Training method of mathematical knowledge point mastering prediction model and prediction system

Abstract

The invention discloses a training method of a mathematical knowledge point mastering prediction model and a prediction system, and belongs to the field of knowledge point mastering prediction. The method comprises the following steps: firstly, acquiring original interaction data of a user in a historical time period and a current time step from an online learning platform, and preprocessing the original interaction data; an embedded layer, a problem encoder, an interaction encoder, a mathematical knowledge point retrieval layer and a prediction network form a mathematical knowledge point mastering prediction model, and the mathematical knowledge point mastering prediction model is trained based on preprocessed interaction data. And updating parameters of the mathematical knowledge point mastering prediction model based on negative logarithm likelihood loss between an answer result prediction value of the next time step output by the minimization model and a corresponding real answer result until a trained mathematical knowledge point mastering prediction model is obtained. The method effectively solves the'impossible four-corner 'problem in a large-scale online learning environment, optimizes training efficiency, reasoning efficiency and prediction performance, considers a forgetting mechanism, and has a good application prospect.

Description

Technical Field

[0001] The present invention belongs to the field of knowledge point mastery prediction, and in particular relates to a training method and a prediction system for a mathematical knowledge point mastery prediction model. Background Art

[0002] Predicting the mastery of mathematical knowledge points is a key research area to improve students' learning efficiency. With the rapid development of online education and artificial intelligence, how to use computer technology to accurately predict students' knowledge mastery status has become an important topic at the intersection of computer science, cognitive science and education. However, online mathematics education faces the "impossible four corners" problem: it is difficult to optimize training efficiency, reasoning efficiency, prediction performance and forgetting mechanism modeling at the same time. In a large-scale learning environment, the number of students is huge and their behaviors are complex, which makes personalized teaching difficult and places extremely high demands on model performance and efficiency. In addition, the knowledge forgetting mechanism significantly affects mathematical learning, and forgetting may cause chain understanding obstacles of logically related knowledge points. To address these challenges, it is necessary to build an efficient and accurate prediction model that can capture knowledge state changes and forgetting mechanisms, support incremental learning, maintain efficient computing and interpretability. The current research focuses of knowledge tracking technology include optimizing deep learning models (such as improving RNN and attention mechanisms), introducing graph neural networks, developing memory-enhanced networks, multimodal data fusion technology, and interpretable artificial intelligence applications. However, current knowledge tracing methods still have some key deficiencies, especially in solving the "impossible four corners" problem: (1) Although Transformer-based models have performed well in terms of performance and training efficiency, they have been criticized for their inference efficiency. These models have high complexity in calculating inter-item weights (i.e., "self-attention") at the sequence level, especially when the sequence length increases, the computational and memory overhead increases significantly. (2) RNN-based methods have performed well in terms of inference efficiency, and achieve efficient step-by-step retrieval and update by maintaining a fixed-length hidden state vector to represent the degree of knowledge mastery. However, such methods have limitations in terms of training efficiency and prediction performance. (3) Other types of models, such as dynamic key-value memory networks (DKVMN) and graph knowledge tracing (GKT), have improved in some aspects, but have not yet fully solved the "impossible four corners" problem. In addition, many existing models are inefficient in modeling long-term dependencies, lack incremental learning capabilities, and cannot adapt to dynamically changing learning environments. The "black box" nature of deep learning models also leads to insufficient interpretability, limiting their application in educational practice. In particular, most existing models have obvious deficiencies in dealing with the forgetting mechanism, making it difficult to accurately capture and predict the knowledge decay process of students. These deficiencies have seriously restricted the widespread application and effectiveness of knowledge tracking technology in actual educational scenarios, and an innovative solution is urgently needed to comprehensively break through these limitations. Summary of the invention

[0003] The purpose of the present invention is to solve the above problems existing in the prior art and to provide a training method and a prediction system for mastering a prediction model of mathematical knowledge points.

[0004] In order to achieve the above-mentioned invention object, the present invention specifically adopts the following technical solutions:

[0005] In a first aspect, the present invention provides a method for training a mathematical knowledge point mastery prediction model, which comprises the following steps:

[0006] S1: Obtaining the original interaction data of the user in the historical time period and the original interaction data of the current time step from the online learning platform, and preprocessing the original interaction data to obtain preprocessed interaction data; wherein each original interaction data consists of a mathematical problem presented to the user at each time step, mathematical knowledge points related to the mathematical problem, and the answer result;

[0007] S2: The preprocessed interaction data is input into the mathematical knowledge point mastery prediction model for training. In the training process of the mathematical knowledge point mastery prediction model, the preprocessed interaction data is first embedded by the embedding layer. Each preprocessed interaction data corresponds to a mathematical problem embedding vector, a mathematical knowledge point embedding vector and an interaction embedding vector. After the mathematical knowledge point embedding vector constitutes the mathematical knowledge point embedding sequence of each time step, the mathematical knowledge point embedding sequence of each time step is input into the question encoder. After being processed by multiple sequentially cascaded question encoding layers, the candidate mathematical knowledge point representation sequence of each time step is obtained. After the interaction embedding vector constitutes the interaction embedding sequence of each time step, the interaction embedding sequence of each time step is input into the interaction encoder. After being processed by multiple sequentially cascaded interaction encoding layers, the candidate interaction representation sequence of each time step is obtained. The candidate interaction representation sequence and the candidate mathematical knowledge point representation sequence are concatenated as the candidate input sequence, and the candidate input sequence of each time step is input into the mathematical knowledge point retriever. After being processed by multiple sequentially cascaded mathematical knowledge point retrieval layers, the corresponding candidate knowledge state representation sequence of each time step is obtained, and the candidate knowledge state representation sequence of each time step is concatenated with the corresponding mathematical problem embedding vector of the next time step and the mathematical knowledge point embedding vector as the embedded spliced ​​sequence of each time step. The embedded spliced ​​sequence is input into the prediction network, and the predicted answer result of the mathematical problem at the next time step is output. The negative log-likelihood loss is calculated based on the predicted answer result of the mathematical problem at the next time step and the corresponding answer result. The parameters of the mathematical knowledge point mastery prediction model are updated based on minimizing the negative log-likelihood loss until the mathematical knowledge point mastery prediction model converges to obtain a trained mathematical knowledge point mastery prediction model.

[0008] Based on the above scheme, each step can be implemented in the following preferred specific manner.

[0009] As a preferred embodiment of the first aspect, in step S2, the specific process of obtaining the mathematical problem embedding vector, the mathematical knowledge point embedding vector and the interaction embedding vector is as follows:

[0010] AS21: A math problem in the preprocessed interaction data is passed through the first embedding layer to obtain a math problem embedding vector;

[0011] AS22: A mathematical knowledge point in the preprocessed interactive data is passed through the second embedding layer and the third embedding layer respectively to obtain a first embedding result and a second embedding result respectively, and a mathematical problem embedding vector corresponding to the mathematical knowledge point is multiplied by the second embedding result to obtain a third embedding result, and the second embedding result and the third embedding result are added together as the mathematical knowledge point embedding vector;

[0012] AS23: Multiply the number of math problems by the answer results in a preprocessed interactive data to obtain a fourth embedding result, add the fourth embedding result and the math knowledge point embedding vector corresponding to the math knowledge point as the fifth embedding result, pass the fifth embedding result through the fourth embedding layer and the fifth embedding layer respectively, and obtain the sixth embedding result and the seventh embedding result respectively, multiply the math problem embedding vector corresponding to the math knowledge point with the seventh embedding result to obtain the eighth embedding result, and add the sixth embedding result, the eighth embedding result and the math knowledge point embedding vector as the interactive embedding vector.

[0013] As a preferred embodiment of the first aspect, in step S2, the specific processing flow of the first question coding layer of the question encoder is: The embedding vector of the mathematical knowledge point at each time step constitutes the The mathematical knowledge point embedding sequence of time steps is used as the input of the first question encoding layer. The mathematical knowledge point embedding sequence is first pre-normalized by the first pre-normalization layer. The pre-normalized mathematical knowledge point embedding sequence is sequentially subjected to the first linear recurrent unit, layer normalization, the first feedforward neural network and Dropout operations to obtain the first encoding result. The first encoding result is compared with the first The embedded sequences of mathematical knowledge points at time steps are added to form a residual connection to obtain the output result of the first question encoding layer.

[0014] As a preferred embodiment of the first aspect, in step S2, the specific processing flow of the first interactive coding layer of the interactive encoder is as follows: The interaction embedding vectors of time steps form the The interactive embedding sequence of time steps is used as the input of the first interactive coding layer. The interactive embedding sequence is first pre-normalized by the second pre-normalization layer. The pre-normalized interactive embedding sequence is sequentially subjected to the second linear recurrent unit, layer normalization, the second feedforward neural network and the Dropout operation to obtain the second encoding result. The second encoding result is compared with the first The interactive embedding sequences of time steps are added to form a residual connection to obtain the output of the first interactive encoding layer.

[0015] As a preferred embodiment of the first aspect, in step S2, the specific processing flow of the first mathematical knowledge point retrieval layer of the mathematical knowledge point retriever is as follows: taking the candidate input sequence of each time step as the input of the first mathematical knowledge point retrieval layer, first pre-normalizing the candidate input sequence through a third pre-normalization layer, and sequentially passing the pre-normalized candidate input sequence through a third linear cyclic unit, layer normalization, a third feedforward neural network, and a Dropout operation to obtain a third encoding result, and combining the third encoding result with the first The candidate input sequences of time steps are added to form a residual connection to obtain the output result of the first mathematical knowledge point retrieval layer.

[0016] As a preferred embodiment of the above-mentioned first aspect, in step S2, the specific processing flow in the prediction network is as follows: taking the embedded concatenated sequence of each time step as input, passing it through three sequentially cascaded linear projection layers in sequence to obtain the linear projection vector of each time step, and using the Sigmoid activation function to perform a nonlinear transformation on the linear projection vector of each time step to obtain the predicted answer result of the math problem at the next time step.

[0017] As a preferred embodiment of the first aspect above, the first linear recurrent unit, the second linear recurrent unit and the third linear recurrent unit all adopt a linear activation function, and the linear activation function is used to take a parameter that gradually decays over time as a weight, and the input of each historical time step is weighted and summed to obtain the output of each linear recurrent unit.

[0018] Furthermore, the output of each linear recurrent unit is specifically expressed as:

[0019]

[0020] in, Indicates The hidden state at the time step; represents the time step index; Indicates Input of historical time steps; Represents input For hidden state The contribution of gradually decays over time.

[0021] In a second aspect, the present invention provides a prediction system for a mathematical knowledge point mastery prediction model, comprising:

[0022] The data acquisition and storage module is used to acquire and store the interaction data of different users in the historical time period from the online learning platform;

[0023] A model acquisition module, used to acquire a mathematical knowledge point mastery prediction model trained according to the training method for a mathematical knowledge point mastery prediction model described in any one of the solutions of the first aspect above;

[0024] The result acquisition module is used to obtain the interaction data of the user to be predicted from the data acquisition and storage module and obtain the current math question to be answered and the corresponding math knowledge points and input them into the math knowledge point mastery prediction model obtained by the model acquisition module, and output the probability prediction value of the answer result of the user to be predicted;

[0025] A result calibration module is used to obtain the probability prediction value of the answer result output by the result acquisition module and perform calibration processing on it, and at the same time calculate the confidence interval of the calibrated probability prediction value of the answer result;

[0026] An online update module is used to form a triplet of the current math question to be answered, the corresponding math knowledge point, and the calibrated probability prediction value of the answer result, and associate it with the ID of the user to be predicted, update the interaction data of the user to be predicted, and add the updated interaction data of the user to be predicted to the data acquisition and storage module;

[0027] An incremental learning module, used to use the interaction data stored in the data acquisition and storage module as an incremental learning sample, and when the amount of interaction data in the data acquisition and storage module reaches a preset interaction data threshold, the interaction data in the data acquisition and storage module is used to retrain the mathematical knowledge point mastery prediction model according to the training method for the mathematical knowledge point mastery prediction model described in any one of the schemes of the first aspect above;

[0028] The storage and display module is used to save the calibrated probability prediction value of the answer result and the corresponding confidence interval, and push them to the user interface of the online learning platform in a preset manner.

[0029] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, a training method for a mathematical knowledge point mastery prediction model as described in any of the schemes of the first aspect above is implemented.

[0030] In a fourth aspect, the present invention provides a computer electronic device comprising a memory and a processor;

[0031] The memory is used to store computer programs;

[0032] The processor is used to implement a training method for a mathematical knowledge point mastery prediction model as described in any scheme of the first aspect when executing the computer program.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] The present invention effectively solves the "impossible four corners" problem by designing a mathematical knowledge point mastery prediction model. While maintaining high prediction performance, the method of the present invention significantly improves the training efficiency and reasoning efficiency of the mathematical knowledge point mastery prediction model. The computational complexity is only 13.15M FLOPs, which is more than 85.8% lower than the existing method; the number of parameters is only 0.11M, which is more than 83.1% lower than the existing method; the training time is only 2.37 seconds, which is more than 73.9% shorter than the existing method.

[0035] The present invention adopts the design of linear recurrent unit, removes the nonlinear activation function in the traditional recurrent neural network, obtains the closed-form solution through matrix decomposition, and realizes efficient parallel computing. In the case of long sequences (>5000 steps), the reasoning time of the present invention increases slowly and steadily, maintaining a sub-second processing speed, while the reasoning time of the existing method increases exponentially. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of the steps of the method of the present invention;

[0037] Figure 2 It is a schematic diagram of the structure of the prediction model for the mathematical knowledge points of the present invention;

[0038] Figure 3 This is a schematic diagram of the comparison results of the inference time of different models under different mathematical learning sequence lengths in this embodiment;

[0039] Figure 4 It is a system block diagram of the present invention. DETAILED DESCRIPTION

[0040] In order to make the above-mentioned purpose, features and advantages of the present invention more obvious and easy to understand, the specific implementation mode of the present invention is described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. The technical features in each embodiment of the present invention can be combined accordingly without conflicting with each other.

[0041] In the description of the present invention, it should be understood that the terms "first" and "second" are only used for the purpose of distinguishing descriptions, and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features.

[0042] like Figure 1 As shown, in a preferred implementation of the present invention, the above-mentioned training method for a mathematical knowledge point mastery prediction model includes the following steps S1 to S2. The specific implementation process is described in detail below.

[0043] 1. Acquisition and preprocessing of interactive data of mathematics learning users

[0044] S1: Obtain the original interaction data of the user in the historical time period and the original interaction data of the current time step from the online learning platform, and preprocess the original interaction data to obtain preprocessed interaction data; wherein each original interaction data consists of a mathematical problem presented to the user at each time step, mathematical knowledge points related to the mathematical problem, and the answer result.

[0045] In step S1 of this embodiment, the original interaction data of the user and the original interaction data of the current time step are obtained from the online learning platform. The specific process of preprocessing the original interaction data is as follows: the original interaction data is cleaned, and repeated original interaction data, invalid information and noise data are removed. If there are missing values ​​in the cleaned interaction data, the missing values ​​are interpolated, and the format of the interpolated interaction data is standardized to ensure the consistency of the interaction data structure, so as to facilitate the subsequent mathematical knowledge point mastering prediction model training and use, and finally obtain the preprocessed interaction data. At the same time, a timestamp is added to each preprocessed interaction data to facilitate the subsequent analysis of the impact of the time interval on the mathematical knowledge state.

[0046] In step S1 of this embodiment, each interaction is represented by a discrete time step, capturing the learner's participation in a question and his subsequent response. time steps, using a triplet To describe an interactive data of mathematics learners, the mathematics learning sequence composed of interactive data can be expressed as .in, represents the length of the mathematics learning sequence, Indicates A unique identifier for the math problem presented to the learner at each time step; Indicates Mathematical knowledge points related to the time step and mathematical problem; Indicates the first record in binary form The answer result of the question in time steps, 1 indicates a correct answer and 0 indicates an incorrect answer. For example, the triple Indicates that the learner is in Time step pairs and mathematical knowledge points Related Mathematical Problems Through this serialization process, the present invention can retain the time sequence information of learners' mathematical problem interactions and provide structured input data for subsequent mathematical knowledge point mastery prediction models.

[0047] It should also be noted that The raw interaction data in a time step can be understood as the raw interaction data in a historical time period. The raw interaction data of the time step can be understood as the raw interaction data of the current time step, which can be obtained by the candidate mathematical problem , Candidate Mathematical Knowledge Points And the candidate answer results The triplet express.

[0048] 2. Training mathematical knowledge points based on linear recurrent units to master the prediction model

[0049] S2: The preprocessed interaction data is input into the mathematical knowledge point mastery prediction model for training. In the training process of the mathematical knowledge point mastery prediction model, the preprocessed interaction data is first embedded by the embedding layer. Each preprocessed interaction data corresponds to a mathematical problem embedding vector, a mathematical knowledge point embedding vector and an interaction embedding vector. After the mathematical knowledge point embedding vector constitutes the mathematical knowledge point embedding sequence of each time step, the mathematical knowledge point embedding sequence of each time step is input into the question encoder. After being processed by multiple sequentially cascaded question encoding layers, the candidate mathematical knowledge point representation sequence of each time step is obtained. After the interaction embedding vector constitutes the interaction embedding sequence of each time step, the interaction embedding sequence of each time step is input into the interaction encoder. After being processed by multiple sequentially cascaded interaction encoding layers, the candidate interaction representation sequence of each time step is obtained. The candidate interaction representation sequence and the candidate mathematical knowledge point representation sequence are concatenated as the candidate input sequence, and the candidate input sequence of each time step is input into the mathematical knowledge point retriever. After being processed by multiple sequentially cascaded mathematical knowledge point retrieval layers, the corresponding candidate knowledge state representation sequence of each time step is obtained, and the candidate knowledge state representation sequence of each time step is concatenated with the corresponding mathematical problem embedding vector of the next time step and the mathematical knowledge point embedding vector as the embedded spliced ​​sequence of each time step. The embedded spliced ​​sequence is input into the prediction network, and the predicted answer result of the mathematical problem at the next time step is output. The negative log-likelihood loss is calculated based on the predicted answer result of the mathematical problem at the next time step and the corresponding answer result. The parameters of the mathematical knowledge point mastery prediction model are updated based on minimizing the negative log-likelihood loss until the mathematical knowledge point mastery prediction model converges to obtain a trained mathematical knowledge point mastery prediction model.

[0050] It should be noted that in step S2 of the present invention, the specific process of obtaining the mathematical problem embedding vector, the mathematical knowledge point embedding vector and the interaction embedding vector is as follows:

[0051] AS21: Pass a math problem in the preprocessed interaction data through the first embedding layer to obtain the math problem embedding vector:

[0052]

[0053] in, represents the first embedding layer; represents the output dimension of the first embedding layer; Indicates The mathematical problem embedding vector for each time step.

[0054] AS22: A mathematical knowledge point in a preprocessed interactive data is passed through the second embedding layer and the third embedding layer respectively to obtain the first embedding result and the second embedding result respectively. The mathematical problem embedding vector corresponding to the mathematical knowledge point is multiplied by the second embedding result to obtain the third embedding result. The second embedding result and the third embedding result are added as the mathematical knowledge point embedding vector:

[0055]

[0056] in, denote the second embedding layer and the third embedding layer respectively; represents the output dimension of the second or third embedding layer; Indicates The embedding vector of mathematical knowledge points at each time step.

[0057] AS23: Multiply the number of math problems by the answer results in a preprocessed interactive data to obtain a fourth embedding result, add the fourth embedding result and the math knowledge point embedding vector corresponding to the math knowledge point as the fifth embedding result, pass the fifth embedding result through the fourth embedding layer and the fifth embedding layer respectively, and obtain the sixth embedding result and the seventh embedding result respectively, multiply the math problem embedding vector corresponding to the math knowledge point by the seventh embedding result to obtain the eighth embedding result, and add the sixth embedding result, the eighth embedding result and the math knowledge point embedding vector as the interactive embedding vector:

[0058]

[0059]

[0060] in, Indicates the number of math problems; represents the fifth embedding result; denote the fourth embedding layer and the fifth embedding layer respectively; Indicates The interaction embedding vector at each time step.

[0061] It should be noted that, in this embodiment, the embedding layer is used to convert the preprocessed interaction data into a vector representation suitable for neural network processing. Among them, the first embedding layer is used to number the math problems into corresponding difficulty values ​​(scalars), the second embedding layer and the third embedding layer do not share the same weights, and the fourth embedding layer and the fifth embedding layer do not share the same weights.

[0062] It should be noted that in step S2 of the present invention, the candidate mathematical problem embedding vector is obtained. And the embedding vector of candidate mathematical knowledge points The specific process can refer to AS21~AS22 above, replacing the math problems and math knowledge points in these two steps with candidate math problems And candidate mathematics knowledge points Implementation, no more details.

[0063] It should be noted that in step S2 of the present invention, the specific processing flow of the first question coding layer of the question encoder is: The embedding vector of the mathematical knowledge point at each time step constitutes the The mathematical knowledge point embedding sequence of time steps The first problem encoding layer uses it as the input. The mathematical knowledge point embedding sequence is first pre-normalized by the first pre-normalization layer. The pre-normalized mathematical knowledge point embedding sequence is sequentially subjected to the first linear recurrent unit (LRU), layer normalization, the first feedforward neural network, and the Dropout operation to obtain the first encoding result. The first encoding result is compared with the first The embedded sequences of mathematical knowledge points at time steps are added to form a residual connection to obtain the output result of the first question encoding layer.

[0064] In this embodiment, when the question encoder needs to process to the When the mathematical knowledge points of time steps are embedded in the sequence, the corresponding That is, the embedding vector of the candidate mathematical knowledge point, which constitutes the The mathematical knowledge point embedding sequence of time steps .

[0065] In this embodiment, after obtaining the output result of the first question coding layer, it is used as the input of the second question coding layer, and is processed according to the specific processing flow of the first question coding layer to obtain the output result of the second question coding layer. This process is repeated continuously, which enhances the mathematical knowledge point to grasp the expression ability and feature extraction ability of the prediction model, and extracts and combines features layer by layer until The question encoder processes the problem and finally obtains a more accurate representation of the candidate mathematical knowledge points, that is, the representation sequence of the candidate mathematical knowledge points corresponding to each time step. The specific processing flow of the problem encoding layer can be expressed as:

[0066]

[0067] in, Represents the Dropout operation; represents a feed-forward neural network; Representation layer normalization; represents a linear recurrent unit; represents the pre-normalization layer; Indicates The candidate mathematical knowledge point representation sequence of time steps; Indicates the number of question encoding layers.

[0068] As can be seen, the question encoder uses multiple question encoding layers to perform sequential learning in the mathematical knowledge point embedding sequence. It generates personalized dynamic representations for each mathematical question item, capturing the changing context during learner interaction, and the generated candidate mathematical knowledge point representation sequence will serve as the input of the mathematical knowledge point retriever.

[0069] It should be noted that in step S2 of the present invention, the specific processing flow of the first interactive coding layer of the interactive encoder is: The interaction embedding vectors of time steps form the time-step interaction embedding sequence The interactive embedding sequence is first pre-normalized by the second pre-normalization layer, and the pre-normalized interactive embedding sequence is sequentially subjected to the second linear recurrent unit (LRU), layer normalization, the second feedforward neural network, and the Dropout operation to obtain the second encoding result. The second encoding result is compared with the first The interactive embedding sequences of time steps are added to form a residual connection to obtain the output of the first interactive encoding layer.

[0070] In this embodiment, after the output result of the first interactive coding layer is obtained, it is used as the input of the second interactive coding layer, and is processed according to the specific processing flow of the first interactive coding layer to obtain the output result of the second interactive coding layer. This process is repeated continuously, which enhances the mathematical knowledge point to grasp the expression ability and feature extraction ability of the prediction model, and extracts and combines features layer by layer until The interaction encoder processes the interaction data in a more accurate way, and finally obtains a more accurate candidate interaction representation, that is, a sequence of candidate interaction representations corresponding to each time step. The specific processing flow of the problem encoding layer can be expressed as:

[0071]

[0072] in, Indicates A sequence of candidate interaction representations for time steps; Indicates the number of interactive encoding layers.

[0073] It can be seen that the interaction encoder processes the learner's interaction history and tracks their mastery of various mathematical knowledge points at different time points. By encoding the sequence of question-answer pairs, a comprehensive knowledge state representation is generated, that is, a sequence of candidate interaction representations at each time step, which is used to reflect the learner's current understanding of different mathematical knowledge points.

[0074] It should be noted that in step S2 of the present invention, for all interaction data in the historical time period, the question encoder will output Candidate mathematical knowledge points represent the sequence , the interactive encoder will output Candidate interaction representation sequence , then concatenate the candidate interaction representation sequence and the candidate mathematical knowledge point representation sequence at the same time step as the candidate input sequence , and process these candidate input sequences in the order of time steps through the mathematical knowledge point retriever, and obtain the candidate knowledge state representation sequence for each time step .

[0075] In this embodiment, when splicing The candidate mathematical knowledge point representation sequence of time steps Interacting with candidate representation sequences The specific splicing method used is as follows:

[0076]

[0077] in, Indicates Candidate input sequence of time steps; represents a concatenation operation, such as the torch.cat operation in PyTorch; [...] represents an array indexing operation in PyTorch; di is the specified dimension parameter.

[0078] It should be noted that in step S2 of the present invention, the specific processing flow of the first mathematical knowledge point retrieval layer of the mathematical knowledge point retriever is as follows: the candidate input sequence of each time step is used as the input of the first mathematical knowledge point retrieval layer, the candidate input sequence is first pre-normalized through the third pre-normalization layer, the pre-normalized candidate input sequence is sequentially subjected to the third linear cyclic unit (LRU), layer normalization, the third feedforward neural network and the Dropout operation to obtain a third encoding result, and the third encoding result is compared with the first The candidate input sequences of time steps are added to form a residual connection to obtain the output result of the first mathematical knowledge point retrieval layer.

[0079] In this embodiment, after the output result of the first mathematical knowledge point retrieval layer is obtained, it is used as the input of the second mathematical knowledge point retrieval layer, and is processed according to the specific processing flow of the first mathematical knowledge point retrieval layer to obtain the output result of the second mathematical knowledge point retrieval layer, and this process is repeated until the output result of the second mathematical knowledge point retrieval layer is obtained. The mathematical knowledge point retrieval layer is processed to finally obtain a more accurate candidate knowledge state representation sequence. The specific processing flow of the mathematical knowledge point retrieval layer can be expressed as:

[0080]

[0081] in, Indicates The candidate knowledge state representation sequence of time steps; Indicates the number of mathematical knowledge point retrieval layers.

[0082] It can be seen that the mathematical knowledge point retriever, as a bridge between the question encoder and the interactive encoder, simulates the cognitive process of problem solving. It uses the representation of the target mathematical problem to query the encoded knowledge state and generate an ability representation to estimate the possibility of correctly answering the candidate question.

[0083] It should be noted that in the problem encoder, interactive encoder and mathematical knowledge point retriever of the present invention, the core technology is based on an improved recurrent neural network architecture, and the key lies in the multi-layer linear recurrent unit (LinearRecurrent Unit, LRU) structure design. The linear recurrent unit encodes the mathematical knowledge point embedding sequence to capture the dependencies between mathematical problems. This process can help the model understand the context and difficulty changes of mathematical problems. This design aims to balance computational efficiency and the ability to capture long-term dependencies in the mathematical learning process.

[0084] In the present invention, the first linear recurrent unit, the second linear recurrent unit and the third linear recurrent unit all adopt a linear activation function, and the linear activation function is used to take a parameter that gradually decays over time as a weight, and the input of each historical time step is weighted and summed to obtain the output of each linear recurrent unit.

[0085] In this embodiment, a linear cycle unit in a problem coding layer is taken as an example to illustrate its main features and design details so that those skilled in the art can understand. The main features and design details of the linear cycle unit are as follows:

[0086] 1) Linear activation function: Unlike traditional RNNs that use nonlinear activation functions (such as tanh or sigmoid), linear recurrent units remove nonlinear activation functions and use linear activation functions. The goal of the linear activation function is to simplify calculations and remove the complexity of nonlinear activations, thereby facilitating parallel calculations and optimization. The mathematical learning state update formula is:

[0087]

[0088] For time series , the linear recurrent unit processes the input at each time step step by step, updating the hidden state .in, Respectively represent The state of the time step; is the state transfer matrix; Indicates The input of the time step, the initial hidden state Defined as the zero vector.

[0089] 2) Recursive expansion: The core of recursive expansion is to use linear relationships to decompose time dependencies into the cumulative sum of historical inputs, thereby avoiding successive recursions at each time step. Since the linear recurrent unit uses a linear activation function, the corresponding mathematical learning state update can derive a closed-form solution:

[0090]

[0091] Calculate the hidden state by recursively expanding the formula When , it can be expressed as the entire historical input The cumulative effect of . Current hidden state is all the historical input The weighted sum of is the state transition matrix The power of , which means the input For hidden state The contribution of gradually decays over time. This closed-form solution lays the foundation for subsequent matrix decomposition and parallel optimization.

[0092] 3) Matrix decomposition: After the state transfer matrix is ​​eigen-decomposed, the corresponding mathematical learning state update process can be simplified as follows:

[0093]

[0094] in, represents the feature matrix; Indicates the corresponding The diagonal matrix of has the following elements on the diagonal: eigenvalue of ; superscript Represents the matrix inversion operation. The decomposed formula form is more convenient for parallel calculation because each eigenvalue and eigenvector can be calculated independently.

[0095] 4) Complex parameterization: Use complex numbers to parameterize eigenvalues:

[0096]

[0097] in, Represents the diagonal matrix corresponding to the state transfer matrix; Indicates eigenvalues; represents the modulus of the eigenvalue, controlling the decay rate of the memory; represents the phase of the eigenvalue, controlling the periodic pattern. , we can control the memory decay rate for different inputs ( The smaller the value, the faster the decay). , the linear recurrent unit can capture periodic patterns (e.g., learning periodic regularities in time series). Thus, the linear recurrent unit can also capture the decay of mathematical knowledge (via ) and cyclical learning models (through .

[0098] 5) Parallel computing: By using the linear characteristics of linear recurrent units, mathematical learning calculations can be decomposed into prefix sum problems, thereby achieving parallel computing:

[0099]

[0100] Part I represents the cumulative contribution of the prefix sum; the second part Indicates the contribution of subsequent input. The essence of the prefix sum problem is to decompose the calculation of the entire sequence into multiple sub-problems and use parallel algorithms (such as Upper / Lower Parallel Computing Algorithm) to solve these sub-problems, thereby reducing the time complexity. Among them, Indicates that at time step Hidden state when is a decay factor introduced in the formula decomposition, indicating that To time step The degree of memory decay between is another decay factor, indicating that To time step This parallelization can significantly improve the training efficiency of long sequences, especially when hardware support (such as GPU) is available.

[0101] 6) Gradient flow control: By carefully tuning the modulus of the eigenvalues, the gradient flow can be controlled to alleviate the gradient vanishing and gradient exploding problems in mathematical learning.

[0102] 7) Multi-scale modeling: By using multiple linear recurrent units with different eigenvalues, both short-term and long-term dependencies can be captured simultaneously.

[0103] 8) Regularization Techniques: During training, constraints or regularization can be imposed on the eigenvalues ​​to prevent overfitting and improve the stability of the linear recurrent unit.

[0104] Through the linear recurrent unit designed in this way, the method of the present invention can achieve a good balance between computational efficiency and model expression ability, providing a powerful and efficient tool for mathematical knowledge point mastery prediction tasks.

[0105] It should be noted that in step S2 of the present invention, The candidate knowledge state representation sequence of time steps The mathematical problem embedding vector corresponding to the next time step And the mathematical knowledge point embedding vector Splicing, as the first The embedded concatenation sequence of time steps :

[0106]

[0107] In this embodiment, when it is necessary to The candidate knowledge state representation sequence of time steps When concatenating the corresponding math problem embedding vector and the math knowledge point embedding vector, the candidate math problem embedding vector is used And the embedding vector of candidate mathematical knowledge points As a candidate knowledge state representation sequence The embedding vectors of mathematical problems and mathematical knowledge points.

[0108] It should be noted that in step S2 of the present invention, the prediction network receives the output from the mathematical knowledge point retriever and the output from the embedding layer, and uses multiple linear projection layers to convert the ability representation into a scalar probability, thereby predicting the response to the mathematical problem at the next time step. In the prediction network, the specific processing flow is as follows: the embedded concatenated sequence of each time step is taken as input, and it is sequentially passed through three sequentially cascaded linear projection layers to obtain the linear projection vector of each time step, and the linear projection vector of each time step is nonlinearly transformed using the Sigmoid activation function to obtain the predicted answer result for the mathematical problem at the next time step.

[0109] In this example, the first linear projection layer in the prediction network Used to map the dimensions of the embedded concatenated sequence to the dimensions , the second linear projection layer Used to map the vector dimension output by the first linear projection layer to the dimension , the third linear projection layer Used to map the vector dimension output by the second linear projection layer to the dimension . Taking the embedded concatenation sequence of time steps as an example, the specific process of passing through three linear projection layers can be expressed as follows:

[0110]

[0111] in, Indicates The linear projection vector of time steps; Represents the output dimension hyperparameter of the linear projection layer, which is used to control the dimension size of feature transformation.

[0112] It should be noted that in step S2 of the present invention, the predicted answer results of the mathematical problems output by the prediction model based on the mathematical knowledge points and the actual answer results in step S1 are calculated as follows: , and use the stochastic gradient descent (SGD) optimizer to update the prediction model parameters according to the negative log-likelihood loss.

[0113]

[0114] in, Indicates The answer result of time steps; Indicates The predicted answer result of a math problem with 10 time steps.

[0115] It should also be noted that in the process of training mathematical knowledge points to master the prediction model, this embodiment specifically adopts the following four optimization strategies:

[0116] 1) Early stopping strategy: Monitor the AUC or ACC indicators on the validation set, and terminate the training if there is no significant improvement after 10 consecutive rounds of training.

[0117] 2) Learning rate adjustment: The initial learning rate range is {0.01, 0.001, 0.005}, and it is dynamically adjusted according to the training performance using a learning rate adjustment strategy that combines preheating and cosine annealing.

[0118] 3) Apply gradient clipping technology during training to prevent gradient explosion problem.

[0119] 4) Evaluation and optimization: Regularly evaluate the performance of the mathematical knowledge point mastery prediction model on the validation set. When the performance of the validation set no longer improves, save the optimal mathematical knowledge point mastery prediction model parameters to complete the training process.

[0120] In summary, if Figure 2 As shown in the figure, the present invention proposes a mathematical knowledge point mastery prediction model based on linear recurrent units, which effectively solves the "impossible four corners" problem in a large-scale online learning environment and optimizes training efficiency, reasoning efficiency and prediction performance. The main innovations include:

[0121] 1) Linear recurrent unit design: The nonlinear activation function in the traditional recurrent unit is removed to achieve a simplified state update expression. The calculation process is further optimized through feature decomposition to obtain a closed-form solution for the state update, which significantly reduces the computational complexity and enables the prediction model to efficiently process long sequence learning data.

[0122] 2) Modular architecture design: A modular architecture consisting of an embedding layer, a question encoder, an interaction encoder, a mathematical knowledge point retriever, and a prediction network is proposed. The question encoder uses linear recurrent units for sequential learning to generate dynamic question representations, the interaction encoder processes the learner's question-response sequence to generate a comprehensive knowledge state representation, and the mathematical knowledge point retriever simulates the cognitive process to realize knowledge state query, thus achieving functional decoupling and flexible combination.

[0123] 3) Knowledge point-based question indexing: A knowledge point-based question indexing method is adopted in the embedding layer, which regards all questions under the same knowledge point as variants of a single representative question, effectively reducing over-parameterization and reducing the complexity of the mathematical knowledge point mastery prediction model.

[0124] 4) Computational optimization strategy: The design of the linear recurrent unit supports highly parallel computing, significantly improving training efficiency. It supports incremental updates of prediction models based on mathematical knowledge points, and can be quickly updated based on new data without frequent full retraining. It greatly reduces the computational complexity of the reasoning process by simplifying recursive formulas.

[0125] It should also be noted that in the present invention, the number of layers of the question encoder, the interactive encoder, and the mathematical knowledge point retriever can be selected according to actual needs. If you want a fast running speed, these layers can be set to be smaller. If you want a high accuracy of the final prediction, these layers can be set to be larger. In this embodiment, the number of layers of the question encoder, the interactive encoder, and the mathematical knowledge point retriever are all 10 layers.

[0126] In order to better demonstrate the specific implementation and technical effects of the present invention, a training method for a mathematical knowledge point mastery prediction model shown in steps S1 to S2 in the above preferred implementation is applied to a specific example.

[0127] Example

[0128] The specific implementation process of the training method for a mathematical knowledge point mastering prediction model adopted in this embodiment is as described above and will not be repeated here.

[0129] The evaluation index of this embodiment uses the most commonly used AUC in the field of knowledge tracking. It is the area under the ROC curve, with a value range of 0 to 1. The larger the AUC value, the better the model effect. The comparison results between the method proposed in the present invention and other methods are shown in Table 1. In Table 1, DKT, DKVMN and SimpleKT are all benchmark methods for predicting the mastery of mathematical knowledge points, and the implementation methods of these benchmark methods are all prior art.

[0130] Table 1. Prediction results of different methods on the mathematics knowledge tracking dataset method AUC(%) DKT 71.88 DKVN 70.73 SimpleKT 75.17 Method of the present invention 92.62

[0131] In order to evaluate the efficiency of the mathematical knowledge point mastery prediction model of the present invention, Table 2 shows the comparison of the present invention with other models in terms of training efficiency. In Table 2, the Transformer-based AKT model, the RNN-based LPKT model, and the FoLiBi model are all representative knowledge tracking (KT) models, and the implementation methods of these knowledge tracking models are all prior art.

[0132] Table 2. Comparison of the training efficiency of the present invention and other models method FLOPs(M) Parameter quantity (M) Training time (seconds) AKT 1131.36 6.07 9.94 LPKT 313.01 1.24 13.24 FoLiBi 92.83 0.65 9.08 The present invention 13.15 0.11 2.37

[0133] It can be seen from Table 2 that: in terms of computational complexity (FLOPs), the computational complexity of the present invention is significantly lower than that of other models, which is only 13.15M FLOPs, which means that the present invention requires the least computing resources when processing mathematical learning data, and is particularly suitable for application in resource-constrained environments; in terms of the number of model parameters, the present invention has the least number of parameters, which is only 0.11M, much lower than other models, which means that the method of the present invention not only reduces the storage requirements of the model, but also reduces the risk of overfitting, making the model easier to generalize to different mathematical learning scenarios; in terms of training time, the training time of the present invention is the shortest, which only takes 2.37 seconds, which means that the present invention can quickly adapt to new mathematical learning data, which is very beneficial for educational environments that require frequent model updates.

[0134] In addition, the mathematical knowledge point mastery prediction model proposed in the present invention has excellent reasoning time performance under different mathematical learning sequence lengths, such as Figure 3 As shown. As the number of steps in the mathematics learning sequence increases, the reasoning time of the mathematics knowledge point mastery prediction model of the present invention increases slowly and steadily, and maintains a sub-second reasoning speed even in a long sequence of 20,000 steps. Compared with the existing LPKT model and AKT model, the mathematics knowledge point mastery prediction model of the present invention shows higher efficiency at all sequence lengths. Especially in the case of long sequences (>5000 steps), the advantages of the mathematics knowledge point mastery prediction model of the present invention are more obvious: the reasoning time of the AKT model grows exponentially, and although the LPKT model performs better, it is still inferior to the mathematics knowledge point mastery prediction model of the present invention. In addition, compared with the AKT model that performs well in short sequences (<5000 steps), the mathematics knowledge point mastery prediction model of the present invention not only maintains competitiveness, but also shows excellent scalability in longer sequences.

[0135] It should also be noted that the training method of the mathematical knowledge point mastery prediction model in the above embodiment can essentially be executed by a computer program or module. Therefore, similarly, based on the same inventive concept, another preferred embodiment of the present invention also provides a mathematical knowledge point mastery prediction model prediction system corresponding to the training method of the mathematical knowledge point mastery prediction model provided in the above embodiment, such as Figure 4 As shown, it includes:

[0136] The data acquisition and storage module is used to acquire and store the interaction data of different users in the historical time period from the online learning platform;

[0137] A model acquisition module, used to acquire a mathematical knowledge point mastery prediction model trained according to the mathematical knowledge point mastery prediction model training method provided in the above embodiment;

[0138] The result acquisition module is used to obtain the interaction data of the user to be predicted from the data acquisition and storage module and obtain the current math question to be answered and the corresponding math knowledge points and input them into the math knowledge point mastery prediction model obtained by the model acquisition module, and output the probability prediction value of the answer result of the user to be predicted;

[0139] A result calibration module is used to obtain the probability prediction value of the answer result output by the result acquisition module and perform calibration processing on it, and at the same time calculate the confidence interval of the calibrated probability prediction value of the answer result;

[0140] An online update module is used to form a triplet of the current math question to be answered, the corresponding math knowledge point, and the calibrated probability prediction value of the answer result, and associate it with the ID of the user to be predicted, update the interaction data of the user to be predicted, and add the updated interaction data of the user to be predicted to the data acquisition and storage module;

[0141] An incremental learning module, used to use the interaction data stored in the data acquisition and storage module as an incremental learning sample, and when the amount of interaction data in the data acquisition and storage module reaches a preset interaction data threshold, the interaction data in the data acquisition and storage module is used to retrain the mathematical knowledge point mastery prediction model according to the training method for the mathematical knowledge point mastery prediction model provided in the above embodiment;

[0142] The storage and display module is used to save the calibrated probability prediction value of the answer result and the corresponding confidence interval, and push them to the user interface of the online learning platform in a preset manner.

[0143] Similarly, based on the same inventive concept, another preferred embodiment of the present invention also provides a computer electronic device corresponding to the training method for the mathematical knowledge point mastery prediction model provided in the above embodiment, which includes a memory and a processor;

[0144] The memory is used to store computer programs;

[0145] The processor is used to implement the training method of the mathematical knowledge point mastery prediction model in the above embodiment when executing the computer program.

[0146] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention.

[0147] Therefore, based on the same inventive concept, another preferred embodiment of the present invention also provides a computer-readable storage medium corresponding to the training method of the mathematical knowledge point mastery prediction model provided in the above embodiment, and a computer program is stored on the storage medium. When the computer program is executed by the processor, the training method of the mathematical knowledge point mastery prediction model in the above embodiment can be implemented.

[0148] It is understandable that the above storage medium may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage. The storage medium may also be a U disk, a mobile hard disk, a magnetic disk or an optical disk, etc., which can store program codes.

[0149] It is understandable that the above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0150] It should also be noted that those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working process of the system described above can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here. In the various embodiments provided in this application, the division of steps or modules in the system and method is only a logical function division, and there may be other division methods in actual implementation, such as multiple modules or steps can be combined or integrated together, and a module or step can also be split.

[0151] The above-described embodiment is only a preferred solution of the present invention, but it is not intended to limit the present invention. A person skilled in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent replacement or equivalent transformation falls within the protection scope of the present invention.

Claims

1. A training method for a mathematical knowledge point mastery prediction model, characterized in that: The following steps are involved: S1: Obtaining the original interaction data of the user in the historical time period and the original interaction data of the current time step from the online learning platform, and preprocessing the original interaction data to obtain preprocessed interaction data; wherein each original interaction data consists of a mathematical problem presented to the user at each time step, mathematical knowledge points related to the mathematical problem, and the answer result; S2: The preprocessed interaction data is input into the mathematical knowledge point mastery prediction model for training. In the training process of the mathematical knowledge point mastery prediction model, the preprocessed interaction data is first embedded by the embedding layer. Each preprocessed interaction data corresponds to a mathematical problem embedding vector, a mathematical knowledge point embedding vector and an interaction embedding vector. After the mathematical knowledge point embedding vector constitutes the mathematical knowledge point embedding sequence of each time step, the mathematical knowledge point embedding sequence of each time step is input into the question encoder. After being processed by multiple sequentially cascaded question encoding layers, the candidate mathematical knowledge point representation sequence of each time step is obtained. After the interaction embedding vector constitutes the interaction embedding sequence of each time step, the interaction embedding sequence of each time step is input into the interaction encoder. After being processed by multiple sequentially cascaded interaction encoding layers, the candidate interaction representation sequence of each time step is obtained. The candidate interaction representation sequence and the candidate mathematical knowledge point representation sequence are concatenated as the candidate input sequence, and the candidate input sequence of each time step is input into the mathematical knowledge point retriever. After being processed by multiple sequentially cascaded mathematical knowledge point retrieval layers, the corresponding candidate knowledge state representation sequence of each time step is obtained, and the candidate knowledge state representation sequence of each time step is concatenated with the corresponding mathematical problem embedding vector of the next time step and the mathematical knowledge point embedding vector as the embedded spliced ​​sequence of each time step. The embedded spliced ​​sequence is input into the prediction network, and the predicted answer result of the mathematical problem at the next time step is output. The negative log-likelihood loss is calculated based on the predicted answer result of the mathematical problem at the next time step and the corresponding answer result. The parameters of the mathematical knowledge point mastery prediction model are updated based on minimizing the negative log-likelihood loss until the mathematical knowledge point mastery prediction model converges to obtain a trained mathematical knowledge point mastery prediction model.

2. A training method for a mathematical knowledge point mastery prediction model as claimed in claim 1, characterized in that: In step S2, the specific process of obtaining the mathematical problem embedding vector, the mathematical knowledge point embedding vector and the interaction embedding vector is as follows: AS21: A math problem in the preprocessed interaction data is passed through the first embedding layer to obtain a math problem embedding vector; AS22: A mathematical knowledge point in the preprocessed interactive data is passed through the second embedding layer and the third embedding layer respectively to obtain a first embedding result and a second embedding result respectively, and a mathematical problem embedding vector corresponding to the mathematical knowledge point is multiplied by the second embedding result to obtain a third embedding result, and the second embedding result and the third embedding result are added together as the mathematical knowledge point embedding vector; AS23: Multiply the number of math problems by the answer results in a preprocessed interactive data to obtain a fourth embedding result, add the fourth embedding result and the math knowledge point embedding vector corresponding to the math knowledge point as the fifth embedding result, pass the fifth embedding result through the fourth embedding layer and the fifth embedding layer respectively, and obtain the sixth embedding result and the seventh embedding result respectively, multiply the math problem embedding vector corresponding to the math knowledge point with the seventh embedding result to obtain the eighth embedding result, and add the sixth embedding result, the eighth embedding result and the math knowledge point embedding vector as the interactive embedding vector.

3. A training method for a mathematical knowledge point mastery prediction model as claimed in claim 1, characterized in that: In step S2, the specific processing flow of the first question encoding layer of the question encoder is: the mathematical knowledge point embedding sequence of the tth time step is formed by the mathematical knowledge point embedding vectors of the 1st, 2nd, ..., t+1th time steps and used as the input of the first question encoding layer, firstly, the mathematical knowledge point embedding sequence is pre-normalized by the first pre-normalization layer, and the pre-normalized mathematical knowledge point embedding sequence is successively subjected to the first linear cyclic unit, layer normalization, the first feedforward neural network and Dropout operation to obtain the first encoding result, and the first encoding result is added to the mathematical knowledge point embedding sequence of the tth time step to form a residual connection to obtain the output result of the first question encoding layer.

4. A training method for a mathematical knowledge point mastery prediction model as claimed in claim 3, characterized in that: In step S2, the specific processing flow of the first interactive coding layer of the interactive encoder is: the interactive embedding vectors of the 1st, 2nd, ..., tth time steps constitute the interactive embedding sequence of the tth time step and use it as the input of the first interactive coding layer, firstly, the interactive embedding sequence is pre-normalized by the second pre-normalization layer, and the pre-normalized interactive embedding sequence is successively subjected to the second linear cyclic unit, layer normalization, the second feedforward neural network and Dropout operation to obtain the second encoding result, and the second encoding result is added to the interactive embedding sequence of the tth time step to form a residual connection to obtain the output result of the first interactive coding layer.

5. A training method for a mathematical knowledge point mastery prediction model as claimed in claim 4, characterized in that: In step S2, the specific processing flow of the first mathematical knowledge point retrieval layer of the mathematical knowledge point retriever is: taking the candidate input sequence of each time step as the input of the first mathematical knowledge point retrieval layer, first pre-normalizing the candidate input sequence through the third pre-normalization layer, and successively passing the pre-normalized candidate input sequence through the third linear cyclic unit, layer normalization, the third feedforward neural network and Dropout operation to obtain the third encoding result, and adding the third encoding result to the candidate input sequence of the tth time step to form a residual connection to obtain the output result of the first mathematical knowledge point retrieval layer.

6. A training method for a mathematical knowledge point mastery prediction model as claimed in claim 1, characterized in that: In step S2, the specific processing flow in the prediction network is as follows: the embedded concatenated sequence of each time step is taken as input, and it is sequentially passed through three sequentially cascaded linear projection layers to obtain the linear projection vector of each time step, and the linear projection vector of each time step is nonlinearly transformed using the Sigmoid activation function to obtain the predicted answer to the math problem at the next time step.

7. A method for training a mathematical knowledge point mastery prediction model as claimed in claim 5, characterized in that: The first linear recurrent unit, the second linear recurrent unit and the third linear recurrent unit all use a linear activation function, which uses a parameter that gradually decays over time as a weight, and performs weighted summation of the input of each historical time step to obtain the output of each linear recurrent unit.

8. A prediction system for a mathematical knowledge point mastery prediction model, characterized in that: include: The data acquisition and storage module is used to acquire and store the interaction data of different users in the historical time period from the online learning platform; A model acquisition module, used to acquire a mathematical knowledge point mastery prediction model trained according to the training method for a mathematical knowledge point mastery prediction model according to any one of claims 1 to 7; The result acquisition module is used to obtain the interaction data of the user to be predicted from the data acquisition and storage module and obtain the current math question to be answered and the corresponding math knowledge points and input them into the math knowledge point mastery prediction model obtained by the model acquisition module, and output the probability prediction value of the answer result of the user to be predicted; A result calibration module is used to obtain the probability prediction value of the answer result output by the result acquisition module and perform calibration processing on it, and at the same time calculate the confidence interval of the calibrated probability prediction value of the answer result; An online update module is used to form a triplet of the current math question to be answered, the corresponding math knowledge point, and the calibrated probability prediction value of the answer result, and associate it with the ID of the user to be predicted, update the interaction data of the user to be predicted, and add the updated interaction data of the user to be predicted to the data acquisition and storage module; An incremental learning module, used to use the interaction data stored in the data acquisition and storage module as an incremental learning sample, and when the amount of interaction data in the data acquisition and storage module reaches a preset interaction data threshold, the interaction data in the data acquisition and storage module is used to retrain the mathematical knowledge point mastery prediction model according to the training method for the mathematical knowledge point mastery prediction model according to any one of claims 1 to 7; The storage and display module is used to save the calibrated probability prediction value of the answer result and the corresponding confidence interval, and push them to the user interface of the online learning platform in a preset manner.

9. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by the processor, the training method for a mathematical knowledge point mastering prediction model as described in any one of claims 1 to 7 is implemented.

10. A computer electronic device, characterized in that: including memory and processor; The memory is used to store computer programs; The processor is used to implement a training method for a mathematical knowledge point mastering prediction model as described in any one of claims 1 to 7 when executing the computer program.

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