System and method for constructing knowledge tracking model based on positive and negative learning transfer

Abstract

The present invention provides a system and method for constructing a knowledge tracking model based on positive and negative learning transfer. The method comprises: constructing a learning transfer graph; modeling direct learning effects, obtaining the transfer effect from one knowledge concept to another based on the knowledge state of the knowledge concept at time step t; aggregating the positive and negative transfer effects of the knowledge concepts and fusing the aggregated results to obtain a fusion result; obtaining the knowledge state under the perception of the transfer effect based on the fusion result, and predicting the probability of a student correctly answering the knowledge concept at the subsequent time step t+1 based on the knowledge state under the transfer effect; constructing an objective function for the LTKT model based on the probability, and minimizing the objective function to obtain a trained LTKT model. The present invention ensures the rationality of updating the knowledge state of all concepts of a student based on the learning transfer graph, thereby improving the performance of the knowledge tracking model.

Description

Technical Field

[0001] The present invention relates to the field of deep learning technology, and in particular to a system and method for constructing a knowledge tracking model based on positive and negative learning transfer. Background Art

[0002] Over the past few years, the application of artificial intelligence (AI) technology has significantly improved the educational practice of intelligent tutoring systems. For example, mainstream massive open online course (MOOC) platforms, such as edX.org, Coursera.org, and aixuexi.com, have used AI to predict students' knowledge states and provide them with personalized learning materials, successfully improving their learning abilities. Consequently, many AI-based knowledge tracing (KT) models have recently been proposed in top conferences or journals. These models can use students' learning logs to predict and track their knowledge states, thereby enhancing the personalized capabilities of MOOC platforms. Generally speaking, the KT task consists of two main parts: 1) estimating students' knowledge states through their interaction logs; and 2) predicting the probability that a student will correctly answer a new exercise in the next time step.

[0003] Existing knowledge tracing models fall into two main categories: traditional models and models based on deep learning. In the past few years, driven by the numerous advantages of deep learning, many researchers have devoted themselves to designing deep learning-based knowledge tracing models, achieving superior results in predicting student performance compared to traditional methods. Deep knowledge tracing, dynamic key-value memory networks for knowledge tracing, and convolutional knowledge tracing are representative early deep knowledge tracing models. However, these models fail to consider the transfer of learning between two concepts and, therefore, produce less accurate predictions.

[0004] In recent years, some researchers have recognized the importance of learning transfer in improving the effectiveness of knowledge tracing. For example, a knowledge tracing model based on graph neural networks, namely graph-based knowledge tracing, was proposed. This model models the learning transfer process based on isomorphic graphs. Similarly, a structure-based knowledge tracing model based on GNN has also been proposed. Unlike GKT, SKT defines the relationship between two different types of knowledge concepts, namely prerequisite relations and similarity relations, and then constructs a heterogeneous graph to represent the knowledge structure. By leveraging multiple relationships in heterogeneous graphs, SKT can model various learning transfer processes between knowledge concepts. Although the performance of knowledge tracing has been significantly improved by considering the impact of learning transfer, existing research has only considered positive learning transfer and ignored the important impact of negative learning transfer on knowledge tracing, which affects the effectiveness of knowledge tracing. Summary of the Invention

[0005] The purpose of the present invention is to provide a system and method for constructing a knowledge tracking model based on positive and negative learning transfer, aiming to solve the problem that traditional technologies have low effectiveness of knowledge tracking due to ignoring the important impact of negative learning transfer on knowledge tracking.

[0006] In a first aspect, the present invention provides a method for constructing a knowledge tracking model based on positive and negative learning transfer, the method comprising:

[0007] A learning transfer graph LTG(V,E) for a given course is constructed based on the historical interactions of students participating in the course, where V = {v1,v2,...,v n ,...,v N} represents N vertices in the graph, each vertex v i ∈V corresponds to a knowledge concept c i ∈C,E={e1,e2,...,e n ,...,e N} represents the set of edges in the graph, and the type of each edge is one of the type set {PTPR, PTSR, NTPR, NTSR};

[0008] Convert the learning interaction into a one-hot vector And according to the one-hot vector Obtaining quantitative impact of direct learning effects t ;

[0009] Modeling direct learning effects to determine the impact of direct learning effects v t Change the knowledge status of knowledge concepts from Evolved to And based on the knowledge state of the knowledge concept at time step t, the positive transfer prerequisite effect, positive transfer similarity effect, negative transfer prerequisite effect, and negative transfer similarity effect from one knowledge concept to another are obtained;

[0010] Summarize the positive transfer effect and negative transfer effect of knowledge concepts to obtain the aggregated result of positive transfer effect and the aggregated results of negative transfer effects And fuse the aggregation results to get the fusion results

[0011] According to the fusion results The knowledge state of the student at time step t based on the transfer effect perception is expressed as And according to the knowledge state under the transfer effect Predict the student's correct answer to knowledge concept c at the subsequent time step t+1 m Probability According to probability Construct the objective function of the LTKT model and minimize the objective function to obtain the trained LTKT model.

[0012] In summary, based on the above-mentioned method of constructing a knowledge tracking model based on positive and negative learning transfer, a new knowledge tracking framework, namely the knowledge tracking model based on positive and negative learning transfer (LTKT model), was introduced. The LTKT model simulates the learning transfer effect between teaching concepts better than existing research by simultaneously considering the impact of positive and negative learning transfer on the knowledge state. Specifically, the LTKT model first proposes a statistical method to construct a learning transfer graph, which models the positive transfer relationship and negative transfer relationship of concepts in a given course. Then, the LTKT model fully considers the learning transfer relationship and learning transfer effect between concepts to ensure the rationality of updating the knowledge state of all concepts of students based on the learning transfer graph, thereby improving the performance of the knowledge tracking model.

[0013] Furthermore, the learning interaction is converted into a one-hot vector And according to the one-hot vector Obtaining quantitative impact of direct learning effects t The steps include:

[0014] For a learning interaction Indicates that the student has a good understanding of the test concept c at time step t i Exercises t The result given is a t ∈{1,0}, the learning interaction is transformed according to the following formula:

[0015]

[0016] The quantitative impact of the direct learning effect v is calculated according to the following formula t :

[0017]

[0018] in, represents the embedding matrix, N represents the total number of concepts, d v Indicates v t The dimension of .

[0019] Furthermore, the direct learning effect is modeled to determine the influence of the direct learning effect v t Change the knowledge status of knowledge concepts from Evolved to The steps of obtaining the positive transfer prerequisite effect, the positive transfer similarity effect, the negative transfer prerequisite effect, and the negative transfer similarity effect from one knowledge concept to another knowledge concept based on the knowledge state of the knowledge concept at time step t include:

[0020] by and the quantified direct learning effect v t As input, the concept c is obtained according to the following formula i The knowledge state at time step t

[0021]

[0022] in, Represents the GRU gate function;

[0023] In the constructed learning transfer graph, given a PTPR edge c i →c j , where c i For the front-wheel drive concept, c j c i The successor concept of , then the concept c is obtained according to the following formula i To concept c j Positive migration prerequisite effect

[0024]

[0025] in, Represents a successor function that returns concept c i All PTPR successor concepts, and Both represent learnable parameters;

[0026] The concept c is obtained according to the following formula i To concept c j Positive transfer similarity effect

[0027]

[0028] The concept c is obtained according to the following formula i The PTSR neighbor pair concept c i Positive transfer similarity effect

[0029]

[0030] in, Indicates the return concept c i Neighbor function of all PTSR neighbors of .

[0031] Furthermore, the direct learning effect is modeled to determine the influence of the direct learning effect v t Change the knowledge status of knowledge concepts from Evolved to The step of obtaining a positive transfer prerequisite effect, a positive transfer similarity effect, a negative transfer prerequisite effect, and a negative transfer similarity effect from one knowledge concept to another based on the knowledge state of the knowledge concept at time step t also includes:

[0032] Given a NTPR edge c i →c j , where c i For the front-wheel drive concept, c j c i The successor concept of , the concept c is calculated according to the following formula i To concept c j Negative transfer prerequisite effect

[0033]

[0034] in, Represents a successor function that returns concept c i All NTPR successor concepts, and Both represent learnable parameters;

[0035] The concept c is calculated according to the following formula i To concept c j Negative transfer similarity effect

[0036]

[0037] The concept c is calculated according to the following formula j Towards concept c i Negative transfer similarity effect of transfer

[0038]

[0039] Among them, the function Represents the retrieval concept c i The neighbor function of all NTSR neighbor concepts, and represents the learnable parameters, Represents a join operation.

[0040] Furthermore, the positive transfer effect and negative transfer effect of the knowledge concept are summarized to obtain the aggregated result of the positive transfer effect. and the aggregated results of negative transfer effects And fuse the aggregation results to get the fusion results The steps include:

[0041] The aggregation results of the positive migration effect were calculated according to the following formula

[0042]

[0043] The aggregation results of negative migration effect were calculated according to the following formula

[0044]

[0045] Among them, α represents a hyperparameter;

[0046] Fusion is performed according to the following formula:

[0047]

[0048] in, and Represent the learnable weight matrix and bias respectively, and β represents a learnable parameter used to calculate each student’s and , MLP(·) represents the multi-layer perception function, and tanh(·) represents the tanh activation function.

[0049] Furthermore, according to the fusion result The knowledge state of the student at time step t based on the transfer effect perception is expressed as And according to the knowledge state under the transfer effect Predict the student's correct answer to knowledge concept c at the subsequent time step t+1 m Probability The steps include:

[0050] The knowledge state under the transfer effect is obtained according to the following formula

[0051]

[0052] in, represents the target student’s knowledge state at time step t-1,

[0053] The probability is calculated according to the following formula

[0054]

[0055] in, represents the learnable weight matrix, represents the learnable bias and σ(·) represents the Sigmoid activation function.

[0056] Furthermore, the probability The steps of constructing the objective function of the LTKT model and minimizing the objective function to obtain the trained LTKT model include:

[0057] The objective function is constructed according to the following formula:

[0058]

[0059] in, Represents the prediction result at each time step t The actual answer result I t The standard cross entropy loss between t =1 means the answer is correct, I t =0 means the answer is incorrect.

[0060] In a second aspect, the present invention provides a system for constructing a knowledge tracking model based on positive and negative learning transfer, the system comprising:

[0061] The transfer graph construction module is used to construct a learning transfer graph LTG(V,E) of a given course based on the historical interactions of students participating in the course, where V = {v1,v2,...,v n ,...,v N} represents N vertices in the graph, each vertex v i ∈V corresponds to a knowledge concept c i ∈C,E={e1,e2,...,e n ,...,e N} represents the set of edges in the graph, and the type of each edge is one of the type set {PTPR, PTSR, NTPR, NTSR};

[0062] Vector conversion module, used to convert learning interactions into a one-hot vector And according to the one-hot vector Obtaining quantitative impact of direct learning effects t ;

[0063] Transfer effect acquisition module, used to model direct learning effects based on the influence of direct learning effects v t Change the knowledge status of knowledge concepts from Evolved to And based on the knowledge state of the knowledge concept at time step t, the positive transfer prerequisite effect, positive transfer similarity effect, negative transfer prerequisite effect, and negative transfer similarity effect from one knowledge concept to another are obtained;

[0064] The fusion module is used to summarize the positive transfer effect and negative transfer effect of knowledge concepts and obtain the aggregated result of the positive transfer effect. and the aggregated results of negative transfer effects And fuse the aggregation results to get the fusion results

[0065] Model training module, used to train The knowledge state of the student at time step t based on the transfer effect perception is expressed as And according to the knowledge state under the transfer effect Predict the student's correct answer to knowledge concept c at the subsequent time step t+1 m Probability According to probability Construct the objective function of the LTKT model and minimize the objective function to obtain the trained LTKT model.

[0066] In a third aspect, the present invention provides a storage medium storing one or more programs, which, when executed by a processor, implement the above-mentioned method for constructing a knowledge tracking model based on positive and negative learning transfer.

[0067] In a fourth aspect, the present invention provides an electronic device, comprising a memory and a processor, wherein:

[0068] The memory is used to store computer programs;

[0069] When the processor is used to execute the computer program stored in the memory, it implements the above-mentioned method for constructing a knowledge tracking model based on positive and negative learning transfer. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Schematic diagram of the structure of a learning transfer graph according to an embodiment of the present invention;

[0071] Figure 2 A flowchart of a method for constructing a knowledge tracking model based on positive and negative learning transfer proposed in one embodiment of the present invention;

[0072] Figure 3 This is an overall framework diagram of a knowledge tracking model based on positive and negative learning transfer in one embodiment of the present invention;

[0073] Figure 4 Schematic diagram of the distribution of student interaction sequence lengths in various data sets according to an embodiment of the present invention;

[0074] Figure 5A distribution diagram of the number of interaction events in various data sets according to an embodiment of the present invention;

[0075] Figure 6 A distribution diagram of the total number of two types of interaction events in various data sets according to an embodiment of the present invention;

[0076] Figure 7 This is a schematic diagram of the structure of a system for constructing a knowledge tracking model based on positive and negative learning transfer proposed in one embodiment of the present invention.

[0077] The following specific embodiments will further illustrate the present invention in conjunction with the above-mentioned drawings. DETAILED DESCRIPTION

[0078] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. Unless otherwise defined, the technical terms or scientific terms used herein should be the common meanings understood by people with ordinary skills in the field to which the present invention belongs. The words "including" and similar words used in this embodiment mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0079] like Figure 1 As shown, the effects of positive and negative transfer on students’ knowledge status are shown. Figure 1 As shown at the bottom of the figure, the six teaching concepts related to mathematics courses (i.e., A, B, C, D, E, and F) are modeled as a learning transfer graph, where nodes represent teaching concepts and edges represent learning transfer relationships between concepts. Specifically, learning transfer relationships include positive transfer relationships and negative transfer relationships. Figure 1 In the figure, green and red edges are used to represent them respectively. Then, the positive and negative transfer relationships can be further identified as prerequisite relationships (represented as directed edges) or similarity relationships (represented as undirected edges). When a concept is connected to another concept through a prerequisite relationship, it means that the former is regarded as the basis of the latter; two concepts connected by a similarity relationship are similar in terms of their content. Figure 1 The middle section shows a student completing a set of exercises in sequence, where each exercise is related to a teaching concept. Figure 1 The correctness of student s’ answer is also marked in the table. Figure 1As shown in Figure 2, after s completes the first exercise related to concept C, his / her knowledge status on concept C is improved, and the updated knowledge status values ​​of all concepts are displayed in the form of a radar chart. Figure 1 . Note that when s’s knowledge state of a particular concept is updated, the knowledge state of all neighboring concepts of that concept in the learning transfer graph will also be updated. For example, when s’s knowledge state of concept C increases, due to the negative transfer relationship between the two concepts, her / his knowledge state of C’s neighbor concept (i.e., D) is updated to a smaller value. For another example, when s’s knowledge state of concept B increases, it triggers an increase in s’s knowledge state of B’s neighbor concept C because there is a positive transfer relationship between the two concepts. When there are both positive and negative transfer relationships between two concepts (such as E and F), s’s knowledge state adjustment of a concept (such as F) depends on s’s knowledge state values ​​of all concepts. In summary, in order to ensure the effectiveness of knowledge tracking based on knowledge structure, it is necessary to simultaneously consider the impact of positive and negative learning transfer on the knowledge state value of each concept in the learning transfer graph.

[0080] In addition, there are two major challenges when considering positive and negative learning transfer:

[0081] 1. Challenge 1: Given a course, how to construct a learning transfer graph for the course, where the teaching concepts in the course are linked by positive transfer relationships and negative transfer relationships.

[0082] 2. Challenge 2: How to reasonably update students’ knowledge status of each concept based on the constructed learning transfer map.

[0083] To address these two challenges, the present invention proposes a deep learning-based knowledge tracking model—the knowledge tracking model based on positive and negative learning transfer (LTKT). This model simultaneously utilizes positive and negative learning transfer relationships between teaching concepts to optimize knowledge tracking performance. To address the first challenge, LTKT proposes a statistical method that constructs a learning transfer graph for a specific course, containing multiple types of learning transfer relationships, based on students' historical interaction data. The solution to the second challenge is to fully consider the direct learning effect (DLE) and learning transfer effect (LTE) to ensure the rationality of updating students' knowledge status of each concept based on the learning transfer graph. Specifically, when a student completes an exercise, a gating function is used to quantify the impact of the exercise results on the knowledge status of the teaching concept tested in the exercise. Subsequently, the impact of the student's exercise results on the knowledge status of other neighboring concepts is considered, which is caused by positive and negative learning transfer effects. The positive and negative transfer effects are modeled using the proven influence propagation perspective. To optimize the impact of positive and negative transfer effects on students' knowledge states of learned concepts, a two-stage fusion strategy is first used to aggregate these effects, taking into account each student's sensitivity to different learning transfer effects. Finally, the aforementioned gating function is used to update the knowledge states of all adjacent concepts in the learning transfer graph based on the aggregated results of positive and negative transfer effects.

[0084] In addition, it should be noted that in the following examples, the symbols used are described and summarized in Table 1, as follows:

[0085] Table 1 Symbols and meanings

[0086]

[0087]

[0088] Furthermore, learning transfer theory shows that the relationships between teaching concepts can be divided into positive transfer relationships and negative transfer relationships. Recent research indicates that positive (or negative) transfer relationships can be further defined as prerequisite relationships or similarity relationships. Therefore, in this invention, a learning transfer graph (LTG) is first defined that encompasses these four types of transfer relationships. Figure 1 An example of an LTG is shown at the bottom of the figure. Each type of migration relationship and its representation in the LTG are explained in detail below:

[0089] Positive transfer prerequisite relation (PTPR): represented as a green directed edge in LTG, in which the predecessor concept in the relationship is considered to be the basis of the successor concept (i.e. the concept being pointed to), and mastering the previous concept promotes the learning of the subsequent concept.

[0090] Positive Transfer Similarity Relation (PTSR): Represented as a green undirected edge in LTG, where the two concepts connected by the edge are similar in content and learning one concept will promote the learning of the other concept.

[0091] Negative Transfer Prerequisite Relationship (NTPR): Represented as a red directed edge in the LTG, this relationship can be interpreted as the predecessor concept being the basis of the successor concept, however, learning the former will interfere with learning the latter.

[0092] Negative Transfer Similarity Relation (NTSR): Represented as a red undirected edge in LTG, this relationship indicates that the two concepts connected together are similar, but learning one of them will inhibit the learning of the other.

[0093] like Figure 2 As shown, a method for constructing a knowledge tracking model based on positive and negative learning transfer provided by an embodiment of the present invention includes steps S101 to S105, wherein:

[0094] Step S101: constructing a learning transfer graph for a given course based on historical interactions of students participating in the course;

[0095] In this step, the main task is to construct a learning transfer graph LTG(V,E) of a given course based on the historical interactions of students participating in the course. In the constructed LTG, each vertex corresponds to a teaching concept of the course, and the edge represents the learning transfer relationship between a pair of concepts. Generally speaking, the teaching concepts of a course are easy to obtain, but determining the learning transfer relationship between concepts is a difficult task. Therefore, this step designs a statistical method to mine the learning transfer relationship between concepts by analyzing the statistical data of students' historical interaction events. It is worth noting that the recency effect is taken into account in the analysis process. Specifically, the recency effect indicates that students tend to forget previous knowledge. Therefore, in the setting of this module, historical interaction events of students that are not adjacent to the current time step are considered to have no effect on the interaction events that occurred in the current time step. The following will introduce in detail the process of mining positive and negative transfer relationships between vertices in LTG. For the convenience of discussion, let Indicates that a student correctly answered the question related to concept c i Let 'i×' represent a student's interaction with concept c. i The related exercises give interactive events for wrong answers. Then, Used to indicate that the interaction event 'j×' occurs during the interaction event after.

[0096] According to the positive transfer theory, if the concept c i The learning of concept c j Through observation and analysis, it is found that the interaction events in students’ historical learning sequence The frequency value of each instance of this interactive event is calculated based on the student's historical learning sequence to determine the positive transfer relationship in LTG. Should be in the event Happens immediately afterwards.

[0097] The connotation of negative transfer theory includes two aspects: (1) Concept c i The concept of learning interference c j Learning; (2) Concept c i The decrease in proficiency reduces c i with c j Cognitive confusion between the two concepts leads to concept c j Following this connotation, when determining the negative transfer relationship between a pair of concepts, the frequency values ​​of the instances of the two interaction events are taken into account, that is, and Likewise, in two events, event 'j×' (or ) is assumed to occur immediately after the event (or 'i×').

[0098] Specifically, regarding the learning transfer graph, a concept set C with N concepts is defined as {c1, c2, ..., c n ,...,c N The learning transfer graph on} is formalized as a graph LTG(V,E) with edge mapping function ψ:E→{PTPR,PTSR,NTPR,NTSR}. Where V={v1,v2,...,v n ,...,v N} represents N vertices in the graph, each vertex v i ∈V corresponds to a concept c i ∈C. E={e1,e2,...,e n ,...,e N} represents the set of edges in the graph, and the type of each edge is one of the type set {PTPR, PTSR, NTPR, NTSR}.

[0099] Regarding the knowledge tracking problem of learning transfer graph, let X={x1,x2,...,x t ,...,x T} represents the student’s historical learning interaction sequence, where the interaction at each time step is represented as x t =(ex t ,a t ), a t ∈{1,0} means practicing ex at time step t t The binary correctness of the concept set C = {c1, c2, ..., c n ,...,c N The goal of the knowledge tracking problem is to model a student’s knowledge state Y = {y1,y2,...,y t ,...,y T}, and predict that the student will correctly answer the new exercise ex at time step t+1 t+1 The probability P(a t+1 |ex t+1 ,X,LTG).

[0100] In addition, it should be noted that in some embodiments, Figure 3 As shown in the figure, the LTKT model uses the positive transfer relationship and negative transfer relationship between teaching concepts to improve the performance of deep knowledge tracking. The model consists of four main components, namely the Learning Transfer Graph Construction (LTGC) component, the Direct Learning Effect (DLE) component, the Learning Transfer Effect (LTE) component and the prediction component. Among them, the LTE component includes three modules: the Positive Transfer Effect (PTE) module, the Negative Transfer Effect (NTE) module and the Learning Transfer Effect Integration (LTEI) module. Figure 3As shown, first, the LTGC component in LTKT is responsible for building a learning transfer graph, which explicitly models the four learning transfer relationships between all teaching concepts. Then, the DLE component is responsible for modeling the direct learning effects between concepts. On this basis, the DLE component updates the target student's knowledge state according to the direct learning effects. Using the learning transfer graph built by the LTGC component and the target student's knowledge state updated by the DLE component as input, the LTE component first models the two learning transfer effects, namely the negative transfer effect and the positive transfer effect, and then adopts a two-stage fusion strategy to fuse the two effects. The fusion result is passed through a gating function The target student's knowledge state is further updated based on the two learning transfer effects. Finally, the prediction component in the LTKT model is implemented to predict whether the target student can correctly answer subsequent exercises using his / her updated knowledge state.

[0101] Step S102: convert the learning interaction into a one-hot vector, and obtain the quantitative impact of the direct learning effect based on the one-hot vector;

[0102] It should be noted that in this step, an exercise to test a certain teaching concept is first given, and the Direct Learning Effect (DLE) component aims to quantify the impact of students’ practice results in the exercise on their knowledge status of the concept. Figure 2 As shown in the lower left part, based on a learning interaction Indicates that the student has a good understanding of the test concept c at time step t i Exercises t The result given is a t ∈{1,0}, the DLE component can be used to calculate the training results for the concept c i The influence of the knowledge state is quantified as a vector v t In order to calculate v t , the DLE component will first learn the interaction Convert to a one-hot vector The specific details are shown in Formula 1:

[0103]

[0104] Quantitative impact of direct learning effects t Calculated by formula 2:

[0105]

[0106] in, represents the embedding matrix, N represents the total number of concepts, d v Indicates v tThe dimension of .

[0107] Step S103: Modeling the direct learning effect to evolve the knowledge state of the knowledge concept based on the influence of the direct learning effect, and obtaining the positive transfer prerequisite effect, positive transfer similarity effect, negative transfer prerequisite effect, and negative transfer similarity effect from one knowledge concept to another based on the knowledge state of the knowledge concept at time step t;

[0108] set up is the student’s knowledge state at the previous time step t-1, Indicates that the student considers the learning interaction at time step t The knowledge state of the direct learning effect brought about by and the quantified direct learning effect v t As input, use the GRU gate function shown in formula 3 Simulate direct learning effects on students' concepts i The impact of the state of knowledge:

[0109]

[0110] Based on the learning transfer relationship between teaching concepts modeled by the constructed learning transfer graph (LTG), the students’ knowledge status of each concept is further updated. i The learning transfer effect simulates the evolution of the target concept c i The knowledge state change of a concept triggers the knowledge state evolution of other concepts. By adopting the positive transfer effect (PTE) and negative transfer effect (NTE), and based on the learning transfer effect between concepts, we ensure the rationality of students' knowledge state update of each concept.

[0111] In addition, the positive transfer prerequisite effect is caused by the positive transfer prerequisite relationship (PTPR). PTPR is represented as a green directed edge in LTG to indicate that the knowledge learned by students about the predecessor concept is beneficial to the learning of the successor concept. Therefore, in order to model the positive transfer prerequisite effect, the PTE module adopts a unidirectional transfer method, that is, transferring the learning effect of the predecessor concept to the successor concept along the directed PTPR edge. Specifically, by modeling the direct learning effect, the concept c i The state of knowledge from Evolved to The concept c learned at time step t i The knowledge of will be transferred to c along the directed PTPR edgei The successor concept c m Given a PTPR edge c i →c j , where c i For the front-wheel drive concept, c j c i The successor concept of i To concept c j Positive migration prerequisite effect It is quantified in the form of formula 4:

[0112]

[0113] in, is a successor function that returns the concept c i All PTPR successor concepts.

[0114] and is a learnable parameter.

[0115] In addition, for the positive transfer similarity effect, the positive transfer similarity relationship (PTSR) between vertices in LTG causes a positive transfer similarity effect. PTSR is represented by a green undirected edge in LTG, indicating that after the knowledge in a concept is learned, it can promote the learning of another concept connected to the concept through PTSR. Therefore, in order to simulate this positive transfer similarity effect, the PTE module adopts a bidirectional transfer method to transfer the learning effect of one concept to other concepts along the undirected PTSR edge. Specifically, when concept c i The knowledge state changes from becomes After that, the concept c learned at time step t i The knowledge of is first transferred to c along two undirected PTSR edges. i PTSR neighbor c p and c e In similarity relations, the improvement of the proficiency of a specific concept will in turn promote the proficiency of its PTSR neighbor concepts, and vice versa, resulting in the proficiency of adjacent concepts being comparable. Therefore, at time step t, according to concept c i The knowledge learned updates the concept c i After the knowledge state of the PTSR neighbors, the concept c i The knowledge state of the concept c i The sum of the positive transfer similarity effects received by all PTSR neighbors of c is used to update. This ensures that adjacent concepts have similar proficiency. In summary, concept c i There are two positive transfer similarity effects between its adjacent concepts. Among them:

[0116] The first category is concept c i To concept c j The positive transfer similarity effect of public

[0117] Quantify in the form of Equation 5:

[0118]

[0119] Among them, the function Back to Concept c i The PTSR neighbor set, and are learnable parameters, Represents a connection (i.e., concat) operation.

[0120] The second is c i PTSR neighbor pair c i The positive transfer similarity effect is expressed as Indicates. The calculation method is shown in Formula 6:

[0121]

[0122] in, Is the return concept c i Neighbor function of all PTSR neighbors of .

[0123] In addition, the negative transfer effect (NTE) module quantifies the influence of negative transfer prerequisite relations and negative transfer similarity relations in the LTG, which are then used to update students' knowledge status of each teaching concept. The negative transfer prerequisite effect is caused by the negative transfer prerequisite relation (NTPR) in the LTG. In the LTG, the NTPR is represented as a red directed edge to indicate that the student's knowledge of the previous concept will interfere with or inhibit the learning of the subsequent concept. Similar to the modeling of the positive transfer prerequisite relationship effect, this embodiment uses a unidirectional transfer method to model the negative transfer prerequisite effect. The negative transfer prerequisite effect transfers the learning effect of the predecessor concept to the subsequent concept along the directed NTPR edge. Specifically, the concept c i The knowledge state changes from Evolved to After that, the concept c learned at time step t i The knowledge of c will be transferred to c along the directed NTPR edge i The successor c n Given a NTPR edge c i →c j , where c i For the front-wheel drive concept, c j ci The successor concept of i To concept c j Negative transfer prerequisite effect It is quantified in the form of formula 7:

[0124]

[0125] in, is a successor function that returns the concept c i All NTPR successor concepts. and is a learnable parameter.

[0126] In addition, the negative transfer similarity effect is caused by the negative transfer similarity relation (NTSR). NTSR is represented as a red undirected edge in LTG, indicating that the knowledge learned by students in a certain concept will interfere with the learning of another concept in the NTSR relationship, and vice versa. Subsequently, similar to the modeling of the positive transfer similarity effect, a bidirectional transfer method is used to model the negative transfer similarity effect. The goal of this method is to transfer the learning effect of one concept to other concepts along the undirected NTSR edge. Specifically, if Figure 2 As shown, in the concept c i The knowledge state is changed from direct learning effect to becomes Afterwards, at time step t, the learned concept c i The knowledge of will first be transferred to concept c along the undirected NTSR edge i NTSR Neighbor c q and c f . Subsequently, concept c i The state of knowledge is absorbed by c i Sent, c i The concept c is updated by the sum of the negative transfer similarity effects received by all its NTSR neighbors, resulting in adjacent concepts having similar proficiency. In summary, concept c i There are two types of negative transfer similarity effects between c and its NTSR neighbors. The first type is c i to c j The negative transfer similarity effect is expressed as It is expressed as quantized in the form of formula 8:

[0127]

[0128] Among them, the function Represents the retrieval concept c i Neighbor functions for all NTSR neighbor concepts. and are learnable parameters, Represents a connection (i.e., concat) operation.

[0129] The second category is c j To c i The negative transfer similarity effect of transfer, The calculation method is shown in Formula 9:

[0130]

[0131] In summary, in addition to considering the impact of direct learning effects on the current knowledge state estimation of a concept, LTKT also considers the learning transfer effect in the LTE component, so that each student's knowledge state can be further updated according to the positive transfer relationship and negative transfer relationship modeled by LTG. Specifically, (1) LTKT mines the learning transfer graph (LTG) from the historical interaction data of all students and models the impact of positive transfer effect and negative transfer effect on students' knowledge state; (2) given a concept c i , when modeling its positive (or negative) transfer antecedent effect, the transfer effect size is determined only by the concept c i When modeling the positive (or negative) transfer similarity effect, the transfer effect size is determined by the concept c i The knowledge state of the concept itself and the knowledge state of the neighboring concepts in the LTG are jointly determined. In addition, the learning transfer caused by the prerequisite relationship only affects the knowledge state of the successor concept in the LTG, while the learning transfer caused by the similarity relationship not only affects the knowledge state of the concept c i The knowledge status of the concept itself also affects the knowledge status of adjacent concepts in the LTG.

[0132] Step S104: Summarizing the positive transfer effects and negative transfer effects of the knowledge concepts to obtain aggregated results of the positive transfer effects and aggregated results of the negative transfer effects, and fusing the aggregated results to obtain a fusion result;

[0133] It should be noted that this step first converts the negative transfer effect (NTE) modules quantified by and ) and the positive transfer effect (PTE) module quantified (i.e. and ) The six learning transfer effects are fused using a two-stage fusion strategy. Then, the LTEI module uses the gating function Based on the aggregated results of all learning transfer effects, the target students’ knowledge status of these concepts is updated.

[0134] Furthermore, this step involves two stages of fusion: (1) Stage 1: Summarize the positive and negative transfer effects of each concept. Given a specific concept c j , it is the concept c iThe successor concept or neighbor concept of c n (c i or c j ), the aggregated result of the positive migration prerequisite effect and the positive migration similarity effect at time step t is recorded as And for c n (c i or c j ), the aggregated results of negative transfer precedent effect and negative transfer similarity effect at time step t are expressed as express. and Calculated by formulas 10 and 11 respectively:

[0135]

[0136] α is a hyperparameter, and its value is set to 0.5 in this embodiment.

[0137] (2) Phase 2: and To perform fusion. Since different students have different knowledge states at time step t-1, the intuition is that students’ sensitivities to positive transfer effects and negative transfer effects may vary depending on their knowledge states. Therefore, the LTEI module uses a multilayer perceptron (MLP) to learn the sensitivity value β of each student at each time step. This sensitivity value will be used to determine the weight ratio of positive transfer effect or negative transfer effect in the fusion process. Specifically, for a concept c n , using formulas 12, 13, and 14 to summarize all positive migration effects at time step t (i.e. ) and the summary results of all negative transfer effects (i.e. ) for further fusion. The final fusion result is recorded as

[0138]

[0139] in, and is a learnable weight matrix and bias. β is a learnable parameter used to calculate each student’s and Since positive migration effect and negative migration effect are two opposite effects, in the calculation When using the negative transfer effect, a minus sign (i.e. '-') needs to be added before the negative transfer effect.

[0140] Step S105: According to the fusion results, the knowledge state representation of the student's knowledge concept at time step t based on the perception of the transfer effect is obtained, and the probability of the student correctly answering the knowledge concept at the subsequent time step t+1 is predicted based on the knowledge state under the transfer effect. The objective function of the LTKT model is constructed according to the probability, and the objective function is minimized to obtain the trained LTKT model.

[0141] Based on the learning behavior of target students, concept c n The integration result of the learning transfer effect at time step t is Given The student's concept c at time step t n The knowledge state perceived by the learning transfer effect is expressed as Calculated by formula 15:

[0142]

[0143] In formula 15, is the same gated recurrent unit (GRU) gate as in Equation 3, represents the target student’s knowledge state at time step t-1. From Equation 15, we can see that Not only does it consider the concept of n Aggregate information (i.e. ), and also considers the embedding of concepts

[0144] In addition, the target student needs to use each concept c at time step t n ∈C after the updated knowledge state (i.e. ) to predict the student’s correct answer to the concept c at the subsequent time step t+1 m Exercise ex for ∈C t+1 Probability Specifically, The calculation formula is shown in Formula 16:

[0145]

[0146] in, is the learnable weight matrix, is the learnable bias, and σ is the Sigmoid activation function.

[0147] Finally, for the LTKT model, the prediction results at each time step t during the training phase are minimized. The actual answer result label I t The standard cross entropy loss between is used to jointly learn all the parameters in LTKT, as shown in Formula 17:

[0148]

[0149] It is worth mentioning that the variable I t It distinguishes whether the target students' answers to the exercises are correct or not, where I t =1 means the answer is correct, I t = 0 indicates an incorrect answer. The objective function is minimized in the mini-batch. Further details on the training are given in Table 2 below:

[0150] Table 2

[0151]

[0152]

[0153] In summary, based on the above-mentioned method of constructing a knowledge tracking model based on positive and negative learning transfer, a new knowledge tracking framework, namely the knowledge tracking model based on positive and negative learning transfer (LTKT model), was introduced. The LTKT model simulates the learning transfer effect between teaching concepts better than existing research by simultaneously considering the impact of positive and negative learning transfer on the knowledge state. Specifically, the LTKT model first proposes a statistical method to construct a learning transfer graph, which models the positive transfer relationship and negative transfer relationship of concepts in a given course. Then, the LTKT model fully considers the learning transfer relationship and learning transfer effect between concepts to ensure the rationality of updating the knowledge state of all concepts of students based on the learning transfer graph, thereby improving the performance of the knowledge tracking model.

[0154] In order to evaluate the effectiveness of the proposed LTKT model, this example uses two publicly available datasets for evaluation. The distribution of the length of student interaction sequences in each dataset is as follows: Figure 4 A brief description of the two datasets is provided below.

[0155] ASSISTments 2015 (ASSIST15): This dataset comes from the online tutoring platform ASSISTments and contains learner interaction records from 2015. ASSIST15 is a "Skill Builder" dataset, which means that when a student reaches a certain standard (usually set to answer 3 exercises correctly in a row), they are considered to have mastered a concept and no further exercises are required after mastery. Among all datasets, this dataset has the shortest average sequence length, such as Figure 4 shown.

[0156] ASSISTments 2009 (ASSIST09): This dataset is also obtained from the ASSISTments online tutoring system, but contains interaction records from 2009 to 2010. This dataset has been widely used by many researchers to evaluate knowledge tracking models. Specifically, ASSIST09 contains two sub-datasets: "Skill Builder data 2009-2010" and "Non-Skill Builder data 2009-2010." The experiments in this example use the latter dataset. In this experiment, only the first teaching concept tested is used to mark the exercises. In addition, this example deletes all records whose correctness labels are not equal to 1 or 0.

[0157] Table 3 below summarizes the statistical characteristics of the datasets. The "proportion of NTPR relations" in Table 3 is calculated using the formula #of NTPR / N×(N-1), and the "proportion of NTSR relations" is calculated using the formula #of NTSR / N×(N-1). Here, N×(N-1) represents the total number of relations in the directed complete graph, and N represents the number of concepts (or vertices) in the graph. As shown in Table 3, the proportion of both types of negative transfer relations (NTPR and NTSR) is higher in the ASSIST15 dataset than in the ASSIST09 dataset.

[0158] Table 3

[0159]

[0160]

[0161] In some embodiments, because no dataset provides an explicit learning transfer graph (LTG(V,E), this embodiment determines the vertex set V and edge set E in the LTG as follows. First, all teaching concepts of the course are used to generate the LTG vertex set V, where each vertex is associated with a different concept. Then, four types of transfer relations (i.e., PTPR, PTSR, NTPR, and NTSR) are described and used to derive the LTG edge set E.

[0162] In order to facilitate the determination of the PTPR and PTSR relationship between each vertex in the LTG, this embodiment first calculates a positive migration statistics matrix (denoted as ), where each element P[i][j]∈P records the event Note that when i=j, P[i][j] is set to 0. At the same time, in order to facilitate the mining of the NTPR and NTSR relationships between the vertices in the LTG, this embodiment also calculates a negative migration statistics matrix Similarly, all N[i][i] values ​​in the matrix where i≤N are all set to 0. For the case where i≠j, the value of N[i][j] is the sum of the two statistical values, i.e., the event Frequency and events frequency of occurrence. Figure 5 and Figure 6 The distribution of interaction events in the log shows that there are enough interactive events in the students’ historical learning logs. and In this case, different types of learning transfer relationships can be determined according to the following statistical strategies.

[0163] To determine the PTPR between vertices, this embodiment calculates a The asymmetric matrix of is used to record the probability of PTPR between each pair of concepts. Specifically, when i≠j, the concept c is calculated using formula 18 i The knowledge of is transferred to concept c in one direction j Then, we introduce the threshold θ PTPR To determine whether there is a PTPR between one concept and another, that is, PT[i][j]≥θ PTPR Represents concept c i To concept c j There is a PTPR relationship between them. The threshold is set to the average value of all elements in PT, as shown in Formula 19:

[0164]

[0165] To determine the PTSR between vertices, this embodiment calculates a To calculate PS, Formula 20 is used to calculate the frequency of concurrent occurrence between two concepts. and When the frequency difference is small, the frequency of concurrency is high, where ∈ = 0.1 is a small positive value to prevent zero division. Then, the maximum and minimum normalization operation is used to convert The values ​​in are normalized to the range [0,1], as shown in Equation 21. Obviously, PS[i][j]∈[0,1] is the probability that there is a PTSR between concept i and concept j. Subsequently, in LTG, if there is a pair of concepts (c i ,c j ), and PS[i][j] is greater than or equal to the set threshold θ PTSR , then they will be connected by a PTSR. Here, the threshold θ PTSR Let it be the average value of PS, as shown in Equation 22:

[0166]

[0167] In order to determine the NTPR between the vertices in LTG, an asymmetric matrix is ​​used. This matrix is ​​expressed as When i≠j, this embodiment uses formula 23 to calculate the probability that there is a negative transfer prerequisite relationship between two concepts. Here, N is the negative transfer statistical matrix. NT[i][j] represents the concept c i The knowledge of the one-way negative transfer to concept c j Then, set a threshold θ NTPR To judge the concept c i and concept c j Is there a relationship between them, that is, if NT[i][j]≥θ NTPR , then NT[i][j]=1. NTPR Set to the average value of NT, as shown in Equation 24:

[0168]

[0169] In order to determine the NTSR between vertices in LTG, this embodiment needs to calculate a symmetric matrix, which is expressed as Specifically, first calculate the concurrent occurrence frequency of each NS[i][j]∈NS(i≠j) according to formula 25 In formula 25, this embodiment sets ∈ to a small positive value of 0.1 to prevent zero division. Then, the maximum and minimum normalization technique is used to convert each The values ​​are normalized to the range [0,1], so as to obtain NS[i][j]∈NS, as shown in Formula 26. Therefore, NS[i][j] is the concept c i With concept c j The probability of negative migration in both directions. Finally, this embodiment also sets a threshold θ for each NS[i][j]∈NS NTSR , to determine a pair of concepts (c i ,c j ) is connected by NTSR in LTG, where θ NTSR Set to the average value of all elements in NS, as shown in Formula 27:

[0170]

[0171] It should be pointed out that when the two concepts c i and c jWhen there is no association, their corresponding statistics (i.e., PT[i][j], PS[i][j], NT[i][j], and NS[i][j]) are set to a small positive value γ instead of 0. This is because simply setting γ = 0 does not guarantee the effectiveness of knowledge tracking based on knowledge structure. In addition, a threshold (i.e., θ) is set to determine whether a certain relationship exists. PTPR ,θ PTSR ,θ NTPR and θ NTSR ). Then, by merging the four types of edges: PTPR, PTST, NTPR, and NTSR, we get the edge set E of LTG.

[0172] In addition, the effectiveness of LTKT was evaluated by comparing it with a set of baseline models. Specifically, four deep learning-based models that do not consider learning transfer were compared, namely Deep Knowledge Tracing (DKT), Regularized Deep Knowledge Tracing (DKT+), Dynamic Key-Value Memory Networks for Knowledge Tracing (DKVMN), and Convolutional Knowledge Tracing (CKT). In addition, four deep learning knowledge tracing models that only consider positive learning transfer between teaching concepts were used as baselines, namely Context-based Knowledge Tracing (ContextKT), Robust Knowledge Tracing with k-Sparse Attention (SPARSEKT), Graph-based Knowledge Tracing (GKT), and Structure-based Knowledge Tracing (SKT), as shown in Table 4.

[0173] Table 4

[0174]

[0175]

[0176] See also Figure 7 , which is a schematic diagram of a system for constructing a knowledge tracking model based on positive and negative learning transfer in one embodiment of the present invention, the system includes:

[0177] The transfer graph construction module 10 is used to construct a learning transfer graph LTG(V,E) of a given course based on the historical interactions of students participating in the course, where V = {v1, v2, ..., v n ,...,v N} represents N vertices in the graph, each vertex v i ∈V corresponds to a knowledge concept c i ∈C,E={e1,e2,...,e n ,...,e N} represents the set of edges in the graph, and the type of each edge is one of the type set {PTPR, PTSR, NTPR, NTSR};

[0178] Vector conversion module 20, used to convert the learning interaction into a one-hot vector And according to the one-hot vector Obtaining quantitative impact of direct learning effects t ;

[0179] The transfer effect acquisition module 30 is used to model the direct learning effect based on the influence of the direct learning effect v t Change the knowledge status of knowledge concepts from Evolved to And based on the knowledge state of the knowledge concept at time step t, the positive transfer prerequisite effect, positive transfer similarity effect, negative transfer prerequisite effect, and negative transfer similarity effect from one knowledge concept to another are obtained;

[0180] Fusion module 40 is used to summarize the positive transfer effect and negative transfer effect of knowledge concepts and obtain the aggregated result of positive transfer effect and the aggregated results of negative transfer effects And fuse the aggregation results to get the fusion results

[0181] Model training module 50 is used to train the model based on the fusion results. The knowledge state of the student at time step t based on the transfer effect perception is expressed as And according to the knowledge state under the transfer effect Predict the student's correct answer to knowledge concept c at the subsequent time step t+1 m Probability According to probability Construct the objective function of the LTKT model and minimize the objective function to obtain the trained LTKT model.

[0182] On the other hand, the present invention further proposes a storage medium having one or more programs stored thereon, which, when executed by a processor, implements the above-mentioned method for constructing a knowledge tracking model based on positive and negative learning transfer.

[0183] On the other hand, the present invention also proposes an electronic device, including a memory and a processor, wherein the memory is used to store computer programs, and the processor is used to execute the computer programs stored in the memory to implement the above-mentioned method of constructing a knowledge tracking model based on positive and negative learning transfer.

[0184] While the embodiments of the present invention have been described in detail above, it will be apparent to those skilled in the art that various modifications and variations of these embodiments are possible. However, it should be understood that such modifications and variations are within the scope and spirit of the present invention as set forth in the claims. Furthermore, the invention described herein is susceptible to other embodiments and may be practiced or implemented in a variety of ways.

Claims

1. A method for constructing a knowledge tracking model based on positive and negative learning transfer, characterized in that: The method comprises: A learning transfer graph LTG(V,E) for a given course is constructed based on the historical interactions of students participating in the course, where V = {v1,v2,...,v n ,...,v N } represents N vertices in the graph, each vertex v i ∈V corresponds to a knowledge concept c i ∈C,E={e1,e2,...,e n ,...,e N } represents the set of edges in the graph, and the type of each edge is one of the type set {PTPR, PTSR, NTPR, NTSR}; Convert the learning interaction into a one-hot vector And according to the one-hot vector Obtaining quantitative impact of direct learning effects t ; Modeling direct learning effects to determine the impact of direct learning effects v t Change the knowledge status of knowledge concepts from Evolved to And based on the knowledge state of the knowledge concept at time step t, the positive transfer prerequisite effect, positive transfer similarity effect, negative transfer prerequisite effect, and negative transfer similarity effect from one knowledge concept to another are obtained; Summarize the positive transfer effect and negative transfer effect of knowledge concepts to obtain the aggregated result of positive transfer effect and the aggregated results of negative transfer effects And fuse the aggregation results to get the fusion results According to the fusion results The knowledge state of the student at time step t based on the transfer effect perception is expressed as And according to the knowledge state under the transfer effect Predict the student's correct answer to knowledge concept c at the subsequent time step t+1 m Probability According to probability Construct the objective function of the LTKT model and minimize the objective function to obtain the trained LTKT model.

2. The method for constructing a knowledge tracking model based on positive and negative learning transfer according to claim 1, characterized in that: The learning interaction is converted into a one-hot vector And according to the one-hot vector Obtaining quantitative impact of direct learning effects t The steps include: For a learning interaction Indicates that the student has a good understanding of the test concept c at time step t i Exercises t The result given is a t ∈{1,0}, the learning interaction is transformed according to the following formula: The quantitative impact of the direct learning effect v is calculated according to the following formula t : in, represents the embedding matrix, N represents the total number of concepts, d v Indicates v t The dimension of .

3. The method for constructing a knowledge tracking model based on positive and negative learning transfer according to claim 2, characterized in that: The direct learning effect is modeled based on the influence of the direct learning effect v t Change the knowledge status of knowledge concepts from Evolved to The steps of obtaining the positive transfer prerequisite effect, the positive transfer similarity effect, the negative transfer prerequisite effect, and the negative transfer similarity effect from one knowledge concept to another knowledge concept based on the knowledge state of the knowledge concept at time step t include: by and the quantified direct learning effect v t As input, the concept c is obtained according to the following formula i The knowledge state at time step t in, Represents the GRU gate function; In the constructed learning transfer graph, given a PTPR edge c i →c j , where c i For the front-wheel drive concept, c j c i The successor concept of , then the concept c is obtained according to the following formula i To concept c j Positive migration prerequisite effect in, Represents a successor function that returns concept c i All PTPR successor concepts, and Both represent learnable parameters; The concept c is obtained according to the following formula i To concept c j Positive transfer similarity effect The concept c is obtained according to the following formula i The PTSR neighbor pair concept c i Positive transfer similarity effect in, Indicates the return concept c i Neighbor function of all PTSR neighbors of .

4. The method for constructing a knowledge tracking model based on positive and negative learning transfer according to claim 3, characterized in that: The direct learning effect is modeled based on the influence of the direct learning effect v t Change the knowledge status of knowledge concepts from Evolved to The step of obtaining a positive transfer prerequisite effect, a positive transfer similarity effect, a negative transfer prerequisite effect, and a negative transfer similarity effect from one knowledge concept to another based on the knowledge state of the knowledge concept at time step t also includes: Given a NTPR edge c i →c j , where c i For the front-wheel drive concept, c j c i The successor concept of , the concept c is calculated according to the following formula i To concept c j Negative transfer prerequisite effect in, Represents a successor function that returns concept c i All NTPR successor concepts, and Both represent learnable parameters; The concept c is calculated according to the following formula i To concept c j Negative transfer similarity effect The concept c is calculated according to the following formula j Towards concept c i Negative transfer similarity effect of transfer Among them, the function Represents the retrieval concept c i The neighbor function of all NTSR neighbor concepts, and represents the learnable parameters, Represents a join operation.

5. The method for constructing a knowledge tracking model based on positive and negative learning transfer according to claim 4, characterized in that: The positive transfer effect and negative transfer effect of the summarized knowledge concepts are obtained to obtain the aggregated result of the positive transfer effect. and the aggregated results of negative transfer effects And fuse the aggregation results to get the fusion results The steps include: The aggregation results of the positive migration effect were calculated according to the following formula The aggregation results of negative migration effect were calculated according to the following formula Among them, α represents a hyperparameter; Fusion is performed according to the following formula: in, and Represent the learnable weight matrix and bias respectively, and β represents a learnable parameter used to calculate each student’s and , MLP(·) represents the multi-layer perception function, and tanh(·) represents the tanh activation function.

6. The method for constructing a knowledge tracking model based on positive and negative learning transfer according to claim 5, characterized in that: According to the fusion results The knowledge state of the student at time step t based on the transfer effect perception is expressed as And according to the knowledge state under the transfer effect Predict the student's correct answer to knowledge concept c at the subsequent time step t+1 m Probability The steps include: The knowledge state under the transfer effect is obtained according to the following formula in, represents the target student’s knowledge state at time step t-1, The probability is calculated according to the following formula in, represents the learnable weight matrix, represents the learnable bias, and σ(·) represents the Sigmoid activation function.

7. The method for constructing a knowledge tracking model based on positive and negative learning transfer according to claim 6, characterized in that: According to the probability The steps of constructing the objective function of the LTKT model and minimizing the objective function to obtain the trained LTKT model include: The objective function is constructed according to the following formula: in, Represents the prediction result at each time step t The actual answer result I t The standard cross entropy loss between t =1 means the answer is correct, I t =0 means the answer is incorrect.

8. A system for constructing a knowledge tracking model based on positive and negative learning transfer, characterized in that: The system comprises: The transfer graph construction module is used to construct a learning transfer graph LTG(V,E) of a given course based on the historical interactions of students participating in the course, where V = {v1,v2,...,v n ,...,v N } represents N vertices in the graph, each vertex v i ∈V corresponds to a knowledge concept c i ∈C,E={e1,e2,...,e n ,...,e N } represents the set of edges in the graph, and the type of each edge is one of the type set {PTPR, PTSR, NTPR, NTSR}; Vector conversion module, used to convert learning interactions into a one-hot vector And according to the one-hot vector Obtaining quantitative impact of direct learning effects t ; Transfer effect acquisition module, used to model direct learning effects based on the influence of direct learning effects v t Change the knowledge status of knowledge concepts from Evolved to And based on the knowledge state of the knowledge concept at time step t, the positive transfer prerequisite effect, positive transfer similarity effect, negative transfer prerequisite effect, and negative transfer similarity effect from one knowledge concept to another are obtained; The fusion module is used to summarize the positive transfer effect and negative transfer effect of knowledge concepts and obtain the aggregated result of the positive transfer effect. and the aggregated results of negative transfer effects And fuse the aggregation results to get the fusion results Model training module, used to train The knowledge state of the student at time step t based on the transfer effect perception is expressed as And according to the knowledge state under the transfer effect Predict the student's correct answer to knowledge concept c at the subsequent time step t+1 m Probability According to probability Construct the objective function of the LTKT model and minimize the objective function to obtain the trained LTKT model.

9. A storage medium, characterized in that: The storage medium stores one or more programs, which, when executed by a processor, implement the method for constructing a knowledge tracking model based on positive and negative learning transfer as described in any one of claims 1 to 7.

10. An electronic device comprising a memory and a processor, wherein: The memory is used to store computer programs; When the processor is used to execute the computer program stored in the memory, it implements the method for constructing a knowledge tracking model based on positive and negative learning transfer as described in any one of claims 1 to 7.

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