Mathematical model-based online education method, apparatus and device, and medium

Abstract

The invention relates to the technical field of online education. The online education method and device based on the mathematical model, the equipment and the medium are provided, and the method comprises the steps that test sequence construction processing is carried out according to a preset educational psychology forgetting curve parameter library, and an antagonism evaluation sequence is generated; performing model compression processing on the knowledge state prediction model to generate a lightweight knowledge tracking model; inputting the antagonism evaluation sequence into a lightweight knowledge tracking model to carry out long-interval forgetting sensitivity test processing, and generating a long-term forgetting sensitivity attenuation rate; performing compression parameter adjustment processing according to the long-term forgetting sensitivity attenuation rate to generate a fidelity compression model; and performing real-time learning behavior data processing through the fidelity compression model to generate an anti-forgetting learning path so as to achieve the technical effects of improving the prediction fidelity of the compression model for the long-interval forgetting characteristic, optimizing the prediction accuracy of the knowledge point long-term memory state and realizing the dynamic anti-forgetting learning path adaptive to the individualized forgetting difference.

Description

Technical Field

[0001] This invention relates to the field of online education technology, and in particular to online education methods, apparatus, equipment and media based on mathematical models. Background Technology

[0002] With the deep integration of artificial intelligence and education, personalized learning through mathematical models has become an industry trend in online education platforms. Knowledge tracing, as a core technology in online education, aims to predict learners' knowledge mastery by analyzing their historical interaction behavior, thereby optimizing learning path planning.

[0003] In traditional techniques, LSTM models are used to adapt to the prediction needs of real-time education scenarios. However, their large number of parameters and high computational complexity make them difficult to deploy efficiently. While traditional model compression techniques can reduce the model size, they can destroy the ability to predict long-term forgetting characteristics. Existing compression methods lack evaluation mechanisms that target educational psychology characteristics and ignore the time-dependent patterns of forgetting curves, leading to distortion in the prediction of long-term memory status of knowledge points. In addition, traditional techniques rely on fixed rules to generate anti-forgetting learning paths, which cannot be dynamically adjusted according to real-time learning behavior and are difficult to adapt to individual forgetting differences, resulting in inaccurate timing of reinforcement practice node insertion. Summary of the Invention

[0004] Therefore, it is necessary to provide online education methods, devices, equipment, and media based on mathematical models to address the aforementioned technical problems, so as to improve the prediction fidelity of compression models for long-term forgetting characteristics, optimize the prediction accuracy of long-term memory status of knowledge points, and achieve the technical effect of dynamic anti-forgetting learning paths that adapt to individual forgetting differences.

[0005] Firstly, this application provides an online education method based on mathematical models, which includes:

[0006] The learner's online interaction logs are preprocessed to generate raw behavioral sequence data; a long short-term memory neural network is trained based on the raw behavioral sequence data to generate a knowledge state prediction model.

[0007] Test sequences are constructed and processed based on a pre-set educational psychology forgetting curve parameter library to generate adversarial assessment sequences; the knowledge state prediction model is compressed to generate a lightweight knowledge tracking model.

[0008] The adversarial evaluation sequence is input into a lightweight knowledge tracing model for long-interval forgetting sensitivity testing to generate a long-term forgetting sensitivity decay rate.

[0009] The compression parameters are adjusted based on the long-term forgetting sensitivity decay rate to generate a high-fidelity compression model; real-time learning behavior data is then processed using the high-fidelity compression model to generate an anti-forgetting learning path.

[0010] In one embodiment, the adversarial evaluation sequence is input into a lightweight knowledge tracing model for long-interval forgetting sensitivity testing to generate a long-term forgetting sensitivity decay rate, including:

[0011] Repeated practice event identification processing is performed on the adversarial evaluation sequence to generate a long-interval node set;

[0012] The adversarial evaluation sequence is input into a lightweight knowledge tracing model for prediction processing, generating compressed model prediction results.

[0013] The adversarial evaluation sequence is input into the knowledge state prediction model for prediction processing, and the prediction result of the original model is generated.

[0014] Based on a long-interval node set, the prediction deviation between the prediction results of the compressed model and the original model is calculated and processed to generate a forgetting sensitivity difference vector.

[0015] The long-term forgetting sensitivity decay rate is generated by statistically normalizing the forgetting sensitivity difference vector using the following formula:

[0016]

[0017] in, Indicates the rate of decline in long-term forgetting sensitivity. This represents the Sigmoid normalization function. Describes the Euclidean norm. Indicates the first The difference vector of each node Represents the baseline difference vector. This indicates a minimum value to prevent division by zero. Represents a set of nodes with long intervals. Indicates the summation index.

[0018] In one embodiment, based on a long-interval node set, a prediction bias calculation is performed on the prediction results of the compressed model and the original model to generate a forgetting sensitivity difference vector, including:

[0019] Based on a long-interval node set, the knowledge point mastery deviation of the prediction results of the compressed model is calculated and processed to generate a cognitive deviation sequence of the compressed model.

[0020] Based on a long-interval node set, the knowledge point mastery deviation of the original model prediction results is calculated and processed to generate the original model cognitive deviation sequence.

[0021] The following formula is used to perform temporal correlation fusion processing on the cognitive bias sequences of the compressed model and the original model to generate a forgetting sensitivity difference vector:

[0022]

[0023] in, Represents the forgetting sensitivity difference vector. This represents the temporal correlation fusion function. Represents a set of nodes with long intervals. Indicates the node's time index. This represents the time decay weighting factor. Indicates time The compressed model of cognitive bias vector, Indicates time The original model cognitive bias vector, This represents the operator for calculating element-level deviations.

[0024] In one embodiment, the adversarial evaluation sequence is input into a lightweight knowledge tracing model for prediction processing to generate a compressed model prediction result, including:

[0025] Temporal feature enhancement processing is performed on the adversarial evaluation sequence to generate a context-aware sequence;

[0026] Using the following formula, the context-aware sequence is input into the forgetting gating unit of the lightweight knowledge tracing model for state transition calculation, generating a dynamic knowledge state matrix:

[0027]

[0028] in, Indicates time step The dynamic knowledge state matrix, Indicates time step Context-aware sequences, Indicates time step The dynamic knowledge state matrix, This represents the set of parameters for a lightweight knowledge tracing model. This represents the state transition function of the forgetting gate unit;

[0029] The following formula is used to map knowledge point mastery based on the dynamic knowledge state matrix, generating compressed model prediction results:

[0030]

[0031] in, This represents the prediction results of the compression model. This represents the dynamic knowledge state matrix after time-series averaging. Represents the weight matrix. This represents the bias vector.

[0032] In one embodiment, compression parameters are adjusted based on the long-term forgetting sensitivity decay rate to generate a high-fidelity compression model, including:

[0033] Abnormal intervals are identified in the long-term forgetting sensitivity decay rate to generate abnormal decay rate features.

[0034] Based on the abnormal characteristics of the decay rate, neuron sensitivity mapping is performed to generate dynamic compression rules.

[0035] The lightweight knowledge tracing model is iteratively adjusted based on dynamic compression rules to generate a high-fidelity compressed model.

[0036] In one embodiment, real-time learning behavior data processing is performed using a high-fidelity compression model to generate a forgetting-resistant learning path, including:

[0037] A dynamic knowledge point state matrix is ​​generated by performing temporal state reasoning on real-time learning behavior data through a high-fidelity compression model.

[0038] The following formula is used to perform time window decay analysis on the dynamic knowledge point state matrix to generate the knowledge point decay probability distribution:

[0039]

[0040] in, Indicates time The probability of knowledge point decay. Representing knowledge points In time The degree of mastery, This represents the decay factor of the forgetting curve. Indicates the time interval parameter. Represents an exponential function;

[0041] Based on the knowledge point decay probability distribution, adaptive insertion of reinforcement practice nodes is performed to generate a learning path resistant to forgetting.

[0042] In one embodiment, a test sequence is constructed based on a pre-set educational psychology forgetting curve parameter library to generate an adversarial assessment sequence, including:

[0043] The critical memory intensity is calculated and processed based on a pre-set educational psychology forgetting curve parameter library to generate a cognitive interference intensity distribution.

[0044] Based on the cognitive interference intensity distribution, long-interval interference events are injected into the initial test sequence to generate enhanced adversarial sequences.

[0045] The knowledge coherence constraint test is performed on the enhanced adversarial sequence to generate an adversarial evaluation sequence.

[0046] Secondly, this application also provides an online education device based on a mathematical model, the device comprising:

[0047] The behavior sequence modeling module is used to preprocess learners’ online interaction logs to generate raw behavior sequence data; based on the raw behavior sequence data, a long short-term memory neural network is trained to generate a knowledge state prediction model.

[0048] The adversarial compression module is used to construct and process test sequences based on a pre-set library of educational psychology forgetting curve parameters, generating adversarial evaluation sequences; and to compress the knowledge state prediction model to generate a lightweight knowledge tracing model.

[0049] The forgetting sensitivity test module is used to input the adversarial evaluation sequence into the lightweight knowledge tracing model for long-interval forgetting sensitivity testing and generate long-term forgetting sensitivity decay rate.

[0050] The Fidelity Learning Path module is used to adjust compression parameters based on the long-term forgetting sensitivity decay rate to generate a Fidelity Compression Model; real-time learning behavior data is processed through the Fidelity Compression Model to generate an Anti-Forgetting Learning Path.

[0051] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of any of the methods in the first aspect of this application.

[0052] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of any of the methods in the first aspect of this application.

[0053] This application provides an online education method, device, equipment, and medium based on a mathematical model. The method includes: preprocessing learners' online interaction logs to generate raw behavioral sequence data; training a long short-term memory neural network based on this data to obtain a knowledge state prediction model; constructing a test sequence to generate an adversarial evaluation sequence by combining a pre-set educational psychology forgetting curve parameter library; compressing the knowledge state prediction model to obtain a lightweight knowledge tracking model; inputting the adversarial evaluation sequence into the lightweight knowledge tracking model to complete a long-interval forgetting sensitivity test to generate a long-term forgetting sensitivity decay rate; adjusting the compression parameters based on the decay rate to obtain a high-fidelity compression model; and then processing real-time learning behavior data through the high-fidelity compression model. This not only improves the prediction fidelity of the compression model for long-interval forgetting characteristics but also optimizes the accuracy of predicting the long-term memory state of knowledge points and enables a dynamic anti-forgetting learning path adapted to individual forgetting differences. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 A flowchart illustrating an online education method based on a mathematical model, as described in one embodiment of the present invention;

[0056] Figure 2 This is a flowchart of a process for adjusting compression parameters based on the long-term forgetting sensitivity decay rate to generate a high-fidelity compression model in one embodiment of the present invention.

[0057] Figure 3 This is a structural diagram of an online education device based on a mathematical model, according to one embodiment of the present invention. Detailed Implementation

[0058] To make the above-mentioned objects, features, and advantages of this application more apparent and understandable, the specific embodiments of this application will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0059] First, the application scenarios of the embodiments of this application are described. In the embodiments of this application, online education methods, devices, equipment, and media based on mathematical models are provided, applicable to scenarios such as online synchronous learning, online training of vocational education skills and knowledge points, and fragmented knowledge learning in adult education.

[0060] In illustrative purposes, the online education methods, devices, equipment, and media based on mathematical models provided in this application embodiment can also be applied to online language learning platforms, online tutoring for professional qualification examinations, online skills enhancement training for internal employees of enterprises, and other application scenarios. These are merely illustrative examples and do not limit the specific application scenarios.

[0061] like Figure 1 As shown, this application provides an online education method based on a mathematical model, which includes:

[0062] S101: Perform log preprocessing on learners' online interaction logs to generate raw behavioral sequence data; train a long short-term memory neural network based on the raw behavioral sequence data to generate a knowledge state prediction model.

[0063] For example, online interaction logs generated by learners in online education scenarios are collected. Preprocessing operations such as effective recording and filtering, redundant information removal, and data format standardization are performed on the online interaction logs to eliminate invalid data and interference information in the online interaction logs, standardize the structure and presentation of the data, ensure the consistency and usability of the data, and generate original behavioral sequence data that meets the standards for subsequent model training.

[0064] Based on the generated raw behavioral sequence data, a basic training framework for a long short-term memory neural network is built. Adaptable sample datasets are divided, and network training parameters that fit the educational scenario are set. Through an iterative training process of forward propagation calculation and backpropagation optimization, the internal parameters of the long short-term memory neural network are continuously adjusted to optimize model performance, reduce the bias of knowledge state prediction, and generate a knowledge state prediction model that can reflect the learner's knowledge mastery.

[0065] S102: Based on a pre-set educational psychology forgetting curve parameter library, test sequences are constructed and processed to generate adversarial evaluation sequences; the knowledge state prediction model is compressed to generate a lightweight knowledge tracking model.

[0066] For example, core parameters of a pre-set educational psychology forgetting curve parameter library are retrieved, and test scenarios with different memory intensities and time intervals are designed by combining the knowledge point association characteristics and learning behavior temporal characteristics. Long-interval forgetting test nodes are incorporated, and after coherence verification and effectiveness screening, an adversarial evaluation sequence is generated.

[0067] Based on the network structure and parameter distribution characteristics of the knowledge state prediction model, the core objectives and performance retention limits of model compression are clearly defined. Appropriate model compression techniques are selected, redundant parameters of the knowledge state prediction model are simplified in a targeted manner, and the network layers are reasonably optimized. During the compression process, the integrity of the model's core prediction functions is continuously monitored to avoid excessive loss of key feature extraction capabilities and knowledge state mapping accuracy. Through multiple rounds of compression effect verification and parameter fine-tuning, a lightweight knowledge tracking model is generated.

[0068] S103: Input the adversarial evaluation sequence into the lightweight knowledge tracing model for long-interval forgetting sensitivity testing to generate the long-term forgetting sensitivity decay rate.

[0069] For example, the adversarial evaluation sequence is format-adapted and validated to conform to the input specifications of the lightweight knowledge tracing model before being input into the model. The model extracts the temporal features and knowledge state information of long-interval forgetting test nodes in the sequence, outputs prediction results through feature mapping and state inference, and quantifies the sensitivity by combining preset evaluation criteria to generate the long-term forgetting sensitivity decay rate.

[0070] S104: Adjust the compression parameters based on the long-term forgetting sensitivity decay rate to generate a high-fidelity compression model; process real-time learning behavior data through the high-fidelity compression model to generate an anti-forgetting learning path.

[0071] For example, the decay rate of long-term forgetting sensitivity is analyzed, and the distribution of compressed parameters of the lightweight knowledge tracing model is combined to clarify the direction and constraints of parameter adjustment, optimize the retention ratio of redundant parameters and the connection mode of network hierarchy, verify the prediction fidelity of the model for long-interval forgetting characteristics, and generate a high-fidelity compressed model after multiple rounds of calibration and verification.

[0072] Real-time learning behavior data is collected, formatted, and effective information is extracted. After meeting the input requirements of the high-fidelity compression model, the data is input into the model. The model analyzes the learner's real-time knowledge status through temporal state reasoning, judges the decline trend by combining the memory decay law, plans reinforcement practice nodes and content according to individual learning behavior differences, and generates an anti-forgetting learning path.

[0073] One embodiment of this application provides an online education method based on a mathematical model, which includes preprocessing learners' online interaction logs to generate raw behavioral sequence data, training a long short-term memory neural network based on this data to obtain a knowledge state prediction model, constructing a test sequence to generate an adversarial evaluation sequence by combining a pre-set educational psychology forgetting curve parameter library, compressing the knowledge state prediction model to obtain a lightweight knowledge tracking model, inputting the adversarial evaluation sequence into the lightweight knowledge tracking model to complete a long-interval forgetting sensitivity test to generate a long-term forgetting sensitivity decay rate, adjusting the compression parameters according to the decay rate to obtain a high-fidelity compression model, and then processing real-time learning behavior data through the high-fidelity compression model. This method can improve the prediction fidelity of the compression model for long-interval forgetting characteristics, optimize the accuracy of long-term memory state prediction of knowledge points, and realize a dynamic anti-forgetting learning path that adapts to individual forgetting differences.

[0074] In one embodiment, the adversarial evaluation sequence is input into a lightweight knowledge tracing model for long-interval forgetting sensitivity testing to generate a long-term forgetting sensitivity decay rate, including:

[0075] (1) Perform repeated practice event identification processing on the adversarial evaluation sequence to generate a long-interval node set.

[0076] For example, all interaction records contained in the adversarial evaluation sequence are classified and grouped according to the corresponding knowledge point type. In the interaction records corresponding to each knowledge point, operation events with the same practice content are identified, and the occurrence position and time information of the above operation events in the adversarial evaluation sequence are marked. Then, the time interval between repeated practice events under the same knowledge point is compared, and practice events with time intervals reaching the long period standard are selected. The sequence nodes corresponding to the above events are summarized and organized to generate a long interval node set.

[0077] The long-interval node set includes adversarial evaluation sequence nodes corresponding to repeated practice events grouped by knowledge points and with time intervals conforming to long-cycle standards.

[0078] (2) Input the adversarial evaluation sequence into the lightweight knowledge tracing model for prediction processing and generate the compressed model prediction results.

[0079] For example, the input data format and field requirements of the lightweight knowledge tracing model are analyzed. By comparing the existing data structure of the adversarial evaluation sequence, the field matching and format conversion of the interaction event data in the sequence are performed, and the necessary feature fields required by the model are supplemented. The input adaptation processing of the adversarial evaluation sequence is completed. The adapted adversarial evaluation sequence is then fed into the lightweight knowledge tracing model, triggering the internal processes of temporal feature extraction, forgetting gating state transition, etc. The model calculates and infers the mastery of knowledge points corresponding to each node in the sequence, and generates the compressed model prediction result.

[0080] The compressed model prediction results include inference data on the mastery of knowledge points at each node, calculated by the lightweight knowledge tracing model based on the adversarial evaluation sequence.

[0081] (3) Input the adversarial evaluation sequence into the knowledge state prediction model for prediction processing to generate the original model prediction results.

[0082] For example, the input specifications and data dimension requirements of the knowledge state prediction model are analyzed, the existing data of the adversarial evaluation sequence are structurally adjusted and dimensionally matched, the integrity and validity of the adjusted data are verified, the input adaptation of the adversarial evaluation sequence and the knowledge state prediction model is completed, the adapted adversarial evaluation sequence is input into the knowledge state prediction model, the long short-term memory feature encoding, knowledge state mapping and other processes of the model are initiated, the model analyzes and judges the mastery of knowledge points corresponding to each node in the sequence, and generates the original model prediction result.

[0083] The original model prediction results include the judgment data on the mastery of knowledge points at each node obtained by the knowledge state prediction model based on the adversarial evaluation sequence analysis.

[0084] (4) Based on the long-interval node set, the prediction deviation between the prediction results of the compressed model and the original model is calculated and processed to generate the forgetting sensitivity difference vector.

[0085] For example, using a long-interval node set as the matching benchmark, the knowledge mastery data of the corresponding nodes in the set is extracted from the prediction results of the compressed model, and the knowledge mastery data of the corresponding nodes in the set is extracted from the prediction results of the original model. The two sets of data are aligned one-to-one at the node level. For each aligned node, the quantization difference between the two sets of mastery data is calculated. The quantization differences of all nodes are integrated into a vector data set in sequence order to generate a forgetting sensitivity difference vector.

[0086] Among them, the forgetting sensitivity difference vector includes a vector formed by integrating the quantitative difference in the knowledge mastery between the prediction results of the compressed model and the prediction results of the original model under the corresponding nodes of the long-interval node set in sequence order.

[0087] (5) The forgetting sensitivity difference vector is statistically normalized using the following formula to generate the long-term forgetting sensitivity decay rate:

[0088]

[0089] in, Indicates the rate of decline in long-term forgetting sensitivity. This represents the Sigmoid normalization function. Describes the Euclidean norm. Indicates the first The difference vector of each node Represents the baseline difference vector. This indicates a minimum value to prevent division by zero. Represents a set of nodes with long intervals. Indicates the summation index.

[0090] For example, the difference data features corresponding to each node are extracted from the forgetting sensitivity difference vector, a benchmark difference vector is introduced as a reference standard, and the difference data of each node is standardized by combining the minimum value of the prevention of division by zero. The standardized difference data is numerically scaled by a normalization function so that the data is within a uniform range. Then, the mean of the scaled difference data of all nodes is calculated and integrated to generate the long-term forgetting sensitivity decay rate.

[0091] Among them, the long-term forgetting sensitivity decay rate is an indicator that reflects the degree of decay in the ability of the lightweight knowledge tracing model to predict long-interval forgetting characteristics after standardization, normalization and mean integration.

[0092] In one embodiment, based on a long-interval node set, a prediction bias calculation is performed on the prediction results of the compressed model and the original model to generate a forgetting sensitivity difference vector, including:

[0093] (1) Based on the long interval node set, the knowledge mastery deviation of the prediction results of the compressed model is calculated and processed to generate the cognitive deviation sequence of the compressed model.

[0094] For example, the node positions corresponding to the long-interval node set in the compressed model prediction results are determined, the knowledge point identifiers corresponding to the above nodes are extracted, the baseline mastery status corresponding to each knowledge point is clarified, the difference between the knowledge point mastery data of these nodes in the compressed model prediction results and the baseline mastery status of the corresponding knowledge points is calculated, and all the calculated difference data are organized according to the node time order of the long-interval node set to generate the cognitive bias sequence of the compressed model.

[0095] The compressed model cognitive bias sequence includes a sequence formed by organizing the difference between the knowledge mastery of the compressed model prediction results and the baseline knowledge mastery of the corresponding knowledge points under the long interval node set in the node time order.

[0096] (2) Based on the long-interval node set, the knowledge point mastery deviation of the original model prediction results is calculated and processed to generate the original model cognitive deviation sequence.

[0097] For example, determine the node positions corresponding to the long-interval node set in the original model prediction results, extract the knowledge point identifiers corresponding to these nodes, clarify the baseline mastery status corresponding to each knowledge point, calculate the difference between the knowledge point mastery data of these nodes in the original model prediction results and the baseline mastery status of the corresponding knowledge points, organize all the calculated difference data according to the node time order of the long-interval node set, and generate the original model cognitive bias sequence.

[0098] The original model cognitive bias sequence includes a sequence formed by organizing the difference between the knowledge mastery of the original model prediction results and the benchmark knowledge mastery of the corresponding knowledge points under the long interval node set in the node time order.

[0099] (3) Using the following formula, perform temporal correlation fusion processing on the cognitive bias sequence of the compressed model and the cognitive bias sequence of the original model to generate a forgetting sensitivity difference vector:

[0100]

[0101] in, Represents the forgetting sensitivity difference vector. This represents the temporal correlation fusion function. Represents a set of nodes with long intervals. Indicates the node's time index. This represents the time decay weighting factor. Indicates time The compressed model of cognitive bias vector, Indicates time The original model cognitive bias vector, This represents the operator for calculating element-level deviations.

[0102] For example, the node time index corresponding to the long interval node set is determined, and a time decay weight factor associated with the node time is introduced. For each node time index, the corresponding compressed model cognitive bias vector in the compressed model cognitive bias sequence is extracted, and the corresponding original model cognitive bias vector in the original model cognitive bias sequence is also extracted. The element-level bias calculation operator is used to perform the corresponding element bias operation on the two vectors. Then, the calculation result is weighted by the time decay weight factor corresponding to the node time index. The weighted results under all node time indices are passed to the time-series correlation fusion function for integration processing to generate a forgetting sensitivity difference vector.

[0103] The forgetting sensitivity difference vector includes the vector result obtained by integrating the cognitive bias sequence of the compressed model and the cognitive bias sequence of the original model after time decay weighting, element-level bias calculation and time series correlation fusion.

[0104] In one embodiment, the adversarial evaluation sequence is input into a lightweight knowledge tracing model for prediction processing to generate a compressed model prediction result, including:

[0105] (1) Perform temporal feature enhancement processing on the adversarial evaluation sequence to generate a context-aware sequence.

[0106] For example, the node structure of the adversarial evaluation sequence is analyzed, and the knowledge point identifier, interaction type, and time step information corresponding to each node are extracted. The above information is sorted in time step order and a node index is established. For each node, the knowledge point interaction features of its preceding consecutive time step nodes are traced, and the knowledge point interaction features of its subsequent adjacent time step nodes are extracted. These preceding and subsequent node features are then associated and bound with the current node features.

[0107] Analyze the interaction frequency and interval characteristics of the same knowledge point at different time steps, and supplement these characteristics into the feature fields of the corresponding nodes. Reorganize the enhanced features of all nodes according to the original time step order to ensure that each node contains its own basic features, the related features of preceding and following nodes, and the temporal sequence features of knowledge point interactions, and generate a context-aware sequence.

[0108] The context-aware sequence includes the basic features of each node, the correlation features between preceding and succeeding nodes, and the temporal features of knowledge point interactions, and is sequence data organized in the original time step order.

[0109] (2) Using the following formula, the context-aware sequence is input into the forgetting gating unit of the lightweight knowledge tracing model for state transition calculation, generating a dynamic knowledge state matrix:

[0110]

[0111] in, Indicates time step The dynamic knowledge state matrix, Indicates time step Context-aware sequences, Indicates time step The dynamic knowledge state matrix, This represents the set of parameters for a lightweight knowledge tracing model. This represents the state transition function of the forgetting gate unit.

[0112] For example, the input field requirements for the forgetting gating unit of the lightweight knowledge tracing model are determined. The data at each time step of the context-aware sequence is split into subfields such as knowledge point features and interaction features, and matched with the input fields of the forgetting gating unit. The dynamic knowledge state matrix of the first time step is initialized with preset initial state data. Starting from the first time step, each time step is processed sequentially: the state transition function of the forgetting gating unit is called, first inputting the dynamic knowledge state matrix of the previous time step, loading parameters such as gating weights and biases from the parameter set of the lightweight knowledge tracing model, then inputting the context-aware sequence data of the current time step, calculating the knowledge state update amount of the current time step through the state transition function, and fusing the update amount with the state of the previous time step to obtain the dynamic knowledge state data of the current time step. After completing all calculations sequentially for each time step, the dynamic knowledge state data of each time step is arranged into a matrix structure according to the time step order to generate the dynamic knowledge state matrix.

[0113] The dynamic knowledge state matrix consists of knowledge point state data obtained from the forgetting gating unit state transition calculation at each time step, arranged in the order of time steps.

[0114] (3) Using the following formula, knowledge point mastery mapping is performed based on the dynamic knowledge state matrix to generate the compressed model prediction results:

[0115]

[0116] in, This represents the prediction results of the compression model. This represents the dynamic knowledge state matrix after time-series averaging. Represents the weight matrix. This represents the bias vector.

[0117] For example, the temporal dimension of the dynamic knowledge state matrix is ​​determined. The arithmetic mean of the state data corresponding to each knowledge point in the matrix is ​​calculated step-by-step to obtain the average state data of each knowledge point over the entire temporal range. This data is then integrated to form a time-averaged dynamic knowledge state matrix. A weight matrix is ​​loaded, and the time-averaged dynamic knowledge state matrix is ​​multiplied by the weight matrix to obtain a preliminary feature mapping result. The bias vector is then added element-wise to this result to complete the linear mapping process. The corresponding normalization function is called to numerically scale the linear mapping result so that the result corresponding to each knowledge point falls within a specified probability interval. The scaled result is then categorized by knowledge point identifier, and the mastery value corresponding to each knowledge point is labeled. This is organized into a structured dataset, generating compressed model prediction results.

[0118] The compressed model prediction results include mastery scores for each knowledge point and a structured dataset categorized by knowledge point identifier.

[0119] like Figure 2 As shown, compression parameters are adjusted based on the long-term forgetting sensitivity decay rate to generate a high-fidelity compression model, including:

[0120] S201: Perform abnormal interval identification processing on the long-term forgetting sensitivity decay rate to generate abnormal decay rate features.

[0121] For example, the model performance evaluation dimension corresponding to the long-term forgetting sensitivity decay rate is clearly defined, and the fluctuation range of this decay rate under normal model operation is determined. The values ​​of the long-term forgetting sensitivity decay rate are distributed and sorted according to the node order of the corresponding long-interval node set, and the matching of the decay rate value corresponding to each node with the normal fluctuation range is compared one by one. The decay rate intervals corresponding to the nodes whose values ​​exceed the normal fluctuation range are selected, and the start and end node positions of the above intervals and the degree of deviation of the decay rate values ​​are recorded. The position information of the above intervals exceeding the ranges and the deviation characteristics are integrated to form structured feature data and generate decay rate anomaly features.

[0122] Among them, the abnormal decay rate features include structured feature data formed by integrating information such as the location of the interval in the decay rate of long-term forgetting sensitivity that exceeds the normal fluctuation range and the degree of numerical deviation.

[0123] S202: Based on the abnormal characteristics of the decay rate, perform neuron sensitivity mapping to generate dynamic compression rules.

[0124] For example, the node positions corresponding to the decay rate anomaly feature are associated with the neuron output layer of the lightweight knowledge tracing model to determine the set of neurons involved in the knowledge state prediction process corresponding to the above nodes. The degree of correlation between the output data of each neuron in this set of neurons and the decay rate anomaly feature is analyzed, and the sensitivity level of the neurons is classified according to the degree of correlation.

[0125] For neurons with different sensitivity levels, corresponding constraints on parameter retention priorities and parameter compression ratios are determined. These priorities and constraints are integrated with the network hierarchy of the lightweight knowledge tracing model to form compression constraints adapted to different neurons, generating dynamic compression rules.

[0126] The dynamic compression rules include a set of rules formed by integrating constraints such as parameter retention priority and compression ratio limits for neurons of different sensitivity levels in the lightweight knowledge tracing model.

[0127] S203: Based on dynamic compression rules, the parameters of the lightweight knowledge tracing model are iteratively adjusted to generate a high-fidelity compressed model.

[0128] For example, dynamic compression rules are loaded to clarify the parameter retention priority and compression ratio limits for each neuron in the lightweight knowledge tracing model. For each network layer of the lightweight knowledge tracing model, parameters corresponding to low-priority neurons are simplified according to the compression ratio specified in the dynamic compression rules, while retaining the core parameters of high-priority neurons. After the first round of parameter adjustment, an adversarial evaluation sequence is input into the adjusted model to recalculate the long-term forgetting sensitivity decay rate and compare the difference between this decay rate and the rate before adjustment. If the decay rate still exhibits abnormal characteristics, the parameters are adjusted again based on the new decay situation, referring to the dynamic compression rules. This process of parameter adjustment and performance verification is repeated until the long-term forgetting sensitivity decay rate of the model is within a normal fluctuation range, generating a faithful compressed model.

[0129] Among them, the fidelity compression model includes an optimized version of the lightweight knowledge tracing model whose long-term forgetting sensitivity decay rate is within the normal fluctuation range after multiple rounds of parameter iteration adjustments.

[0130] In one embodiment, real-time learning behavior data processing is performed using a high-fidelity compression model to generate a forgetting-resistant learning path, including:

[0131] (1) Real-time learning behavior data is processed by time-series state reasoning through a high-fidelity compression model to generate a dynamic knowledge point state matrix.

[0132] For example, real-time learning behavior data is collected, and the knowledge point identifiers, interaction operation types, and corresponding operation time step information contained therein are extracted. The data is then formatted and supplemented with the time series feature fields required by the high-fidelity compression model to ensure that the data structure matches the input specifications of the high-fidelity compression model.

[0133] The normalized real-time learning behavior data is input into the high-fidelity compression model in chronological order, triggering the model's internal temporal state inference process. The model, combined with its stored knowledge state mapping rules, performs state analysis on the knowledge point interaction information at each time step, calculating the mastery state data of each knowledge point at the corresponding time step. All calculated mastery state data are then arranged in a matrix according to the dimensions of time step and knowledge point, generating a dynamic knowledge point state matrix.

[0134] The dynamic knowledge point status matrix includes mastery status data for different knowledge points at each time step, arranged in a matrix according to the time step and knowledge point dimensions.

[0135] (2) Using the following formula, perform time window decay analysis on the dynamic knowledge point state matrix to generate the knowledge point decay probability distribution:

[0136]

[0137] in, Indicates time The probability of knowledge point decay. Representing knowledge points In time The degree of mastery, This represents the decay factor of the forgetting curve. Indicates the time interval parameter. This represents an exponential function.

[0138] For example, the range of the time window is determined, and based on this range, knowledge point mastery status data within the corresponding time interval in the dynamic knowledge point state matrix is ​​extracted to clarify the mastery degree of each knowledge point at the corresponding time step. A forgetting curve decay factor and time interval parameter are introduced, and combined with the mastery degree of each knowledge point, a decay trend analysis is performed on the state change of each knowledge point within the time window to calculate the degree of decay of each knowledge point at the current time step. The decay degrees of all knowledge points are classified and organized according to the knowledge point identifier to form a decay probability data set corresponding to each knowledge point, generating a knowledge point decay probability distribution.

[0139] The knowledge point decay probability distribution includes the decay probability data of each knowledge point at the current time step, which is a set organized according to the knowledge point identifier.

[0140] (3) Based on the knowledge point decay probability distribution, adaptive insertion of reinforcement practice nodes is performed to generate anti-forgetting learning paths.

[0141] For example, the data in the knowledge point decay probability distribution is categorized into levels to determine the required level of reinforcement practice corresponding to different decay probabilities. For each knowledge point, corresponding reinforcement practice content is matched according to its decay probability level. Simultaneously, the timing of inserting reinforcement practice nodes is determined by combining real-time learning behavior data reflecting the learning progress. These reinforcement practice nodes are then aligned temporally with the knowledge point learning nodes in the original learning path, adjusting the node arrangement to suit the learning pace and ensuring that the interval between reinforcement practice nodes and the corresponding knowledge point learning nodes conforms to the principles of memory consolidation. All the adjusted nodes are integrated to form a structured learning process, generating an anti-forgetting learning path.

[0142] The anti-forgetting learning path includes the original learning path nodes and adaptively inserted reinforcement practice nodes, forming a structured learning process after being aligned in sequence and adapted to the rhythm.

[0143] In one embodiment, a test sequence is constructed based on a pre-set educational psychology forgetting curve parameter library to generate an adversarial assessment sequence, including:

[0144] (1) The critical memory intensity is calculated and processed according to the pre-set educational psychology forgetting curve parameter library to generate the cognitive interference intensity distribution.

[0145] For example, a pre-built database of educational psychology forgetting curve parameters is retrieved, and core parameters such as memory decay cycle, knowledge retention threshold, and repetition reinforcement coefficient are analyzed to clarify the memory characteristic parameters corresponding to different types of knowledge points. Combining the difficulty and relevance of knowledge points, the calculation dimensions and weight allocation of critical memory intensity are determined. Through comprehensive analysis of each parameter, the minimum intensity standard required to maintain effective memory for each knowledge point is calculated. Then, based on the differences in critical memory intensity, different levels of interference intensity intervals are divided. Finally, the interference intensity levels and interval ranges corresponding to all knowledge points are integrated to generate a cognitive interference intensity distribution.

[0146] The cognitive interference intensity distribution includes the interference intensity level and range corresponding to each knowledge point, and the distribution data is formed by classifying and integrating the knowledge point type and memory characteristics.

[0147] (2) Based on the cognitive interference intensity distribution, the initial test sequence is subjected to long-interval interference event injection processing to generate enhanced adversarial sequences.

[0148] For example, the arrangement order of knowledge points, time interval settings, and knowledge point coverage of the initial test sequence are analyzed to clarify the knowledge point attributes and temporal relationships of each node in the sequence. Based on the distribution of cognitive interference intensity, a corresponding interference event type is matched for each knowledge point, and the time interval standard for long-interval interference events is determined. This standard must conform to the memory decay law in a pre-set educational psychology forgetting curve parameter library.

[0149] In the initial test sequence, node gaps that meet the long interval requirement are selected, and interference events associated with the corresponding knowledge points are injected to ensure that the interference events can both trigger memory interference effects and not undermine the core testing objectives of the knowledge points. The sequence after the interference events are injected undergoes node integration and temporal calibration to generate a reinforced adversarial sequence.

[0150] The enhanced adversarial sequence includes the basic structure of the initial test sequence, long-interval interference events injected according to the cognitive interference intensity distribution, and sequence data formed by time-series calibration and node integration.

[0151] (3) Perform knowledge coherence constraint testing on the enhanced adversarial sequence to generate an adversarial evaluation sequence.

[0152] For example, constraints on knowledge coherence are determined, which include the rationality of logical connections between knowledge points, the naturalness of temporal arrangement, and the boundary of the correlation between interfering events and original knowledge points. The reinforcement adversarial sequence is examined node by node in order, analyzing whether the logical connection between adjacent knowledge points is smooth, whether the injection of interfering events affects the coherence of knowledge transfer, and whether the long interval setting conforms to memory rules and testing requirements.

[0153] For any inconsistencies found during the testing process, their positions are adjusted or their content is optimized, and invalid interference events that severely disrupt the coherence are removed. After completing the local adjustments, the overall sequence is reviewed for coherence to ensure that it retains the adversarial testing function while meeting the coherence requirements of knowledge logic and temporal arrangement, thus generating an adversarial evaluation sequence.

[0154] Among them, the adversarial evaluation sequence includes test sequences that retain long-interval interference events and meet the knowledge coherence requirements after being tested for knowledge coherence constraints, local adjustments and overall review.

[0155] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0156] In one embodiment, such as Figure 3 As shown, this application also provides an online education device 300 based on a mathematical model, the device 300 comprising:

[0157] The behavior sequence modeling module 301 is used to preprocess the learner's online interaction logs to generate raw behavior sequence data; and to train a long short-term memory neural network based on the raw behavior sequence data to generate a knowledge state prediction model.

[0158] The adversarial compression module 302 is used to construct and process test sequences based on a pre-set educational psychology forgetting curve parameter library to generate adversarial evaluation sequences; and to perform model compression processing on the knowledge state prediction model to generate a lightweight knowledge tracking model.

[0159] The forgetting sensitivity test module 303 is used to input the adversarial evaluation sequence into the lightweight knowledge tracing model for long-interval forgetting sensitivity test processing, and generate the long-term forgetting sensitivity decay rate.

[0160] The high-fidelity learning path module 304 is used to adjust the compression parameters according to the long-term forgetting sensitivity decay rate to generate a high-fidelity compression model; and to process real-time learning behavior data through the high-fidelity compression model to generate an anti-forgetting learning path.

[0161] Specifically, the behavior sequence modeling module 301 collects learners' online interaction logs, performs log preprocessing operations such as valid record filtering, redundant information removal, and data format standardization on the online interaction logs, eliminates invalid content and interference information in the online interaction logs, standardizes the structure and presentation of the data, ensures the consistency and usability of the data, and generates raw behavior sequence data.

[0162] Based on the generated raw behavioral sequence data, a training framework for a long short-term memory neural network is built, a suitable sample dataset is divided, network training parameters that fit the educational scenario are set, and the internal parameters of the long short-term memory neural network are continuously adjusted through an iterative training process of forward propagation calculation and backpropagation optimization to optimize model performance, reduce the bias of knowledge state prediction, and generate a knowledge state prediction model.

[0163] The raw behavioral sequence data includes learner online interaction behavior data that has been preprocessed from logs and meets the subsequent model training criteria. The knowledge state prediction model includes a long short-term memory neural network model that can reflect learners' knowledge mastery.

[0164] The adversarial compression module 302 retrieves a pre-set educational psychology forgetting curve parameter library, combines the knowledge point association characteristics and learning behavior temporal characteristics, designs test scenarios with different memory intensities and time intervals, incorporates long-interval forgetting test nodes, and generates an adversarial evaluation sequence after sequence coherence verification and validity screening.

[0165] The compression target and performance baseline of the knowledge state prediction model are clearly defined, an appropriate model compression technology is selected, redundant parameters of the knowledge state prediction model are simplified and network layers are optimized. The integrity of the core prediction function is monitored during the process. After multiple rounds of effect verification and parameter fine-tuning, a lightweight knowledge tracing model is generated.

[0166] The adversarial evaluation sequence includes test sequences that incorporate long-interval forgetting check nodes and conform to knowledge logic and temporal coherence. The lightweight knowledge tracing model includes a simplified version of the knowledge state prediction model that retains core prediction functions after parameter simplification and hierarchical optimization.

[0167] The forgetting sensitivity test module 303 performs format adaptation and verification on the adversarial evaluation sequence to make it conform to the input specifications of the lightweight knowledge tracing model. After that, it is input into the lightweight knowledge tracing model. The model extracts the temporal features and knowledge state information of long-interval forgetting test nodes in the sequence, outputs the prediction results through feature mapping and state inference, and quantifies the sensitivity by combining the preset evaluation criteria to generate the long-term forgetting sensitivity decay rate.

[0168] Among them, the long-term forgetting sensitivity decay rate includes an indicator that reflects the degree of decay in the ability of the lightweight knowledge tracing model to predict long-interval forgetting characteristics.

[0169] The 304 module of the high-fidelity learning path analyzes the decay rate of long-term forgetting sensitivity, combines the compression parameter distribution of the lightweight knowledge tracing model, clarifies the direction and constraints of parameter adjustment, optimizes the retention ratio of redundant parameters and the connection mode of network hierarchy, verifies the model's prediction fidelity for long-interval forgetting characteristics, and generates a high-fidelity compressed model after multiple rounds of calibration and verification.

[0170] Real-time learning behavior data is collected, formatted, and effective information is extracted. After meeting the input requirements of the high-fidelity compression model, the data is input into the high-fidelity compression model. The model analyzes the learner's knowledge status in real time through temporal state reasoning, judges the decline trend by combining the memory decay law, and plans reinforcement practice nodes and content according to individual learning behavior differences to generate anti-forgetting learning paths.

[0171] The high-fidelity compression model includes an optimized version of a lightweight knowledge tracing model that achieves high fidelity in predicting long-interval forgetting characteristics after parameter adjustments. The anti-forgetting learning path consists of original learning nodes and adaptively inserted reinforcement practice nodes, forming a structured learning process adapted according to time sequence and rhythm.

[0172] The forgetting sensitivity test module 303 is also used for:

[0173] Repeated practice event identification processing is performed on the adversarial evaluation sequence to generate a long-interval node set;

[0174] The adversarial evaluation sequence is input into a lightweight knowledge tracing model for prediction processing, generating compressed model prediction results.

[0175] The adversarial evaluation sequence is input into the knowledge state prediction model for prediction processing, and the prediction result of the original model is generated.

[0176] Based on a long-interval node set, the prediction deviation between the prediction results of the compressed model and the original model is calculated and processed to generate a forgetting sensitivity difference vector.

[0177] The long-term forgetting sensitivity decay rate is generated by statistically normalizing the forgetting sensitivity difference vector using the following formula:

[0178]

[0179] in, Indicates the rate of decline in long-term forgetting sensitivity. This represents the Sigmoid normalization function. Describes the Euclidean norm. Indicates the first The difference vector of each node Represents the baseline difference vector. This indicates a minimum value to prevent division by zero. Represents a set of nodes with long intervals. Indicates the summation index.

[0180] The forgetting sensitivity test module 303 is also used for:

[0181] Based on a long-interval node set, the knowledge point mastery deviation of the prediction results of the compressed model is calculated and processed to generate a cognitive deviation sequence of the compressed model.

[0182] Based on a long-interval node set, the knowledge point mastery deviation of the original model prediction results is calculated and processed to generate the original model cognitive deviation sequence.

[0183] The following formula is used to perform temporal correlation fusion processing on the cognitive bias sequences of the compressed model and the original model to generate a forgetting sensitivity difference vector:

[0184]

[0185] in, Represents the forgetting sensitivity difference vector. This represents the temporal correlation fusion function. Represents a set of nodes with long intervals. Indicates the node's time index. This represents the time decay weighting factor. Indicates time The compressed model of cognitive bias vector, Indicates time The original model cognitive bias vector, This represents the operator for calculating element-level deviations.

[0186] The forgetting sensitivity test module 303 is also used for:

[0187] Temporal feature enhancement processing is performed on the adversarial evaluation sequence to generate a context-aware sequence;

[0188] Using the following formula, the context-aware sequence is input into the forgetting gating unit of the lightweight knowledge tracing model for state transition calculation, generating a dynamic knowledge state matrix:

[0189]

[0190] in, Indicates time step The dynamic knowledge state matrix, Indicates time step Context-aware sequences, Indicates time step The dynamic knowledge state matrix, This represents the set of parameters for a lightweight knowledge tracing model. This represents the state transition function of the forgetting gate unit;

[0191] The following formula is used to map knowledge point mastery based on the dynamic knowledge state matrix, generating compressed model prediction results:

[0192]

[0193] in, This represents the prediction results of the compression model. This represents the dynamic knowledge state matrix after time-series averaging. Represents the weight matrix. This represents the bias vector.

[0194] The Fidelity Learning Path module 304 is also used for:

[0195] Abnormal intervals are identified in the long-term forgetting sensitivity decay rate to generate abnormal decay rate features.

[0196] Based on the abnormal characteristics of the decay rate, neuron sensitivity mapping is performed to generate dynamic compression rules.

[0197] The lightweight knowledge tracing model is iteratively adjusted based on dynamic compression rules to generate a high-fidelity compressed model.

[0198] The Fidelity Learning Path module 304 is also used for:

[0199] A dynamic knowledge point state matrix is ​​generated by performing temporal state reasoning on real-time learning behavior data through a high-fidelity compression model.

[0200] The following formula is used to perform time window decay analysis on the dynamic knowledge point state matrix to generate the knowledge point decay probability distribution:

[0201]

[0202] in, Indicates time The probability of knowledge point decay. Representing knowledge points In time The degree of mastery, This represents the decay factor of the forgetting curve. Indicates the time interval parameter. Represents an exponential function;

[0203] Based on the knowledge point decay probability distribution, adaptive insertion of reinforcement practice nodes is performed to generate a learning path resistant to forgetting.

[0204] The anti-compression module 302 is also used for:

[0205] The critical memory intensity is calculated and processed based on a pre-set educational psychology forgetting curve parameter library to generate a cognitive interference intensity distribution.

[0206] Based on the cognitive interference intensity distribution, long-interval interference events are injected into the initial test sequence to generate enhanced adversarial sequences.

[0207] The knowledge coherence constraint test is performed on the enhanced adversarial sequence to generate an adversarial evaluation sequence.

[0208] In one embodiment, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0209] In one embodiment, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the above-described method embodiments.

[0210] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The components described as separate parts may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0211] The above-described embodiments are merely illustrative of several implementation methods of the embodiments of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the embodiments of this application, and these modifications and improvements all fall within the protection scope of the embodiments of this application.

Claims

1. An online education method based on mathematical models, characterized in that, The method includes: The learner's online interaction logs are preprocessed to generate raw behavioral sequence data; a long short-term memory neural network is trained based on the raw behavioral sequence data to generate a knowledge state prediction model. Test sequences are constructed and processed based on a pre-set educational psychology forgetting curve parameter library to generate adversarial evaluation sequences; the knowledge state prediction model is compressed to generate a lightweight knowledge tracking model. The adversarial evaluation sequence is input into the lightweight knowledge tracing model for long-interval forgetting sensitivity testing to generate a long-term forgetting sensitivity decay rate. The compression parameters are adjusted based on the long-term forgetting sensitivity decay rate to generate a high-fidelity compression model; real-time learning behavior data is processed using the high-fidelity compression model to generate an anti-forgetting learning path.

2. The online education method based on a mathematical model according to claim 1, characterized in that, The step of inputting the adversarial evaluation sequence into the lightweight knowledge tracing model for long-interval forgetting sensitivity testing to generate a long-term forgetting sensitivity decay rate includes: The adversarial evaluation sequence is processed to identify repeated practice events, generating a long-interval node set; The adversarial evaluation sequence is input into the lightweight knowledge tracing model for prediction processing to generate compressed model prediction results. The adversarial evaluation sequence is input into the knowledge state prediction model for prediction processing to generate the original model prediction result; Based on the long-interval node set, the prediction deviation of the compressed model prediction result and the original model prediction result is calculated to generate a forgetting sensitivity difference vector. The long-term forgetting sensitivity decay rate is generated by statistically normalizing the forgetting sensitivity difference vector using the following formula: in, Indicates the rate of decline in long-term forgetting sensitivity. This represents the Sigmoid normalization function. Describes the Euclidean norm. Indicates the first The difference vector of each node Represents the baseline difference vector. This indicates a minimum value to prevent division by zero. Represents a set of nodes with long intervals. Indicates the summation index.

3. The online education method based on a mathematical model according to claim 2, characterized in that, The step of calculating the prediction deviation between the compressed model prediction result and the original model prediction result based on the long-interval node set, and generating a forgetting sensitivity difference vector, includes: Based on the long-interval node set, the knowledge point mastery deviation of the prediction results of the compressed model is calculated and processed to generate a cognitive deviation sequence of the compressed model. Based on the long-interval node set, the knowledge point mastery deviation of the original model prediction results is calculated and processed to generate the original model cognitive deviation sequence. The following formula is used to perform time-series correlation fusion processing on the cognitive bias sequence of the compressed model and the cognitive bias sequence of the original model to generate the forgetting sensitivity difference vector: in, Represents the forgetting sensitivity difference vector. This represents the temporal correlation fusion function. Represents a set of nodes with long intervals. Indicates the node's time index. This represents the time decay weighting factor. Indicates time The compressed model of cognitive bias vector, Indicates time The original model cognitive bias vector, This represents the operator for calculating element-level deviations.

4. The online education method based on a mathematical model according to claim 2, characterized in that, The step of inputting the adversarial evaluation sequence into the lightweight knowledge tracing model for prediction processing to generate compressed model prediction results includes: The adversarial evaluation sequence is subjected to temporal feature enhancement processing to generate a context-aware sequence; The context-aware sequence is input into the forgetting gating unit of the lightweight knowledge tracing model using the following formula to perform state transition calculations and generate a dynamic knowledge state matrix: in, Indicates time step The dynamic knowledge state matrix, Indicates time step Context-aware sequences, Indicates time step The dynamic knowledge state matrix, This represents the set of parameters for a lightweight knowledge tracing model. This represents the state transition function of the forgetting gate unit; The following formula is used to perform knowledge point mastery mapping based on the dynamic knowledge state matrix to generate the prediction result of the compressed model: in, This represents the prediction results of the compression model. This represents the dynamic knowledge state matrix after time-series averaging. Represents the weight matrix. This represents the bias vector.

5. The online education method based on a mathematical model according to claim 1, characterized in that, The step of adjusting compression parameters based on the long-term forgetting sensitivity decay rate to generate a high-fidelity compression model includes: The long-term forgetting sensitivity decay rate is subjected to abnormal interval identification processing to generate abnormal decay rate features; Based on the abnormal decay rate characteristics, neuron sensitivity mapping is performed to generate dynamic compression rules. The lightweight knowledge tracing model is iteratively adjusted based on the dynamic compression rules to generate the high-fidelity compression model.

6. The online education method based on a mathematical model according to claim 1, characterized in that, The step of processing real-time learning behavior data through the fidelity compression model to generate a forgetting-resistant learning path includes: The real-time learning behavior data is processed by the fidelity compression model to perform temporal state reasoning to generate a dynamic knowledge point state matrix. The following formula is used to perform time window decay analysis on the dynamic knowledge point state matrix to generate the knowledge point decay probability distribution: in, Indicates time The probability of knowledge point decay. Representing knowledge points In time The degree of mastery, This represents the decay factor of the forgetting curve. Indicates the time interval parameter. Represents an exponential function; Based on the knowledge point decay probability distribution, adaptive insertion of reinforcement practice nodes is performed to generate the anti-forgetting learning path.

7. The online education method based on a mathematical model according to claim 1, characterized in that, The step of constructing test sequences based on a pre-set educational psychology forgetting curve parameter library to generate adversarial assessment sequences includes: The critical memory intensity is calculated based on the pre-set educational psychology forgetting curve parameter library to generate a cognitive interference intensity distribution. Based on the cognitive interference intensity distribution, the initial test sequence is processed by long-interval interference event injection to generate an enhanced adversarial sequence. The knowledge coherence constraint test is performed on the enhanced adversarial sequence to generate the adversarial evaluation sequence.

8. An online education device based on a mathematical model, characterized in that, The device includes: The behavior sequence modeling module is used to preprocess the learner's online interaction logs to generate raw behavior sequence data; and to train a long short-term memory neural network based on the raw behavior sequence data to generate a knowledge state prediction model. The adversarial compression module is used to construct and process test sequences based on a pre-set educational psychology forgetting curve parameter library to generate adversarial evaluation sequences; and to perform model compression processing on the knowledge state prediction model to generate a lightweight knowledge tracking model. The forgetting sensitivity testing module is used to input the adversarial evaluation sequence into the lightweight knowledge tracing model for long-interval forgetting sensitivity testing to generate a long-term forgetting sensitivity decay rate. The high-fidelity learning path module is used to adjust compression parameters based on the long-term forgetting sensitivity decay rate to generate a high-fidelity compression model; and to process real-time learning behavior data through the high-fidelity compression model to generate an anti-forgetting learning path.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the online education method based on a mathematical model as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the online education method based on a mathematical model as described in any one of claims 1 to 7.

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