An intelligent teaching auxiliary method and system based on a large language model

Abstract

The present application belongs to the technical field of artificial intelligence education, and relates to an intelligent teaching auxiliary method and system based on a large language model. The method comprises: obtaining text data, voice data and eye movement trajectory data of students, and performing feature extraction to construct a three-dimensional cognitive state tensor model; a cognitive state tensor decomposition constraint optimization function is constructed, the tensor is decomposed, and a core tensor and a factor matrix are output; a teaching strategy is generated, feature correlation is realized through definition of a cross-modal kernel function; the tensor decomposition parameters are dynamically adjusted; and an updated teaching strategy is output. The present application can capture the cognitive change trajectory of learners from multiple dimensions, significantly improve the accuracy and comprehensiveness of cognitive state representation through a cross-modal kernel function and a gradient coupling mechanism, and construct a cognitive state tensor decomposition constraint optimization function to describe the evolution law of the cognitive state, and capture the continuous change characteristics of the cognitive state over time through the dynamic constraint conditions of the time factor matrix.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of artificial intelligence education, and in particular relates to an intelligent teaching auxiliary method and system based on a large language model. BACKGROUND

[0002] At present, with the rapid development of artificial intelligence technology, intelligent teaching systems, as an important carrier of educational informatization, are profoundly changing the traditional teaching mode. Intelligent teaching systems can greatly improve teaching efficiency and learning outcomes by automatically analyzing learner status and generating teaching strategies to provide decision support for educators. In the context of large-scale online education and distance learning, intelligent teaching systems can effectively address the problem of insufficient teacher resources, realize the educational philosophy of teaching students in accordance with their aptitude, and meet the diverse educational needs of a lifelong learning society.

[0003] Various technical routes have been formed in the field of existing intelligent teaching systems. Teaching systems based on knowledge graphs construct hierarchical association networks between subject knowledge points to realize learning path planning and knowledge point recommendation. Systems based on learning behavior analysis use sequence models to process learning trajectory data to predict knowledge point mastery and learning difficulties. Systems based on natural language processing analyze learners' text answers to assess understanding depth and concept confusion. Systems based on multimedia analysis use audio and video processing techniques to capture learners' emotional state and attention distribution. These technical solutions have been applied in various educational scenarios and have achieved certain teaching effects.

[0004] Although existing intelligent teaching technology has made significant progress, there are still some deficiencies. First, existing systems rely on single-modal data for analysis. Since cognitive processes inherently involve multi-channel information processing, single-modal analysis cannot fully capture learners' internal cognitive changes, resulting in incomplete state representation. Second, existing cognitive modeling methods mostly use static representation frameworks, which fail to effectively capture time-varying factors such as memory decay and attention fluctuations, resulting in insufficient prediction accuracy for long-term learning processes. Third, traditional teaching strategy generation lacks a systematic theoretical framework, making it difficult to balance cognitive goals and teaching costs while ignoring key teaching constraints, resulting in poor strategy feasibility. In addition, existing systems generally lack a closed-loop feedback mechanism, making it difficult to dynamically adjust parameters based on learning outcomes and address individual differences. SUMMARY

[0005] To solve the above technical problems, the present application provides an intelligent teaching auxiliary method and system based on a large language model.

[0006] In a first aspect, the present application provides an intelligent teaching auxiliary method based on a large language model, comprising:

[0007] Text data, speech data and eye movement trajectory data of students are acquired, feature extraction is performed, and a three-dimensional cognitive state tensor model is constructed;

[0008] A cognitive state tensor decomposition constraint optimization function is constructed, the cognitive state tensor is subjected to tensor decomposition with a constraint condition, and a core tensor and a factor matrix are outputted;

[0009] A teaching strategy is generated according to the core tensor and the factor matrix;

[0010] Feature correlation is realized by defining a cross-modal kernel function;

[0011] The tensor decomposition parameters are dynamically adjusted according to the strategy execution result and the feature correlation degree, and the updated core tensor and factor matrix are obtained;

[0012] An updated teaching strategy is outputted according to the updated core tensor and factor matrix.

[0013] In a second aspect, the present application provides an intelligent teaching auxiliary system based on a large language model, comprising a multi-modal data processing unit, a cognitive state modeling unit, a teaching strategy generation unit, a multi-modal fusion unit, a feedback control unit and an update output unit;

[0014] The multi-modal data processing unit is used for acquiring text data, speech data and eye movement trajectory data of students, performing feature extraction, and constructing a three-dimensional cognitive state tensor model;

[0015] The cognitive state modeling unit is used for constructing a cognitive state tensor decomposition constraint optimization function, performing tensor decomposition on the cognitive state tensor with a constraint condition, and outputting a core tensor and a factor matrix;

[0016] The teaching strategy generation unit is used for generating a teaching strategy according to the core tensor and the factor matrix;

[0017] The multi-modal fusion unit is used for realizing feature correlation by defining a cross-modal kernel function;

[0018] The feedback control unit is used for dynamically adjusting tensor decomposition parameters according to a strategy execution result and a feature correlation degree, and obtaining an updated core tensor and factor matrix;

[0019] The update output unit is used for outputting an updated teaching strategy according to the updated core tensor and factor matrix.

[0020] On the basis of the above technical solution, the present application can also be improved as follows.

[0021] Further, text data, speech data and eye movement trajectory data of students are acquired, feature extraction is performed, and a three-dimensional cognitive state tensor model is constructed, comprising:

[0022] According to the text data, a text feature vector is calculated; let be the input text sequence, be the classification identifier of the model, be the semantic vector dimension, represent a real number, be a real number vector space of dimension d, then the text feature vector is represented as:

[0023] ;

[0024] According to the speech data, a speech feature matrix is calculated; let be the speech spectrogram, be the Mel cepstrum coefficient extraction method, be the cepstrum coefficient order, be a real number matrix space of dimension D, then the speech feature matrix is represented as:

[0025] ;

[0026] According to the eye movement trajectory data, an eye movement feature function is calculated; let be the eye movement trajectory data, be the time horizontal gaze coordinates, be the time vertical gaze coordinates, be the time pupil diameter, be the gaze density function, be the start time of the teaching segment, be the end time of the teaching segment, be the feature dimension, be a real number vector space of dimension D, then the eye movement feature function is represented as:

[0027] ;

[0028] Let the cognitive state tensor be , , be the total number of knowledge points, be the number of time slices, be the number of modalities, be the feature dimension of each modality, be the trainable weight parameter, be the feature vector of the modality at time , then the three-dimensional cognitive state tensor model is represented as:

[0029] .

[0030] Further, the cognitive state tensor decomposition constraint optimization function is constructed, comprising: Let the cognitive state tensor be Let the core tensor be Let the knowledge point factor matrix be Let the time factor matrix be Let the modality factor matrix be Let the tensor decomposition constraint optimization function be The Frobenius norm be The regularization coefficient be And The unit matrix be The cognitive state tensor decomposition constraint optimization function is represented as:

[0031] ;

[0032] Let the knowledge point sparsity adjustment parameter be The core tensor rank constraint value be The diagonal element of the extraction matrix be The rank of the core tensor The constraint condition is represented as:

[0033] .

[0034] Further, the cognitive state tensor is subjected to tensor decomposition with constraints, and the core tensor and the factor matrix are output, and further comprising imposing an orthogonal constraint on the factor matrix; Let the The first row vector of the time factor matrix The first row vector of the time factor matrix be The exponential decay term be The periodic term be The standard Euclidean inner product be The teaching cycle parameter be The memory decay rate be The orthogonal constraint imposed on the factor matrix is represented as:

[0035] .

[0036] Further, the teaching strategy is generated according to the core tensor and the factor matrix, comprising:

[0037] A mixed integer nonlinear programming model of the teaching strategy is constructed according to the core tensor and the knowledge point factor matrix;

[0038] Let​ is a teaching strategy vector, represents the selection of the th knowledge point, is a knowledge point factor matrix of the current teaching period, is a knowledge point factor matrix of the previous teaching period, and are weight coefficients, is the teaching cost of the th knowledge point, is a teaching method constraint matrix, is a teaching method threshold vector, is the maximum number of knowledge points for a single teaching, is a set of conflict knowledge point pairs, is a core tensor, is a tensor mod product, is the Frobenius norm, then the mixed integer nonlinear programming model of the teaching strategy is represented as:

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] The mixed integer nonlinear programming model of the teaching strategy is solved by using a branch and bound algorithm, and the objective function value corresponding to the optimal teaching strategy is output.

[0044] Further, feature association is achieved by defining a cross-modal kernel function, including:

[0045] modality factor matrix and original features, define a cross-modal kernel function;

[0046] Let and be multi-modal input samples, be the number of modalities, be the th feature mapping function of the modality, be the weight matrix of the modality , be the modality association matrix, , be the kernel scale parameter, be the th modality feature vector of the sample , be the cross-modal kernel function value, then the cross-modal kernel function is represented as:

[0047] ;

[0048] Let be the cross-modal coupling coefficient, be the gradient of the modal mapping to the modal input, be the gradient vector of the kernel function to the modal input feature, be the hidden space mapping function of the modal, satisfying the gradient coupling condition:

[0049] ;

[0050] Output modal correlation matrix.

[0051] Further, for the feature mapping function, a nonlinear transformation is realized by a multilayer perceptron, and the LeakyReLU activation function is selected as the hidden layer activation function, and the weight matrix is updated through a differentiable convex optimization layer; let be the number of batch samples, denote the weighted norm, be the kernel scale parameter of the iteration update, used to control the sensitivity of the distance metric in the kernel function, be the th multimodal input sample in the batch, be the th multimodal input sample in the batch, each multimodal input sample containing text, speech, and eye movement three modal features, be the multimodal joint mapping function, which maps the original feature space sample to the unified hidden space representation, be the iteration round counter, be dimensional modal correlation matrix, be the number of modalities; the kernel scale parameter is dynamically adjusted according to the feature distribution, denoted as:

[0052] .

[0053] Further, let be the predicted cognitive state tensor, be the predicted value reconstructed by tensor decomposition, be the L2 norm of the vector, be the cognitive state prediction error, and the cognitive state tensor is , ;

[0054] The cognitive state prediction error is represented as:

[0055] ;

[0056] Let be the teaching strategy weight of the n th teaching cycle, be the teaching strategy weight of the n th teaching cycle, , be the PID control parameters, be the prediction error of the n th teaching cycle, be the prediction error of the n th teaching cycle, be the prediction error of the n th teaching cycle, be the prediction error of the n th teaching cycle, be the prediction error of the n th teaching cycle, be the teaching cycle cumulative variable, be the prediction error of the n th teaching cycle, be the teaching strategy weight adjusted by the PID controller, represented as:

[0057] ;

[0058] Let be the maximum number of knowledge points allowed in the n th teaching cycle, be the capacity adjustment step size, be the cognitive state prediction error change rate, be the sign function, be the floor function, then the dynamic adjustment of the teaching capacity constraint is represented as:

[0059] .

[0060] The beneficial effects of the present application are:

[0061] (1) The present application constructs a dynamic cognitive state representation model through multi-modal data fusion and tensor decomposition, realizes the collaborative analysis of text, speech and eye movement data in the teaching process, effectively overcomes the problem of incomplete single modal information, can capture the cognitive change trajectory of learners from multiple dimensions, through the cross-modal kernel function and gradient coupling mechanism, makes the system can identify the implicit correlation pattern between each modal, significantly improves the accuracy and comprehensiveness of cognitive state representation;

[0062] ​(2) The application constructs a cognitive state tensor decomposition constraint optimization function to describe the evolution law of the cognitive state, and separates the core tensor and the factor matrix to represent the potential characteristics of the three dimensions of knowledge points, time and modalities, so that the teaching system can deeply understand the memory decay law and attention fluctuation pattern in the learning process. The cognitive state tensor decomposition constraint optimization function not only has good interpretability, but also captures the continuous change characteristics of the cognitive state over time through the dynamic constraint conditions of the time factor matrix, thereby providing accurate quantitative basis for subsequent teaching strategy generation. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 A principle diagram of an intelligent teaching auxiliary method based on a large language model is provided for the embodiment 1 of the application.

[0064] Figure 2 A principle diagram of an intelligent teaching auxiliary system based on a large language model is provided for the embodiment 2 of the application. DETAILED DESCRIPTION

[0065] To make the objectives, technical solutions and advantages of the embodiments of the application clearer, the technical solutions in the embodiments of the application will be described below in connection with the drawings in the embodiments of the application. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments of the application. The components of the embodiments of the application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0066] Embodiment 1

[0067] As an embodiment, as shown in the accompanying drawings, to solve the above technical problems, the embodiment provides an intelligent teaching auxiliary method based on a large language model, which comprises the following steps: Figure 1

[0068] Acquiring text data, voice data and eye movement trajectory data of students, and performing feature extraction to construct a three-dimensional cognitive state tensor model;

[0069] Constructing a cognitive state tensor decomposition constraint optimization function, performing tensor decomposition on the cognitive state tensor with constraint conditions, and outputting a core tensor and a factor matrix;

[0070] Generating a teaching strategy according to the core tensor and the factor matrix;

[0071] Realizing feature association by defining a cross-modal kernel function;

[0072] According to the strategy execution result and the feature association degree, dynamically adjusting the tensor decomposition parameters to obtain an updated core tensor and factor matrix;

[0073] According to the updated core tensor and factor matrix, outputting an updated teaching strategy.​

[0074] The application realizes the collaborative analysis of text, voice and eye movement data in the teaching process by constructing a dynamic cognitive state representation model through multi-modal data fusion and tensor decomposition, effectively overcomes the problem of incomplete information of a single mode, can capture the cognitive change trajectory of learners from multiple dimensions, and through the cross-modal kernel function and gradient coupling mechanism, the system can identify the implicit correlation pattern between modes, significantly improving the accuracy and comprehensiveness of cognitive state representation.

[0075] The application constructs a cognitive state tensor decomposition constraint optimization function to describe the evolution law of cognitive state, separates the core tensor and factor matrix to represent the potential characteristics of the three dimensions of knowledge points, time and modes, so that the teaching system can deeply understand the memory decay law and attention fluctuation pattern in the learning process. The cognitive state tensor decomposition constraint optimization function not only has good interpretability, but also captures the continuous change characteristics of cognitive state with time through the dynamic constraint condition of time factor matrix, providing accurate quantitative basis for subsequent teaching strategy generation.

[0076] Optionally, the text data, voice data and eye movement trajectory data of the student are acquired and feature extraction is performed to construct a three-dimensional cognitive state tensor model, comprising:

[0077] The text feature vector is calculated according to the text data; let be the input text sequence, be the classification identifier of the model, be the semantic vector dimension, represent a real number, be a real number vector space of dimension, then the text feature vector is represented as:

[0078] ;

[0079] The voice feature matrix is calculated according to the voice data; let be the voice spectrogram, be the mel cepstrum coefficient extraction method, be the cepstrum coefficient order, be a real number matrix space of dimension, then the voice feature matrix is represented as:

[0080] ;

[0081] The eye movement feature function is calculated according to the eye movement trajectory data; let be the eye movement trajectory data, be the horizontal gaze coordinates of time , be the time The vertical gaze coordinates, For time The diameter of the pupil, Let gaze density function be the function of gaze. The starting time of the teaching segment. This is the end time of the teaching segment. For feature dimension, for In a real vector space of dimension 1, the eye-tracking feature function is expressed as:

[0082] ;

[0083] Let the cognitive state tensor be... , , The total number of knowledge points. The number of time slices, For the number of modes, For each modal feature dimension, For trainable weight parameters, For the first Mode in time The feature vectors are then represented by the three-dimensional cognitive state tensor model as follows:

[0084] .

[0085] Through the above processing steps, the alignment and fusion of heterogeneous teaching data in a unified mathematical representation space were achieved, laying a data foundation for the subsequent cognitive state analysis and strategy generation of the system.

[0086] The Tucker decomposition framework is used to decompose the standardized feature tensor into a modal product of the core tensor and the factor matrix. The decomposition objective function is defined as a weighted sum of the reconstruction error and the regularization term.

[0087] Optionally, construct the cognitive state tensor decomposition constrained optimization function, including: setting For the cognitive state tensor, The core tensor represents cross-modal knowledge associations. For the knowledge point factor matrix, For time factor matrix, The modal factor matrix, For tensor Modular product, It is the Frobenius norm. and The regularization coefficient is . If the identity matrix is ​​used, then the cognitive state tensor decomposition constrained optimization function is expressed as:

[0088] ;

[0089] The physical interpretability of the decomposition results is guaranteed by imposing three constraints: first, the knowledge point factor matrix is required to be sparse to prevent overfitting and maintain feature stability; second, the time factor matrix is required to be column-wise unitized to ensure the scale consistency of the temporal features; and finally, the rank of the core tensor is limited to a pre-set threshold to capture the main cross-modal association patterns.

[0090] Let be the knowledge point sparsity adjustment parameter, be the core tensor rank constraint value, be the diagonal elements of the extraction matrix, denote the rank of the core tensor , then the constraint condition is expressed as:

[0091] .

[0092] Optionally, the cognitive state tensor is subjected to constrained tensor decomposition, and the core tensor and factor matrices are output, which also includes imposing an orthogonal constraint on the factor matrices.

[0093] Let be the i-th row vector of the time factor matrix , be the i-th row vector of the time factor matrix, be the exponential decay term, be the periodic term, be the standard Euclidean inner product, be the teaching period parameter, be the memory decay rate, then imposing an orthogonal constraint on the factor matrices is expressed as: .

[0094] .

[0095] For the characteristics of the time dimension, a dynamic constraint condition is introduced to strengthen the temporal continuity, and the inner product of the adjacent time slice factor vectors satisfies the exponential decay periodic law.

[0096] The alternating least squares method is used for optimization and solution, and the core tensor and each factor matrix are iteratively updated. After each iteration, the factor matrices are subjected to normalization projection: projecting into the Frobenius sphere, unitizing the column vectors of , and realizing the low-rank approximation of the core tensor through singular value decomposition. After the optimization process converges, the decomposition results of , ,​​ and to downstream modules for policy generation.

[0097] The above process realizes the interpretable modeling of multi-modal cognitive state, and the core tensor encodes the cross-modal interaction mode. The factor matrix represents the knowledge point correlation strength, time evolution law and mode contribution weight respectively, and provides quantitative basis for system adaptive policy generation.

[0098] Based on the analysis results of cognitive state, an optimized teaching scheme is generated, and the specific implementation is as follows:

[0099] According to the core tensor and the knowledge point factor matrix , a multi-objective optimization function is constructed to balance the cognitive development demand and the teaching implementation cost, and the objective function is defined as a weighted double criterion optimization form:

[0100] .

[0101] Optionally, according to the core tensor and the factor matrix, a teaching strategy is generated, including:

[0102] According to the core tensor and the knowledge point factor matrix, a mixed integer nonlinear programming model of teaching strategy is constructed;

[0103] Let be the teaching strategy vector, represent the selection of the th knowledge point, be the knowledge point factor matrix of the current teaching period, be the knowledge point factor matrix of the previous teaching period, and be the weight coefficient, be the teaching cost of the th knowledge point, be the teaching method constraint matrix, be the teaching method threshold value vector, be the maximum number of knowledge points for single teaching, be the conflict knowledge point pair set, be the core tensor, be the tensor mod product, be the Frobenius norm, then the mixed integer nonlinear programming model of the teaching strategy is expressed as:

[0104] ;

[0105] The feasibility and effectiveness of the teaching scheme are ensured by imposing three constraints. First, the teaching method adaptability constraint is introduced:

[0106] ;

[0107] This constraint forces the teaching strategy to comply with the preset pedagogical principles, such as the knowledge point correlation strength requirement under the guidance of constructivism.

[0108] Secondly, set the knowledge point capacity constraint:

[0109] ;

[0110] Maximum number of knowledge points in a single teaching represents the maximum number of knowledge points allowed to be covered in a single teaching cycle, whose value is dynamically adjusted by the feedback control module. This constraint prevents cognitive overload and ensures teaching quality. Preferably, the initial value is set to 10.

[0111] Finally, define the conflict avoidance constraint:

[0112] ;

[0113] This constraint avoids including mutually interfering knowledge points in the teaching plan at the same time, such as the timing conflict between prerequisite knowledge points and advanced knowledge points.

[0114] Solve the mixed integer nonlinear programming model of the teaching strategy using the branch and bound algorithm, and output the objective function value corresponding to the optimal teaching strategy. First, take the continuous relaxation problem as the lower bound estimate, and gradually approach the optimal solution by iteratively partitioning the feasible region and calculating the boundary values; introduce the cut plane technique to accelerate convergence and add effective inequalities to eliminate non-integer solutions; finally output the binary strategy vector , where , represents the selection of the th knowledge point into the current teaching cycle, is the optimal solution of the teaching strategy mixed integer nonlinear programming model, i.e., the optimal teaching strategy vector finally output by the algorithm; is the th component or element in the optimal teaching strategy vector .

[0115] By generating the teaching strategy according to the core tensor and factor matrix as described above, the quantitative generation and optimization of the teaching strategy are realized. Under the premise of ensuring the compliance of the teaching method, the dynamic balance between cognitive development goals and resource investment costs is achieved, providing executable plan guidance for subsequent teaching implementation.

[0116] This invention utilizes a mixed-integer programming method to achieve multi-objective optimization of teaching strategies. By balancing two key indicators—changes in cognitive state and teaching costs—it generates the optimal teaching plan within a constrained framework. This strategy generation mechanism considers multiple constraints, including pedagogical adaptability, knowledge point capacity, and conflict avoidance, ensuring the practicality and feasibility of the teaching strategies and effectively addressing the lack of theoretical basis for strategy generation in traditional teaching systems.

[0117] Optionally, feature association can be achieved by defining a cross-modal kernel function, including:

[0118] Modal factor matrix and original features, define cross-modal kernel function;

[0119] set up and For multimodal input samples, For the number of modes, For the first Modal feature mapping function, For modality The weight matrix, The modal incidence matrix, , For kernel scale parameters, For the sample The Modal eigenvectors If the value is a cross-modal kernel function, then the cross-modal kernel function is expressed as:

[0120] ;

[0121] A cross-modal kernel function is constructed to achieve feature alignment and interaction. The kernel function is defined as an exponential distance metric. This kernel function measures the similarity of cross-modal samples through weighted Mahalanobis distance. The exponential transformation maps linearly inseparable features to a high-dimensional separable space.

[0122] set up For cross-modal coupling coefficients, For the first Modal mapping pairs of the first Gradient of modal input, For kernel function on the 1st The gradient vector of the modal input features. For the first The latent space mapping function of the modality satisfies the gradient coupling condition as follows:

[0123] ;

[0124] The gradient coupling constraint condition is introduced to strengthen the inter-modal correlation. The constraint is realized through a back propagation algorithm, which forces the gradient update paths of different modalities to produce a synergistic effect in the hidden space. Preferably, the coupling coefficient matrix satisfies the row normalization condition.

[0125] The output modal correlation matrix is output.

[0126] Optionally, for the feature mapping function, a nonlinear transformation is realized through a multilayer perceptron, and the hidden layer activation function is selected as a LeakyReLU activation function. The weight matrix is updated through a differentiable convex optimization layer; let be the number of batch samples, denote the weighted norm, be the kernel scale parameter after the th iteration update, which is used to control the sensitivity of the distance metric in the kernel function, be the th multimodal input sample in the batch, be the th multimodal input sample in the batch, each of which contains text, speech, and eye movement modal features, be a multimodal joint mapping function that maps the original feature space sample to a unified hidden space representation, be an iteration round counter, be a modal correlation matrix of dimension , and the number of modalities; the kernel scale parameter is dynamically adjusted according to the feature distribution, and is denoted as:

[0127] .

[0128] An alternating optimization strategy is adopted to jointly train the mapping function and the weight matrix. For the mapping function , a nonlinear transformation is realized through a multilayer perceptron, and the hidden layer activation function is preferably a LeakyReLU to alleviate the gradient vanishing problem. The weight matrix is updated through a differentiable convex optimization layer to ensure its semi-definiteness to maintain the effectiveness of the distance metric.

[0129] The output modal correlation matrix provides a quantitative basis for cross-modal dependency for dynamic adjustment of system parameters. Through the above process, deep semantic alignment and collaborative representation of multimodal features such as text, speech, and eye movement are realized, providing a unified fusion feature space for subsequent cognitive state modeling.

[0130] By monitoring the difference between the predicted value and the actual observation of the cognitive state in real time, an error signal driven parameter adjustment mechanism is constructed. The cognitive state prediction error is defined as the normalized difference of the multi-modal tensor.

[0131] Optionally, the tensor decomposition parameters are dynamically adjusted according to the policy execution result and the feature correlation degree, including:

[0132] Let be the predicted cognitive state tensor, be the predicted value reconstructed by tensor decomposition, be the L2 norm of the vector, be the cognitive state prediction error, and the cognitive state tensor be , ;

[0133] The cognitive state prediction error is expressed as:

[0134] ;

[0135] The error term quantifies the system prediction ability and serves as the core feedback signal of the control loop. A proportional-integral-derivative control (PID control) algorithm is used to adjust the weight parameters of the policy generation module.

[0136] Let be the teaching strategy weight of the th teaching cycle, be the teaching strategy weight of the th teaching cycle, , and be the PID control parameters, be the prediction error of the th teaching cycle, be the teaching cycle cumulative variable, be the prediction error value of the th teaching cycle, the teaching strategy weight is adjusted using the PID controller, which is expressed as:

[0137] ;

[0138] Let be the maximum number of knowledge points allowed in the th teaching cycle, be the capacity adjustment step size, be the cognitive state prediction error change rate, be the sign function, be the floor function, then the dynamic adjustment of the teaching capacity constraint is expressed as:

[0139] .

[0140] A double-level feedback mechanism is established: the bottom layer of fast response layer performs parameter fine-tuning once every teaching period, and the top layer of slow adaptation layer re-trains the cognitive state model every K periods. The core tensor is frozen during re-training, and only the factor matrices , 、 and are updated to maintain the stability of the cross-modal association pattern. Preferably, the re-training period number K = 5 to balance the model adaptability and computational overhead.

[0141] By establishing a double-level feedback mechanism, a complete "perception-decision-execution" closed-loop control circuit is formed, realizing the collaborative optimization of teaching strategy parameters and system constraint thresholds, and guaranteeing the robustness and adaptability of the system in the dynamic teaching environment.

[0142] The present application introduces a closed-loop feedback control mechanism to dynamically adjust system parameters, and by comparing the differences between the predicted cognitive state and the actual observation results in real time, the PID control algorithm is used to update the teaching strategy weight and knowledge point capacity constraint. This adaptive adjustment mechanism enables the system to optimize the teaching plan in real time according to the learning effect, significantly improving the adaptability of the teaching system to individual differences, and realizing precise intervention and continuous optimization in the intelligent teaching process.

[0143] Embodiment 2

[0144] Based on the same principles as the method shown in Embodiment 1 of the present application, an intelligent teaching auxiliary system based on a large language model is also provided in the embodiments of the present application, which includes a multi-modal data processing unit, a cognitive state modeling unit, a teaching strategy generation unit, a multi-modal fusion unit, a feedback control unit and an update output unit;

[0145] The multi-modal data processing unit is used to obtain text data, speech data and eye movement trajectory data of students, and perform feature extraction to construct a three-dimensional cognitive state tensor model;

[0146] The cognitive state modeling unit is used to construct a cognitive state tensor decomposition constraint optimization function, and perform tensor decomposition on the cognitive state tensor with constraint conditions to output the core tensor and the factor matrix;

[0147] The teaching strategy generation unit is used to generate a teaching strategy according to the core tensor and the factor matrix;

[0148] The multi-modal fusion unit is used to realize feature association by defining a cross-modal kernel function;

[0149] The feedback control unit is used to dynamically adjust the tensor decomposition parameters according to the strategy execution results and the feature association degree to obtain the updated core tensor and factor matrix;

[0150] An update output unit is configured to output the updated teaching strategy according to the updated core tensor and the factor matrix.

[0151] Optionally, the text data, the voice data and the eye movement trajectory data of the student are acquired, and feature extraction is performed to construct a three-dimensional cognitive state tensor model, including:

[0152] The text feature vector is calculated according to the text data; let be the input text sequence, be the classification identifier of the model, be the semantic vector dimension, represent a real number, be a real number vector space with dimension d, then the text feature vector is represented as:

[0153] ;

[0154] The voice feature matrix is calculated according to the voice data; let be the voice spectrogram, be the mel cepstrum coefficient extraction method, be the cepstrum coefficient order, be a real number matrix space with dimension D, then the voice feature matrix is represented as:

[0155] ;

[0156] The eye movement feature function is calculated according to the eye movement trajectory data; let be the eye movement trajectory data, be the horizontal gaze coordinates at time , be the vertical gaze coordinates at time , be the pupil diameter at time , be the gaze density function, be the start time of the teaching segment, be the end time of the teaching segment, be the feature dimension, be a real number vector space with dimension D, then the eye movement feature function is represented as:

[0157] ;

[0158] Let the cognitive state tensor be , , be the total number of knowledge points, be the number of time slices, is the number of modalities, is the dimension of each modality feature, is the trainable weight parameter, is the first modality feature vector at time , then the three-dimensional cognitive state tensor model is represented as:

[0159] .

[0160] Optionally, a cognitive state tensor decomposition constraint optimization function is constructed, comprising: is the cognitive state tensor, is the core tensor, representing cross-modality knowledge association, is the knowledge point factor matrix, is the time factor matrix, is the modality factor matrix, is the tensor mod product, is the Frobenius norm, and is the regularization coefficient, is the identity matrix, then the cognitive state tensor decomposition constraint optimization function is represented as:

[0161] .

[0162] Let be the knowledge point sparsity adjustment parameter, be the core tensor rank constraint value, be the diagonal element of the extraction matrix, represent the rank of , then the constraint condition is represented as:

[0163] .

[0164] Optionally, the cognitive state tensor is subjected to tensor decomposition with constraints, and the core tensor and the factor matrix are output, and further comprising imposing an orthogonal constraint on the factor matrix; Let be the first row vector of the time factor matrix , be the first row vector of the time factor matrix, be the exponential decay term, be the periodic term, be the standard Euclidean inner product, be the teaching cycle parameter, be the memory decay rate, then the orthogonal constraint on the factor matrix is represented as:

[0165] .

[0166] Optionally, teaching strategies can be generated based on the core tensor and factor matrix, including:

[0167] Based on the core tensor and the knowledge point factor matrix, a mixed-integer nonlinear programming model for teaching strategies is constructed.

[0168] set up For teaching strategy vectors, Indicates the selection of the first One knowledge point, This is the knowledge point factor matrix for the current teaching cycle. This is the knowledge point factor matrix of the previous teaching cycle. and These are the weighting coefficients. For the first The teaching cost of each knowledge point For the pedagogical constraint matrix, This is the threshold vector for achieving teaching methodology standards. This represents the maximum number of knowledge points covered in a single lesson. For a set of conflicting knowledge points, For the core tensor, For tensor Modular product, If the Frobenius norm is used, then the mixed-integer nonlinear programming model of the teaching strategy is expressed as:

[0169] ;

[0170] ;

[0171] ;

[0172] ;

[0173] The branch-and-bound algorithm is used to solve the mixed-integer nonlinear programming model of teaching strategies, and the objective function value corresponding to the optimal teaching strategy is output.

[0174] Optionally, feature association can be achieved by defining a cross-modal kernel function, including:

[0175] Modal factor matrix and original features, define cross-modal kernel function;

[0176] set up and For multimodal input samples, For the number of modes, For the first Modal feature mapping function, For modality The weight matrix, The modal incidence matrix, , For kernel scale parameters, For the sample The Modal eigenvectors If the value is a cross-modal kernel function, then the cross-modal kernel function is expressed as:

[0177] ;

[0178] set up For cross-modal coupling coefficients, For the first Modal mapping pairs of the first Gradient of modal input, For kernel function on the 1st The gradient vector of the modal input features. For the first The latent space mapping function of the modality satisfies the gradient coupling condition as follows:

[0179] ;

[0180] Output the modal correlation matrix.

[0181] Optionally, for the feature mapping function, a nonlinear transformation is implemented using a multilayer perceptron, with the LeakyReLU activation function chosen for the hidden layer, and the weight matrix... Update the layer by optimizing the differentiable convexity; let... This represents the batch sample size. Denotes the weighted norm. For the first The kernel scale parameter, updated in the next iteration, is used to control the sensitivity of the distance metric in the kernel function. For the first in the batch A multimodal input sample, For the first in the batch Each of the multimodal input samples contains three modal features: text, speech, and eye-tracking. This is a multimodal joint mapping function that maps samples from the original feature space. Mapped to a unified latent space representation For the iteration round counter, for 3D modal correlation matrix For modal number; kernel scale parameter Dynamically adjusted based on feature distribution, expressed as:

[0182] .

[0183] Optionally, the tensor decomposition parameters can be dynamically adjusted based on the strategy execution results and feature correlation, including:

[0184] set up To predict the cognitive state tensor, These are the predicted values ​​from tensor decomposition reconstruction. Let L2 norm be the vector. The cognitive state prediction error is given by the cognitive state tensor. , ;

[0185] The cognitive state prediction error is expressed as:

[0186] ;

[0187] set up For the first The weight of teaching strategies in each teaching cycle For the first The weight of teaching strategies in each teaching cycle , and For PID control parameters, For the first Prediction error for each teaching cycle Add variables to the teaching cycle. For the first The prediction error value for each teaching cycle, adjusted using a PID controller to adjust the weights of the teaching strategy, is expressed as follows:

[0188] ;

[0189] set up For the first The maximum number of knowledge points allowed per teaching cycle. To adjust the step size for capacity, The rate of change of the prediction error for cognitive state. For symbolic functions, If the function is a floor function, then the dynamic adjustment of the teaching capacity constraint is expressed as:

[0190] .

[0191] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A large language model-based intelligent teaching assistance method, characterized in that, The method comprises the following steps: Text data, speech data and eye movement trajectory data of students are acquired, and feature extraction is performed to construct a three-dimensional cognitive state tensor model, including: calculating a text feature vector according to the text data; setting for the input text sequence, for the classification identifier of the model, for the semantic vector dimension, representing a real number, for a real number vector space of dimension, then the text feature vector is represented as: ; calculating a speech feature matrix according to the speech data; setting as the speech spectrogram, as the mel cepstrum coefficient extraction method, as the cepstrum coefficient order, as a real number matrix space of dimension, then the speech feature matrix is represented as: ; calculating an eye movement feature function according to the eye movement trajectory data; setting as the eye movement trajectory data, as the time horizontal gaze coordinates, as the time vertical gaze coordinates, as the time pupil diameter, as the gaze density function, as the starting time of the teaching segment, as the ending time of the teaching segment, as the feature dimension, as a real number vector space of dimension, then the eye movement feature function is represented as: ; setting the cognitive state tensor as , , as the total number of knowledge points, as the number of time slices, as the number of modalities, as the feature dimension of each modality, as the trainable weight parameter, as the feature vector of the modality at time , then the three-dimensional cognitive state tensor model is represented as: ; constructing a cognitive state tensor decomposition constraint optimization function, performing tensor decomposition on the cognitive state tensor with constraints, and outputting a core tensor and a factor matrix; generating a teaching strategy according to the core tensor and the factor matrix; realizing feature association by defining a cross-modal kernel function; dynamically adjusting tensor decomposition parameters according to the strategy execution result and the feature association degree, obtaining an updated core tensor and factor matrix; outputting an updated teaching strategy according to the updated core tensor and the factor matrix. 2.The intelligent teaching assistance method based on a large language model of claim 1, wherein, The cognitive state tensor decomposition constraint optimization function is constructed, including: is a cognitive state tensor, is a core tensor, representing cross-modal knowledge association, is a knowledge point factor matrix, is a time factor matrix, is a modal factor matrix, is a tensor modular product, is a Frobenius norm, and is a regularization coefficient, is a unit matrix, and the cognitive state tensor decomposition constraint optimization function is represented as: ； Let be the knowledge point sparsity adjustment parameter, be the core tensor rank constraint value, be the extraction matrix diagonal element, denote the rank of the core tensor , then the constraint condition is expressed as: 。 3.The intelligent teaching assistance method based on a large language model of claim 1, wherein, The cognitive state tensor is decomposed under constraints, outputting the core tensor and factor matrix. This also includes applying orthogonal constraints to the factor matrix. Time factor matrix The row vectors The first of the time factor matrix row vectors It is an exponentially decaying term. It is a periodic term. The standard Euclidean inner product. For teaching cycle parameters, To represent the memory decay rate, applying orthogonal constraints to the factor matrix is ​​expressed as: 。 4.The intelligent teaching assistance method based on a large language model of claim 1, wherein, The method for generating a teaching strategy according to the core tensor and the factor matrix comprises the following steps: constructing a mixed integer nonlinear programming model of the teaching strategy according to the core tensor and the knowledge point factor matrix; Let be the teaching strategy vector, be the number of teaching periods, denote the selection of the th knowledge point, be the knowledge point factor matrix of the current teaching period, be the knowledge point factor matrix of the previous teaching period, and be the weight coefficient, be the teaching cost of the th knowledge point, be the teaching method constraint matrix, be the teaching method threshold vector, be the maximum number of knowledge points for a single teaching, be the set of conflicting knowledge point pairs, be the core tensor, be the tensor mod product, be the Frobenius norm, then the mixed integer nonlinear programming model of the teaching strategy is represented as: ； ； ； ； solving the mixed integer nonlinear programming model of the teaching strategy by using a branch and bound algorithm, and outputting a target function value corresponding to an optimal teaching strategy.

5. The intelligent teaching assistance method based on a large language model according to claim 1, characterized in that, The method for realizing feature association by defining a cross-modal kernel function comprises the following steps: defining a cross-modal kernel function by using a modal factor matrix and an original feature; Let and be a multi-modal input sample, be the number of modalities, be the feature mapping function of the -th modality, be the weight matrix of the -th modality, be the modality correlation matrix, , be the kernel scale parameter, be the -th modality feature vector of the sample , be the cross-modality kernel function value, then the cross-modality kernel function is represented as: ； Let be the cross-modal coupling coefficient, be the gradient of the modal mapping with respect to the modal input, be the gradient vector of the kernel function with respect to the modal input feature, be the hidden space mapping function of the modal, satisfying the gradient coupling condition ； outputting a modal association matrix.

6. The intelligent teaching assistance method based on a large language model according to claim 5, characterized in that, For the feature mapping function, a nonlinear transformation is realized by a multi-layer perceptron, and the LeakyReLU activation function is selected for the hidden layer activation function, and the weight matrix is updated by differentiable convex optimization layer; set is the batch size, represents the weighted norm, is the kernel scale parameter after the iterative update, which is used to control the sensitivity of the distance metric in the kernel function, is the multi-modal input sample in the batch, is the multi-modal input sample in the batch, each multi-modal input sample contains text, speech and eye movement three modal features, is a multi-modal joint mapping function that maps the original feature space sample to a unified hidden space representation, is an iteration round counter, is a dimensional modal correlation matrix, is the number of modalities; the kernel scale parameter is dynamically adjusted according to the feature distribution, which is represented as: 。 7. The intelligent teaching assistance method based on a large language model according to claim 1, characterized in that, The method for dynamically adjusting tensor decomposition parameters according to the strategy execution result and the feature association degree comprises the following steps: Let be the predicted cognitive state tensor, be the predicted value of the tensor decomposition reconstruction, be the L2 norm of a vector, be the cognitive state prediction error, the cognitive state tensor is , be the total number of knowledge points, be the number of time slices, be the number of modalities, ; a cognitive state prediction error is represented as: ； Let be the teaching strategy weight for the th teaching cycle, be the teaching strategy weight for the th teaching cycle, , and be the PID control parameters, be the prediction error for the th teaching cycle, be the teaching cycle cumulative variable, be the prediction error value for the th teaching cycle, the teaching strategy weight is adjusted by the PID controller, which is expressed as: ； Let be the maximum number of knowledge points allowed for the current teaching cycle, be the capacity adjustment step size, be the cognitive state prediction error change rate, be the sign function, be the floor function, then the dynamic adjustment of the teaching capacity constraint is represented as: 。 8. An intelligent teaching assistance system based on a large language model, characterized by, The method comprises the following steps: A multi-modal data processing unit is configured to acquire text data, speech data and eye movement trajectory data of a student, and perform feature extraction to construct a three-dimensional cognitive state tensor model, including: calculating a text feature vector according to the text data; setting for an input text sequence, for a classification identifier of the model, for a semantic vector dimension, representing a real number, for a real number vector space of dimension d, the text feature vector is represented as: ; calculating a speech feature matrix according to the speech data; setting for a speech spectrogram, for a mel cepstrum coefficient extraction method, for a cepstrum coefficient order, for a real number matrix space of dimension D, the speech feature matrix is represented as: ; calculating an eye movement feature function according to the eye movement trajectory data; setting for eye movement trajectory data, for a time horizontal gaze coordinate, for a time vertical gaze coordinate, for a time pupil diameter, for a gaze density function, for a start time of a teaching segment, for an end time of a teaching segment, for a feature dimension, for a real number vector space of dimension d, the eye movement feature function is represented as: ; setting a cognitive state tensor as , , for a total number of knowledge points, for a number of time slices, for a number of modalities, for a feature dimension of each modality, for a trainable weight parameter, for a feature vector of the th modality at time , the three-dimensional cognitive state tensor model is represented as: ; constructing a cognitive state tensor decomposition constraint optimization function, performing tensor decomposition on the cognitive state tensor with constraints, and outputting a core tensor and a factor matrix; generating a teaching strategy according to the core tensor and the factor matrix; realizing feature association by defining a cross-modal kernel function; dynamically adjusting tensor decomposition parameters according to the strategy execution result and the feature association degree, obtaining an updated core tensor and factor matrix; outputting an updated teaching strategy according to the updated core tensor and the factor matrix.

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