CN117057422B - Knowledge tracking system for global knowledge convergence sensing - Google Patents
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Abstract
The invention provides a knowledge tracking system for global knowledge convergence sensing, and belongs to the technical field of knowledge tracking; the system comprises: the system comprises a knowledge graph construction module, a knowledge perception module, a knowledge convergence module, an updating module and a prediction module. According to the knowledge tracking system for global knowledge convergence sensing, provided by the invention, the spatial positions of knowledge points in the learning process of a learner are considered when the knowledge state of the learner is tracked, and the spatial position relation between the knowledge points is mined by utilizing a self-attention mechanism, so that each knowledge point can sense other knowledge points; the invention inputs the representing characteristics and the state characteristics of all knowledge points to the model when tracking the knowledge state of the learner, combines the knowledge structure of the learner, and inputs the current examination knowledge points and the first-order neighbor knowledge point information and the higher-order neighbor knowledge point information to the model, thereby tracking the knowledge state of the learner more accurately.
Description
Technical Field
The invention relates to the technical field of knowledge tracking, in particular to a knowledge tracking system for global knowledge convergence sensing.
Background
Bayesian knowledge tracking (Bayesian Knowledge Tracing, BKT) models the learner's knowledge state by modeling the learner's knowledge level through a dynamic bayesian network, creating dynamic transitions between knowledge states. The method adopts a hidden Markov model (Hidden Markov Model, HMM) to treat the knowledge state of a learner as hidden variables, wherein the HMM has two states, namely a potential node for indicating a student to grasp a knowledge point and a binary observation node for indicating whether the student correctly solves a problem, so as to track the knowledge state of the learner in the answering process. Deep knowledge tracking (Deep Knowledge Tracing, DKT) uses a recurrent neural network (Recurrent Neural Networdk, RNN) or Long Short-Term Memory (LSTM) or gated loop unit (Gate Recurrent Unit, GRU) to track the knowledge state of students, generating a hidden state vector representing the learner's knowledge state, RNN is typically used to process problem performance predictions for single knowledge points, LSTM and GRU are typically used for problem performance predictions for multiple knowledge points, so that DKT implicitly models complex knowledge point relationships. Dynamic Key Value Memory Network (DKVMN) allows network to keep multiple hidden state vectors and read and write respectively, uses a Key matrix to store concepts, uses a value matrix to store the grasping state of students to concepts, and can accurately indicate specific knowledge state of students on each concept through the two matrix DKVMN models. The Graph-based knowledge tracking model (Graph-based Knowledge Tracing, GKT) applies a Graph neural network, the knowledge points and knowledge point dependency relationships are respectively represented as nodes and continuous edges of the Graph, and the mutual influence among the knowledge points is modeled through the topological relationship of the knowledge points. Although the four models achieve good results in predicting future answering situations of students, indirect interaction of knowledge points is not explicitly modeled, and only local knowledge state changes are considered by the models.
The most similar prior art implementation to the present invention is Graph-based Knowledge Tracing (GKT). The model builds a graph of knowledge point relation, explicitly learns knowledge point states, and reconstructs knowledge tracking tasks into time sequence node classification problems in the graph neural network, so that prediction accuracy can be improved without any additional information.
Classical knowledge tracking models, such as bayesian knowledge tracking (Bayesian Knowledge Tracing), deep knowledge tracking (Deep Knowledge Tracing) Dynamic Key-Value Memory Networks for Knowledge Tracing and Graph-based knowledge tracking (Graph-based Knowledge Tracing), track the knowledge state of students with problem interaction data, which do not take into account the indirect interactions of knowledge points through knowledge point relationships. Specifically, BKT does not model knowledge point relationships and thus ignores the interaction of knowledge points; DKT implicitly models knowledge point relationships through a single knowledge state vector but ignores the connections between indirectly related knowledge points; the DKVMN models the correlation of local knowledge points by calculating the examination weight of the knowledge points in the current problem, but ignores the correlation of all knowledge points; the GKT takes the first-order neighbor knowledge points of the current problem examination knowledge points as influence objects, and neglects the influence of the high-order neighbor knowledge points on the current problem examination knowledge points. The model can be enabled to contain more abundant information by inputting all knowledge point characteristics into the model, so that the phenomenon of 'in general' low generalization of the model is avoided.
Disclosure of Invention
The invention provides a knowledge tracking system for global knowledge convergence sensing, which is used for solving the defects in the prior art.
The invention provides a knowledge tracking system for global knowledge convergence perception, which comprises: the system comprises a knowledge graph construction module, a knowledge perception module, a knowledge convergence module, an updating module and a prediction module;
the knowledge graph construction module is used for obtaining a knowledge point representation matrixAnd knowledge point relation matrixThereby constructing a knowledge graph; wherein L is the total number of knowledge points, d k The embedding dimension of the knowledge points; wherein a node in the knowledge graph represents a knowledge point;
the knowledge perception module is used for acquiring a distance matrix of the knowledge points relative to the current examination knowledge points based on the knowledge graphDistance matrix E t Coding to obtain a spatial position matrix of knowledge points>Modeling knowledge point representations of knowledge point awareness to each other by self-attentional mechanisms>Modeling interactions between knowledge point representations;
the knowledge aggregation module is used for determining the order of each node, constructing a knowledge state diagram, separating nodes with different orders into different diagrams, and describing the mutual influence among knowledge point states through state migration aggregation;
the updating module is used for updating knowledge states through the knowledge propagation function and the GRU gating circulating unit and describing state updating after each knowledge point is mutually influenced;
and the prediction module is used for outputting the probability of correctly answering the problem at the next moment by the learner according to the updated result of the knowledge state.
The invention provides a knowledge tracking system for global knowledge convergence perception, which has the following beneficial effects:
the invention considers the spatial position of the knowledge points in the learning process of the learner when tracking the knowledge state of the learner; the existing model does not consider the point, and the invention uses a self-attention mechanism to mine the spatial position relation among knowledge points so that each knowledge point can sense other knowledge points.
The invention inputs the representing characteristics and the state characteristics of all knowledge points to the model when tracking the knowledge state of the learner, and the existing model mostly only considers the representing characteristics and the state characteristics of the current examined knowledge points and the related knowledge points, ignores a large amount of knowledge point information and cannot accurately track the knowledge state of the learner. According to the invention, in combination with the knowledge structure of the learner, the current examination knowledge point and the first-order neighbor knowledge point information are input into the model, and the higher-order neighbor knowledge point information is also input, so that the knowledge state of the learner is tracked more accurately.
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In order to more clearly illustrate the invention or the technical solutions of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a knowledge tracking system for global knowledge convergence awareness provided by the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that in the description of embodiments of the present invention, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
FIG. 1 is a schematic structural diagram of a knowledge tracking system for global knowledge convergence sensing, that is, a structure diagram of a knowledge tracking model for global knowledge sensing, provided by the present invention, as shown in FIG. 1, the system includes: the system comprises a knowledge graph construction module, a knowledge perception module, a knowledge convergence module, an updating module and a prediction module;
the knowledge graph construction module is used for obtaining a knowledge point representation matrixAnd knowledge point relation matrixThereby constructing a knowledge graph; wherein L is the total number of knowledge points, d k The embedding dimension of the knowledge points; wherein a node in the knowledge graph represents a knowledge point;
the knowledge perception module is used for acquiring a distance matrix of the knowledge points relative to the current examination knowledge points based on the knowledge graphDistance matrix E t Coding to obtain a spatial position matrix of knowledge points>Modeling knowledge point representations of knowledge point awareness to each other by self-attentional mechanisms>Modeling interactions between knowledge point representations;
the knowledge aggregation module is used for determining the order of each node, constructing a knowledge state diagram, separating nodes with different orders into different diagrams, and describing the mutual influence among knowledge point states through state migration aggregation;
the updating module is used for updating knowledge states through the knowledge propagation function and the GRU gating circulating unit and describing state updating after each knowledge point is mutually influenced;
and the prediction module is used for outputting the probability of correctly answering the problem at the next moment by the learner according to the updated result of the knowledge state.
The above modules are described in one-to-one manner.
(1) Knowledge graph construction module
The knowledge graph construction module is used for acquiring a knowledge point representation matrix and a knowledge point relation matrix so as to construct a knowledge graph.
First, knowledge points are embedded and expressed to obtain a knowledge point expression matrixWherein L is the total number of knowledge points, d k Is the embedding dimension of the knowledge points. Then, obtaining knowledge point sequence relation from the learner answer sequence, and obtaining knowledge point relation matrix by statistics>Finally, K is represented according to knowledge points c And knowledge point relation E t Constructing a knowledge graph
Specifically, first, a knowledge point representation matrix K is obtained c . Setting a learning embedded matrix A and setting a knowledge point c i Is represented by (c) i ) Mapped as a distributed real value vector k i ：
k i ＝O(c i )·A T ，
Wherein,d k is the embedding dimension. Similarly, an embedded representation vector for each knowledge point can be obtained: k (k) 1 ；...；k i ；...；k L And splicing the knowledge points to obtain a knowledge point representation matrix:
K c ＝[k 1 ；...；k i ；...；k L ]，
wherein, [ -; carrying out]The vector is represented as a concatenation of vectors into a matrix,
then, obtaining a knowledge point relation matrix E t . Acquiring the sequence relation of the knowledge points from the learner response sequence, and when the learner responds to the examination knowledge point c i After the problem of (2), the next moment answers the examination knowledge point c j Is regarded as the knowledge point c i 、c j There is a precedence relationship and is directed, i.e. c i →c j . If knowledge point c i And c j C is the more times of the sequential examination i 、c j The closer the order relation of (2) is, the matrix E is obtained by statistical probability t ：
Wherein,in the answer to the history problem, n i,j Indicating the learner's answer to the knowledge point c i After the problem of (2), then answer the examination knowledge point c j The number of exercises of Sigma k n i,k Representing the examination knowledge point c i Then the sum of the number of times of examination of other knowledge points is made.
Finally, constructing a knowledge graphthe knowledge graph of the learner at time t is +.>C＝{c 1 ,c 2 ,...,c L A set of nodes, each node representing a knowledge point; e= { (c) i ,c j )|c i ,c j E, C is the set of continuous edges at the current moment, (C) i ,c j ) Representing knowledge point c i And c j A relationship exists; k (K) c Representing a matrix for the knowledge points; e (E) t Is knowledge point relation matrix and also serves as adjacent matrix of current time graph, E t (i, j) is node c i And c j Weight of the connecting edge between E t (i, j) > 0, then c i And c j There is a border between them.
(2) Knowledge sensing module
The knowledge awareness module is used to model interactions, including direct and indirect, between knowledge point representations. Firstly, obtaining a distance matrix of knowledge points relative to the current examination knowledge pointsThen, the distance matrix is encoded to obtain a spatial position matrix of knowledge points +.>Finally, knowledge point representations of knowledge point mutual perceptions are modeled by self-attentive mechanisms +.>Thereby modeling interactions between knowledge point representations.
The method comprises the following steps:
firstly, obtaining a distance matrix E' of a knowledge point relative to a current examination knowledge point t Adjoining knowledge graph to matrix E t Conversion to a distance matrix E' t A negative logarithmic conversion method is used:
E′ t ＝-dln(E t )，
wherein,d is a scale factor. Distance value E' t The smaller (i, j), the c i And c j The closer the spatial locations in the knowledge graph, the closer their relationship. Distance matrix E' t Only the distance between each node and its first-order neighbor node is included to obtain the distance between each node and node c i Distance matrix E ' is calculated using Dijkstra's algorithm ' t Converted into a distance matrix E t ：
E″ t (i,j)＝d(c i ,c j ),1≤j≤L，
Wherein,d(c i ,c j ) For node c i And node c j Is a minimum distance of (2).
Each node is then associated with node c i The sine and cosine functions can capture and distinguish the space position information of the nodes, and the sine and cosine functions with different frequencies are used for connecting a certain node c j And node c i Is encoded to obtain node c j Spatial position encoding p of (2) j ：
Wherein,2i represents p j 2i+1 represents p j Is a bit of the odd number of (b). The spatial position coding of each node can be obtained by the same method: p is p 1 ,...,p j ,...,p L . Splicing them to obtain the spatial position coding matrix PE of the current moment t ：
PE t ＝[p 1 ；...；p j ；...；p L ]，
Wherein,the j-th row in (a) is node c j Spatial position encoding of (a) is provided.
Finally, the spatial position codes of the nodes are fused into knowledge point representation, and knowledge point representation of the perceived spatial position is obtained through a self-attention mechanismThereby modeling knowledge points and current knowledge point c of different spatial positions i Is a different degree of interaction:
wherein W is q Is a learnable query matrix, W k Is a learnable key matrix, W v Is a matrix of values that can be learned,
(3) Knowledge gathering module
The knowledge convergence module is used for modeling interaction between knowledge point states, including direct influence and indirect influence. First determining the order of each node, then constructing a knowledgeStatus diagramAnd separating the nodes of different orders into different graphs, and finally, depicting the mutual influence among knowledge point states through state migration aggregation.
The method comprises the following steps:
first, a certain node c in the knowledge graph is determined j The order s of each node is obtained by Dijkstra algorithm (shortest path algorithm) j ：
s j ＝d(c j ,c i )，
Wherein d (c) i ,c j ) Is through a matrix sgn (E t ) The shortest path length thus obtained, sgn is obtained by multiplying E t A step function with a value mapping of 0 or 1.
The order of each node in the knowledge graph is similarly available: s is(s) 1 ,s 2 ,...,s L 。
Then constructing a knowledge state diagram, and defining the knowledge state diagram at the current moment:n is the knowledge graph of the current moment->Maximum value of the node orders:
N＝max(s 1 ,s 2 ,...,s L )。
for knowledge state diagramSubgraph of (a)>G n,t ＝(C n,t ,E n,t ,H n,t ,E n,t )，C n,t ＝{c j |c j ∈C,s j Not less than n is c i N-order neighbor node and higher-order neighbor node set, E n,t ＝{(c i ,c j )|c i ,c j ∈C n,t The } is a set of edges, +.>For the knowledge point state representation corresponding to each node, F is the dimension of the knowledge point state, E n,t ＝E t Is the adjacency matrix of the figure.
And finally, migrating the aggregated knowledge state. G N,t To G 0,t The state information in the method is converged from a high level to a low level, and the migration aggregation process comprises the following steps: step 1: graph G of the time to be immediately before 0,t-1 State information H of (2) 0,t-1 Graph G migrating to the current time n,t The method comprises the steps of carrying out a first treatment on the surface of the Step 2: map G n+1,t The state information of the transition to the next-level graph G n,t The method comprises the steps of carrying out a first treatment on the surface of the Step 3: in graph G n,t In the method, state information of the (n+1) -th order node and the (n) -th order node is aggregated to the (n) -th order; step 4: repeating the steps 1, 2 and 3 from G N,t Converging to G 0 So that at the current time t, all node state information is aggregated to c i . Step 5: and aggregating the answer results of the knowledge points of the examination of the problems at the current moment.
The steps 1 to 5 are further described below.
Step 1: will know the state diagram of the previous momentGraph G in (a) 0,t-1 The state information of (1) is migrated to the nth order graph G at the current moment n,t ，
Step 2: the previous first-order graph G at the current time n+1,t Migration of state features of intermediate nodes to graph G n,t In (a):
H n,t ＝H 0,t-1 ，
H n,t ＝H n+1,t 。
step 3: recording node c j In graph G n,t In (a) is in the state ofThe node state of the n+1-th implies its higher orderNode states, aggregating the node states of the n+1th to the nth order nodes, which exist in the graph G n+1,t But not in the graph G n,t In which their set is S:
&representing and (i.e., sum), the state information of the different nodes in the set S is aggregated to the current node c i To a different extent, each node is assigned an attention coefficient through a single layer feedforward neural network to represent a different degree of aggregation:
wherein, [ ·, ]]Representing stitching of vectors into a longer vector, alpha ij For node c j Is used for the concentration factor of (a),is a learnable weight vector +.>Is a weight matrix which can be learned, +.>Is the status of the aggregated knowledge points. The n+1th order node state is aggregated to the n order node state by using multi-head attention, and an average aggregation mode with low calculation cost and low overfitting risk is adopted in consideration of the calculation efficiency and generalization capability of the model:
wherein M is the number of heads of multi-head attention, W m For the weight matrix of the mth head,
step 4: and the like, repeating the steps 1, 2 and 3 from G N Converging to G 0 Finally, the node c is caused to i The state information contains all node state information.
Step 5: knowledge point representation embedded in perceived spatial locationResult r of answer t As input for knowledge state update:
wherein r is t ∈{0,1} L For the answer result of the current problem,for the state after the result of the polymerization as input for the update +.>
(4) Update module
The updating module is used for updating the knowledge state of the learner. Propagating the function f through knowledge tran 、f self Updating knowledge state with GRU gate control circulation unit to describe state update after each knowledge point is mutually influenced, wherein f tran Is the knowledge point c i Information direction c j A propagated function, f self Is the information to the self knowledge point c i A propagated function.
The method comprises the following steps:
through f tran 、f self Self-update or propagation update of function modeling knowledge point state:
wherein f 1 、f 2 、f 3 Is MLP. Update node c j ∈C 0,t The state at time t+1 is:
wherein,is a gated loop unit.
S50: and a prediction module.
The prediction module is used for predicting response performance of the learner at the next moment.
The method comprises the following steps:
outputting the probability of the learner correctly answering the problem at the next moment according to the updated result of the knowledge state:
wherein,is the probability of correctly answering the problem, f out Is MLP, W out Is a weight matrix, b out Is offset. Through the method, the t+1 moment examination knowledge point c can be obtained j Predictive probability of correct answers to questions of (a).
Based on the knowledge tracking system (model) of global knowledge convergence perception provided by the invention, the results of the performed experiments are shown in table 1. Table 1 shows AUC values of different models under different data sets, wherein AUC is an area surrounded by a working characteristic curve of a subject and a coordinate axis, the index is generally used for representing a prediction effect of the model, and the higher the AUC value is, the better the prediction performance of the model is.
Wherein DKT (Deep Knowledge Tracing) is a first depth knowledge tracking model, DKVMN (Dynamic key-value memory networks for knowledge tracing) is a knowledge tracking model of Dynamic key values versus memory network, GKT (Graph-based knowledge tracing: modeling student proficiency using Graph neural network) is a knowledge tracking model based on graphs, and GKAP-KT is a model provided by the invention.
Table 1 comparison of AUC of different models
In summary, the knowledge tracking system for global knowledge convergence sensing provided by the invention has the following beneficial effects:
(1) The invention considers the spatial position of the knowledge points in the learning process of the learner when tracking the knowledge state of the learner. The existing model does not consider the point, and the invention uses a self-attention mechanism to mine the spatial position relation among knowledge points so that each knowledge point can sense other knowledge points.
(2) The invention inputs the representing characteristics and the state characteristics of all knowledge points to the model when tracking the knowledge state of the learner, and the existing model mostly only considers the representing characteristics and the state characteristics of the current examined knowledge points and the related knowledge points, ignores a large amount of knowledge point information and cannot accurately track the knowledge state of the learner. According to the invention, in combination with the knowledge structure of the learner, the current examination knowledge point and the first-order neighbor knowledge point information are input into the model, and the higher-order neighbor knowledge point information is also input, so that the knowledge state of the learner is tracked more accurately.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (2)
1. A knowledge tracking system for global knowledge convergence awareness, comprising: the system comprises a knowledge graph construction module, a knowledge perception module, a knowledge convergence module, an updating module and a prediction module;
the knowledge graph construction module is used for obtaining a knowledge point representation matrixAnd knowledge point relation matrixThereby constructing a knowledge graph; wherein L is the total number of knowledge points, d k The embedding dimension of the knowledge points; wherein a node in the knowledge graph represents a knowledge point;
the knowledge graph construction module is specifically used for:
setting a learning embedded matrix A and setting a knowledge point c i Is represented by (c) i ) Mapped as a distributed real value vector k i Distributed real value vector k i Stitching to generate a knowledge representation matrix K c ；
Establishing a knowledge point relation matrix based on the acquired knowledge point first-and-later relation;
establishing a knowledge graph based on the knowledge point relation matrix; expressed as:
wherein c= { C 1 ,c 2 ,...,c L A set of nodes, each node representing a knowledge point; e= { (c) i ,c j )|c i ,c j E, C is the set of continuous edges at the current moment, (C) j ,c j ) Representing knowledge point c j And knowledge point c j A relationship exists; k (K) c Representing a matrix for the knowledge points; e (E) t Is knowledge point relation matrix, also serves as knowledge graph adjacent matrix at current moment, E t (i, j) is node c i And node c j Weighting of the connecting edges;
the knowledge point relation matrix is established based on the acquired knowledge point first-and-later relation, and the specific formula is as follows:
wherein E is t For knowledge point relation matrix, n i,j Indicating the learner's answer to the knowledge point c i After the problem of (2), then answer the examination knowledge point c j The number of exercises of Sigma k n i,k Representing the examination knowledge point c i Then the sum of the times of examination of other knowledge points is made;
the knowledge perception module is used for acquiring a distance matrix of the knowledge points relative to the current examination knowledge points based on the knowledge graphDistance matrix E t Coding to obtain a spatial position matrix of knowledge points>Modeling knowledge point representations of knowledge point awareness to each other by self-attentional mechanisms>Modeling interactions between knowledge point representationsSounding;
the knowledge perception module is specifically used for:
adjoining knowledge graph matrix E by negative logarithmic transformation method t Conversion to a distance matrix E' t And then the distance matrix E 'is obtained by utilizing the shortest path algorithm' t Converted into a distance matrix E t ；
Splicing the spatial position codes of each node into a spatial position code matrix PE at the current moment t ：PE t ＝[p 1 ；...；p j ；...；p L ]Wherein, the method comprises the steps of, wherein,the j-th row in (a) is node c j Spatial position encoding of (a); and, in addition, the method comprises the steps of,
wherein,2i represents p j 2i+1 represents p j Odd bits of (2);
fusing the spatial position codes of the nodes into knowledge point representations, and obtaining knowledge point representations of perceived spatial positions through a self-attention mechanismThe method comprises the following steps:
wherein W is q Is a learnable query matrix, W k Is a cocoaLearning key matrix, W v Is a matrix of values that can be learned,
the knowledge aggregation module is used for determining the order of each node, constructing a knowledge state diagram, separating nodes with different orders into different diagrams, and describing the mutual influence among knowledge point states through state migration aggregation;
the knowledge gathering module is specifically configured to:
the method comprises the steps of obtaining the order of each node in a knowledge graph: s is(s) 1 ,...s j ,...,s L The method comprises the steps of carrying out a first treatment on the surface of the Wherein s is j ＝d(c j ,c i ) And d (c) i ,c j ) Is through a matrix sgn (E t ) The shortest path length thus obtained, sgn is a step function in which the value in Et is mapped to 0 or 1;
constructing a knowledge state diagram at the current moment:n is the knowledge graph of the current moment->Maximum value in intermediate node order:
for knowledge state diagramSubgraph G of (1) n,t ＝(C n,t ,E n,t ,H n,t ,E n,t ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein C is n,t ＝{c j |c j ∈C,s j Not less than n is c i N-order neighbor node and higher-order neighbor node set, E n,t ＝{(c i ,c j )|c i ,c j ∈C n,t And is the set of edges,for each node corresponding knowledge point state representation, F is the dimension of the knowledge point state，E n,t ＝E t ；
Will G N,t To G 0,t The state information in the knowledge point state is converged from a high level to a low level to describe the mutual influence between the knowledge point states through state migration aggregation;
wherein G is to N,t To G 0,t The state information in (1) is converged from a high order to a low order, and specifically comprises:
step 1: will know the state diagram of the previous momentGraph G of (2) 0,t-1 The state information of (1) is migrated to the nth order graph G at the current moment n,t ；
Step 2: first-order graph G at current time n+1,t Migration of state features of intermediate nodes to graph G n,t In (a):
H n,t ＝H 0,t-1 ，H n,t ＝H n+1,t ；
step 3: recording node c j In graph G n,t In (a) is in the state ofAggregating node states of the n+1th to nth order nodes to be present in graph G n+1,t But not in the graph G n,t As set S:
the state information of different nodes in the set S is aggregated to the current node c i To a different extent, each node is assigned an attention coefficient through a single layer feedforward neural network to represent a different degree of aggregation:
wherein, [ ·, ]]Representing stitching vectors into a longer directionAmount, alpha ij For node c j Is used for the concentration factor of (a),is a learnable weight vector +.>Is a weight matrix which can be learned; />The knowledge point state after aggregation;
aggregation of the n+1th order node states to the nth order node states using multi-headed attention, average aggregation approach:
wherein M is the number of heads of multi-head attention, W m For the weight matrix of the mth head,
step 4: and so on, from G N Converging to G 0 Finally, the node c is caused to i The state information comprises all node state information;
step 5: knowledge point representation embedded in perceived spatial locationResult r of answer t As input for knowledge state update:
wherein r is t ∈{0,1} L For the answer result of the current problem,for the state after the result of the polymerization as input for the update +.>
The updating module is used for updating knowledge states through the knowledge propagation function and the GRU gating circulating unit and describing state updating after each knowledge point is mutually influenced; the method comprises the following steps:
through f tran 、f self Self-update or propagation update of function modeling knowledge point state:
wherein f 1 、f 2 、f 3 Is MLP, update node c j ∈C 0,t The state at time t+1 is:
wherein,is a gated loop unit;
and the prediction module is used for outputting the probability of correctly answering the problem at the next moment by the learner according to the updated result of the knowledge state.
2. The knowledge tracking system of claim 1, wherein the outputting the probability of the learner correctly answering the problem at the next time according to the updated result of the knowledge state comprises:
wherein,is the probability of correctly answering the problem, f out Is a multi-layer sensor, W out Is a weight matrix, b out Is offset.
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