CN116976434B - Knowledge point diffusion representation-based knowledge tracking method and storage medium - Google Patents
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Abstract
The invention discloses a knowledge tracking method based on knowledge point diffusion representation, which comprises the following steps: acquisition oftA time answer sequence and a knowledge point representation graph and a knowledge point state graph; calculating weights to update the knowledge point representation graph and the knowledge point state graph, and obtaining knowledge point representation and knowledge point state representation; forward diffusion is carried out to obtain knowledge point representation and knowledge point state representation; back diffusion is carried out to obtain knowledge point representation, knowledge point state representation and knowledge point state relation; according to the back diffusion result, obtaintKnowledge point representation and knowledge point grasp state at +1 time, and obtained from knowledge point grasp statetKnowledge point state diagram at +1 moment; the state is mastered through the knowledge points, and the behavior of the learner on the problems is predicted. The knowledge points and the correlations thereof and the knowledge point states and correlations thereof are aggregated, the knowledge state of a learner is deduced, the characterization of the knowledge point relationships and the knowledge point state relationships is added in the modeling process, and the knowledge point modeling method has better effectiveness and interpretation for modeling of the knowledge state.
Description
Technical Field
The invention relates to the technical field of knowledge tracking, in particular to a knowledge tracking method based on knowledge point diffusion representation and a storage medium.
Background
In recent years, knowledge tracking models have made significant progress in modeling the knowledge state of learners and the correctness of answers to predicted problems. Deep knowledge tracking (Deep Knowledge Tracing, DKT) is a representation of this type of model, which characterizes problems with problem information, and represents knowledge state with hidden vectors. Subsequent related work improved on the basis of DKT, taking knowledge points of problem examination into account, and introducing new model structures to improve knowledge point characterization and knowledge state representation capabilities. Corresponding knowledge point characterization is obtained from the problem information, and then the knowledge state of the learner is deduced through the knowledge points. In order to further improve the modeling effect of the knowledge state, the subsequent research introduces a mapping process between knowledge points and knowledge point states on the basis of problem characterization. The methods firstly express the problem as a knowledge point, then establish the association between the knowledge point expression and the knowledge point state, and finally deduce the knowledge state.
Current knowledge-based research, while having made some progress, still presents a number of problems and challenges. Classical knowledge tracking, such as bayesian knowledge tracking (Bayesian Knowledge Tracing, BKT), deep knowledge tracking (Deep Knowledge Tracing, DKT) and Dynamic Key-Value Memory Networks for Knowledge Tracing, DKVMN), mainly characterizes the representation of knowledge points or models a single knowledge point state, and good results are obtained under certain conditions, but they ignore the relationship between knowledge point states. Although the relation among knowledge point states is considered in the follow-up part research, the knowledge point states are not fused with related information such as knowledge point representation in the modeling process, the derived knowledge state representation capacity is limited, and the prediction accuracy of the model still has room for improvement.
Disclosure of Invention
Aiming at least one defect or improvement requirement of the prior art, the invention provides a knowledge tracking method and a storage medium based on knowledge point diffusion representation, knowledge points and correlations thereof and knowledge point states and correlations thereof are cooperatively aggregated through a diffusion model, so that the knowledge state of a learner is deduced, the characterization of the knowledge point relations and the knowledge point state relations is added in the modeling process, and the knowledge tracking method and the storage medium have better effectiveness and interpretation for modeling of the knowledge state.
To achieve the above object, according to a first aspect of the present invention, there is provided a knowledge tracking method based on knowledge point spread representation, the method comprising:
obtaining a learnertTime-of-day answer sequence and knowledge point representationKnowledge Point state diagram->The method comprises the steps of carrying out a first treatment on the surface of the The answer sequence comprises the problem->Answer result->And knowledge Point->；
Calculate a first weightAnd a second weight->To update the knowledge point representation +.>And knowledge point state diagramThe method comprises the steps of carrying out a first treatment on the surface of the Wherein the first weight +.>And said second weight +.>Is the investigation weight of the problem for the knowledge points;
aggregating the knowledge point representation graph after updatingAnd the knowledge point state diagram +.>Obtaining a first knowledge point representation +.>And a first knowledge point status representation +.>；
Forward diffusing the first knowledge point representationObtaining a second knowledge point representation +.>The method comprises the steps of carrying out a first treatment on the surface of the Forward diffusing said first knowledge point state representation +.>Obtaining a second knowledge point state representation +.>；
Back-diffusing the second knowledge point representationObtaining a third knowledge point representation +.>And a third knowledge point state representationThe method comprises the steps of carrying out a first treatment on the surface of the Back diffusing said second knowledge point state representation +.>Obtaining knowledge point state relation->；
Representing according to the third knowledge pointObtainingtKnowledge point representation at time +1 +.>The method comprises the steps of carrying out a first treatment on the surface of the Representing +.about.according to the third knowledge point state>And the knowledge point status relationship->Obtaining knowledge point mastering state->And grasp the status +.>ObtainingtKnowledge point state diagram at time +1 +.>；
Acquisition oftProblem at +1 timeAnd knowledge Point->Grasping the status by combining the knowledge points>Predicting the problem of learner>Is a manifestation of (a) in the future.
Further, the knowledge tracking method based on knowledge point diffusion representation further comprises the following steps:
the knowledge point representation graphExpressed as:
；
wherein,representing a knowledge point set, the elements in the set being knowledge points +.>；Is knowledge point->A set of relations, wherein->Representing knowledge pointsiAnd (3) withjA relationship of interactions between;Is a knowledge point feature matrix;Is a knowledge point relation characteristic matrix;
the knowledge point state diagramExpressed as:
；
wherein,is a knowledge point state set, and elements in the set are knowledge point states;is a set of knowledge point state relations, wherein +.>Representing knowledge point statesiAnd (3) withjA relationship of interactions between;Is a knowledge point state feature matrix;Is a knowledge point state relation feature matrix;
will exercise problemsMapping into a distributed real value vector:
；
wherein,and->For embedding matrix->Indicate the problem->The effect and impact on each knowledge point;
calculate a first weightThe method comprises the following steps:
；
updating the knowledge point representationIs to use the first weight +.>Updating the knowledge point feature matrixThe method comprises the following steps:
the method comprises the steps of carrying out a first treatment on the surface of the The above-mentioned updating means using the described knowledge point feature matrix +.>And the first weight +.>Feature matrix +_as new knowledge point>；
The first weight is processed through MLPConversion to the second weight->：
；
Updating knowledge point state diagramsIs to use the second weight +.>Updating the knowledge point state feature matrixThe method comprises the following steps:
the method comprises the steps of carrying out a first treatment on the surface of the The above-mentioned updating means that the feature matrix is +.>And the second weightAs a new knowledge point state feature matrix +.>。
Further, the knowledge tracking method based on knowledge point diffusion representation further comprises the following steps:
calculating updated knowledge point representationAnd updated knowledge point state diagram +.>First attention weight between nodes +.>：
Wherein,weight matrix shared for neighbor nodes, +.>The first attention weight is a weight coefficient between nodes;
weighting the first attention weightNormalizing to obtain a second attention weight +.>：
；
Mapping updated knowledge pointsAnd updated knowledge point state diagram +.>The middle node and neighbor nodes thereof perform aggregation representation:
；
wherein,for an embedded weight matrix +.>The number of neighbor nodes, which are nodes, +.>Aggregating representations for nodes;
by setting upKMultiple attention layers of independent attention mechanisms, and updated knowledge point representation diagramAnd updated knowledge point state diagram +.>The aggregation of the edges of (a) represents:
；
wherein, thereinIs edge->Adjacent edge number of (2),>is an edge aggregation representation;
fusing the node aggregation representation and the edge aggregation representation to obtain a first knowledge point representationAnd a first knowledge point status representation +.>The following are provided:
the node is an updated knowledge point representation graphMiddle->And said edge is said knowledge point representation +.>Middle->When substituting the above expression to obtain the first knowledge point representation +.>The method comprises the following steps:
；
；
wherein,、the knowledge point representation is +.>An embedding matrix of the node aggregate representation and the edge aggregate representation;
a state diagram of the knowledge point after the node is updatedMiddle->And said edge is said knowledge point state diagram +.>Middle->When substituting the above expression to obtain the first knowledge point state representation +.>The method comprises the following steps:
；
；
wherein,、the knowledge point state diagrams are respectively->An embedding matrix of the node aggregate representation and the edge aggregate representation.
Further, the knowledge tracking method based on knowledge point diffusion representation further comprises the following steps:
gradually adding Gaussian noiseFor forward diffusion in the i step, knowledge points after forward diffusion represent a calculation method as follows:
；
the knowledge point state calculation method after forward diffusion comprises the following steps:
；
wherein i represents a forward diffusion step, and the value of i is a positive integer of 1~I;
；；representing variance->Is the average value of (2);
substituting i=i in the above formula to obtain second knowledge point representation as forward diffusion resultAnd a second knowledge point state representation +.>。
Further, the knowledge tracking method based on knowledge point diffusion representation further comprises the following steps:
at the second knowledge point representationIs integrated with learning result data->Obtaining knowledge point representation integrated into learning result data +.>：
；
Further, the learning result data is represented by knowledge pointsFor initial value, iterate stepwise to +.>The iterative method is expressed as:
；
wherein,for the learning result data, < >>A weight matrix corresponding to the learning result data;An approximation model representing noise removal during back diffusion;
sequentially iterating according to the above to obtain a third knowledge point representation as the back diffusion result。
Further, the knowledge tracking method based on knowledge point diffusion representation further comprises the following steps:
at the second knowledge point representationIs incorporated with the first weight +.>Obtaining knowledge point state integrated with first weight +.>：
；
Further, to incorporate knowledge point state of first weightFor initial value, iterate stepwise to +.>The iterative method is expressed as:
；
wherein,an approximation model representing noise removal during back diffusion;
sequentially iterating according to the above to obtain a third knowledge point state representation as the back diffusion result。
Further, the knowledge tracking method based on knowledge point diffusion representation further comprises the following steps:
state representation at the second knowledge pointIs incorporated with the second weight +.>Obtaining knowledge point state relation which is integrated with second weight +.>：
；
Further, the knowledge point state relation of the second weight is integratedFor initial value, iterate stepwise to +.>The iterative method is expressed as:
；
wherein,an approximation model representing noise removal during back diffusion;
sequentially iterating according to the above to obtain knowledge point state relation as the back diffusion result。
Further, the knowledge tracking method based on knowledge point diffusion representation further comprises the following steps:
according to the knowledge point state relationFeature matrix related to knowledge point state>Calculating to obtain the related weight：
；
Further incorporating the third knowledge point state representationObtaining the knowledge point mastering state +.>：
。
Further, the knowledge tracking method based on knowledge point diffusion representation further comprises the following steps:
calculating knowledge state vectors：
；
Wherein,is a problem->The distributed real-valued vector of the map,
predicting problem pairs of learnerThe expression conditions are as follows:
。
according to a second aspect of the present invention there is also provided a storage medium storing a computer program executable by an access authentication device, the computer program, when run on the access authentication device, causing the access authentication device to perform the steps of any one of the methods described above.
In general, the above technical solutions conceived by the present invention, compared with the prior art, enable the following beneficial effects to be obtained:
(1) The knowledge point diffusion representation-based knowledge tracking method provided by the invention constructs a knowledge point representation graph and a knowledge point state graph when tracking the knowledge state of students. The knowledge point state diagram represents knowledge point states and interrelationships thereof. Knowledge points and correlations thereof and knowledge point states and correlations thereof are cooperatively aggregated through a diffusion model, so that the knowledge state of a learner is deduced.
(2) According to the knowledge tracking method based on knowledge point diffusion representation, the representation of the knowledge point relation and the knowledge point state relation is added in the knowledge state modeling process, the knowledge state of a learner is fused and deduced on the basis, and the knowledge tracking method has better effectiveness and interpretation for knowledge state modeling.
(3) According to the knowledge tracking method based on knowledge point diffusion representation, the influence of the problems on the knowledge point investigation weight is introduced when the knowledge state of students is tracked, the influence of the relation between knowledge points and the relation between knowledge point states on the knowledge point state is modeled, and the influence of the problems on different investigation degrees of all knowledge points is increased in modeling the knowledge point state by combining with an actual learning process.
(4) According to the knowledge point diffusion representation-based knowledge tracking method, when the knowledge state of students is tracked, the diffusion model is combined to represent the evolution process of the knowledge points, firstly, the knowledge point representation diagram and the knowledge point state diagram are subjected to forward diffusion to obtain the representation of the knowledge points in the hidden space, secondly, the forward diffusion result is input into reverse diffusion, and the updated knowledge point representation and knowledge point state representation are generated by combining learning end data and related weights. Thereby obtaining a knowledge point representation graph and a knowledge point state graph after answering, and constructing a logical link of knowledge point evolution in the training process of the learner. According to the invention, knowledge points are represented in a diffusion mode by combining learning characteristics, so that the knowledge points have good effectiveness and interpretation.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a knowledge tracking method based on knowledge point diffusion representation according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a knowledge tracking model based on knowledge point diffusion representation according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The terms first, second, third and the like in the description and in the claims and in the above drawings, are used for distinguishing between different objects and not necessarily for describing a particular sequential or chronological order. Furthermore, the terms "comprise" and "have," as well as any variations thereof, are intended to cover a non-exclusive inclusion. For example, a process, method, system, article, or apparatus that comprises a list of steps or elements is not limited to only those listed steps or elements but may include other steps or elements not listed or inherent to such process, method, article, or apparatus.
As shown in fig. 1-2, as a first embodiment of the present invention, there is provided a knowledge tracking method based on knowledge point spread representation, the method in this embodiment including two steps of constructing a knowledge tracking model and predicting a learner response situation using the knowledge tracking model.
Wherein, the knowledge tracking model construction comprises the following steps:
obtaining a learnertTime-of-day answer sequence and knowledge point representationKnowledge Point state diagram->The method comprises the steps of carrying out a first treatment on the surface of the The answer sequence comprises the problem->Answer result->And knowledge Point->。
Calculate a first weightAnd a second weight->To update the knowledge point representation +.>And knowledge point state diagramThe method comprises the steps of carrying out a first treatment on the surface of the Wherein the first weight->And a second weight->Is the investigation weight of the problem for the containing knowledge points.
Aggregating the knowledge point representation graph after updatingAnd the knowledge point state diagram +.>Obtaining a first knowledge point representation +.>And a first knowledge point status representation +.>。
Forward diffusing the first knowledge point representationObtaining a second knowledge point representation +.>The method comprises the steps of carrying out a first treatment on the surface of the Forward diffusing said first knowledge point state representation +.>Obtaining a second knowledge point state representation +.>。
Back-diffusing the second knowledge point representationObtaining a third knowledge point representation +.>And a third knowledge point state representationThe method comprises the steps of carrying out a first treatment on the surface of the Back diffusing said second knowledge point state representation +.>Obtaining knowledge point state relation->。
Representing according to the third knowledge pointObtainingtKnowledge point representation at time +1 +.>The method comprises the steps of carrying out a first treatment on the surface of the Representing +.about.according to the third knowledge point state>And the knowledge point status relationship->Obtaining knowledge point mastering state->And grasp the status +.>ObtainingtKnowledge point state diagram at time +1 +.>。
The method for predicting the answering state of the learner by using the knowledge tracking model mainly comprises the following steps:
acquisition oftProblem at +1 timeAnd knowledge Point->Grasping the status by combining the knowledge points>Predicting the problem of learner>Is a manifestation of (a) in the future.
The learner answering the questions contained in the information in the sequenceAnswer result->Knowledge Point->And connotation, extension and other relations among knowledge points. After the learner answers the problems, the answering results of the problems can influence the relevant knowledge point states to different degrees, so that the representation of the knowledge point state diagram is changed, and meanwhile, the update of the knowledge point state is influenced by the knowledge point representation diagram. The knowledge point representation and knowledge point state diagram evolve with the training process, and the modeling in this embodiment includes the knowledge point representation and knowledge point state diagram described above. Knowledge point representation at time t is marked +.>The knowledge point state diagram at time t is marked as +.>。
The knowledge points and the relation thereof, the knowledge point states and the relation thereof and other information are represented, and the method specifically comprises the following steps:
first, a knowledge point representation is defined：
。
Knowledge point representationConsists of a plurality of nodes and connecting lines (namely edges) between the nodes. In this embodiment, <' > a->Is a set of nodes, i.e. a set of knowledge points, the elements in the set being knowledge points +.>；Is a set of edges, i.e. a set of relationships between knowledge points, +.>Representing knowledge pointsiAnd (3) withjThe relationship of the interaction between the two involves +.>To->The representation of the connotation or extension relation exists between the two, and a graph fusion algorithm is adopted to obtain the fused edges under the condition that a plurality of relations coexist;Is a knowledge point feature matrix, initially denoted +.>。Is a relational feature matrix, initially expressed as +.>。
Knowledge points at initial timeIs characterized by->Knowledge points represent feature matrices marked +.>. Relation features of knowledge points->Initializing:
，
wherein,，the feature matrix of the relation is initialized to +.>. Through analyzing the association relation between the problems and the knowledge points in the learning answer sequence and combining labeling the connotation and extension relation of the knowledge points, the knowledge point representation graph can be constructed.
Next, define a knowledge point state diagram：
。
Similar to the knowledge point representation, wherein,is a set of nodes in the graph or knowledge point states,is a set of edges, i.e. a set of relationships between knowledge point states,/->Representing knowledge point statesiAnd (3) withjThe interaction relation is initially the relation between knowledge points, and the subsequent combination of knowledge points represents the diffusion result of the graph and the updating of learning data information in the diffusion process into the relation between knowledge points.Is a knowledge point state feature matrix, initially denoted +.>。Is a state relation feature matrix, initially expressed as +.>。
Initial state relation feature matrixRepresenting the matrix by knowledge points->Obtained by MLP transformation:
。
as learning progresses, knowledge point representation changes dynamically along with learning exercise of a learner, and in order to represent the change process of the knowledge points, the module updates a knowledge point representation diagram and a knowledge point state diagram by combining the current answer questions, and diffuses the knowledge point representation diagram and the knowledge point state diagram by using a diffusion model to obtain hidden space representations of the knowledge point representation and the knowledge point state, and is used for deducing the relationship between the knowledge states and generating updated knowledge state representations. The specific operation is as follows:
firstly, calculating the investigation weight of the current problem for the knowledge points, wherein the investigation weight is the correlation weight between the problem and the knowledge points, and reflects the emphasis degree of the problem for investigating each knowledge point. The calculated problem is referred to as a first weight in this embodiment for the investigation weight containing knowledge pointsAnd a second weight->。
Assume that the total number of exercises isQWill exercise problemsMapping into a distributed real value vector:
，
wherein,and->For embedding matrix->Indicate the problem->Effect and impact on each knowledge point. The problems to be answered at present have different investigation emphasis degrees on knowledge points, so that the states of the knowledge points are affected to different degrees, and the correlation weights of the problems and the knowledge points are further obtainedHeavy, using distributed real-valued vectorsCalculating the knowledge point feature matrix of the same knowledge point representation graph to obtain a first weight +.>：
，
Wherein,. Multiplying the first weight with the knowledge point feature matrix to update the knowledge point representation:
,
wherein, the left side of the upper partIs the updated knowledge point feature matrix.
The first weight obtained above is applied by MLPSecond weight for transition to problem and knowledge point state>：
，
Wherein,. Multiplying the second weight with the knowledge point state feature matrix to obtain an updated representation of the knowledge point state:
,
left side of the upper partIs the updated knowledge point state feature matrix, i.e. the knowledge point state representation. In this embodiment, updating means that after the knowledge point feature matrix or the knowledge point state feature matrix is multiplied by the corresponding weight, the knowledge point feature matrix or the knowledge point state feature matrix is represented by a new value.
Further, the advanced idea of the diffusion model is to learn the generated data, initial input, through the progressive noise process of diffusionAre sampled data points in the real data distribution. Forward diffusion process parameterized as Markov chainBy gradually adding a small amount of noise, this eventually results in a pure gaussian distribution to corrupt the original input data points:
。
from the following componentsDeriving the diffusion result->：
,
The diffusion result at any diffusion time can be expressed, namely:
。
the diffusion model is applied to the embodiment, the knowledge point representation graph and the knowledge point state graph are taken as objects, the knowledge point representation graph and the knowledge point state graph are mapped to the hidden space by virtue of a forward diffusion process, the space reflects the internal structure and the essential information of the knowledge points and the relation thereof, and the diffusion result of the knowledge point representation graph and the knowledge point state graph is obtained from the internal structure and the essential information. The method comprises the following specific steps:
the related weights of the graph will be represented by the problem and knowledge pointsKnowledge point representation with updated node representation +.>Aggregation representation is performed by first calculating a first attention weight between nodes:
，
wherein,weight matrix shared for neighbor nodes, +.>For the weight coefficients between nodes, knowledge points are +.>Normalizing the selection of all neighbor nodes to obtain a second attention weight:
，
wherein,is knowledge pointiNeighbor node number,/-, of (a)>Is->Knowledge point ++obtained by normalization of softmax activation function>Attention weights with neighboring nodes.
Second, nodes in the graph are to beAnd its neighbor nodes perform aggregate representation:
，
wherein,for an embedded weight matrix +.>Is knowledge point->Neighbor node number,/-, of (a)>The representation is aggregated for the nodes.
By setting upKMultiple attention layers of independent attention mechanisms, the edges in the figure are represented in aggregate:
，
wherein,is edge->Adjacent edge number of (2),>is an aggregate representation of edges.
Knowledge point representation according to the previous descriptionConsists of a plurality of nodes and connecting lines (namely edges) between the nodes. In this embodiment, <' > a->Is a collection of nodes, +.>Is a collection of edges, and thus the aggregate result of the fused nodes and edges represents knowledge points as follows:
；
；
wherein,、knowledge point representation respectively->An embedding matrix of node aggregate representations and said edge aggregate representations;，，。
Knowledge point state diagramThe diffusion representation of (a) is similar to the knowledge point representation of +.>And (3) diffusion representation, namely aggregating knowledge point states and edges representing state relations in the knowledge point state diagram, and fusing to obtain the representation of the knowledge point state diagram, wherein the representation is as follows:
；
；
wherein,、the knowledge point state diagrams are respectively->An embedding matrix of node aggregate representations and edge aggregate representations;，，。
Further, to represent the change process of the intrinsic structure and the implication logic of the knowledge points, the first knowledge point is representedMapping into hidden space by diffusion process:
first, a forward diffusion process is defined: assuming that the relational expression of knowledge points obeys a certain data distribution, i.e.，
In the process, from the initial inputStarting, gradually go to->Added Gaussian noise->A series of noisy samples will eventually be produced:Wherein the step size of each step is controlled by the variance. Variance->Constant sequence set to linearly increase with average value +.>Diffusion result data for the same current time step +.>Is a product of (a) and (b). Data samples +.>Gradually losing its distinguishable characteristics. Finally, when->When (I)>Corresponding to an isotropic gaussian distribution. The process is represented as follows:
。
it can be found that during forward diffusion, the conditional probability distribution of the state at the next moment depends only on the state at the current moment, i.e. has markov-compliant properties, and therefore, using parametric reconstruction, at a given momentInitial inputThe above formula is rewritten under the condition that +.>：
。
To sum up, the firstThe diffusion vector of a step can be expressed as:
,
wherein,，。
thus, the first knowledge point representation is entered for the initial inputThe knowledge point representation map distribution of any diffusion time step can be represented, and the final forward diffusion result is represented by a second knowledge point>。
The same as the diffusion updating process of the knowledge point representation, the distribution of the knowledge point state diagram at any moment:
,
at given initial inputCan be calculated directly under the condition of +.>：
，
Thus, the first knowledge point state representation is entered for the initial inputCan show the knowledge point state diagram distribution of any forward diffusion time step, and the final forward diffusion result is a second knowledge point state representation +.>。
The forward diffusion process noise the data and the reverse process is the process of removing noise. Reverse diffusion processI.e. the generation process by mimicking each pair of time steps of the forward diffusion process +.>The series of noise added before is progressively removed in reverse. However, since it is difficult to estimate the true back diffusion process, a model is constructed +.>To approximate these conditional probabilities in order to perform the back diffusion process:
，/>
finally, the diffusion result of the forward process is mapped from the hidden space to the back display space, and the data with the characteristics are restored and generated.
In the back-diffusion generation of knowledge point representation, the back-diffusion process is equally divided intoStep, every step is->The result of each step of back diffusion is expressed as:. In the back diffusion process, when the variance of each step +.>For a sufficiently small time, the result of the sampling is also a gaussian distribution, which is difficult to estimate, so that the initial input +_ is introduced by parameterization techniques>By learning Gaussian noise->To approximate->The original formula is rewritten:
，
wherein:
，
from the initial input has been derived in the forward processIndicates the diffusion result->Otherwise, can pass->Representation->：
The rearranged representation is as follows:
，
it can be found that the mean value is subjected toAnd->Is the result of the back diffusion process, input +.>Is known and therefore only needs to be obtainedThe entire back diffusion process can be represented.
The learning data of the learner in practice can influence the back diffusion process, and the learning result data influencing the knowledge state of the learner is combinedTo enhance the relationship between modeling knowledge points, and to perform fusion representation:
，
wherein,for fusing learning result data->Is a knowledge point representation of (c).
Prediction by training a modelApproximating the noise to be removed for each step:
，
the iteration formula for each step is obtained as follows:
，
wherein,. Finally, the back-diffusion result of the knowledge point representation is obtained, namely the third knowledge point representation +.>And updating the current knowledge point representation as the knowledge point representation of the next moment +.>。
Similar to the process of generating knowledge point representation by back diffusion, the knowledge point representation is subjected to diffusion resultsAssociated weights of state diagram combined with knowledge points>Updating to knowledge point state representation +.>:
,
Corresponding noiseThe method comprises the following steps:
，
the iterative formula for each step is:
。
finally, the characteristic back diffusion generating result comprising knowledge point representation, knowledge point relation and the like, namely third knowledge point state representation, can be obtainedAnd is used for generating the current knowledge point state by fusing the knowledge point state relation subsequently. In this embodiment, the first knowledge point represents +.>Is a knowledge point representation>After the middle node and the edge, learning data are merged, and then the third knowledge point state representation +.>Therefore, the third knowledge point state represents +.>Not only the knowledge points, but also the relations between the knowledge points.
The knowledge point state relation is initially defined as a relation between knowledge points, and in the learning process, the relation between knowledge point states influences the change degree of the knowledge point states. In the back diffusion process, the diffusion results at adjacent moments are distinguished as removed noise, namely the influence of the knowledge point state relation on the knowledge point state is reflected as the change of the diffusion state at the adjacent moments. Thus, useApproximating the noise removed at each step, representing the second knowledge point state +.>The course of the gradual change of knowledge state is represented by back diffusion.
Similar to the back diffusion generation of knowledge point representation, the influence weight of the problem on the knowledge point state is combinedRepresenting the status of knowledge points after diffusion +.>Updating to knowledge point status relation representation +.>：
，
Noise of back diffusion process of corresponding knowledge point state diagramThe method comprises the following steps:
，
and (3) obtaining an iterative process of back diffusion generation of the knowledge point state relation diagram:
。
the obtained knowledge point state relationFeature matrix related to knowledge point state>Calculating to obtain the related weightAnd combining the third knowledge point state representation +.>Fusion is expressed as the current knowledge point mastery state +.>：
，/>
。
Wherein,finally, an updated knowledge point state diagram can be obtained, and the updated knowledge point state diagram is taken as a knowledge point state diagram +.>。
Finally, grasping the state according to the knowledge points obtained by modelingThe response situation of the learner at the next moment is predicted, and the prediction method comprises the following steps:
considering that different investigation weights of problems on knowledge points can cause different difficulties of the problems, the knowledge points are mastered into the stateAnd the distributed problem vector to be answered +.>Splicing and obtaining knowledge state vector via full connection layer with activation function>The knowledge point state and the relation between knowledge point states, learning behavior and other data are contained, and the data are as follows:
。
finally, through the output layer provided with the Sigmoid activation function, the methodAs input, predict learner's problem +.>The behavior is as follows:
。
as a further embodiment of the present invention, a comparison of the knowledge tracking model of the present invention with other prior art is provided, wherein the comparison uses three data sets and utilizes the predictive method to learn about problemsIs anticipated->And the actual answer result->In comparison, AUC comparison results for each model method are shown in table 1:
TABLE 1 comparison of the invention with the prior art
The present invention also provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of the above method. The computer readable storage medium may include, among other things, any type of disk including floppy disks, optical disks, DVDs, CD-ROMs, micro-drives, and magneto-optical disks, ROM, RAM, EPROM, EEPROM, DRAM, VRAM, flash memory devices, magnetic or optical cards, nanosystems (including molecular memory ICs), or any type of media or device suitable for storing instructions and/or data.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (5)
1. A knowledge tracking method based on knowledge point spread representation, comprising:
obtaining a learnertTime-of-day answer sequence and knowledge point representationKnowledge Point state diagram->The method comprises the steps of carrying out a first treatment on the surface of the The answer sequence comprises the problem->Answer result->And knowledge Point->；
Calculate a first weightAnd a second weight->To update the knowledge point representation +.>And knowledge point state diagram->The method comprises the steps of carrying out a first treatment on the surface of the Wherein the first weight +.>And said second weight +.>Is the investigation weight of the problem for the knowledge points;
aggregating the knowledge point representation graph after updatingAnd the knowledge point state diagram +.>Obtaining a first knowledge point representation +.>And a first knowledge point status representation +.>；
Forward diffusing the first knowledge point representationObtaining a second knowledge point representation +.>The method comprises the steps of carrying out a first treatment on the surface of the Forward diffusing said first knowledge point state representation +.>Obtaining a second knowledge point state representation +.>；
Back-diffusing the second knowledge point representationObtaining a third knowledge point representation +.>And third knowledge point state representation +.>The method comprises the steps of carrying out a first treatment on the surface of the Back diffusing said second knowledge point state representation +.>Obtaining knowledge point state relation->；
Representing according to the third knowledge pointObtainingtKnowledge point representation at time +1 +.>The method comprises the steps of carrying out a first treatment on the surface of the Representing +.about.according to the third knowledge point state>And the knowledge point status relationship->Obtaining knowledge point mastering state->And is combined withMastering the state according to the knowledge points>ObtainingtKnowledge point state diagram at time +1 +.>；
Acquisition oftProblem at +1 timeAnd knowledge Point->Grasping the status by combining the knowledge points>Predicting the problem of learner>Is a manifestation of (2);
aggregating the knowledge point representation graph after updatingAnd the knowledge point state diagram +.>Obtaining a first knowledge point representation +.>And a first knowledge point status representation +.>The method specifically comprises the following steps:
calculating updated knowledge point representationAnd updated knowledge point state diagram +.>First attention weight between nodes +.>：
Wherein,weight matrix shared for neighbor nodes, +.>The first attention weight is a weight coefficient between nodes;knowledge point representing time ti；Knowledge point representing time tj；
Weighting the first attention weightNormalizing to obtain a second attention weight +.>：
；
Mapping updated knowledge pointsAnd updated knowledge point state diagram +.>The middle node and neighbor nodes thereof perform aggregation representation:
；
wherein,for an embedded weight matrix +.>The number of neighbor nodes, which are nodes, +.>Aggregating representations for nodes;
by setting upKMultiple attention layers of independent attention mechanisms, and updated knowledge point representation diagramAnd updated knowledge point state diagram +.>The aggregation of the edges of (a) represents:
；
wherein, thereinIs edge->Adjacent edge number of (2),>is an edge aggregation representation;
fusing the node aggregate representation and the edge aggregate representationObtaining a first knowledge point representationAnd a first knowledge point status representation +.>The following are provided:
the node is an updated knowledge point representation graphMiddle->And said edge is said knowledge point representation +.>Middle->When substituting the above expression to obtain the first knowledge point representation +.>The method comprises the following steps:
；
；
wherein,、the knowledge point representation is +.>Is the section of (1)An embedding matrix of a point aggregate representation and the edge aggregate representation;
a state diagram of the knowledge point after the node is updatedMiddle->And said edge is said knowledge point state diagram +.>Middle->When substituting the above expression to obtain the first knowledge point state representation +.>The method comprises the following steps:
；
；
wherein,、the knowledge point state diagrams are respectively->An embedding matrix of the node aggregate representation and the edge aggregate representation;
forward diffusing the first knowledge point representationObtain the firstTwo knowledge points represent +.>The method comprises the steps of carrying out a first treatment on the surface of the Forward diffusing said first knowledge point state representation +.>Obtaining a second knowledge point state representation +.>The specific method comprises the following steps:
gradually adding Gaussian noiseFor forward diffusion in the i step, knowledge points after forward diffusion represent a calculation method as follows:
；
the knowledge point state calculation method after forward diffusion comprises the following steps:
；
wherein i represents a forward diffusion step, and the value of i is a positive integer of 1~I;
；；representing variance->Is the average value of (2);
substituting i=i in the above formula, respectively, to obtain the diffusion as forward diffusionSecond knowledge point representation of the resultAnd a second knowledge point state representation +.>；
Back-diffusing the second knowledge point representationObtaining a third knowledge point representation +.>The specific method comprises the following steps:
at the second knowledge point representationIs integrated with learning result data->Obtaining knowledge point representation integrated into learning result data +.>：
；
Further, the learning result data is represented by knowledge pointsFor initial value, iterate stepwise to +.>The iterative method is expressed as:
；
wherein,for the learning result data, < >>A weight matrix corresponding to the learning result data;an approximation model representing noise removal during back diffusion;
sequentially iterating according to the above to obtain a third knowledge point representation as the back diffusion result；
Back-diffusing the second knowledge point representationObtaining a third knowledge point state representation +.>The specific method comprises the following steps:
at the second knowledge point representationIs incorporated with the first weight +.>Obtaining knowledge point state integrated with first weight：
；
Further, to incorporate knowledge point state of first weightFor initial value, iterate stepwise to +.>The iterative method is expressed as:
；
wherein,an approximation model representing noise removal during back diffusion;
sequentially iterating according to the above to obtain a third knowledge point state representation as the back diffusion result；
Back-diffusing the second knowledge point state representationObtaining knowledge point state relation->The specific method comprises the following steps:
state representation at the second knowledge pointIs incorporated with the second weight +.>Obtaining knowledge point state relation which is integrated with second weight +.>：
；
Further, the knowledge point state relation of the second weight is integratedFor initial value, iterate stepwise to +.>The iterative method is expressed as:
；
wherein,an approximation model representing noise removal during back diffusion;
sequentially iterating according to the above to obtain knowledge point state relation as the back diffusion result。
2. The knowledge tracking method based on knowledge point spread representation according to claim 1, wherein:
calculate a first weightAnd a second weight->To update the knowledge point representation +.>And knowledge point state diagram->The method specifically comprises the following steps:
the knowledge point tableDiagram of the drawingsExpressed as:
；
wherein,representing a knowledge point set, the elements in the set being knowledge points +.>；Is knowledge point->A set of relations, wherein->Representing knowledge pointsiAnd (3) withjA relationship of interactions between;Is a knowledge point feature matrix;Is a knowledge point relation characteristic matrix;
the knowledge point state diagramExpressed as:
；
wherein,is a knowledge point state set, and elements in the set are knowledge point states;is a set of knowledge point state relations, wherein +.>Representing knowledge point statesiAnd (3) withjA relationship of interactions between;Is a knowledge point state feature matrix;Is a knowledge point state relation feature matrix;
will exercise problemsMapping into a distributed real value vector:
；
wherein,and->For embedding matrix->Indicate the problem->The effect and impact on each knowledge point;
calculate a first weightThe method comprises the following steps:
；
updating the knowledge point representationIs to use the first weight +.>Updating the knowledge point feature matrix +.>The method comprises the following steps:
the method comprises the steps of carrying out a first treatment on the surface of the The above-mentioned updating means using the described knowledge point feature matrix +.>And the first weight +.>Feature matrix +_as new knowledge point>；
The first weight is processed through MLPConversion to the second weight->：
；
Updating knowledge point state diagramsIs to use the second weight +.>Updating the knowledge point state feature matrix +.>The method comprises the following steps:
the method comprises the steps of carrying out a first treatment on the surface of the The above-mentioned updating means that the feature matrix is +.>And the second weight +.>As a new knowledge point state feature matrix +.>。
3. The knowledge tracking method based on knowledge point spread representation according to claim 1, wherein:
representing according to the third knowledge point stateAnd the knowledge point status relationship->Obtaining knowledge point mastering state->The specific method comprises the following steps:
according to the knowledge point state relationFeature matrix related to knowledge point state>Calculating to obtain the relevant weight->：
；
Further incorporating the third knowledge point state representationObtaining the knowledge point mastering state +.>：
。
4. A knowledge tracking method based on knowledge point spread representation according to claim 3, characterized in that:
acquisition oftProblem at +1 timeAnd knowledge Point->Grasping the status by combining the knowledge points>Predicting the problem of learner>The specific method is as follows:
calculating knowledge state vectors：
；
Wherein,is a problem->The distributed real-valued vector of the map,
predicting problem pairs of learnerThe expression conditions are as follows:
。
5. a storage medium storing a computer program executable by an access authentication device, the computer program, when run on the access authentication device, causing the access authentication device to perform the steps of the method of any one of claims 1 to 4.
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