A method, device and equipment for analyzing online learning effect based on symbolic regression

Abstract

The present application discloses a method, device and equipment for analyzing online learning effects based on symbolic regression, the method comprising: obtaining an initial data set containing multi-layer node equation instances by random sampling based on a general operator set; training an initial operator filter according to the initial data set to obtain a target operator filter; sampling based on students' real online learning data and the target operator filter to obtain a function operator set; analyzing the students' real online learning data and the function operator set to generate students' online learning effect equations. The present invention trains the operator filter by generating an initial data set containing multi-layer node equation instances, and finally obtains a function operator set, predicts the effectiveness of the operator, thereby improving the efficiency of the search, and can directly learn and discover mathematical expressions describing the relationship between learners and knowledge points from the data, thereby providing more accurate and efficient personalized learning support.

Description

Technical Field

[0001] The present application relates to the technical field of data analysis, and more specifically, to an online learning effect analysis method, device and equipment based on symbolic regression. Background Art

[0002] With the development of Internet technology and multimedia tools, online learning has become an important part of the modern education system. In particular, online practice systems provide students with a convenient way to learn and apply knowledge in a virtual environment by providing a variety of questions and exercises. These systems not only enrich learning resources, but also enable educators to monitor students' learning progress and understanding by collecting learning data. By analyzing this data, educators can gain a deep understanding of students' cognitive patterns and learning strategies, thereby providing support for the implementation of personalized teaching strategies.

[0003] In the prior art, AFM (Additive Factor Model) is generally used to analyze learning effects. AFM is a refined learning analysis model that analyzes students' learning process by breaking down learning tasks into different skills or knowledge points. The model believes that students' performance in completing specific learning activities can be regarded as a direct reflection of their mastery of relevant knowledge and skills. The AFM model uses mathematical equations to represent students' problem-solving ability and assumes that students' performance is the cumulative result of their ability to master each factor (i.e., knowledge point or skill).

[0004] However, due to the significant differences in learning needs and strategies across disciplines, this method in the existing technology may not work well when dealing with highly domain-specific datasets. It also faces certain limitations in the application of personalized learning, especially when dealing with diverse and personalized learning paths. Each student's learning journey is unique, and the linear and additive assumptions of the AFM model may not be able to fully capture the subtle differences between individuals, thus affecting the accuracy and effectiveness of the model in designing personalized learning plans for each student. Summary of the invention

[0005] In response to at least one defect or improvement need in the prior art, the present invention provides a method, device and equipment for analyzing online learning effects based on symbolic regression, which are used to solve the problem that the AFM model in the prior art does not perform well when processing data sets with high domain specificity. The learning ability or skill level of each student is fully described by a set of fixed parameters in the model, which cannot fully capture the subtle differences between individuals, thereby affecting the accuracy and effectiveness of the model in designing personalized learning plans for each student.

[0006] To achieve the above object, according to a first aspect of the present invention, a method for analyzing online learning effects based on symbolic regression is provided, comprising:

[0007] An initial data set containing multi-layer node equation instances is obtained by random sampling based on a set of universal operators;

[0008] The initial operator filter is trained according to the initial data set to obtain the target operator filter;

[0009] Based on the students' real online learning data and the target operator filter, sampling is performed to obtain a set of function operators;

[0010] Analyze students' real online learning data and function operator sets to generate students' online learning effect equations.

[0011] In a possible implementation, an initial data set containing multi-layer node equation instances is obtained by random sampling based on a set of universal operators, including:

[0012] The number of paths between the independent variable and the dependent variable is randomly selected according to the set of universal operators;

[0013] Data sampling is performed on each path to determine multiple independent variables, connecting edges and neuron outputs;

[0014] An equation instance is established based on independent variables, connecting edges and neuron outputs to obtain an initial data set.

[0015] In a possible implementation, each path includes at least two layers of nodes; data sampling is performed on each path to determine multiple independent variables, connecting edges, and neuron outputs, including:

[0016] Randomly select nodes and independent variable sets at each layer and generate node connection edges and independent variable connection edges;

[0017] Evenly distribute sampling of node connection edges and independent variable connection edges within a first preset range, and evenly distribute sampling of independent variable sets within a second preset range;

[0018] The neuron output is calculated based on the sampled independent variable set, node connection edges, and independent variable connection edges.

[0019] In a possible implementation, the initial operator filter is trained according to the initial data set to obtain the target operator filter, including:

[0020] Input the initial data set into the initial operator filter for feature encoding to obtain learning features;

[0021] Mapping the learned features to the probability space where the operator exists to predict the existence of the operator;

[0022] When the prediction results meet the preset requirements, the target operator filter is obtained.

[0023] In a possible implementation, sampling is performed based on students' real online learning data and a target operator filter to obtain a set of function operators, including:

[0024] Input the students' real online learning data into the target operator filter, and output the existence probability matrix;

[0025] The existence probability matrix is ​​processed into temperature using the sampling temperature function;

[0026] Operator sampling is performed on the temperature-processed existence probability matrix to obtain a set of function operators.

[0027] In one possible implementation, the sampling temperature function is:

[0028] Among them, p i is the i-th element in the existence probability matrix, p j is the jth element in the existence probability matrix, and T is the sampling temperature.

[0029] In a possible implementation, the real online learning data of students and a set of function operators are analyzed to generate an equation for the online learning effect of students, including:

[0030] A multi-layer feedforward neural network is used to linearly map the students' real online learning data and the function operator set to obtain a linear output;

[0031] The multi-layer feedforward neural network is used to perform nonlinear transformation on the linear output and obtain the equation of students' online learning effect.

[0032] According to a second aspect of the present invention, there is also provided an online learning effect analysis method based on symbolic regression, comprising:

[0033] A data preparation module, which is configured to obtain an initial data set containing multi-layer node equation instances by random sampling based on a set of universal operators;

[0034] A model training module, which is configured to train an initial operator filter according to an initial data set to obtain a target operator filter;

[0035] An operator sampling module is configured to perform sampling based on students' real online learning data and a target operator filter to obtain a set of function operators;

[0036] The data analysis module is configured to analyze students' real online learning data and a set of function operators to generate an equation for students' online learning effects.

[0037] According to the third aspect of the present invention, there is also provided an online learning effect analysis device based on symbolic regression, which includes at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program, and when the computer program is executed by the processing unit, the processing unit performs any step of the above-mentioned online learning effect analysis method based on symbolic regression.

[0038] According to a fourth aspect of the present invention, there is also provided a storage medium storing a computer program executable by an access authentication device, wherein when the computer program runs on the access authentication device, the access authentication device executes any of the steps of the online learning effect analysis method based on symbolic regression described above.

[0039] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0040] (1) The present invention provides a method for describing the student learning process based on symbolic regression. An initial data set containing multi-layer node equation instances is obtained by random sampling of a general operator set to construct an operator filter, and the operator filter is trained by the initial data set. Operator sampling is then performed to determine the function operator set. The operator that is most likely to generate a meaningful mathematical expression can be pre-analyzed and identified. The subtle differences between individuals can be captured by predicting the effectiveness of the operator rather than randomly searching the entire operation space, thereby significantly improving the search efficiency and the performance of the final model, which is conducive to improving the accuracy and effectiveness of designing a personalized learning plan for each student.

[0041] (2) By using the method provided by the present invention to describe the student learning process based on symbolic regression, mathematical expressions describing the complex relationship between learners and knowledge points can be learned and discovered from the data, reducing the reliance on expert prior knowledge. Mathematical expressions are regarded as components of a neural network, where each neuron can represent a variable or an operator, and the connections between neurons represent the operational relationship in the formula. This method not only reflects the intrinsic structure of the data, but also precisely regulates the generation process by controlling the network hierarchy, the selection of operators, and the distribution of variables. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0043] Figure 1A flowchart of an embodiment of an online learning effect analysis method based on symbolic regression provided by the present invention;

[0044] Figure 2 The present invention provides Figure 1 A schematic flow chart of an embodiment of step S101;

[0045] Figure 3 The present invention provides Figure 2 A flowchart of an embodiment of step S202;

[0046] Figure 4 The present invention provides Figure 1 A schematic diagram of a flow chart of an embodiment of step S102;

[0047] Figure 5 The present invention provides Figure 1 Schematic diagram of a flow chart of an embodiment of step S103 in FIG.

[0048] Figure 6 A schematic diagram of the structure of an embodiment of an online learning effect analysis device based on symbolic regression provided by the present invention;

[0049] Figure 7 A schematic diagram of the structure of a synchronous tracking flying welding device for real-time measurement of battery height provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0051] The terms "first", "second", "third", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices.

[0052] The present invention provides a method, device and equipment for describing a student's learning process based on symbolic regression, which are described below respectively.

[0053] See also Figure 1, Figure 1 A flowchart of an embodiment of an online learning effect analysis method based on symbolic regression provided by the present invention is provided. In a specific embodiment of the present invention, an online learning effect analysis method based on symbolic regression is disclosed, comprising:

[0054] S100, performing random sampling based on a universal operator set to obtain an initial data set including multi-layer node equation instances;

[0055] S200, training the initial operator filter according to the initial data set to obtain a target operator filter;

[0056] S300, sampling based on the students' real online learning data and the target operator filter to obtain a function operator set;

[0057] S400, analyzing students' real online learning data and function operator sets to generate students' online learning effect equations.

[0058] In the above embodiment, the online learning effect analysis method provided by the present invention needs to be implemented through an improved symbolic regression method, and needs to be implemented through the ONEQL (Operator Navigation enhanced Equation Learner) model. ONEQL automates and optimizes the learning process of mathematical expressions by combining symbolic neural networks and advanced operator navigation systems. The ONEQL model is innovative based on the traditional multi-layer feedforward neural network, and embeds mathematical functions such as sine, cosine, exponential, etc. directly as operators of activation functions into the network structure, so that the entire network can directly learn and express complex mathematical relationships. Through the pre-trained operator filter, the ONEQL model can evaluate and select the operators that are most helpful in explaining the data before training, which not only optimizes the learning process, but also reduces the model complexity and improves the computational efficiency. In addition, the ONEQL model uses gradient clipping technology to maintain numerical stability during training. This strategy significantly improves the performance and reliability of the model in complex data environments.

[0059] The ONEQL model provides an innovative solution to overcome the limitations of the AFM model in processing educational data analysis through automated symbolic neural networks. This approach enables the model to learn and discover mathematical expressions that describe the complex relationships between learners and knowledge points directly from the data, reducing the reliance on expert prior knowledge. In addition, the pre-trained operator filter (ON) of the ONEQL model optimizes the learning efficiency and prediction accuracy of the model through intelligent filtering of mathematical functions in the process. This enables the ONEQL model to flexibly adapt in various disciplines and different learning environments, improving the implementation effect of personalized education. Through these strategies, the ONEQL model effectively expands the scope of application of the AFM model and enhances its performance and interpretation in complex educational data analysis.

[0060] The ONEQL model optimizes the search process by introducing a pre-trained operator filter (Operator Navigation, ON). This method adds a machine learning strategy to the traditional symbolic regression framework, improving the learning efficiency and expression ability of the model when processing complex data.

[0061] Compared with the prior art, the method provided in this embodiment describes the student learning process based on symbolic regression. An initial data set containing multi-layer node equation instances is obtained by random sampling of a general operator set to construct an operator filter, and the operator filter is trained by the initial data set. Operator sampling is then performed to determine the function operator set. The operators that are most likely to generate meaningful mathematical expressions can be analyzed and identified in advance. The subtle differences between individuals are captured by predicting the effectiveness of the operators rather than randomly searching the entire operation space, thereby significantly improving the efficiency of the search and the performance of the final model, which is conducive to improving the accuracy and effectiveness of designing personalized learning plans for each student.

[0062] See also Figure 2 , Figure 2 The present invention provides Figure 1 In some embodiments of the present invention, random sampling based on a universal operator set is performed to obtain an initial data set containing multi-layer node equation instances, including:

[0063] S110, randomly selecting the number of paths between the independent variable and the dependent variable according to the universal operator set;

[0064] S120, sampling data for each path to determine multiple independent variables, connecting edges, and neuron outputs;

[0065] S130, establishing an equation instance according to independent variables, connecting edges and neuron outputs to obtain an initial data set.

[0066] In the above embodiments, the general operator set generally includes various mathematical functions (such as addition, subtraction, multiplication, division, exponentiation, logarithm, etc.), logical operators (such as AND, OR, NOT, etc.), comparison operators (such as greater than, less than, equal to, etc.) and possible activation functions (such as ReLU, Sigmoid, Tanh, etc.). As a preferred embodiment, the general operator set used in the present invention is specifically: The number of paths in the present invention is n∈[1,2], which can be a fixed value or a random value within a certain range.

[0067] It should be noted that the independent variable set X represents the learning characteristics of students (such as student ID, knowledge point ID and cumulative learning times, etc.), while the dependent variable (that is, neuron output) set Y represents the degree of students' knowledge mastery (such as learning accuracy, that is, the ratio of the number of correct questions in the test to the total number of questions). i represents the i-th element in the independent variable set X. Similarly, y j It represents the jth element in the dependent variable set Y.

[0068] In the ONEQL model, mathematical expressions are considered to be composed of the neurons of the EQL network and the edges of their weights, where the neurons in the input layer and the output layer represent variables, the weighted sum between layers represents addition, the activation function represents the operator, and the connection edge represents the constant. Since the fully connected operation generated by directly selecting the first and second layer operators will make the formula too complicated, the complexity of the equation instance is limited by defining the path to ensure that each path from the output y to the input variable is only connected by a limited number of neurons. In order to make the probabilities of one layer of operators and two layers of operators consistent in the present invention, the probability of the second layer operator taking id is set to 0.5, and the other probabilities remain consistent. For each path, it can be represented as an equation instance, which describes the relationship between the independent variable and the dependent variable, including the selected connection edges and weights.

[0069] By repeating the above steps (S110-S120), multiple equation instances can be generated and combined into an initial data set, which will contain multiple samples, each of which represents a different equation instance. The sampling step based on the universal operator set includes selecting the number of paths, randomly configuring the nodes and connecting edges of the network layer, and obtaining the output y through multiple samplings. The generated equation instances and related data are stored in the data set D for subsequent network training and analysis.

[0070] See also Figure 3 , Figure 3 The present invention provides Figure 2In some embodiments of the present invention, each path includes at least two layers of nodes; data sampling is performed on each path to determine multiple independent variables, connecting edges and neuron outputs, including:

[0071] S121, randomly select each layer of nodes and independent variable sets and generate node connection edges and independent variable connection edges;

[0072] S122, uniformly distribute and sample the node connection edges and the independent variable connection edges within a first preset range, and uniformly distribute and sample the independent variable set within a second preset range;

[0073] S123. Calculate neuron output based on the sampled independent variable set, node connection edges, and independent variable connection edges.

[0074] In the above embodiment, it is first necessary to determine the number of layers of the neural network and the number of nodes in each layer, which can be fixed or randomly generated according to certain rules or constraints. A portion of the available independent variable set is randomly selected as the independent variable of the current path, and these independent variables may be feature values, input data or other information. Then, according to the structure of the neural network, the connection edges between nodes (node ​​connection edges) and the connection edges from independent variables to nodes (independent variable connection edges) are generated. The connection edges can be expressed as weights or parameters, which will be used to calculate the output of the neuron.

[0075] It should be noted that the first preset range refers to the range for uniformly distributed sampling. This range can be the value range of the weight, the value range of the independent variable, etc. It can be fixed or adjusted according to the specific situation. For each node connection edge and independent variable connection edge, uniformly distributed sampling is performed within the first preset range to generate corresponding weights or parameter values. These values ​​will be used for subsequent neuron output calculations. For the selected set of independent variables, uniformly distributed sampling is performed within the second preset range to generate specific independent variable values, which will serve as the input of the neural network.

[0076] The output of the neuron is calculated using the sampled set of independent variables, node connections, and independent variable connections (i.e., weights or parameters) through the forward propagation algorithm. This usually involves passing the input data (independent variables) to the neuron through the connection edges (applying weights and activation functions) and calculating the activation value of the neuron. Based on the activation function of the neuron and the weight of the connection edge, we can calculate the output value of the neuron. This output value will be used as the input of the next layer of neurons, or as the final output of the entire neural network (if the current layer is the output layer).

[0077] In a preferred embodiment of the present invention, firstly, the second layer nodes are randomly selected, and then the connection edges E1 are generated, where E1~U(-2,2), and the following connection edges are uniformly sampled in the same range. Then, the number of first layer nodes n∈[1,2] is randomly selected, and the first layer operators are randomly selected and connection edges are generated for uniform distribution sampling. Then, the independent variable set is randomly selected. Then generate the connection edges for uniform distribution sampling. Sample the independent variable set X 100 times, and each independent variable follows the uniform distribution U(-5,5). Finally, calculate the output, y, based on the sampled independent variables, edges, and neurons, and get an equation instance containing 100 data points.

[0078] See also Figure 4 , Figure 4 The present invention provides Figure 1 FIG. 1 is a flow chart of an embodiment of step S200 in FIG. 1 . In some embodiments of the present invention, training the initial operator filter according to the initial data set to obtain the target operator filter includes:

[0079] S210, inputting the initial data set into the initial operator filter to perform feature encoding to obtain learning features;

[0080] S220, mapping the learning features to the probability space where the operator exists to predict the existence of the operator;

[0081] S230: When the prediction result meets the preset requirements, a target operator filter is obtained.

[0082] In the above embodiments, an initial data set (usually containing a series of samples and corresponding labels or features) is input into an initial operator filter. This filter can be a predefined model structure, such as a neural network, decision tree or other machine learning model, etc. Feature encoding is the process of converting raw data into a form that the model can understand. In this case, feature encoding may involve preprocessing of the data (such as scaling, normalization, one-hot encoding, etc.), as well as converting raw features into internal representations that can be used by the model.

[0083] Once the learning features are extracted, the model needs to map them to the probability space where the operator exists. This is usually achieved by applying an activation function (such as Sigmoid function or Softmax function) to the output layer of the model, which can map any real number to the probability space (for example, the interval [0, 1]). The model will predict the probability of the operator's existence based on the learning features. This prediction process may involve adjusting the parameters within the model, which are learned through the training process.

[0084] Finally, it is necessary to evaluate whether the prediction results of the model meet the preset requirements. The preset requirements may include indicators such as model accuracy, recall rate, F1 score, etc., depending on the nature and needs of the problem. If the prediction results of the model meet the preset requirements, then it can be said that the model has been trained and can be regarded as a target operator filter. Otherwise, the model needs to be further trained or adjusted until its prediction results meet the requirements.

[0085] It is understandable that in practice, this training process may be iterative, that is, the model will update its internal parameters based on the difference between its predicted results and the actual results to gradually improve its predictive ability. In addition, in order to avoid overfitting (i.e., the situation where the model performs well on the training data but performs poorly on new data), it is usually necessary to use validation sets and test sets to evaluate the performance of the model and take some regularization measures (such as early stopping, dropout, etc.) during the training process.

[0086] See also Figure 5 , Figure 5 The present invention provides Figure 1 In some embodiments of the present invention, sampling is performed based on the student's online real learning data and the target operator filter to obtain a function operator set, including:

[0087] S310, inputting the students' real online learning data into the target operator filter, and outputting an existence probability matrix;

[0088] S320, performing temperature processing on the existence probability matrix using a sampled temperature function;

[0089] S330, performing operator sampling on the temperature-processed existence probability matrix to obtain a set of function operators.

[0090] In the above embodiment, the real data of students' online learning is used as input, which may include students' answer records, learning progress, interaction status, etc. These data are input into the trained target operator filter. Based on these input data, the target operator filter outputs an existence probability matrix. Each row of this matrix may represent a possible function operator, and each column may represent a specific learning situation or data point. The value in the matrix represents the probability of the existence of the function operator in this situation.

[0091] The sampling temperature function is a tool for adjusting the sampling process. By adjusting the sampling temperature, the "randomness" or "determinism" of the sampling can be controlled. At higher temperatures, the sampling process is more random, and some function operators with lower probability of existence but still possible may be sampled; while at lower temperatures, the sampling process is more inclined to select function operators with higher probability of existence. The sampling temperature function is used to temperature-process the existence probability matrix. Specifically, each value in the existence probability matrix can be divided by a temperature parameter (usually a number greater than 1), and then the result can be mapped through an appropriate function (such as the Sigmoid function) to obtain a new matrix. This new matrix is ​​the existence probability matrix after temperature processing.

[0092] After obtaining the temperature-normalized existence probability matrix, operator sampling can be performed. The sampling process usually involves randomly selecting an element from each row (i.e., each possible function operator) according to the existence probability. Since the existence probability has been temperature-normalized before, this sampling process will take into account the existence probabilities of different function operators in different learning situations and make selections accordingly. Specifically, the Roulette Wheel Selection algorithm or similar methods can be used for sampling. The basic idea of ​​this method is to assign an interval on the "roulette wheel" to each element according to its existence probability, and then randomly select a point to see which interval the point falls in, and then select the element corresponding to the interval. In this way, a set of function operators can be obtained, and each element in this set is randomly sampled after considering the existence probability of function operators in different learning situations.

[0093] In some embodiments of the present invention, the sampling temperature function is:

[0094] Among them, p i is the i-th element in the existence probability matrix, p j is the jth element in the existence probability matrix, and T is the sampling temperature.

[0095] In the above embodiment, in order to control the randomness of sampling from the predicted probability distribution, the sampled existence probability matrix is ​​subjected to temperature processing. After processing, the operator is sampled N times, and each sampling obtains a set of function operators Λ. At this time, |Λ|<|Ω|, and the pre-pruning of EQL is realized. Then, the eigenvector of the operator is converted into a function list and provided to N EQL models. For the training of the EQL model, a gradient-based Adam optimization is designed to reduce the loss function.

[0096] In some embodiments of the present invention, the student's online real learning data and the function operator set are analyzed to generate the student's online learning effect equation, including:

[0097] A multi-layer feedforward neural network is used to linearly map the students' real online learning data and the function operator set to obtain a linear output;

[0098] The multi-layer feedforward neural network is used to perform nonlinear transformation on the linear output and obtain the equation of students' online learning effect.

[0099] In the above embodiment, EQL is a multi-layer feedforward neural network, which uses mathematical symbols (such as sin, cos, exp, etc.) as activation functions, but the input layer does not participate in the actual calculation, so there are L-1 hidden layers and output layers involved in data processing. This model is suitable for describing complex learning and memory processes. For the lth layer, l = 1, 2, ..., L-1, its linear mapping calculation process can be described as:

[0100] In each hidden layer l, EQL transforms the learning feature a of the previous layer into (l-1) Convert to the linear output z of the current layer (l) . The formula for the linear mapping is:

[0101] z (l) =W (l) ·a (l-1) +b (l) ;

[0102] Where W (l) is the weight matrix of the lth layer, b (l) is the bias vector of the lth layer, a (l-1) is the learned feature representation of the previous layer. In EQL, this weighted summation process can be regarded as a representation of the addition operation on the input.

[0103] The nonlinear transformation calculation process can be described as:

[0104] In each hidden layer l, EQL transforms the linear output z into (l) Convert to the learning feature representation a of the current layer (l) .

[0105] Specifically, if the lth layer has u unary operators f1,f2,…,f u and v binary operators g1,g2,…,g v , using a set of these operators Perform activation function conversion, where each operator σ belongs to the global operator set Ω = {id, sin, cos, ..., mul}. Considering that the binary operator merges two linear outputs into one output, in the lth layer,

[0106]

[0107] Here ⊙ represents the set z (l) Applied element-wise to Λ (l) For example, if in a layer l, we choose the operator set Λ (l) =[id, sin, mul], corresponding to z (l) is [z1,z2,z3,z4], then the activation value a (l) =[z1,sin(z2),z3×z4].

[0108] Nonlinear transformations are used to simulate processes such as memory decay and cognitive processing in students. For example, if the operators sin and exp are selected at a certain layer, the learning feature representation of this layer is a (l) The linear output z is transformed by these functions (l) , forming a more complex expression of learning dynamics.

[0109] The output layer (layer L) directly outputs the prediction results, such as the student’s final grade or knowledge level, without applying an activation function, which can be expressed as:

[0110]

[0111] where z (L) is the weighted input of the output layer, W (L) is the weight matrix of the output layer, b (L) is the bias vector of the output layer.

[0112] The training goal of EQL is to combine the mean squared error (MSE) and L1 regularization term in the loss function to enhance the sparsity of the model. The specific expression is as follows:

[0113]

[0114] Where λ is a regularization parameter that controls the sparsity of weights, thereby preventing overfitting and enhancing the interpretability of the model, ensuring that the model can clearly reflect the key factors in the student’s learning process.

[0115] The present invention also uses Geometry Area (1996-97) and IWT Self-Explanation Study 1 (Spring 2009), which were previously used to test the AFM and LFA models. Geometry Area (1996-97) involves geometry and uses a mastery learning algorithm to sort tasks. IWT Self-Explanation Study 1 uses multiple fixed sequences based on experimental design and involves the study of English articles. The present invention analyzes the knowledge mastery rules of students in the above two data sets, and therefore selects the test records of no less than 10 students as the experimental data set, and one-hot encodes the students and knowledge points.

[0116] The present invention uses a stratified sampling method to process the data set to ensure that the distribution ratio of the training set and the test set of each student is 7:3. The experimental setting of the ONEQL-FM model is 3, the L1 regularization coefficient is 0.0001, the learning rate is 0.001, and the number of training rounds is 4000.

[0117] On the two datasets of Geometry Area (1996-97) and IWT Self-Explanation Study 1 (Spring 2009), based on the input features of the AFM model, ONEQL-FM found better regular expressions, and the results are shown in Table 1. As can be seen from the table, on these two datasets, the ONEQL-FM model has higher accuracy (ACC) and area under the curve (AUC), lower root mean square error (RMSE) and mean absolute error (MAE), and performs better than the AFM model, as shown in Table 1:

[0118] Table 1 Experimental results of model prediction performance comparison

[0119]

[0120] In order to reveal the learners’ knowledge mastery rules fitted by the two methods, the formulas output by AFM and ONEQL-FM are further analyzed in detail. For example, in the dataset IWT Self-Explanation Study 1, student S7 did knowledge point KC 11 The answers to the first 8 questions are [0,1,1,0,1,1,0,1]. 11 I have tested opp(KC before 11 ,9)=8 times, predicting student S7 in knowledge point KC 11The probability of answering question 9 correctly (the true label is 1). For the sake of simplicity, the non-zero terms in the formula are left. The fitting results of the two methods are shown in Table 2. Among them, one-hot encoding S7 = 1, KC 11 =1, the result of AFM is calculated to be 0.459, and the result of ONEQL-FM is 0.601, which is closer to 1, as shown in Table 2:

[0121] Table 2 Comparison experimental results of model prediction performance

[0122]

[0123] This is mainly due to the characteristics of the AFM prior formula. As learning progresses, its growth rate gradually slows down and tends to stabilize, and it is easily limited by the initial ability of students. In the learning process, people usually need more time and effort to master basic concepts and skills in the initial stage, and progress is relatively slow. However, as knowledge and skills accumulate, the speed of learning gradually accelerates, and the learning effect shows rapid growth, which can be well reflected by the linear and exponential combination of a+b.

[0124] When answering the i-th question of knowledge point KC6, the knowledge mastery of student S0 can be expressed by the following formula: 0.0087*S0+0.0015*opp(KC6,i)+0.6784*

[0125] Where S0 = 1. From the formula, it can be seen that student S0 has a strong ability and can still give the correct answer with a high probability even if he has not practiced enough on the questions related to knowledge point KC6.

[0126] In order to better implement the online learning effect analysis method based on symbolic regression in the embodiment of the present invention, on the basis of the online learning effect analysis method based on symbolic regression, correspondingly, please refer to Figure 6 , Figure 6 This is a schematic diagram of the structure of an embodiment of an online learning effect analysis device based on symbolic regression provided by the present invention. The embodiment of the present invention provides an online learning effect analysis device 600 based on symbolic regression, including:

[0127] A data preparation module 610 is configured to obtain an initial data set containing multi-layer node equation instances by random sampling based on a set of universal operators;

[0128] A model training module 620, which is configured to train the initial operator filter according to the initial data set to obtain a target operator filter;

[0129] An operator sampling module 630 is configured to perform sampling based on the student's online real learning data and the target operator filter to obtain a function operator set;

[0130] The data analysis module 640 is configured to analyze the students' real online learning data and the function operator set to generate the students' online learning effect equation.

[0131] It should be noted here that: the device 600 provided in the above embodiment can implement the technical solutions described in the above method embodiments. The specific implementation principles of the above modules or units can refer to the corresponding contents in the above method embodiments, which will not be repeated here.

[0132] See also Figure 7 , Figure 7 A schematic diagram of the structure of a synchronous tracking flying welding device for real-time measurement of battery height provided by an embodiment of the present invention. Based on the above-mentioned online learning effect analysis method based on symbolic regression, the present invention also provides an online learning effect analysis device based on symbolic regression. The online learning effect analysis device based on symbolic regression can be a computing device such as a mobile terminal, a desktop computer, a notebook, a palm computer, and a server. The online learning effect analysis device based on symbolic regression 700 includes a processor 710, a memory 720, and a display 730. Figure 7 Only some components of the synchronous tracking flying welding equipment for real-time measurement of battery height are shown, but it should be understood that it is not required to implement all the components shown, and more or fewer components may be implemented instead.

[0133] In some embodiments, the memory 720 may be an internal storage unit of the online learning effect analysis device 700 based on symbolic regression, such as a hard disk or memory of the online learning effect analysis device 700 based on symbolic regression. In other embodiments, the memory 720 may also be an external storage device of the online learning effect analysis device 700 based on symbolic regression, such as a plug-in hard disk, a smart memory card (SmartMedia Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. equipped on the online learning effect analysis device 700 based on symbolic regression. Further, the memory 720 may also include both an internal storage unit of the online learning effect analysis device 700 based on symbolic regression and an external storage device. The memory 720 is used to store application software and various types of data installed in the online learning effect analysis device 700 based on symbolic regression, such as the program code for installing the online learning effect analysis device 700 based on symbolic regression. The memory 720 may also be used to temporarily store data that has been output or is to be output. In one embodiment, the memory 720 stores an online learning effect analysis program 740 based on symbolic regression, and the online learning effect analysis program 740 based on symbolic regression can be executed by the processor 710, thereby realizing the online learning effect analysis method based on symbolic regression of each embodiment of the present application.

[0134] In some embodiments, the processor 710 may be a central processing unit (CPU), a microprocessor or other data processing chip, used to run program codes or process data stored in the memory 720, such as executing an online learning effect analysis method based on symbolic regression.

[0135] In some embodiments, the display 730 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, etc. The display 730 is used to display information on the online learning effect analysis device based on symbolic regression 700 and to display a visual user interface. The components 710-730 of the online learning effect analysis device based on symbolic regression 700 communicate with each other through a system bus.

[0136] In one embodiment, when the processor 710 executes the online learning effect analysis program 740 based on symbolic regression in the memory 720, the steps in the online learning effect analysis method based on symbolic regression are implemented.

[0137] This embodiment also provides a computer-readable storage medium, on which an online learning effect analysis program based on symbolic regression is stored. When the online learning effect analysis program based on symbolic regression is executed by a processor, the following steps are implemented:

[0138] An initial data set containing multi-layer node equation instances is obtained by random sampling based on a set of universal operators;

[0139] The initial operator filter is trained according to the initial data set to obtain the target operator filter;

[0140] Based on the students' real online learning data and the target operator filter, sampling is performed to obtain a set of function operators;

[0141] Analyze students' real online learning data and function operator sets to generate students' online learning effect equations.

[0142] In summary, the present invention provides a method for describing the student learning process based on symbolic regression. An initial data set containing multi-layer node equation instances is obtained by random sampling of a general operator set to construct an operator filter, and the operator filter is trained by the initial data set. Operator sampling is then performed to determine the function operator set. The operators that are most likely to generate meaningful mathematical expressions can be analyzed and identified in advance. The subtle differences between individuals are captured by predicting the effectiveness of the operators rather than randomly searching the entire operation space, thereby significantly improving the search efficiency and the performance of the final model, which is conducive to improving the accuracy and effectiveness of designing personalized learning plans for each student.

[0143] The present application also provides a computer-readable storage medium on which a computer program is stored, and when the program is executed by a processor, the steps of the above method are implemented. The computer-readable storage medium may include, but is not limited to, any type of disk, including a floppy disk, an optical disk, a DVD, a CD-ROM, a micro drive, and a magneto-optical disk, a ROM, a RAM, an EPROM, an EEPROM, a DRAM, a VRAM, a flash memory device, a magnetic card or an optical card, a nanosystem (including a molecular memory IC), or any type of medium or device suitable for storing instructions and / or data.

[0144] It should be noted that, for the aforementioned method embodiments, for the sake of simplicity, they are all expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the described order of actions, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

[0145] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0146] In the several embodiments provided in the present application, it should be understood that the disclosed devices can be implemented in other ways. For example, the device embodiments described above are only schematic, such as the division of the units, which is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some service interfaces, and the indirect coupling or communication connection of devices or units can be electrical or other forms.

[0147] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0148] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0149] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a memory, including a number of instructions to enable a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned memory includes: U disk, read-only memory (ROM), random access memory (RAM), mobile hard disk, disk or optical disk and other media that can store program code.

[0150] A person of ordinary skill in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable memory, which can include: a flash drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, etc.

[0151] The above is only an exemplary embodiment of the present disclosure, and the scope of the present disclosure cannot be limited thereto. That is, any equivalent changes and modifications made according to the teachings of the present disclosure are still within the scope of the present disclosure. After considering the specification and practicing the disclosure here, those skilled in the art will easily think of the implementation scheme of the present disclosure. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary technical means in the technical field not recorded in the present disclosure. The description and examples are regarded as exemplary only, and the scope and spirit of the present disclosure are defined by the claims.

[0152] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0153] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for analyzing online learning effects based on symbolic regression, characterized in that: include: An initial data set containing multi-layer node equation instances is obtained by random sampling based on a set of universal operators; Training an initial operator filter according to the initial data set to obtain a target operator filter; Sampling based on the students' real online learning data and the target operator filter to obtain a set of function operators; Analyze the student's real online learning data and the function operator set to generate an online learning effect equation for the student; The step of training the initial operator filter according to the initial data set to obtain the target operator filter includes: Inputting the initial data set into the initial operator filter for feature encoding to obtain learning features; Mapping the learning features to the probability space where the operator exists to predict the existence of the operator; When the prediction result meets the preset requirements, a target operator filter is obtained; The sampling based on the student's real online learning data and the target operator filter to obtain a set of function operators includes: Inputting the student's online real learning data into the target operator filter, and outputting an existence probability matrix; Performing temperature processing on the existence probability matrix using a sampled temperature function; Operator sampling is performed on the temperature-processed existence probability matrix to obtain a set of function operators.

2. The online learning effect analysis method based on symbolic regression according to claim 1, characterized in that: The initial data set containing multi-layer node equation instances is obtained by random sampling based on the universal operator set, including: Randomly selecting the number of paths between the independent variable and the dependent variable according to the universal operator set; Data sampling is performed on each path to determine multiple independent variables, connecting edges and neuron outputs; An equation instance is established according to the independent variables, the connecting edges and the neuron outputs to obtain the initial data set.

3. The online learning effect analysis method based on symbolic regression according to claim 2, characterized in that: Each path includes at least two layers of nodes; the data sampling of each path to determine multiple independent variables, connecting edges and neuron outputs includes: Randomly select nodes and independent variable sets at each layer and generate node connection edges and independent variable connection edges; The node connection edges and the independent variable connection edges are uniformly sampled within a first preset range, and the independent variable set is uniformly sampled within a second preset range; The neuron output is calculated based on the sampled independent variable set, node connection edges, and independent variable connection edges.

4. The online learning effect analysis method based on symbolic regression according to claim 1, characterized in that: The sampling temperature function is: ; in, is the first elements, is the first elements, is the sampling temperature.

5. The online learning effect analysis method based on symbolic regression according to claim 1, characterized in that: The step of analyzing the student's online real learning data and the function operator set to generate the student's online learning effect equation includes: Using a multi-layer feedforward neural network, linear mapping is performed on the student's online real learning data and the function operator set to obtain a linear output; The linear output is nonlinearly transformed using a multi-layer feedforward neural network to obtain an equation for the student's online learning effect.

6. An online learning effect analysis device based on symbolic regression, characterized in that: include: A data preparation module, which is configured to obtain an initial data set containing multi-layer node equation instances by random sampling based on a set of universal operators; A model training module, configured to train an initial operator filter according to the initial data set to obtain a target operator filter; An operator sampling module, which is configured to perform sampling based on the student's online real learning data and the target operator filter to obtain a function operator set; A data analysis module, configured to analyze the student's real online learning data and the function operator set to generate an online learning effect equation for the student; The step of training the initial operator filter according to the initial data set to obtain the target operator filter includes: Inputting the initial data set into the initial operator filter for feature encoding to obtain learning features; Mapping the learning features to the probability space where the operator exists to predict the existence of the operator; When the prediction result meets the preset requirements, a target operator filter is obtained; The sampling based on the student's real online learning data and the target operator filter to obtain a set of function operators includes: Inputting the student's online real learning data into the target operator filter, and outputting an existence probability matrix; Performing temperature processing on the existence probability matrix using a sampled temperature function; Operator sampling is performed on the temperature-processed existence probability matrix to obtain a set of function operators.

7. An online learning effect analysis device based on symbolic regression, characterized in that: It includes at least one processing unit and at least one storage unit, wherein the storage unit stores a computer program, and when the computer program is executed by the processing unit, the processing unit executes the steps of the online learning effect analysis method based on symbolic regression according to any one of claims 1 to 5.

8. A storage medium, characterized in that: It stores a computer program executable by an access authentication device. When the computer program runs on the access authentication device, the access authentication device executes the steps of the online learning effect analysis method based on symbolic regression as described in any one of claims 1 to 5.

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