Knowledge tracking model construction system and method based on positive and negative learning migration

Abstract

The invention provides a system and a method for constructing a knowledge tracking model based on positive and negative learning migration. The method comprises the following steps: constructing a learning migration graph; modeling the direct learning effect, and obtaining a migration effect from the knowledge concept to the knowledge concept based on the knowledge state of the knowledge concept at the time step t; summarizing the positive migration effect and the negative migration effect of the knowledge concept, and fusing the aggregation results to obtain a fusion result; and obtaining a knowledge state under migration effect perception according to a fusion result, predicting a probability that the students correctly answer knowledge concepts in a subsequent time step t + 1 according to the knowledge state under the migration effect, constructing an objective function about an LTKT model according to the probability, and minimizing the objective function to obtain a trained LTKT model. According to the invention, reasonability of updating knowledge states of all concepts of students based on the learning migration graph can be ensured, so that the performance of the knowledge tracking model is improved.

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] In the past few years, with the application of artificial intelligence (AI) technology, the educational practice of intelligent tutoring systems has been significantly improved. For example, mainstream massive online open course (MOOC) platforms, such as edX.org, Coursera.org, aixuexi.com, etc., use AI technology to predict students' knowledge status and provide students with personalized learning materials, which successfully improves students' learning ability. Therefore, many AI-based knowledge tracing (KT) models have been proposed in some top conferences or journals recently. These models can predict and track students' knowledge status using their learning logs to enhance the personalization function of MOOC platforms. In general, the KT task includes two main parts: 1) estimating students' knowledge status through their interaction logs; 2) predicting the probability that students will correctly answer a new exercise in the next time step.

[0003] There are two main categories of existing knowledge tracing models: traditional models and models based on deep learning technology. In the past few years, due to the many advantages of deep learning, many researchers have devoted themselves to designing knowledge tracing models based on deep learning technology and have achieved better results in student performance prediction than traditional methods. Deep knowledge tracing, dynamic key-value memory networks for knowledge tracing, and convolutional knowledge tracing are representative deep knowledge tracing models proposed earlier. However, these models do not consider the learning transfer between two concepts and can only produce less accurate prediction results.

[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, is proposed, which 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 multiple learning transfer processes between knowledge concepts. Although the performance of knowledge tracing has been significantly improved by considering the impact of learning transfer, existing studies have 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 the students participating in the course, where V = {v1,v2,...,v n ,...,v N} represents the 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 Get quantified impact of direct learning effectv t ;

[0009] Modeling the direct learning effect based on the impact 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;

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

[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, according to the above-mentioned method of constructing a knowledge tracking model based on positive and negative learning transfer, a new knowledge tracking framework is introduced, namely the knowledge tracking model based on positive and negative learning transfer (LTKT model). 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 Get quantified impact of direct learning effectv t The steps include:

[0014] For a learning interaction Indicates that the student has a good understanding of the 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 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 the time step t include:

[0020] by and the direct learning effect v was quantified 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 All 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 for all PTSR neighbors of .

[0031] Furthermore, 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 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 the 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 , then 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 All 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

[0038]

[0039] Among them, the function Represents the search 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 aggregate result of negative migration effect And fuse the aggregation results to get the fusion result The steps include:

[0041] The aggregation result of the positive migration effect was calculated according to the following formula

[0042]

[0043] The aggregation result of negative migration effect was calculated according to the following formula

[0044]

[0045] Among them, α represents a hyperparameter;

[0046] The fusion is performed according to the following formula:

[0047]

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

[0049] Further, 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 the students participating in the course, where V = {v1,v2,...,v n ,...,v N} represents the 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 Get quantified impact of direct learning effectv t ;

[0063] Transfer effect acquisition module, used to model direct learning effect, based on the influence of 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;

[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 aggregate result of negative migration effect And fuse the aggregation results to get the fusion result

[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, the 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, the above-mentioned method for constructing the knowledge tracking model based on positive and negative learning transfer is implemented. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a schematic diagram of the structure of a learning transfer graph exemplified in one 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 It 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 A schematic diagram of the distribution of the lengths of student interaction sequences in various data sets exemplified in an embodiment of the present invention;

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

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

[0076] Figure 7 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 implementation manner 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 in the present invention, all other embodiments obtained by ordinary technicians in this field without 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 usual meanings understood by people with general 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 the mathematics course (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 Then, the positive and negative transfer relations can be further identified as prerequisite relations (represented as directed edges) or similarity relations (represented as undirected edges). When a concept is connected to another concept through a prerequisite relation, it means that the former is regarded as the basis of the latter; two concepts connected by a similarity relation 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 Figure 1As shown in Figure 2, after s completed the first exercise related to concept C, his / her knowledge status on concept C was improved, and the updated knowledge status values ​​of all concepts were 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 states of all neighboring concepts of that concept in the learning transfer graph are also 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] In response to the above two challenges, the present invention proposes a knowledge tracking model based on deep learning, namely, a knowledge tracking model based on positive and negative learning transfer (LTKT), which simultaneously utilizes positive and negative learning transfer relationships between teaching concepts to optimize the performance of knowledge tracking. To solve the first challenge, LTKT proposes a statistical method that constructs a learning transfer graph containing multiple types of learning transfer relationships for a specific course based on students' historical interaction data. The solution to the second challenge is to fully consider the direct learning effect (DLE) and the 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 by the exercise. Subsequently, the impact of the student's exercise results on the knowledge status of other neighbor concepts is considered, which is caused by positive and negative learning transfer effects. The positive transfer effect and the negative transfer effect are modeled using the proven influence propagation viewpoint. In order to optimize the impact of positive and negative transfer effects on the knowledge state of the concepts learned by students, a two-stage fusion strategy is first used to aggregate these effects, in which the sensitivity value of each student to different learning transfer effects is taken into account. Finally, the above-mentioned gating function is used to update the knowledge state values ​​of all adjacent concepts in the learning transfer graph based on the aggregation results of positive and negative transfer effects.

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

[0085] Table 1 Symbols and meanings

[0086]

[0087]

[0088] In addition, it is known from the learning transfer theory that the relationship between teaching concepts can be divided into positive transfer relationships and negative transfer relationships. Recent studies have shown that positive (or negative) transfer relationships can be further determined as prerequisite relationships or similarity relationships. Therefore, in the present invention, a learning transfer graph (LTG) containing these four types of transfer relationships is first defined. 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 as follows:

[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 promotes the learning of the other.

[0091] Negative Transfer Prerequisite Relation (NTPR): Represented as a red directed edge in the LTG, this relationship can be interpreted as the predecessor concept being the basis for the successor concept, however, learning the former interferes 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: construct 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) for 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 considered 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 who 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 the concept c j Through observation and analysis, it is found that the interaction events in the 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 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 Similarly, 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 the 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 by x t =(ex t ,a t ), a t ∈{1,0} means practicing ex at time step t t The binary correctness of 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, and on this basis, the DLE component updates the target student's knowledge state according to the direct learning effect. 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 two learning transfer effects, namely negative transfer effect and positive transfer effect, and then adopts a two-stage fusion strategy to fuse these two effects. The fused result is passed through a gating function To further update the target student's knowledge state according to 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: converting the learning interaction into a one-hot vector, and obtaining the quantitative impact of the direct learning effect according to 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 the knowledge status of the concept. Figure 2 As shown in the lower left part of Indicates that the student has a good understanding of the concept c at time step t i Exercises t The result given is a t ∈{1,0}, the DLE component can be used to apply the training results to 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] Quantification 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 knowledge concept to knowledge concept 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, It means that the student considers the learning interaction at time step t Then, and the direct learning effect v was quantified 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 the negative transfer effect (NTE), and based on the learning transfer effect between concepts, the rationality of students' knowledge state update for each concept is ensured.

[0111] In addition, the positive transfer prerequisite effect is caused by the positive transfer prerequisite relation (PTPR). The PTPR is represented as a green directed edge in the 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 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 are learnable parameters.

[0115] In addition, for the positive transfer similarity effect, the positive transfer similarity relationship (PTSR) between vertices in LTG induces the 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 particular concept will in turn promote the proficiency of its PTSR neighbor concepts, and vice versa, resulting in the proficiency of neighboring 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 achieves 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 formula 5:

[0118]

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

[0120] The second is c i The 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 for 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 relationship (NTPR) in the LTG. In the LTG, the NTPR is represented as a red directed edge to indicate that students' 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 adopts 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 will be transferred to c along the directed NTPR edge i The successor of 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 are learnable parameters.

[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 what students learn in a certain concept will interfere with the learning of another concept in the NTSR relation, 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 of 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 knowledge state 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 NTSR neighbors, resulting in adjacent concepts having similar proficiency. i There are two types of negative transfer similarity effects between them and their 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 search 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 is expressed as Indicates that 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 LTG.

[0132] Step S104: Summarize 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 fuse the aggregated results to obtain fused results;

[0133] It should be noted that this step first converts the negative transfer effect (NTE) module 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 a 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 the fusion of two stages: (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 result of negative transfer prerequisite effect and negative transfer similarity effect at time step t is expressed as express. and Calculated by formulas 10 and 11 respectively:

[0135]

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

[0137] (2) Phase 2: and Since different students have different knowledge states at time step t-1, the intuition is that students’ sensitivity to positive and negative transfer effects may vary due to their different knowledge states. Therefore, the LTEI module uses a multilayer perceptron (MLP) to learn the sensitivity value β of each student at each time step, which will be used to determine the weight ratio of positive or negative transfer effects 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 and Since positive migration effect and negative migration effect are two opposite effects, in calculating 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 result, 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 the 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 knowledge state of the target student at time step t-1. From formula 15, we can see that Not only does it consider the concept 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’s updated knowledge state (i.e. ) to predict the student’s correct answer about 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 result at each time step t during the training phase is 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 means the answer is incorrect. The objective function is minimized in the mini-batch. For further details on the training, see Table 2 below:

[0150] Table 2

[0151]

[0152]

[0153] In summary, according to the above-mentioned method of constructing a knowledge tracking model based on positive and negative learning transfer, a new knowledge tracking framework is introduced, namely the knowledge tracking model based on positive and negative learning transfer (LTKT model). 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 the student interaction sequences in each dataset is shown in 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 the interaction records of learners in 2015. ASSIST15 is a "Skill Builder" dataset, that is, 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 more exercises are required after mastering it. 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, namely "Skill Builder data 2009-2010" and "Non-Skill Builder data 2009-2010". The latter dataset is used in the experiment of this embodiment. In the experiment, only the first teaching concept examined is used to mark the exercises. In addition, this embodiment deletes all records whose correctness labels are not equal to 1 or 0.

[0157] Table 3 below summarizes the statistical characteristics of the above datasets. The value of the "proportion of NTPR relations" in Table 3 is obtained by the formula #of NTPR / N×(N-1), and the value of the "proportion of NTSR relations" is calculated by the formula #of NTSR / N×(N-1). Among them, 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 (i.e., NTPR and NTSR) in the ASSIST15 dataset is higher than that in the ASSIST09 dataset.

[0158] Table 3

[0159]

[0160]

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

[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 The occurrence frequency of . 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 ​​for i≤N in the matrix are set to 0. For i≠j, the value of N[i][j] is the sum of the two statistical values, that is, the event Frequency and events frequency of occurrence. Figure 5 and Figure 6 The distribution of interaction events in the above table 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 concept, 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 A symmetric matrix is ​​constructed to record the probability of PTSR between each pair of concepts. To calculate PS, Formula 20 is used to calculate the frequency of concurrent occurrence between two concepts. and When occurs frequently and 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 Formula 21. Obviously, PS[i][j]∈[0,1] is the probability that there is a bidirectional 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 Set it as the average value of PS, as shown in Formula 22:

[0166]

[0167] In order to determine the NTPR between vertices in LTG, an asymmetric matrix is ​​used, which 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 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 techniques are used to convert each The values ​​are normalized to the range [0,1], thus obtaining NS[i][j]∈NS, as shown in Formula 26. Thus, 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 is evaluated by comparing it with a set of baseline models. Specifically, four deep learning-based models that do not consider learning transfer are 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 are 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 below:

[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, and 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 the 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 Get quantified impact of direct learning effectv 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 to obtain the aggregated result of the positive transfer effect and the aggregate result of negative migration effect And fuse the aggregation results to get the fusion result

[0181] Model training module 50 is 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.

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

[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, so as to implement the above-mentioned method for constructing a knowledge tracking model based on positive and negative learning transfer.

[0184] Although the embodiments of the present invention are described in detail above, it is obvious to those skilled in the art that various modifications and variations can be made to these embodiments. However, it should be understood that such modifications and variations are within the scope and spirit of the present invention as described in the claims. Moreover, the present invention described herein may have other embodiments and may be implemented or realized 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 the students participating in the course, where V = {v1,v2,...,v n ,...,v N } represents the 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 Get quantified impact of direct learning effectv t ; Modeling the direct learning effect based on the impact 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; Summarize the positive and negative transfer effects of knowledge concepts to obtain the aggregated results of the positive transfer effect and the aggregate result of negative migration effect And fuse the aggregation results to get the fusion result 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 Get quantified impact of direct learning effectv t The steps include: For a learning interaction Indicates that the student has a good understanding of the 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 the time step t include: by and the direct learning effect v was quantified 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 All 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 for all PTSR neighbors of .

4. The method for constructing a knowledge tracking model based on positive and negative learning transfer according to claim 3 is 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 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 the 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 , then 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 All 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 Among them, the function Represents the search 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 knowledge concept are summarized to obtain the aggregated result of the positive transfer effect. and the aggregate result of negative migration effect And fuse the aggregation results to get the fusion result The steps include: The aggregation result of the positive migration effect was calculated according to the following formula The aggregation result of negative migration effect was calculated according to the following formula Among them, α represents a hyperparameter; The fusion is performed according to the following formula: in, and denote the learnable weight matrix and bias respectively, and β denotes a learnable parameter used to calculate each student’s and , MLP(·) represents the multi-layer perceptron 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 the students participating in the course, where V = {v1,v2,...,v n ,...,v N } represents the 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 Get quantified impact of direct learning effectv t ; Transfer effect acquisition module, used to model direct learning effect, based on the influence of 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; 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 aggregate result of negative migration effect And fuse the aggregation results to get the fusion result 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 the 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 1-7.

Images