Knowledge tracking model fusing dynamic edge weight and forgetting gating

Abstract

The invention relates to a knowledge tracking model fusing dynamic edge weight and forgetting gating, and aims to solve the problems that an existing knowledge tracking model cannot effectively model dynamic association of knowledge points and neglects a memory recession effect. According to the method, by constructing a time sequence diagram neural network, based on a learnable time attenuation factor and an attention mechanism, the edge weight between knowledge points is dynamically adjusted, and self-adaptive modeling of the incidence relation evolving along with time and learning behaviors is achieved. Furthermore, according to the Ebbinghaus forgetting curve theory, personalized forgetting rate parameters are defined, and the generated memory intensity is embedded into the LSTM unit to serve as a gating signal, so that the influence of knowledge decline on the cognitive state of the student is explicitly simulated. The invention also provides a hierarchical fusion architecture, which combines the time sequence behavior sequence and the map structure information, and improves the prediction precision and generalization ability of the model. According to the method, chain state degradation caused by knowledge forgetting can be accurately identified, and a theoretical basis and decision support are provided for intelligent recommendation of personalized review paths in an adaptive learning system.

Description

Technical Field

[0001] The present invention belongs to the field of educational artificial intelligence technology, and specifically relates to a knowledge tracking model that integrates dynamic edge weights and forgetting gating to accurately predict students' knowledge status and generate personalized learning recommendations. Background Art

[0002] Knowledge tracing (KT) is a core technology in personalized learning systems. Its goal is to dynamically predict a student's mastery of knowledge points by analyzing their historical answer sequences. While traditional deep knowledge tracing models (such as DKT and DKVMN) have made some progress in sequence modeling using recurrent neural networks, they still suffer from two key flaws: First, they treat knowledge points as independent entities, ignoring the inherent structured connections within subject matter, resulting in a lack of interpretability in reasoning about knowledge state transfer; second, they fail to explicitly account for forgetting patterns in human cognition, making it difficult to capture knowledge decay and cascading forgetting during long-term learning.

[0003] Among existing improved methods, the GKT model models knowledge point relationships through a static knowledge graph. However, its fixed edge weights cannot reflect the dynamic changes in association strength during the learning process, such as increased associations after review and decreased associations after long periods of inactivity. While the HawkesKT model uses a time-point process to simulate the temporal dependencies of knowledge activation, it fails to effectively couple the forgetting effect with the evolution of graph structure. Furthermore, most current knowledge tracking models are based solely on single behavioral sequence data and lack the integration of multimodal cognitive evidence (such as memory strength and semantic associations). This limits the model's predictive accuracy and generalization capabilities in complex educational scenarios.

[0004] Specifically, existing technologies have the following three major limitations: (1) static graph structures cannot adapt to the dynamic evolution of the strength of knowledge point associations at different learning stages; (2) the forgetting effect is only modeled as a global time decay, failing to establish an explicit association between it and changes in the knowledge network topology; and (3) isomorphic graph modeling makes it difficult to distinguish between multiple types of knowledge interaction patterns, such as concept dependencies and method applications. These problems have severely restricted the application of knowledge tracking models in actual educational scenarios.

[0005] To address the above issues, the inventors proposed a knowledge tracking model that integrates dynamic edge weights and forgetting gating in their previous research. They constructed a dynamic knowledge point correlation network through a temporal graph neural network, and combined the time decay factor with the attention mechanism to achieve adaptive adjustment of edge weights. At the same time, they introduced the Ebbinghaus forgetting curve theory, established personalized forgetting rate parameters, and embedded memory strength as a gating signal into the LSTM cell state update process. Summary of the Invention

[0006] The present invention proposes a knowledge tracking model that integrates dynamic edge weights and forget gating, which specifically includes the following steps:

[0007] The time interval is used to measure the "forgetting degree" of a knowledge point. The longer the time interval, the longer the knowledge point has not been reviewed, and the lower its retention strength in the student's memory may be. The time interval is used as an input to calculate the memory strength function and further participates in controlling the forgetting weight of the cell state in the gating mechanism, reflecting the need to model the long-term memory decay effect during the learning process. The last interaction time interval of the knowledge point is defined as ,in Representing knowledge points The last time it was practiced.

[0008] Introducing a learnable global decay factor . Through back-propagation end-to-end optimization, the constraint is positive (using Ensure non-negativity). For any two knowledge point nodes i and j, under the premise that there is a structural association, the decay function of their edge weight evolution over time is defined as .

[0009] The dynamic edge weight mechanism effectively enhances the time perception ability of the knowledge graph, helps capture the evolution trend of the learner's knowledge structure in the long-term learning process, and provides a more timely structural basis for the feature aggregation of subsequent graph neural network layers. (Just practiced recently), the edge weight is close to the initial value . , the edge weight approaches zero, indicating that the association is broken due to long-term lack of practice. When the value is small, that is, when two knowledge points have been practiced together recently or related questions have been answered frequently, Close to 1.

[0010] The dynamic edge weights approach their initial values, reflecting a strong correlation in knowledge structure. If the two knowledge points are large, they have not been reviewed or used together for a long time, and their edge weights gradually decay and approach 0, indicating that the association between the knowledge points has weakened or even broken over time.

[0011] In the process of edge weight construction, the attention mechanism is introduced to dynamically perceive and model the correlation between knowledge points using the current cognitive state of students, so as to further improve the ability to express the local dependency relationship between knowledge points in dynamic graph modeling. The current hidden state (from LSTM) and the embedding vector of the knowledge point are projected into the query space and key space respectively. , .in, is the learnable parameter matrix, is the hidden layer dimension. A scaled dot product attention mechanism is introduced during the construction of the dynamic adjacency matrix to calculate the attention weight of each knowledge point relative to the current state, thereby modeling the strength of the association between the student's current cognitive state and the knowledge point.

[0012] Computing knowledge points by scaling dot product attention The associated weight relative to the current state The time-decayed edge weights and attention weights are integrated in a linear superposition manner to obtain the dynamic edge weights that are ultimately used for feature propagation in graph neural networks.

[0013] For any pair of knowledge point nodes i and j with structural connections, first calculate their time interval-based decay edge weight and attention-based semantic weight, then sum them proportionally to form the final edge weight. Linearly superimpose the time decay edge weight and attention weight to obtain the final dynamic edge weight.

[0014]

[0015] in, is the balance coefficient (initialized to 1, which can be learned and adjusted).

[0016] The dynamic edge weights are used to perform graph convolution operations to update the feature representation of knowledge point nodes, thereby more accurately capturing the interactive relationship between structural information and students' cognitive states. The constructed dynamic graph is subjected to multi-layer graph convolution calculations using the graph neural network structure. Each layer of graph convolution operations is performed based on the dynamic edge weights. Update the knowledge point representation, .

[0017] A modeling mechanism based on the Ebbinghaus forgetting curve is introduced to calculate the memory strength of knowledge points over time. This memory information is embedded in the sequence modeling process, improving the model's ability to perceive and predict long-term knowledge decay. Based on the Ebbinghaus forgetting curve, memory strength decays exponentially with time without review, and the decay rate is mathematically modeled based on individual differences and the complexity of the knowledge points.

[0018] The time interval reflects the length of time students haven't reviewed a particular knowledge point. A larger value indicates a higher likelihood of forgetting the knowledge point. This interval value is used as a key variable in the subsequent memory strength calculation formula to enable continuous quantitative modeling of the forgetting process. This processing step provides fundamental temporal information for subsequent Ebbinghaus curve modeling and forgetting gating mechanisms.

[0019] Knowledge points , calculate the current time Last practice time Interval . Define knowledge points In time The memory strength is ,Right now .

[0020] along with Increase, It decreases monotonically, showing a trend of rapid decline followed by a flattening trend, which is consistent with the actual law in human cognitive psychology that the rate of forgetting knowledge slows down over time. This is used to control the update amplitude of knowledge states in neural networks. By introducing this dynamic quantitative indicator, we can explicitly simulate the decline in knowledge mastery caused by forgetting, thereby improving the model's ability to model long-term memory evolution trends.

[0021] By introducing learnable Parameters are used to achieve fine-grained modeling of the forgetting trends of different knowledge points. It also supports the identification and intervention of "high-risk forgetting knowledge points" in subsequent personalized recommendation strategies, which helps to improve the cognitive rationality and personalized teaching ability of the learning system. Different knowledge points have significant differences in cognitive complexity and usage frequency in the knowledge structure, and their speed of forgetting may also be different. Instead of using a global unified forgetting coefficient, an independent decay coefficient is set for each knowledge point k. , and use it as a parameter in the end-to-end optimization process during model training. End-to-end optimization is performed through backpropagation, and positive constraints are imposed on variables. Introducing subject prior constraints: For mathematical knowledge points (such as "calculus"), initialization It is higher than the liberal arts category (such as “Historical Events”), which is consistent with the cognitive load theory.

[0022] A joint optimization strategy combining the Softplus function and the L1 regularization term is adopted to effectively suppress the overfitting phenomenon of the model and improve the generalization ability. This strategy significantly reduces the complexity of the parameter space while maintaining the expressive power of the model through the synergy of nonlinear transformation and sparsity constraints. , . Optimization method based on Softplus function and L1 regularization term. Apply L1 regularization to avoid overfitting .

[0023] Traditional LSTM models usually use input gates, forget gates, and output gates to control the update of cell states. These gating mechanisms usually rely on Sigmoid activation functions to generate probability values ​​between 0 and 1, which can only represent the binary decision of "whether to update" and cannot directly reflect the strength of memory. Introducing memory strength as a gating signal achieves precise control of cell state updates, thereby improving the memory capacity and computational efficiency of time series models such as recurrent neural networks (RNNs) or long short-term memory networks (LSTMs). Serves as a gating signal for cell state updates . Indicates that the current cell state should strongly retain historical information; Indicates that the current cell state should almost completely forget historical information and only rely on new input updates.

[0024] Bidirectional long short-term memory network is used as the basic framework for temporal behavior modeling, specifically for modeling and analyzing student answer sequence data. This modeling method can effectively capture the temporal dependencies and cognitive patterns of students in the answering process, providing technical support for personalized learning analysis and intelligent teaching systems. Temporal behavior modeling (BiLSTM) is performed, and the student answer sequence is input. ,in To ensure answer accuracy, the BiLSTM model uses a bidirectional processing mechanism to simultaneously consider the forward temporal information (from question 1 to question n) and the backward temporal information (from question n to question 1) of the answer sequence, thereby more comprehensively capturing the evolution of students' cognitive states during the answering process.

[0025] A knowledge tracking model that integrates dynamic edge weights and forget gates takes student answer sequences as input data, where the input features of each time step t are It represents the correctness of the student's answer to question t, and its value is a binary label {0,1}. , indicating that the answer to the question is wrong; , indicating that the answer to the question is correct. This time series of binary labels can reflect the dynamic changes in students' knowledge acquisition process, providing basic data for subsequent cognitive diagnosis and personalized teaching. Forward LSTM processing sequentially processes the input sequence from t=1 to t=n and calculates the forward hidden state. Backward LSTM processing sequentially processes the input sequence from t=n to t=1 and calculates the backward hidden state. Bidirectional fusion concatenates the forward and backward hidden states by time step to obtain a complete bidirectional hidden state for subsequent temporal behavior analysis.

[0026] The multi-dimensional and multi-level feature extraction system can efficiently extract discriminative feature representations from the original input data, providing high-quality feature support for subsequent model training and decision-making. .

[0027] Graph structure modeling (dynamic GNN), input dynamic edge weights +Knowledge point embedding . Perform feature aggregation The GNN layer uses multi-hop neighborhood aggregation to capture high-order knowledge point dependencies. Nodes represent knowledge points, and each knowledge point node is embedded as a d-dimensional vector , obtained by encoding the course knowledge structure through pre-trained language model. The edge represents the relationship between knowledge points, and each edge contains dynamic edge weight , which represents the association strength between knowledge point i and knowledge point j at time t.

[0028] The knowledge graph is constructed using a heterogeneous graph structure, and the edge weight can be dynamically adjusted based on students' historical answering behavior, knowledge transfer rules, or teaching feedback. Time-series-aware edge weight update, edge weight Evolving over time, it reflects the dynamic changes in knowledge dependencies (the relationship between knowledge points that students are weak in at the beginning and strengthen in the later stages). . Use periodic functions to encode time intervals .

[0029] Answer result coding .

[0030] Dynamic propagation of knowledge point embedding, node embedding The message passing mechanism propagates on the graph to achieve dynamic knowledge fusion. Through the multi-layer message passing of dynamic GNN, the model achieves feature aggregation. Local knowledge point association, the first layer GNN aggregates the features of directly related knowledge points (1-hop neighbors). High-order knowledge dependency, the m-th layer GNN aggregates the knowledge features of m-hop neighbors to capture indirect associations (such as the migration path of knowledge point A→B→C). Edge weight Regulate the intensity of message transmission so that the model pays more attention to strongly related knowledge points.

[0031] Through learnable gating weights , dynamically adjust the fusion ratio of time series features and graph features. Gate weight calculation . Perform feature fusion . Temporal feature vector hidden state From the BiLSTM time series model. Graph feature vector ,from dynamic GNN.

[0032] The prediction layer, the system's final output module, accurately predicts a student's probability of mastering each knowledge point based on the integrated features. This module utilizes a carefully designed probabilistic prediction architecture, combined with educational cognitive theory models, to output probability values ​​that meet the requirements of educational metrology, providing a reliable basis for personalized learning diagnosis and instructional decision-making.

[0033] Prediction layer , output students' understanding of knowledge points The probability of mastery. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is the overall framework diagram of the embodiment.

[0035] Figure 2 This is the overall architecture diagram of the present invention.

[0036] Figure 3 Detailed diagram of forget gated LSTM.

[0037] Figure 4 Detailed diagram of the multimodal fusion module. DETAILED DESCRIPTION

[0038] Mathematical knowledge point tracking and analysis

[0039] Input data:

[0040] Student answer sequence:

[0041] Question 1: Knowledge point "Quadratic equation", correct answer (1)

[0042] Question 2: Knowledge point "Factorization", wrong answer (0)

[0043] Question 3: Knowledge point "Quadratic equation", correct answer (1)

[0044] Question 4: Knowledge point "quadratic function graph", wrong answer (0)

[0045] Question 5: Knowledge point “Factorization”, correct answer (1).

[0046] Processing flow:

[0047] Dynamic edge weight calculation, initialization of knowledge point association graph:

[0048] Initial edge weight ("quadratic equation" ↔ "factorization") = 0.8

[0049] Initial value of edge weight ("factorization" ↔ "quadratic function image") = 0.6.

[0050] Time decay adjustment:

[0051] In question 5, the last interaction time interval between "factorization" and "quadratic equation" is Δt=2 (question), and the attenuation edge weight is 0.8×e^(-0.2×2)≈0.54.

[0052] The attention weight (based on the current hidden state) is calculated to be 0.3, and the final dynamic edge weight = 0.54 + 0.3 = 0.84.

[0053] Forget Gating Modeling

[0054] The knowledge point "Factorization" was practiced in questions 2 and 5, with a time interval of Δt=3 (questions), and memory strength = e^(-0.15×3)≈0.64.

[0055] LSTM forget gate signal: g_t=0.64, retaining 36% of the historical cell state and 64% relying on new input updates.

[0056] Feature fusion and prediction

[0057] BiLSTM output time series features: h_t=[0.7, 0.2, 0.9, 0.1, 0.8]

[0058] Dynamic GNN output graph features: z_t=[0.6, 0.3, 0.7, 0.4]

[0059] Gated fusion: g_t=0.6 (temporal weight), fused feature = 0.6×h_t + 0.4×z_t.

[0060] Prediction layer output:

[0061] Probability of mastering "quadratic equations": 92%

[0062] Probability of mastering “factorization”: 78%

[0063] Probability of mastering “quadratic function graph”: 65%.

[0064] This paper proposes a knowledge tracking model that integrates dynamic edge weights and forgetting gating. Through dynamic graph neural networks and time series modeling technology, it solves the key defects of traditional knowledge tracking models in the dynamic evolution of knowledge point associations and the modeling of forgetting effects.

[0065] By using a time decay factor and attention mechanism, the strength of associations between knowledge points is adaptively adjusted to capture the dynamic changes in knowledge structure during the learning process. For example, the edge weights of knowledge points are enhanced after review, while the edge weights of long-unpracticed points are decayed, which is more consistent with actual learning patterns. Based on the Ebbinghaus forgetting curve, memory strength is quantified and embedded into the LSTM cell state update process to explicitly simulate the effect of knowledge decay. Combining the temporal behavior characteristics of BiLSTM with the structured knowledge characteristics of dynamic GNNs, adaptive fusion is achieved through learnable gating weights to comprehensively capture the evolution of students' cognitive states. Dynamic edge weight visualization reveals the evolutionary path of knowledge point associations (such as the change in strength from "factorization → quadratic function"). The forgetting gating signal directly reflects the degree of memory decay, providing a basis for teaching decisions.

[0066] In summary, the present invention improves the prediction accuracy and educational applicability of the knowledge tracking model through the collaborative innovation of dynamic edge weights and forgetting gating.

Claims

1. A knowledge tracking model integrating dynamic edge weights and forget gates, characterized by: The following steps are involved: S1. Build a temporal knowledge graph and dynamically adjust the edge weights between knowledge points based on the time decay factor and attention mechanism; S2. Quantify students’ personalized forgetting rate and embed memory strength into LSTM gated units to simulate knowledge decay effects. S3. Design a hierarchical fusion architecture to combine temporal behavior sequences with graph structure features for joint prediction; S4. Training a joint model of dynamic graph neural network and forget gate enhancement; S5. Identify chain knowledge state degradation based on model output and generate personalized review path recommendations.

2. A knowledge tracking model integrating dynamic edge weights and forget gates according to claim 1, characterized in that: The specific steps of dynamically adjusting edge weights in step S1 include: Calculate knowledge point pairs Last interaction interval: ； Through the learnable decay factor Adjust the initial edge weights: ； Linearly superimpose the time-decayed edge weight and the attention weight to obtain the final dynamic edge weight: 。 3. The knowledge tracking model integrating dynamic edge weights and forget gate according to claim 2 is characterized in that: The specific steps of quantifying the forgetting rate in step S2 include: Defining knowledge points based on the Ebbinghaus forgetting curve In time Memory strength: ； in It is a personalized forgetting rate. The larger the value, the faster the forgetting (such as complex knowledge points). , 1 means complete memory, and close to 0 means complete forgetfulness. Memory Strength Embedded as a gating signal to the LSTM cell state update: ； in: : Remains of historical memory ( attenuation), : Current input information (such as answer results), : Input gate, controls the amount of new information written.

4. The knowledge tracking model integrating dynamic edge weights and forget gate according to claim 1 is characterized in that: The implementation of the layered fusion architecture in step S3 includes: Temporal behavior feature extraction: Encoding the answer sequence through BiLSTM , output hidden state , Graph structure feature extraction: based on dynamic edge weights Perform graph convolution operations and output node representations , Gated feature fusion: Dynamically balance the contribution weights of two types of features: ； Among them, the gate weight calculation is: ； : Sigmoid function, the output value range is [0,1], which represents the contribution weight of the time series feature.

5. The knowledge tracking model integrating dynamic edge weights and forget gate according to claim 4 is characterized in that: The gating weight The educational scenario explanation includes: when (Emphasis on timing): It is recommended to practice repeatedly to consolidate short-term memory. when (Focus on the map): Recommended extended training on related knowledge points.

6. The knowledge tracking model integrating dynamic edge weights and forget gate according to claim 5, characterized in that: The specific parameters for model training in step S4 are set as: Hidden layer dimensions , learning rate (Adam optimizer); Regularization coefficient , dynamic edge weight balance coefficient ; The training set: validation set: test set is divided in 7:2:1 time order.

7. The knowledge tracking model integrating dynamic edge weights and forget gate according to claim 6, characterized in that: The logic for generating the review path recommendation in step S5 is: (1) Detecting knowledge state degradation: Calculating cognitive state ; (2) Sort by forgetting intensity priority: ； in, It is the importance index of knowledge points.

8. A knowledge tracking model that implements any one of claims 1-7 and integrates dynamic edge weights and forget gates, characterized in that: include: Dynamic graph construction module: a time-series graph neural network that updates the association strength of knowledge points in real time; Forget gating calculation module: generates memory strength gating signals based on the Ebbinghaus curve; Multimodal fusion prediction module: a gated attention mechanism that combines temporal behavior and graph structure; Decision support module: output state degradation warning and personalized learning strategy.

Images