comprehensive expert will be responsible for the final summary and refinement of these three sets of collaboratively revised professional reports; based on the hierarchical relationship of Bloom's theory, the performance patterns of students in different cognitive dimensions will be analyzed; finally, a structured, personalized, multi-dimensional cognitive diagnostic report will be generated, clearly identifying the highest effective cognitive level achieved by students in each knowledge point and their weak links. To enhance the semantic depth of the diagnosis, a large language model is used to perform fine-grained analysis of the problem-solving process and output qualitative conclusions: not mastered, weakly mastered, well mastered, and excellent mastered; to achieve algorithm integration, these conclusions are mapped to numerical indicators. The final knowledge point mastery level is calculated using a linear weighted fusion strategy: ； in, As a balance factor, .

7. The adaptive learning path planning method based on knowledge graphs and multi-agent systems according to claim 1, characterized in that: 1) The intent analysis agent: Utilizes a large language model fine-tuned for the education domain, and employs a prompting engineering guidance model to perform deep semantic parsing of the original query, accurately extracting key semantic elements and mapping them into a standardized, structured intent representation; this process can be formally represented as: ； in, This indicates that the large language model, fine-tuned with data from the education sector, possesses the ability to recognize intent and generate structured data. Its model parameters; for The raw natural language statements entered by the user at any given moment; The structured intent representation of the model output; 2) The knowledge point retrieval agent: Utilizes the high-performance embedding model nomic-embed-text to construct a user intent and knowledge graph. Semantic mapping; firstly, the discrete knowledge points in the graph are mapped to the structured intent. The vectors are projected onto a unified high-dimensional dense vector space, and then vector similarity is calculated in this semantic space to filter the candidate set. ； in, This represents a vectorization function for a knowledge graph based on nomic-embed-text, used to construct a semantic index space; It is an isomorphic intent encoding function. It is a retrieval algorithm based on vector similarity calculation; 3) The user profile analysis agent: responsible for real-time tracking and dynamic modeling of the user's cognitive state; based on the user's historical interaction logs, it uses the logical reasoning ability of a large model to identify the distribution patterns of knowledge gaps and the absence of prerequisite dependencies, and realizes the iterative evolution of the user profile through a state update function. ； in, Represents the user's current step The cognitive state vector, Representing the user's steps in the previous time period The cognitive state vector, Represents the time step The collection of user learning behavior logs; It is an update function driven by fine-tuning the LLM; 4) The path planning agent: As the core decision-making unit of the system, its function is to make decisions based on the input set of knowledge concepts. Learner's current status and knowledge graphs Output a unique learning path; employ a state-aware sequence generation mechanism to directly construct the target path based on the knowledge graph's topology and learner profile; the generation process, while satisfying knowledge dependency constraints, incorporates the learner's current cognitive state. As a condition for generating the model, a logically coherent learning sequence that conforms to the individual's cognitive level is generated. This process is mathematically formalized as a direct mapping function from the state space to the path space: ； in, This represents a path generation function; by integrating the structural information of the knowledge graph with the learner's feature vector, this function directly outputs an optimal path that conforms to subject-specific logic and meets personalized learning needs. ; 5) The path evaluation agent: its input is the inference chain and candidate learning paths generated by the path planning agent described above, and its output is the evaluation result (Approved or Rejected) and structured feedback for the path; the path evaluation agent is based on the policy evaluation idea in reinforcement learning, and constructs a hierarchical constraint satisfaction mechanism to evaluate the generated paths. Dual verification of execution logic and adaptability; Based on the verification results, the system performs binary decision-making; if a constraint violation is detected, the path review agent generates a structured feedback signal, driving the path planning agent to perform multiple rounds of policy iteration and replanning until an optimal path that satisfies all constraints is generated, thereby achieving robust closed-loop optimization.

8. The adaptive learning path planning method based on knowledge graphs and multi-agent systems according to claim 7, characterized in that, The dual verification includes: (1) Logical consistency constraints: Check path Does it strictly adhere to the dependencies in the knowledge graph G, for any knowledge point in the path? All prerequisite knowledge points must satisfy the following: ； in, For knowledge points The set of prerequisite dependencies in the graph; This represents the set of knowledge that the learner has currently mastered; (2) Multidimensional adaptability constraints: Based on satisfying the logical constraints, the agent further evaluates whether the path adequately responds to the user's learning intent. First, does the core knowledge point include the assessment path? Next, is the assessment path tailored to the weaknesses identified in the learner's cognitive diagnosis? Key areas of emphasis were strengthened.

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