Learning path recommendation method based on distribution awareness and graph-constrained semantic feedback

Abstract

This invention relates to a learning path recommendation method based on distribution-awareness and graph-constrained semantic feedback, belonging to the field of online education technology. The method includes: constructing a dual knowledge graph composed of a prerequisite relationship graph and a similarity relationship graph; using a knowledge tracking model to diagnose students' cognitive states, generating a virtual candidate exercise set by a large-scale planning language model, and mapping it to a real question bank through semantic retrieval and entity locking to form an executable path; analyzing the distribution pattern of expected accuracy deviation through distribution-aware gating to distinguish between global deviations and local cognitive bottlenecks; when a local bottleneck is detected, a diagnostic model performs problem analysis and concept confusion detection under the topological constraints of the dual knowledge graph, generating semantic diagnostic feedback; the large-scale planning language model rewrites abnormal concept-related exercises accordingly while retaining normal exercises unchanged; iterating the above steps until convergence. This invention achieves interpretable personalized learning path recommendation, significantly improving knowledge improvement rate and diagnostic accuracy.

Description

Technical Field

[0001] This invention relates to the field of online education technology, and in particular to learning path recommendation technology, knowledge tracking technology, knowledge graph technology, and Large Language Model (LLM) application technology, specifically a learning path recommendation method based on distributed perception and graph-constrained semantic feedback. Background Technology

[0002] Learning Path Recommendation (LPR) refers to automatically generating an ordered sequence of learning resources (such as exercises) for students, enabling them to effectively improve their knowledge level upon completion of the sequence. The input to a LPR system typically includes students' historical answer records and structured information about subject knowledge concepts, while the output is an executable learning path composed of actual exercises. Unlike product recommendations in traditional e-commerce platforms, the ultimate goal of path recommendation in the education field is not to cater to user preferences, but to improve students' actual cognitive state. This places higher demands on the cognitive adaptability of the recommendations and the effectiveness of teaching.

[0003] Existing learning path recommendation methods mainly follow three technical routes. The first type of approach is based on the combination of knowledge graphs and knowledge tracing (KT): it uses knowledge graphs to describe the prerequisite dependencies between knowledge points, and uses knowledge tracing models (such as the deep knowledge tracing model DKT based on Long Short-Term Memory networks LSTM) to infer the learner's mastery of each knowledge concept based on their historical answer sequences. Then, it plans a recommended path based on the graph topology and cognitive state. The advantage of this type of approach is that the path conforms to the logical structure of the knowledge system, but its recommendation process is usually unidirectional—after the path is generated, there is a lack of evaluation feedback and dynamic correction mechanisms for the recommendation effect.

[0004] The second approach incorporates the generative capabilities of Large Language Models (LLMs). Leveraging their superior natural language understanding and logical reasoning abilities, LLMs can generate instructionally relevant exercises based on students' cognitive states. However, when directly applied to exercise generation, LLMs face the illusion problem: they may generate illogical or non-existent virtual exercises, impacting the feasibility of recommended paths. Furthermore, when requiring LLMs to assess knowledge mastery based on quantitative metrics, the models tend to output conservative scores (reaching the middle range) to avoid extreme misjudgments, lacking sensitivity in identifying localized structural cognitive deficiencies.

[0005] The third approach attempts to combine knowledge tracing with a large language model to form a closed loop. The large language model generates candidate learning paths based on the student's current cognitive state, and the knowledge tracing model performs a prospective simulation evaluation of these paths and outputs a numerical knowledge improvement score (denoted as ). The large language model adjusts its generation strategy based on this value to generate paths in the next round. This approach improves upon the previous two approaches in terms of adaptability.

[0006] However, the aforementioned third type of closed-loop scheme still has the following four technical shortcomings in practical applications:

[0007] First, the granularity of the feedback signal is too coarse. The knowledge tracing model only provides a coarse-grained estimate of the amount of knowledge improvement. This scalar can only indicate the overall effectiveness of the path, but it cannot tell the large language model which specific knowledge concept the student encountered a cognitive obstacle, nor can it indicate the nature of the obstacle—for example, whether it is due to weak prior knowledge (prerequisite gap) or confusion with similar concepts. The large language model can only make blind global adjustments based on this (such as uniformly reducing the difficulty of all exercises), and the corrective operations lack direction and specificity, resulting in low efficiency.

[0008] Second, there is a lack of ability to differentiate between different types of cognitive abnormalities. When simulation assessment results are unsatisfactory, there are actually two distinct types of abnormalities: when the predicted mastery of most concepts deviates from the target level, the overall difficulty parameters need to be adjusted; when the predicted mastery of individual concepts deviates significantly, root cause diagnosis and targeted correction are required. Existing solutions treat these two types of abnormalities equally, failing to address local cognitive bottlenecks in a targeted manner.

[0009] Third, the diagnostic process lacks structured constraints. If an attempt is made to introduce diagnostic functions into the closed loop to compensate for the lack of feedback granularity, the diagnostic model, lacking external knowledge structure constraints, may produce erroneous analytical results through its free inference—for example, incorrectly attributing students' answer errors caused by conceptual confusion to a lack of prior knowledge, thereby generating incorrect corrective suggestions that actually worsen the quality of the learning path.

[0010] Fourth, single-model self-evaluation bias. Homogeneous large language models simultaneously undertake the dual responsibilities of path generation and diagnostic evaluation, which may introduce evaluation bias—that is, the model tends to give an optimistic evaluation of the paths it generates, similar to the cognitive bias of humans acting as both player and referee. Simply introducing a self-reflection mechanism cannot completely avoid this inherent flaw.

[0011] In summary, existing solutions have shortcomings in four dimensions: feedback granularity, anomaly discrimination capability, diagnostic constraints, and model collaboration. Therefore, how to construct a personalized learning path recommendation method that can accurately locate the root causes of cognitive impairment under structured knowledge constraints, alleviate self-assessment bias through heterogeneous model collaboration, and provide educationally interpretable gradient signals for path correction at the semantic level has become an urgent technical problem to be solved in this field. Summary of the Invention

[0012] The technical problem this invention aims to solve is that in existing closed-loop learning path recommendation schemes, the feedback signal is a single numerical value and lacks the ability to distinguish cognitive abnormalities and diagnostic constraints. At the same time, the single model, which takes into account both generation and evaluation, has self-evaluation bias, resulting in a lack of directionality and accuracy in path correction, and failing to effectively solve the local cognitive structural bottlenecks of students.

[0013] This invention addresses the aforementioned technical problems through the following technical features: It distinguishes between global difficulty bias and local cognitive bottlenecks through a distributed perception gating mechanism (solving the anomaly differentiation problem); it determines the specific root cause type of the bottleneck through graph constraint diagnosis based on dual knowledge graph topology queries (solving the problems of diagnostic constraints and feedback granularity); it assigns path generation and cognitive diagnosis to two independent large language model instances with different parameter scales through a heterogeneous dual-agent architecture (solving the single-model self-evaluation bias problem); and it ensures that each exercise in the recommended path comes from a real question bank through semantic retrieval and entity locking mechanisms (solving the entity illusion problem generated by large language models). These features form a cascading triggering closed loop, collaboratively achieving self-correction of the learning path.

[0014] The technical solution of the present invention to solve the above-mentioned technical problems is as follows.

[0015] A learning path recommendation method based on distribution awareness and graph-constrained semantic feedback includes the following steps:

[0016] Step 1: Construct a dual knowledge graph offline, the dual knowledge graph including a prerequisite relationship graph. Similarity graph ,in Record the prerequisite dependencies between knowledge concepts. Record the semantic similarity relationships between knowledge concepts;

[0017] Step 2: Use a knowledge tracing model to model the student's historical answer sequence and obtain the student's current mastery vector of each knowledge concept. ;

[0018] Step 3: Based on the preset mastery threshold From mastering the degree vector Select the weak concept set from the middle

[0019] Step 4: Develop a large language model based on the backbone and a set of weak concepts. Student knowledge state vector And the expected value of the ideal accuracy Generate a virtual candidate problem set consisting of reference problems. ;

[0020] Step 5: Map each reference exercise in the virtual candidate exercise set to an actual exercise in the real question bank through semantic matching to form an executable candidate path. ;

[0021] Step 6: Use a knowledge-tracking model to analyze candidate paths A prospective simulation was conducted to calculate the expected accuracy rate of students after completing the candidate paths, and to calculate the expected cognitive deviation of the candidate set for each weak concept. ;

[0022] Step 7: Calculate the number of meaningful deviations from concepts, distinguish between global difficulty alignment deviations and local cognitive structural bottlenecks, and trigger the diagnostic process only when a local structural bottleneck is identified; otherwise, the main planning large language model will regenerate a virtual candidate exercise set composed of reference exercises, and return to step 6.

[0023] Step 8: When a local structural bottleneck is detected, the diagnostic model traverses the aforementioned prior relationship graph. Similarity graph Perform topological queries, root cause analysis and conceptual confusion detection, and generate natural language diagnostic feedback text containing root cause analysis and corrective suggestions. ;

[0024] Step 9: Transfer the diagnostic feedback text Input the main planning large language model, and rewrite the exercises in the candidate exercise set that are only associated with abnormal concepts, while keeping the exercises corresponding to normal concepts unchanged;

[0025] Step 10: Repeat steps 6 to 9 until the expected deviation in mastery converges to the preset tolerance threshold. Within or reaching the maximum number of iterations Output the final learning path;

[0026] Furthermore, in step 1, the offline construction process of the dual knowledge graph includes: extracting all knowledge concept nodes from the subject knowledge system. ,in The total number of knowledge concepts is used; text descriptions are generated from knowledge point names using a large language model, and a prerequisite relationship graph is automatically constructed using Graph Retrieval Augmentation (GraphRAG) technology. ,in Denotes the set of directed pre-dependency edges, where each edge is a pre-dependency edge. Master the knowledge points You must first learn the knowledge points. Based on the semantic representation of knowledge concepts, the semantic similarity between concepts is calculated. For concept pairs that exceed a preset similarity threshold, undirected edges are constructed to form a similarity graph. ,in Represents the set of undirected semantically similar edges, where each edge... Representing knowledge points With knowledge points Because they are highly similar in semantics or application scenarios, students are likely to confuse the two during the learning process.

[0027] Furthermore, in step 2, the specific process of initial cognitive state diagnosis includes: obtaining the student's cognitive state up to the current time. Historical interaction sequence ,in For a moment Interactive exercise index, The corresponding answer score is assigned (0 for incorrect, 1 for correct). The learning record is input into a pre-trained Deep Knowledge Tracking (DKT) model, which uses a recurrent neural network to capture the cognitive state dependencies across time steps and outputs the student's mastery vector of each knowledge concept at the current time t. , of which element Strictly defined as students at all times knowledge concepts The probability of prediction.

[0028] Furthermore, in step 3, the specific process of screening weak concepts includes: traversing the mastery degree vector. All conceptual components within this framework will have a mastery level below a preset threshold. The concept is categorized into the weak concept set. ,in Used to define the scope of concepts that students have not yet effectively mastered and that require targeted teaching intervention.

[0029] Furthermore, in step 4, the specific process of generating the initial path includes: the backbone planning large language model receiving the set of weak concepts. Student knowledge state vector As the input feature space; under the domain alignment constraint, for For each target concept, a targeted reference exercise is generated, with the content of the exercise strictly consistent with the teaching objectives of the target concept; under cognitive load calibration constraints, the exercise is designed based on a pre-set ideal accuracy expectation. The inherent cognitive difficulty of each reference exercise is calibrated so that the expected accuracy rate of students in completing the exercise gradually approaches that of the target. ; Output by A virtual candidate problem set consisting of reference problems. Each reference exercise is accompanied by a tag indicating its target concept.

[0030] Furthermore, in step 5, the specific process of semantic retrieval and entity locking includes: processing the virtual candidate exercise set... Each reference exercise It uses a text encoder to convert its text content into semantic vectors. ; In the pre-built vector index of the real question bank, retrieve and The frontmost cosine similarity One candidate entity exercise; formerly Each candidate selects the entity exercise with the highest match to the target concept tag as the locked result, replacing the original reference exercise's position in the path; complete all. Once the entities for each exercise are locked, executable candidate paths are formed. ,in All of these are exercises from a real question bank.

[0031] Furthermore, in step 7, the specific process of distributed perception gating judgment includes: for each concept in the knowledge concept space... Calculate its expected accuracy Deviation from the ideal cognitive load range Set the hyperparameters for the gating shunt boundary. and cognitive deviation tolerance threshold The system formally defines the set of core exception concepts. Let the cardinality of this set of anomalies (i.e., the number of concepts with meaningful deviations) be . .when When the deviation exhibits a uniform distribution, the system identifies it as a global difficulty alignment deviation. After regenerating a virtual candidate exercise set composed of reference exercises from the backbone planning large language model, it returns to step 6 without triggering subsequent diagnostic procedures. When the system determines that there is a local peak in the deviation distribution, it determines that there is a local cognitive structural bottleneck and triggers step 8.

[0032] Furthermore, in step 8, the specific process of graph constraint diagnosis includes: for the set of abnormal concepts... Each concept in First, repair the relationship diagram. Perform a topology query to retrieve data. The system retrieves the direct prior concepts and simultaneously searches for students' mastery of these foundational concepts to determine whether insufficient mastery of prior concepts is hindering the learning of the current concept; in the similarity graph... Perform a neighborhood query to extract the results from the neighborhood. The top with the highest topological correlation indivual( The model uses similarity-based concept confusion to diagnose whether students have made incorrect analogies between the current concept and adjacent concepts; the diagnostic model organizes the above analysis results into structured natural language diagnostic feedback text. The text explicitly identifies the pedagogical roots of students’ learning difficulties (such as preconcept deficiencies or surface semantic confusion) and outputs fine-grained exercise adjustment strategies, which are then distributed to the planning large model.

[0033] Furthermore, in step 9, the specific process of feedback-driven local self-correction includes: parsing the diagnostic feedback text. The list of marked abnormal concepts is used to identify a subset of normal exercises in the candidate exercise set P where the concepts are not marked as abnormal. Strict immutability protection is applied to the exercise text in this subset, prohibiting any modification. For the subset of exercises in the candidate exercise set associated with abnormal concepts, the diagnostic feedback text is used to further analyze the text. The specific correction strategies are rewritten non-linearly one by one: for problems with insufficient prior knowledge, scaffolded sub-problems are embedded in the target exercises to reduce the cognitive threshold caused by weak prior concepts through structured step-by-step prompts; for problems with concept confusion, contrastive semantic distractors are injected into the target exercises to help students distinguish the boundaries between the target concept and its confused neighboring concepts through explicit contrast design.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0035] First, by employing a distributed perception gating mechanism, the system automatically distinguishes between global deviations and local bottlenecks using statistical distribution of deviations, triggering subsequent diagnostics only for the latter. This avoids the inefficient computational overhead caused by indiscriminate full rewriting and ensures that local cognitive problems are accurately identified and addressed, rather than being overwhelmed by global adjustments.

[0036] Second, the diagnostic mechanism, based on graph constraints, limits the scope of reasoning in the analysis to the topological query results of the prior relation graph and similarity graph. The diagnostic model cannot freely infer the causes of bottlenecks; its output must be based on verifiable graph topological relationships. This constraint effectively reduces the risk of diagnostic illusion and ensures that the root cause analysis results are traceable and educationally interpretable.

[0037] Third, by using a structured semantic feedback mechanism, the single numerical score in the traditional closed-loop scheme is upgraded to a structured diagnostic text that includes abnormal concept identification, bottleneck type, root cause explanation and rewriting strategy. This provides clear directional instructions and traceable educational basis for path correction, solving the fundamental defect that numerical feedback cannot tell "which concept has what problem and how to modify it".

[0038] Fourth, by using strategy freezing and targeted rewriting mechanisms, the accuracy of the correction is guaranteed while avoiding destructive reconstruction of the already verified and effective problem sequences. This ensures that each round of self-correction only applies to local concepts with real cognitive bottlenecks, and the parts of the path that have been evaluated through simulation remain stable, thus achieving continuous convergence rather than oscillation during the iteration process.

[0039] Fifth, through semantic retrieval and entity locking mechanisms, vector retrieval technology is used to map the reference intent generated by the large language model to the actual exercises in the real question bank, ensuring that every exercise pushed to the students comes from the real question bank, thus eliminating the risk of execution feasibility of virtual unexecutable exercises generated by the large language model.

[0040] Sixth, through a heterogeneous dual-agent architecture, path generation and cognitive diagnosis are assigned to two independent large language model instances with different parameter scales—the planning model focuses on heuristic teaching and learning question generation, and the diagnosis model focuses on restricted diagnostic reasoning, thereby achieving decoupling of responsibilities and effectively alleviating the self-verification bias introduced by a single model simultaneously undertaking the roles of generation and evaluation. Attached Figure Description

[0041] Figure 1 The following is an overall flowchart of the method of the present invention, showing steps 1 to 10. Detailed Implementation

[0042] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this description, those skilled in the art can make various equivalent modifications to the invention, and these equivalent forms also fall within the scope defined in this application.

[0043] Overall Solution Overview

[0044] The overall process of the learning path recommendation method based on distribution-awareness and graph-constrained semantic feedback proposed in this invention is as follows: Figure 1As shown. Its core logic is as follows: The system first constructs a dual knowledge graph offline (step 1), then obtains the student's current cognitive state and filters weak concepts (steps 2-3), generates an initial virtual candidate exercise set by the backbone planning large language model (step 4), maps it to an executable path in the real question bank through semantic retrieval and entity locking (step 5), uses a knowledge tracking model to perform a prospective simulation evaluation of the path (step 6), and then analyzes the distribution of the deviation of the expected mastery on each concept through distribution-aware gating (step 7). If a local cognitive bottleneck is detected, the system triggers graph constraint diagnosis (step 8), determines the root cause of the bottleneck under the topological constraints of the dual knowledge graph, and generates a structured diagnostic text; then, based on the diagnostic text, it performs strategy freezing and targeted rewriting on the candidate path (step 9), and finally sends the corrected path back to the evaluation stage, iterating until convergence (step 10). The detailed implementation of each step is described below.

[0045] Key symbols and parameter definitions

[0046] For ease of understanding, the following lists the core symbols involved in this invention and their definitions: Represents the knowledge concept space, in which The total number of knowledge concepts; Indicates students' understanding of the concept The current level of mastery is output by the knowledge tracking model; The target is the expected accuracy, which corresponds to the ideal difficulty range of the Zone of Proximal Development (ZPD), typically with a value of 0.7. A threshold value of 0.5 is typically used to filter weak concepts. This represents the lower boundary of the zone of proximal development, typically with a value of 0.4. The tolerance threshold for cognitive deviation is typically set at 0.05. This is the hyperparameter for the gated shunt boundary, typically set to 2.0; The number of candidates to be retrieved for an entity; The number of iterations, typically 3.

[0047] Step 1: Offline construction of dual knowledge graphs

[0048] The dual knowledge graphs are built offline before system deployment, including a pre-built relationship graph. Similarity graph .

[0049] First, repair the relationship diagram. This is a directed acyclic graph. The direction of the edges represents the prerequisite dependencies between knowledge concepts: edges Master the knowledge points You must first learn the knowledge points. This graph is constructed by automatically extracting prerequisite edges from concept description text using Graph Retrieval Enhanced Generation (GraphRAG) technology. The construction process is as follows: first, all knowledge concept nodes are extracted from the subject knowledge system. Then, using a large language model, a text description containing the core teaching content, prerequisites, and typical application scenarios of each knowledge point is generated from its name. All text descriptions are then input into the GraphRAG workflow—which automatically outputs a set of prerequisite dependency edges E_pre between concepts through four steps: text segmentation, entity extraction, relation detection, and community discovery. This workflow eliminates the need for manual experts to annotate prerequisite relations pair by pair, significantly reducing the cost of knowledge graph construction.

[0050] Similarity graph It is an undirected graph. (Edges) Representing knowledge points With knowledge points Because they are highly similar in semantics or application scenarios, students easily confuse the two during the learning process. The construction method is to use a text encoder (such as Sentence-BERT or text-embedding-3 model) to encode each concept... The text description is mapped to a semantic vector. ; for all concepts Calculate cosine similarity ;Will Exceeding the preset similarity threshold Concept pairs (typically 0.75) are constructed as undirected edges. It should be noted that the concept... and Semantic similarity means that the two share a lot of vocabulary and overlapping application scenarios, but it does not mean that they have a prerequisite dependency relationship. Semantic similarity is a sufficient condition for confusion, but not a sufficient condition for a prerequisite relationship.

[0051] Step 2: Initial diagnosis of cognitive state

[0052] Given a student up to the current time Historical interaction sequence ,in For a moment Interactive exercise index, The corresponding score is assigned (0 for an incorrect answer, 1 for a correct answer). At each time step... The system maps the problem representations and answers to low-dimensional dense vectors, and performs a concatenation operation to construct a joint input vector. :

[0053] ;

[0054] in and They represent the exercises respectively. and answer performance One-hot encoded vector; and For learnable embedding weight matrix, This indicates the total number of questions in the question bank. and , respectively, represent the embedding dimensions of the exercise features and the answer features; ⊕ indicates the vector concatenation operation.

[0055] LSTM sequence modeling. Embedding time sequences into sequences. Gradually feed the data into the Long Short-Term Memory (LSTM) network. In the... In this step, the LSTM unit captures the evolution of students' learning cognition through the following gating mechanism:

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] in, , , These are the input gate, forget gate, and output gate vectors of the LSTM, respectively. The state of the memory unit; This is the hidden state vector at the current time step; Element-wise activation function; ⊙ represents element-wise vector multiplication; all and All of these are trainable grid parameters.

[0062] Cognitive mastery prediction. The current hidden state after the LSTM completes its forward propagation. A high-dimensional knowledge mastery space vector is output by performing non-linear mapping through fully connected layers and functions. :

[0063] ;

[0064] in The vector represents the total number of knowledge concepts. The element Strictly defined as students at all times knowledge concepts The model predicts the probability of success. It is trained using standard binary cross-entropy as the loss function.

[0065] Step 3: Weakness Concept Screening

[0066] Traversing and mastering the degree vector Construct a set of weak concepts from all conceptual components. , The threshold for filtering weak concepts is typically set at 0.5. The concepts in the middle are the target concepts that currently require targeted teaching interventions, and their quantity is... .like If the set is empty (i.e., the student's mastery of all concepts is not less than 0.5), the system determines that the student does not require additional teaching intervention and the recommendation process ends.

[0067] Step 4: Initial Path Generation

[0068] Initial path generation is performed by the backbone planning large language model (Planner LLM). This model is a planning model in a heterogeneous dual-agent architecture, focusing on heuristic teaching exercise creation and path planning.

[0069] The model receives the following input feature space: a set of weak terms. Student knowledge state vector Target ideal accuracy expected value A set of virtual candidate exercises, along with a few example exercises, is provided as hints. The set of virtual candidate exercises is generated under the following three constraints:

[0070] (a) Domain alignment constraints: for Each target concept in Generate a reference exercise that is targeted at teaching, and the content of the exercise is strictly in line with... The teaching objectives must be consistent and must not deviate from the conceptual boundaries.

[0071] (b) Cognitive Load Calibration Constraint: Calibrate the inherent cognitive difficulty of each reference exercise to a level that requires effort but allows students to succeed—according to Vygotsky's Zone of Proximal Development (ZPD) theory, the expected accuracy of the exercise should asymptotically approach a certain level. . A score of 0.7 indicates that students' expected accuracy in completing the exercises is approximately 70%. This level of difficulty avoids both overly easy exercises that lack cognitive stimulation and overly difficult exercises that cause frustration.

[0072] (c) Style consistency constraint: Inherit the mathematical rigor, problem syntax and structural format of the example exercises.

[0073] Model output by A virtual candidate problem set consisting of reference problems. Each reference exercise is followed by a tag for its target concept, formatted as "[Target Concept: ]".

[0074] Step 5: Semantic Retrieval and Entity Locking

[0075] The purpose of the entity locking mechanism is to map reference exercises generated by the large language model to actual exercises in the real question bank, ensuring the executability of the recommended path. The specific process is as follows:

[0076] (a) Text vectorization: for virtual candidate exercise sets Each reference exercise It uses a sentence-level text encoder to convert its text content into semantic vectors. .

[0077] (b) Vector retrieval: Retrieve data from a pre-built vector index in the real question bank (based on the FAISS approximate nearest neighbor retrieval database) and related data. The frontmost cosine similarity One candidate entity exercise, The typical value is 3. The FAISS index is built offline before system deployment, encoding the text of all entity exercises in the question bank into vectors and establishing an index structure.

[0078] (c) Concept label matching: For the previous For each entity exercise in the candidate set, calculate its associated set of knowledge concepts. With target concept label Similarity:

[0079] ;

[0080] Select the entity exercises with the highest similarity as the locked results. Replace the original reference exercises .

[0081] (d) Complete all Once the entities for each exercise are locked, executable candidate paths are formed. Each of them All exercises are from real question banks. The entity locking mechanism has significant engineering implications: it limits the creativity of the large language model to the level of generating instructional intent, while the specific exercises delivered to students come from a quality-verified real question bank, ensuring the physical executability of the path.

[0082] Step 6: Knowledge Tracking Simulation Assessment

[0083] Use the knowledge tracking model trained in step 2 to analyze candidate paths. Conduct a prospective simulation assessment. The simulation process is as follows: Assume that students follow... Complete the exercises in the correct order. For the first exercise... Exercises Based on the student's current hidden state Based on the characteristics of the exercises, a knowledge tracing model is used to predict the probability of answering correctly, and then simulated answer results are generated based on probability sampling. (Bernoulli distribution). The knowledge tracing model updates the hidden state accordingly. (Complete) After simulating the exercise, the model outputs a vector representing the student's expected mastery level after completing the path. This vector encodes the system's prediction of students' mastery of each concept after completing the recommended path.

[0084] Step 7: Distributed sensing gating judgment

[0085] Distributed perception gating is one of the core innovative mechanisms of this invention. The key design idea of ​​this mechanism is: instead of simply comparing whether the expected level of mastery has been met, it analyzes the distribution pattern of deviation in the knowledge concept space, and distinguishes different types of cognitive abnormalities accordingly.

[0086] To eliminate random noise in the cognitive simulation process, the system introduces a tolerance threshold. Deviations are filtered out. Based on this, the system formally defines a set of core anomaly concepts. for:

[0087] ;

[0088] Let the cardinality of this set of anomalies (i.e., the number of concepts with meaningful deviations) be . The system will... With boundary hyperparameters By comparing the results, different control flow bifurcations are activated:

[0089] ·when Time (uniformly distributed bias): It is determined that the candidate set generally exhibits a global difficulty alignment bias. Control flow is then fed back to the Planner LLM to regenerate a full set of virtual candidate sets. And return to step 5;

[0090] ·when Time (concentrated distribution of deviations): It is determined that the current path is limited only by a few bottleneck concepts, belonging to a localized structural cognitive impairment. The control flow then activates the diagnostic model, relying on... and The above set of abnormal concepts Root cause analysis and obfuscation detection are performed to generate semantic diagnostic text. The planning model only applies to the candidate set. Involving The exercises in the specified range are rewritten in a targeted manner, while the exercises in the remaining matching ranges remain unchanged. After correction, the system returns to the "Exercise Retrieval and Entity Locking" stage to update the corresponding exercises.

[0091] The engineering significance of gating mechanisms lies in the fact that, in most cases, poor path performance is due to the global difficulty of the exercises not meeting expectations, thus avoiding the need to trigger subsequent costly diagnostic and rewriting processes. Taking the MOOCCubeX dataset as an example, actual test data shows that approximately 65% ​​to 75% of evaluation failures are due to global bias. The introduction of distributed awareness gating can reduce the trigger frequency of diagnostics and rewriting to about 25% to 35%, significantly reducing the average response latency of the system.

[0092] Step 8: Graph Constraint Diagnosis

[0093] This step is performed by a diagnostic model, which is a diagnostic model within a heterogeneous dual-agent architecture, focusing on constrained diagnostic reasoning and analysis. Its core design constraint is that diagnostic reasoning is not a free inference by the diagnostic model, but rather is strictly constrained by the results of topological queries from the dual knowledge graph. The role of the diagnostic model is to organize and represent the query results, rather than to replace the graph in performing causal inference.

[0094] The diagnostic model only shows local cognitive impairment in gating decisions (i.e. It is triggered and awakened when [a certain condition is met]. The core task of this module is to target the core set of exception concepts. Topological root cause tracing and confusion detection are performed on a dual-structure graph, whose input feature space is interwoven with three heterogeneous dimensions:

[0095] 1. Characteristics of target cognitive bias: Input the core abnormal concept of the current step and its current mastery level output in the DKT simulator. .

[0096] 2. Topological Pre-Basis Features: Through the prior relationship graph Perform a one-hop reverse topology query to extract... The system retrieves the direct set of prerequisite concepts and simultaneously searches for students' mastery of these basic concepts to determine whether insufficient mastery of prerequisite concepts is hindering the learning of the current concept.

[0097] 3. High-dimensional semantic confusion features: Through similarity graphs Perform nearest neighbor search to extract the results from the previous page. The highest topological correlation Similarity confusion is used to diagnose whether students are making incorrect analogies between the current concept and adjacent concepts.

[0098] In a formal sense, the virtual tutor adopts the aforementioned heterogeneous graph representation context and generates instructive semantic diagnostic text plaintext through deterministic reasoning. :

[0099] ;

[0100] in Refers to diagnostic models.

[0101] The text explicitly identifies the pedagogical roots of students’ learning difficulties (such as prior concept deficiencies or surface semantic confusion) and outputs fine-grained exercise adjustment strategies, which are then distributed to the main planning model.

[0102] Step 9: Feedback-driven local self-correction

[0103] When the diagnostic plaintext output by the diagnostic model in step 8 is received Subsequently, the planning model ceased its blind global iterations and instead performed localized, targeted self-corrections. The model was forced to strictly freeze the exercise text for the remaining fitting intervals, focusing only on the relevant... The conceptual deficiencies in the exercises are rewritten non-linearly to ensure that the reconstructed content has an explicit pedagogical gradient:

[0104] ;

[0105] in Refers to the planning model. Refers to the first A set of iterative exercises.

[0106] Step 10: Iterative Optimization and Convergence

[0107] (a) in the After the candidate path is self-corrected in the next iteration, the corrected candidate path is obtained. Return to step 6 to re-execute the prospective simulation assessment using the knowledge tracing model, and obtain the updated expected mastery vector. .

[0108] (b) Convergence Judgment: If the prediction accuracy of the candidate path converges to the target interval after iteration, convergence is determined—the student's cognitive problem has been effectively alleviated, and the expected mastery of the candidate path on abnormal concepts tends to stabilize. The iteration is terminated, and the current candidate path is output as the final learning path. .

[0109] (c) If the number of iterations reaches the preset maximum number of steps If the convergence condition is still not met when the value is typically 3, compare the knowledge improvement rate calculated in step 6 across all historical iterations. ,choose The highest-performing path is output as the final learning path. Knowledge improvement rate. The definition of

[0110] ;

[0111] in This is the initial test score. The final test score after completing the path. This represents the highest possible score on the test. This indicator directly quantifies the actual gain in a student's knowledge state after completing the recommended path; a higher value indicates a more significant teaching effect.

[0112] Example

[0113] The technical effects of the present invention will be verified below through specific experimental data.

[0114] 1. Dataset

[0115] This embodiment uses three real online education datasets for experimental verification: (a) the MOOCCubeX dataset, sourced from a massive online open course platform, covering multiple knowledge domains of mathematics, containing 13,091 students, 156 exercises, 71 knowledge concepts, and 1,206,646 interaction records; (b) the MOOPer dataset, sourced from student answer records of an adaptive learning platform, containing 26,603 students, 1,756 exercises, 1,360 knowledge concepts, and 2,007,572 interaction records; and (c) the XES3G5M dataset, sourced from a large-scale online math practice system, covering the math knowledge system from grades 3 to 5 of primary school, containing 16,378 students, 6,006 exercises, 828 knowledge concepts, and 4,803,902 interaction records, characterized by long sequence interactions, with an average of over 200 answer records per student. Students with fewer than 10 interaction records were removed from each dataset, and students were randomly divided into training, validation, and test sets in an 8:1:1 ratio. 2. Implementation Parameter Settings

[0116] The main language model for backbone planning uses Qwen2-32B, and the diagnostic model uses DeepSeek-V4-pro. The knowledge tracing model adopts the DKT architecture, implemented based on LSTM. Key hyperparameter settings are as follows: weak concept screening threshold. =0.5, Target Ideal Accuracy Expected Value =0.7, lower boundary of the zone of proximal development =0.4, cognitive deviation tolerance threshold Gated shunt boundary hyperparameters =2.0, Entity-locked search The maximum number of iterations, T_max, is 3. The text encoder uses the Sentence-BERT model with a vector dimension of 768. The vector index is built based on the FAISS library, using an IVF256 (Inverted File with 256 clusters) and PQ64 (Product Quantization with 64 sub-vectors) index structure.

[0117] 3. Evaluation Indicators

[0118] The effectiveness of the learning path (using) (This can be calculated using the following formula:)

[0119] ;

[0120] As the primary evaluation metric, it is used in comparison to traditional recommended evaluation metrics (such as Normalized Diminished Cumulative Gain (NDCG) and Precision). It directly quantifies the actual gain in students' knowledge status after completing the path, which is more consistent with the fundamental goal of educational recommendations—to promote meaningful and measurable knowledge progress.

[0121] 4. Comparison Methods

[0122] To verify the technical contributions of each feature of this invention, the following comparison method is set up:

[0123] (a) FISM (Factorization Similarity Model): A classic recommendation model based on similarity matrices, used to provide a performance reference for static recommendations.

[0124] (b) GEHRL (Hierarchical Reinforcement Learning): A cutting-edge approach that combines Knowledge Trace (KT) with hierarchical reinforcement learning. This model continuously tracks students' knowledge status and uses reinforcement learning to plan and recommend educational goals.

[0125] (c)SKarRec (Structure and Knowledge-Aware Concept Recommendation Representation Learning Framework): A model that uses a large language model to construct textual descriptions of learning items and combines knowledge tracking and graph neural networks for recommendation.

[0126] (d) LPRekL (Knowledge Tracking and Large Language Model Enhancement Learning Path Recommendation): A generative recommendation framework that deeply integrates knowledge tracking and large language models. It evaluates candidate paths generated by large language models through knowledge tracking to form a basic closed loop.

[0127] 5. Experimental Results and Analysis

[0128] Table 1. Knowledge improvement rate of each model on the three datasets ( Comparison results

[0129] FISM 0.2428 0.2407 0.0165 GEHRL 0.3446 0.4973 0.2318 SKarRec 0.3593 0.4641 0.2671 LPReKL 0.3885 0.4852 0.3002 Method of the present invention 0.4089 0.5028 0.3175

[0130] As shown in Table 1, the method of this invention achieved the best knowledge improvement rate on all three datasets. On the MOOCCubeX dataset, the method of this invention... The efficiency score reached 0.4089, representing an improvement of approximately 68.4% compared to the traditional collaborative filtering method FISM (0.2428) and approximately 5.3% compared to the closed-loop baseline LPRekL (0.3885). On the MOOPer dataset, the proposed method achieved... The score reached 0.5028, an improvement of approximately 1.1% compared to GEHRL (0.4973) and approximately 3.6% compared to LPRekL (0.4852). On the XES3G5M dataset, due to its characteristics of long sequence interactions and finer concept granularity, all methods showed improved performance. While the absolute values ​​are generally low, the method of this invention still achieves the best result at 0.3175, which is about 5.8% higher than LPRekL (0.3002). These results demonstrate that this invention, through the cascading synergy of three mechanisms—distributed sensing gating, graph constraint diagnosis, and semantic feedback rewriting—effectively overcomes the shortcomings of existing closed-loop schemes, such as the lack of directionality and diagnostic constraints in single numerical feedback. It exhibits stable and consistent performance advantages across datasets of different sizes and features.

[0131] Four ablation variants were set up to quantify the independent contribution of each core component: (a) variant without semantic feedback – semantic diagnostic feedback was removed, and the correction signal in the self-correcting loop was degenerated into a single numerical bias; (b) variant without graph constraints – the topological constraints of the dual knowledge graph were removed, and diagnosis was performed only based on the student knowledge state vector without performing graph topology queries; (c) variant without distribution-aware gating – the gating mechanism was replaced with a simple global threshold judgment, without distinguishing between global bias and local bottlenecks; (d) variant without entity locking – the semantic retrieval and entity locking modules were removed, and the reference exercises generated directly by the planning model were used as the final recommendation results.

[0132] Table 2. Knowledge enhancement rate of each variant on three datasets in ablation experiments ( )contrast

[0133] Complete method 0.4089 0.5028 0.3175 w / o Semantic Feedback 0.3925 0.4890 0.3040 w / o Graph Constraints 0.3980 0.4955 0.3095 w / o Distribution-Aware Gating 0.4035 0.5000 0.3140 w / o Entity Locking 0.4065 0.5015 0.3160

[0134] The above ablation experiment results collectively demonstrate that semantic feedback mechanism, graph constraint diagnosis, distributed sensing gating, and entity locking each make irreplaceable independent contributions to the technical effect of the present invention, and the combination of the four features produces synergistic gains that exceed their individual effects.

[0135] As shown in Table 2, the performance degradation caused by removing the semantic feedback mechanism (without semantic feedback, i.e., the feedback signal degenerates into a single numerical bias) is the most significant: on the MOOCCubeX dataset. The score decreased from 0.4089 to 0.3925, a drop of approximately 4.0%, ranking first in terms of degradation across all three datasets. This result quantitatively verifies, from an ablation perspective, the core value of semantic feedback in this invention—the root cause analysis and directional rewriting instructions carried by natural language diagnostic text, providing far richer pedagogical gradient information for path correction than a single numerical score. Removing graph constraint diagnostics (w / o GraphConstraints) also leads to significant degradation, especially on the XES3G5M dataset. The performance dropped to 0.3095, validating the role of structured knowledge constraints in ensuring diagnostic accuracy: Without graph topology query constraints, the diagnostic model's free inference led to incorrect root cause attribution, causing subsequent rewriting direction deviations. Removing distribution-aware gating (without distribution-aware gating) failed to distinguish between global deviations and local bottlenecks, triggering full diagnosis and rewriting for all deviated concepts, resulting in increased computational overhead and decreased performance. Removing entity locking (without entity locking) also caused a slight performance decrease, confirming the engineering necessity of limiting the creativity of large language models to generating instructional intent and delivering exercises from a real question bank.

Claims

1. A learning path recommendation method based on distribution-awareness and graph-constrained semantic feedback, characterized in that, Includes the following steps: Step 1: Construct a dual knowledge graph offline, the dual knowledge graph including a prerequisite relationship graph. Similarity graph ,in Record the prerequisite dependencies between knowledge concepts. Record the semantic similarity relationships between knowledge concepts; Step 2: Use a knowledge tracing model to model the student's historical answer sequence and obtain the student's current mastery vector of each knowledge concept. ; Step 3, based on the preset mastery threshold From mastering the degree vector Select the weak concept set from the middle ; Step 4: The large language model is based on the set of weak concepts. Student knowledge state vector And the expected value of the target ideal accuracy Generate a virtual candidate problem set consisting of reference problems. ; Step 5: Through semantic matching, each reference exercise in the virtual candidate exercise set is mapped to an actual exercise in the real question bank, forming an executable candidate path. ; Step 6: Use a knowledge tracing model to analyze candidate paths. Perform prospective simulations to calculate the predicted mastery vector after students complete the candidate paths. ; Step 7, Calculate the expected mastery vector The distribution of deviations from the target ideal accuracy in each concept is analyzed. The number of meaningful deviation concepts is used to distinguish between global difficulty alignment deviations and local cognitive structural bottlenecks. The diagnostic process is triggered only when a local structural bottleneck is identified. Otherwise, the main planning large language model regenerates a virtual candidate exercise set composed of reference exercises, and the process returns to step 6. Step 8: When a local structural bottleneck is detected, the diagnostic model traverses the prior relationship graph. Similarity graph Perform topological queries, root cause analysis and conceptual confusion detection, and generate natural language diagnostic feedback text containing root cause analysis and corrective suggestions. ; Step 9: Transfer the diagnostic feedback text Input the main planning large language model, and rewrite the exercises in the candidate exercise set that are only associated with abnormal concepts, while keeping the exercises corresponding to normal concepts unchanged; Step 10: Repeat steps 6 to 9 until the expected deviation in mastery converges to the preset tolerance threshold. Within or reaching the maximum number of iterations Output the final learning path.

2. The learning path recommendation method based on distribution-awareness and graph-constrained semantic feedback according to claim 1, characterized in that, In step 1, the offline construction process of the dual knowledge graph includes: Extract all knowledge concept nodes from the subject knowledge system. ,in The total number of knowledge concepts is used; text descriptions are generated from knowledge point names using a large language model, and a prerequisite relationship graph is automatically constructed using Graph Retrieval Augmentation (GraphRAG) technology. ,in Denotes the set of directed pre-dependency edges, where each edge is a pre-dependency edge. Master the knowledge points You must first learn the knowledge points. Based on the semantic representation of knowledge concepts, the semantic similarity between concepts is calculated. For concept pairs that exceed a preset similarity threshold, undirected edges are constructed to form a similarity graph. ,in Represents the set of undirected semantically similar edges, where each edge... Representing knowledge points With knowledge points Because they are highly similar in semantics or application scenarios, students are likely to confuse the two during the learning process.

3. The learning path recommendation method based on distribution-awareness and graph-constrained semantic feedback according to claim 1, characterized in that, In step 2, the specific process of initial cognitive state diagnosis includes: obtaining the student's cognitive state up to the current moment. Historical interaction sequence ,in For a moment Interactive exercise index, The corresponding answer score is assigned (0 for incorrect, 1 for correct). The learning record is input into a pre-trained Deep Knowledge Tracking (DKT) model, which uses a recurrent neural network to capture the cognitive state dependencies across time steps and outputs the student's mastery vector of each knowledge concept at the current time t. , of which element Strictly defined as students at all times knowledge concepts The probability of prediction.

4. The learning path recommendation method based on distribution-awareness and graph-constrained semantic feedback according to claim 1, characterized in that, In step 5, the specific process of semantic retrieval and entity locking includes: processing the virtual candidate exercise set. Each reference exercise It uses a text encoder to convert its text content into semantic vectors. ; In the pre-built vector index of the real question bank, retrieve and The front with the highest cosine similarity One candidate entity exercise; formerly Each candidate selects the entity exercise with the highest match to the target concept tag as the locked result, replacing the original reference exercise's position in the path; complete all. Once the entities for each exercise are locked, executable candidate paths are formed. ,in All of these are exercises from a real question bank.

5. The learning path recommendation method based on distribution-awareness and graph-constrained semantic feedback according to claim 1, characterized in that, In step 7, the specific process of distributed perception gating judgment includes: for each concept in the knowledge concept space... Calculate its expected accuracy Deviation from the ideal cognitive load range Set the hyperparameters for the gating shunt boundary. and cognitive deviation tolerance threshold The system formally defines the set of core exception concepts. Let the cardinality of this set of anomalies (i.e., the number of concepts with meaningful deviations) be . ;when When the deviation exhibits a uniform distribution, the system identifies it as a global difficulty alignment deviation. After regenerating a virtual candidate exercise set composed of reference exercises from the backbone planning large language model, it returns to step 6 without triggering subsequent diagnostic procedures. When the system determines that there is a local peak in the deviation distribution, it determines that there is a local cognitive structural bottleneck and triggers step 8.

6. The learning path recommendation method based on distribution-awareness and graph-constrained semantic feedback according to claim 1, characterized in that, In step 8, the specific process of graph constraint diagnosis includes: for the set of abnormal concepts Each concept in First, repair the relationship diagram. Perform a topology query and retrieve data. The system retrieves the direct prior concepts and simultaneously searches for students' mastery of these foundational concepts to determine whether insufficient mastery of prior concepts is hindering the learning of the current concept; in the similarity graph... Perform a neighborhood query to extract the results from the neighborhood. The top with the highest topological correlation indivual( The model uses similarity-based concept confusion to diagnose whether students have made incorrect analogies between the current concept and adjacent concepts; the diagnostic model organizes the above analysis results into structured natural language diagnostic feedback text. The text explicitly identifies the pedagogical roots of students’ learning difficulties (such as preconcept deficiencies or surface semantic confusion) and outputs fine-grained exercise adjustment strategies, which are then distributed to the planning large model.

7. The learning path recommendation method based on distribution-awareness and graph-constrained semantic feedback according to claim 1, characterized in that, In step 9, the specific process of feedback-driven local self-correction includes: parsing the diagnostic feedback text. The list of marked abnormal concepts is used to identify a subset of normal exercises in the candidate exercise set P where the concepts are not marked as abnormal. Strict immutability protection is applied to the exercise text in this subset, prohibiting any modification. For the subset of exercises in the candidate exercise set associated with abnormal concepts, the diagnostic feedback text is used to further analyze the text. The specific correction strategies are rewritten non-linearly one by one: for problems with insufficient prior knowledge, scaffolded sub-problems are embedded in the target exercises to reduce the cognitive threshold caused by weak prior concepts through structured step-by-step prompts; for problems with concept confusion, contrastive semantic distractors are injected into the target exercises to help students distinguish the boundaries between the target concept and its confused neighboring concepts through explicit contrast design.

8. The learning path recommendation method based on distribution-awareness and graph-constrained semantic feedback according to claim 1, characterized in that, The planning large language model and the diagnostic model adopt two independent large language model instances with different parameter scales: the planning large language model is used for teaching creation and path planning, and the diagnostic model is used for analysis, diagnosis and root cause tracing; the two models are independently optimized for generation capability and diagnostic accuracy, respectively, forming a heterogeneous dual-agent architecture with decoupled responsibilities.

9. The learning path recommendation method based on distribution-awareness and graph-constrained semantic feedback according to claim 1, characterized in that, In step 10, the specific process of iterative optimization includes: in the first step... After the next iteration, the corrected candidate path will be... Return to step 6 for re-evaluation; if the prediction accuracy of the candidate path converges to the target interval, then convergence is determined, and the current path is output; if the number of iterations reaches the preset maximum value... Convergence, selecting the knowledge improvement rate across all historical iterations. Output the highest path.

10. A learning path recommendation system based on distribution-aware and graph-constrained semantic feedback, characterized in that, include: A dual knowledge graph construction module is used for offline construction, including a prerequisite relationship graph. Similarity graph The dual knowledge graph, in which Record the prerequisite dependencies between knowledge concepts. Record the semantic similarity relationships between knowledge concepts; The cognitive state diagnosis module is used to model students' historical answer sequences using a knowledge tracing model, and obtain the student's current mastery vector of each knowledge concept. And based on a preset mastery threshold Filtering the set of weak concepts ; The large language model module is designed for use with a set of weak concepts. Student knowledge state vector And the expected value of the target ideal accuracy Generate a virtual candidate problem set consisting of reference problems. ; The semantic retrieval and entity locking module is used to map virtual candidate questions to actual questions in the real question bank through semantic matching, forming executable candidate paths. ; The knowledge tracing simulation evaluation module is used to evaluate candidate paths. Perform a prospective simulation to calculate the expected mastery vector of students after completing the candidate paths. ; The distributed sensing gating module is used to calculate the expected mastery vector. The distribution pattern of deviations from the target ideal accuracy expectation value across various concepts is used to distinguish between global difficulty alignment deviations and local cognitive structural bottlenecks by statistically analyzing the number of meaningful deviation concepts. The diagnostic process is triggered only when local structural bottlenecks are identified. The diagnostic module is used to traverse the prior relation graph when a local structural bottleneck is detected. Similarity graph Perform topological queries, conduct root cause analysis and concept confusion detection, and generate natural language diagnostic feedback text containing root cause analysis and correction suggestions. ; Feedback-driven local self-correction module, used to adjust diagnostic feedback text. For the candidate exercise set, exercises that are only associated with abnormal concepts are rewritten in a targeted manner, while the exercises corresponding to normal concepts are retained unchanged; The iterative optimization control module controls the iterative execution of simulation evaluation, gating judgment, graph constraint diagnosis, and local self-correction until the convergence condition is met or the maximum number of iterations is reached. Output the final learning path .

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