A knowledge tracking system and method based on multi-algorithm adaptive switching

Abstract

The application discloses a kind of knowledge tracking system and method based on multi-algorithm adaptive switching.System includes data acquisition module, bayesian knowledge tracker, deep knowledge tracker, item response theory tracker and algorithm adaptive switching module.Data acquisition module obtains the historical answering interaction sequence of student on target knowledge point.Bayesian knowledge tracker adopts four-parameter bayesian model to independently and in parallel track mastery probability.Algorithm adaptive switching module automatically selects tracking strategy according to sequence length: when sequence length is less than first preset threshold, item response theory tracker estimation result is used;When sequence length is between first and second preset threshold, deep knowledge tracker prediction value and item response theory tracker estimation value are weighted and fused;When sequence length is greater than or equal to second preset threshold, deep knowledge tracker prediction result is used.The application is suitable for multi-algorithm adaptive switching knowledge tracking.

Description

Technical Field

[0001] This invention relates to the field of knowledge tracking in intelligent education, specifically to a knowledge tracking system and method based on adaptive switching of multiple algorithms. Background Technology

[0002] With the deepening application of artificial intelligence technology in education, knowledge tracing has become a core technology of intelligent teaching systems. Knowledge tracing dynamically assesses students' mastery of various knowledge points by analyzing their historical test performance, providing data support for personalized learning path planning and teaching intervention. However, existing knowledge tracing technologies have the following technical shortcomings:

[0003] Limitation 1: A single algorithm cannot handle both cold start and data-rich scenarios. Existing intelligent teaching systems typically employ a single knowledge tracing algorithm. Item Response Theory (IRT) provides stable ability estimation when data is sparse, but its accuracy is lower than deep learning models when data is abundant. Deep Knowledge Tracing (DKT) can capture complex sequence patterns when data is abundant, but its prediction bias is large and prone to overfitting during the cold start phase due to a lack of training data. Bayesian Knowledge Tracing (BKT) has good interpretability, but its parameter estimation is unstable when data is sparse and it cannot fully utilize sequence information. A single algorithm cannot simultaneously adapt to all stages from sparse to abundant data, resulting in inaccurate evaluation during the cold start phase and limited accuracy during the data-rich phase.

[0004] Defect 2: Abrupt algorithm switching lacks a smooth transition mechanism. Although some systems attempt to switch between multiple algorithms, the switching logic often adopts a discrete "either / or" strategy—using algorithm A when there is little data and algorithm B when there is a lot of data. The instantaneous switching causes a jump in the estimated value, resulting in discontinuous changes in the assessment of student mastery, which affects the stability and interpretability of downstream teaching decisions.

[0005] Deficiency 3: Fixed BKT parameters lack adaptive adjustment capability. Existing BKT models typically use four fixed parameters (prior probability, learning transfer probability, guessing probability, and error probability), which cannot dynamically adjust the parameters based on students' actual performance. When students' answering patterns change significantly, the fixed guessing and error probabilities cannot accurately reflect students' true answering behavior, leading to an accumulation of mastery estimation bias.

[0006] Deficiency 4: Lack of a forgetting decay mechanism in knowledge tracking. Existing knowledge tracking models typically update mastery levels solely based on the sequence of answers, without considering the impact of time on memory retention. If students haven't practiced a particular knowledge point for a long time, even with a high historical mastery level, their actual mastery may decline due to forgetting. Existing systems cannot simulate this forgetting process, leading to inflated mastery assessments and a lack of targeted follow-up review plans.

[0007] Defect 5: The three algorithms operate independently, lacking a collaborative output mechanism. Existing systems typically only expose the output of a single algorithm. The BKT, DKT, and IRT algorithms run independently, preventing the caller from flexibly selecting the optimal tracker output based on the characteristics of the problem type, thus failing to realize the collaborative value of multiple algorithms at the application layer. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a knowledge tracking system and method based on multi-algorithm adaptive switching, so as to overcome the technical defects of the prior art, such as the inability of a single algorithm to take into account different data volume scenarios, abrupt algorithm switching, fixed BKT parameters, lack of forgetting decay, and independent algorithm output.

[0009] The present invention achieves the above objectives by adopting the following technical solution: Firstly, the present invention provides a knowledge tracking system based on multi-algorithm adaptive switching, comprising:

[0010] The data acquisition module is used to acquire the student's historical answer interaction sequence on the target knowledge point. The interaction sequence contains several answer records, and each answer record includes a knowledge point identifier and a correctness indicator.

[0011] The Bayesian knowledge tracker uses a four-parameter Bayesian model to track the mastery probability of each knowledge point. The four parameters include the prior non-mastery probability, learning transfer probability, guessing probability, and error probability. The Bayesian knowledge tracker updates the mastery probability in real time based on the student's answer results using the Bayesian update formula and runs independently in parallel with other trackers.

[0012] The deep knowledge tracker uses a deep knowledge tracking model with a recurrent neural network structure to predict the mastery probability of each knowledge point using the interaction sequence as input.

[0013] The Item Response Theory Tracker uses an ability assessment model based on Item Response Theory to estimate students' potential ability parameters through their answer performance and map them to the probability of mastering each knowledge point.

[0014] The algorithm adaptive switching module automatically selects one or a combination of two of the deep knowledge tracker and the item response theory tracker for mastery estimation based on the sequence length of the interaction sequence, and outputs the tracking result of the Bayesian knowledge tracker as an independent baseline.

[0015] When the sequence length is less than a first preset threshold, the algorithm adaptive switching module uses the estimation result of the project response theory tracker as the mastery output;

[0016] When the sequence length is greater than or equal to the first preset threshold and less than the second preset threshold, the algorithm adaptive switching module performs a weighted fusion of the predicted value of the deep knowledge tracker and the estimated value of the project response theory tracker, and uses the fusion result as the mastery output.

[0017] When the sequence length is greater than or equal to the second preset threshold, the algorithm adaptive switching module uses the prediction result of the deep knowledge tracker as the mastery output.

[0018] Furthermore, the weighted fusion method of the algorithm adaptive switching module when the sequence length is greater than or equal to the first preset threshold and less than the second preset threshold is as follows:

[0019] Calculate the fusion weight, which is equal to the sequence length divided by the second preset threshold;

[0020] The degree of mastery is equal to the fusion weight multiplied by the predicted value of the deep knowledge tracker plus a first product, where the first product is 1 minus the fusion weight multiplied by the estimated value of the project response theory tracker.

[0021] Furthermore, the project response theory tracker employs a two-parameter logistic model, which includes a discrimination parameter and a difficulty parameter.

[0022] The batch estimation of the potential capability parameters adopts an iterative estimation method: the potential capability parameters are initialized with initial values, and the first and second derivatives are calculated in each iteration. The iteration is terminated when the absolute value of the second derivative is less than the preset convergence accuracy; otherwise, the potential capability parameters are updated by dividing the first derivative by the second derivative. The iteration convergence condition is that the absolute value of the update is less than the preset update threshold. The value range of the potential capability parameters is limited to the preset value range.

[0023] The project response theory tracker also supports online gradient updates: calculate the correct probability under the current potential ability parameters, calculate the first difference, the first difference is the actual answer result minus the correct probability, the gradient is equal to the discrimination parameter multiplied by the first difference, the updated potential ability parameters are equal to the current potential ability parameters plus the preset learning rate multiplied by the gradient, and the mastery is obtained by transforming the potential ability parameters through the logistic function.

[0024] Furthermore, the deep knowledge tracker adopts a long short-term memory network structure, with the input dimension being the number of knowledge points multiplied by a preset encoding multiple, and the hidden layer dimension being a preset hidden dimension value.

[0025] The interactive encoding method is as follows: multiply the knowledge point number by the preset encoding multiple and add the correct flag bit as the offset. When the answer is correct, the correct flag bit is incremented by 1 and when the answer is incorrect, the correct flag bit is incremented by 0. Set the corresponding position to 1 in the all-zero vector with a length equal to the number of knowledge points multiplied by the preset encoding multiple to generate the one-hot encoding vector of the current interaction.

[0026] The network weights are initialized using a preset method: the weight matrix input to the hidden weight matrix is ​​randomly sampled within the target interval. The lower limit of the target interval is a preset initialization constant divided by a first sum (where the lower limit is a negative square root of the target interval), and the upper limit of the target interval is the same preset initialization constant divided by the first sum (where the upper limit is a positive square root of the target interval). The first sum is the input dimension plus the hidden dimension. The weight matrix input to the hidden weight matrix is ​​randomly sampled within the second target interval. The lower limit of the second target interval is a preset initialization constant divided by a second sum (where the lower limit is a negative square root of the target interval), and the upper limit of the second target interval is the same preset initialization constant divided by the second sum (where the upper limit is a positive square root of the target interval). The second sum is the hidden dimension multiplied by a third preset constant. The forget gate bias is initialized to a first preset value, and the remaining biases are initialized to the second preset value.

[0027] The forward propagation process sequentially calculates the input gate, forget gate, output gate, and candidate memory units. The output layer maps the hidden states to the mastery probability of each knowledge point through the softmax function.

[0028] Furthermore, the deep knowledge tracker has a cold start rollback mechanism:

[0029] When the length of the interaction sequence of the target knowledge point is less than the first preset threshold, the mastery estimate of the project response theory tracker is directly used as the backoff output of the deep knowledge tracker.

[0030] Furthermore, the Bayesian update method is as follows: When a student answers correctly, a first product factor is calculated, which is the prior mastery probability multiplied by a first factor, where the first factor is 1 minus the error probability; a second product factor is calculated, which is 1 minus the prior mastery probability multiplied by the guess probability; the posterior mastery probability is equal to the first product factor divided by the sum of the first and second product factors; when a student answers incorrectly, a third product factor is calculated, which is the prior mastery probability multiplied by the error probability; a fourth product factor is calculated, which is 1 minus the prior mastery probability multiplied by a second factor, where the second factor is 1 minus the guess probability; the posterior mastery probability is equal to the third product factor divided by the sum of the third and fourth product factors; then, the new posterior probability is updated using the learning transition probability, where the new posterior probability is equal to the posterior probability plus a third factor, where the third factor is 1 minus the posterior probability multiplied by the learning transition probability.

[0031] Furthermore, the Bayesian knowledge tracker also features a parameter adaptation mechanism and a forgetting decay mechanism:

[0032] The parameter adaptive mechanism is as follows: when the number of observed data reaches the preset number of triggers, the guessing probability and the error probability are adjusted according to the historical answer accuracy. If the accuracy is greater than the first preset accuracy threshold, the guessing probability and the error probability are each reduced by a preset step size. If the accuracy is less than the second preset accuracy threshold, the guessing probability and the error probability are each increased by the preset step size. The adjustment range is limited to between the preset lower limit and the preset upper limit.

[0033] The forgetting decay mechanism is as follows: the final mastery is equal to the current mastery probability multiplied by a first coefficient plus a fifth product factor, where the first coefficient is 1 minus the decay factor, the fifth product factor is the prior unmastered probability multiplied by the decay factor, and the decay factor is equal to the number of interaction records raised to the power of the preset decay rate.

[0034] Furthermore, the knowledge tracking system also includes a unified API interface. The Bayesian knowledge tracker, the deep knowledge tracker, and the project response theory tracker all expose knowledge mastery query and update interfaces through the unified API interface. The caller selects the corresponding tracker result according to the question type.

[0035] Secondly, this invention provides a knowledge tracing method based on multi-algorithm adaptive switching, applied to the aforementioned knowledge tracing system based on multi-algorithm adaptive switching, comprising the following steps:

[0036] Step S1: Obtain the student's historical answer interaction sequence on the target knowledge point;

[0037] Step S2: Determine the sequence length of the interaction sequence;

[0038] Step S3: When the sequence length is less than the first preset threshold, the student's potential ability parameters are estimated using the item response theory tracker, and the potential ability parameters are mapped to the mastery probability through the logistic function, which is then used as the final mastery output.

[0039] Step S4: When the sequence length is greater than or equal to the first preset threshold and less than the second preset threshold, start the deep knowledge tracker to perform forward propagation calculation on the interaction sequence, obtain the predicted value of the deep knowledge tracker, and at the same time obtain the estimated value of the item response theory tracker. Calculate the fusion weight, which is equal to the sequence length divided by the second preset threshold with an upper limit of 1.0. The fusion mastery is equal to the fusion weight multiplied by the predicted value of the deep knowledge tracker plus a sixth product factor, which is 1 minus the fusion weight multiplied by the estimated value of the item response theory tracker. Output the fusion mastery as the final mastery.

[0040] Step S5: When the sequence length is greater than or equal to the second preset threshold, start the deep knowledge tracker to perform a complete forward propagation calculation on the interaction sequence, and output the probability value of the corresponding knowledge point after the output layer is mapped by the softmax function as the final mastery output.

[0041] Step S6: The Bayesian knowledge tracker runs independently of steps S3 to S5 in parallel. It performs Bayesian updates based on each answer result and outputs a structured knowledge point mastery probability as an independent baseline tracking result.

[0042] Furthermore, the knowledge tracking method also includes step S7: when the Bayesian knowledge tracker triggers parameter adaptation when the observed data reaches a preset number of triggers: calculate the historical answer accuracy rate; if the accuracy rate is greater than the first preset accuracy rate threshold, the guess probability and the error probability are each reduced by a preset step size; if the accuracy rate is less than the second preset accuracy rate threshold, the guess probability and the error probability are each increased by the preset step size, and the adjustment range is limited to between the preset lower limit value and the preset upper limit value.

[0043] The Bayesian knowledge tracker introduces forgetting decay when calculating mastery: the decay factor is equal to the number of interaction records raised to the power of the preset decay rate, and the final mastery is equal to the current mastery probability multiplied by the first coefficient plus the seventh product factor, where the first coefficient is 1 minus the decay factor, and the seventh product factor is the prior non-mastery probability multiplied by the decay factor.

[0044] Compared with the prior art, the present invention has the following advantages:

[0045] This invention employs a multi-algorithm adaptive switching approach to balance cold start and long-term accuracy. It utilizes IRT to provide stable capability estimation when data is sparse (e.g., sequence length < 5 sequences), and DKT to capture complex sequence interaction patterns when data is abundant (e.g., sequence length ≥ 10 sequences). A smooth transition from IRT to DKT is achieved through alpha-weighted fusion of sequences between 5 and 10, overcoming the technical limitation of a single algorithm in handling different data volumes and achieving a balance between cold start and long-term accuracy.

[0046] Weighted fusion enables a smooth transition during algorithm switching. This invention employs a linear weighted fusion strategy with alpha = length / 10 for sequences with lengths between 5 and 10. The fusion weight continuously varies from 0.5 to 1.0, avoiding jumps in estimated values ​​during algorithm switching and ensuring the temporal continuity of mastery assessment and the stability of downstream decision-making.

[0047] BKT parameter adaptation improves model fitting accuracy. This invention triggers parameter adaptation when 20 data points are observed, dynamically adjusting the guess probability and error probability based on historical accuracy (lowering guess and error probabilities when accuracy is high, and increasing them when accuracy is low). This allows the BKT model to adaptively adjust parameters according to students' actual answering patterns, improving the accuracy of mastery estimation.

[0048] The forgetting decay mechanism simulates the memory curve. This invention introduces a forgetting decay factor (decay rate of 0.1 to the power of n) based on the number of interactive records in the BKT mastery calculation. When students have not practiced for a long time, their mastery automatically decays towards the prior probability, simulating the Ebbinghaus forgetting curve. This makes the mastery assessment closer to the students' actual memory state and provides a more accurate basis for subsequent review arrangements.

[0049] DKT cold start rollback ensures availability of sparse data. This invention incorporates a cold start rollback mechanism in DKT, directly using the estimated value of IRT as the output of DKT when the length of the interaction sequence is less than 5, thus avoiding prediction bias caused by overfitting when training data is insufficient.

[0050] A unified API interface enables collaborative output of multiple algorithms. This invention exposes the outputs of three trackers—BKT, DKT, and IRT—simultaneously through a unified API interface. Callers can flexibly select the optimal tracker based on the characteristics of the question type (e.g., BKT for conceptual questions, DKT for sequence questions, and IRT for cold starts), realizing the collaborative value of multiple algorithms at the application layer and improving the system's flexibility and scalability. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the overall architecture of the knowledge tracking system based on multi-algorithm adaptive switching provided in an embodiment of the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0053] Example 1: System Overall Architecture

[0054] Reference Figure 1 The knowledge tracking system based on multi-algorithm adaptive switching described in this invention includes a data acquisition module, a Bayesian knowledge tracker (BKT), a deep knowledge tracker (DKT), an item response theory tracker (IRT), an algorithm adaptive switching module, and a unified API interface.

[0055] The data acquisition module receives externally input student answer records, groups them according to student identifier and knowledge point identifier, and constructs a historical answer interaction sequence for each student on each knowledge point. Each answer record contains a knowledge point identifier (…). ), Correctness indicator ( (1 indicates correct, 0 indicates incorrect) and a timestamp. The interaction sequence is arranged in ascending order of timestamp.

[0056] The BKT tracker, DKT tracker, and IRT tracker operate in parallel, each independently maintaining an estimate of the student's knowledge state. The algorithm adaptive switching module reads the interaction sequence from the data acquisition module and, based on the sequence length, decides whether to use IRT estimation, DKT+IRT fusion, or DKT prediction as the main output, while using the output of the BKT tracker as an independent baseline. The outputs of all three trackers are exposed through the unified API interface.

[0057] Example 2: Algorithm Adaptive Switching Decision Process

[0058] The decision-making process of the adaptive switching module of the algorithm of this invention includes the following steps:

[0059] Step A01: Read the historical question-answering interaction sequence on the target knowledge point from the data acquisition module and record the sequence length L.

[0060] Step A02: Determine whether the sequence length L is less than the first preset threshold (5 sequences). If L < 5, proceed to step A03; otherwise, proceed to step A04.

[0061] Step A03 (IRT Cold Start Path): Call the IRT tracker to estimate the mastery level of the knowledge point, output the IRT estimate as the final mastery level, and end the decision-making process.

[0062] Step A04: Determine whether the sequence length L is less than the second preset threshold (10 sequences). If L < 10 (i.e., 5 ≤ L < 10), proceed to step A05; otherwise (L ≥ 10), proceed to step A07.

[0063] Step A05 (fusion path): Use the DKT tracker to perform forward propagation on the interaction sequence to obtain the DKT prediction value; use the IRT tracker to obtain the IRT estimate value. Calculate the fusion weight alpha = L / 10, with an upper limit of 1.0 for alpha.

[0064] Step A06: Calculate the fusion mastery = alpha × DKT predicted value + (1 - alpha) × IRT estimated value, output the fusion mastery as the final mastery, and end the decision-making process.

[0065] Step A07 (DKT Dominant Path): Call the DKT tracker to perform a complete forward propagation of the interaction sequence. After the output layer is mapped by the softmax function, the probability value corresponding to the target knowledge point is taken as the DKT prediction value, and the output is the final mastery level.

[0066] The following are specific application examples of the three decision paths of this invention:

[0067] Example 1: IRT Cold Start Path (L < 5)

[0068] In a specific application example of this invention, a student is learning the concept of "logarithmic function" for the first time, with only 3 answer records (L=3 < 5). The three records are: question 1 answered incorrectly (y=0), question 2 answered correctly (y=1), and question 3 answered incorrectly (y=0). Due to the extremely small amount of data, the DKT model cannot be effectively trained (it is prone to overfitting). Therefore, the system does not call DKT and directly uses the IRT tracker for estimation.

[0069] The IRT tracker obtains the difficulty parameter *b* and discrimination parameter *a* of three questions—all three questions are of medium difficulty (b1=0.2, b2=0.5, b3=0.8), and the discrimination parameter *a* is 1.0 for each question. The Newton-Raphson iterative method is used to estimate the potential ability parameter *θ*: initially *θ*=0, it converges to *θ*≈-0.32 after three iterations. After logistic transformation, the mastery is calculated as *mastery* = 1 / (1+1.377) ≈ 0.421.

[0070] This estimate reflects a slightly below-average level of mastery (0.5) in this knowledge point, consistent with the student's performance of answering only 1 out of 3 questions correctly. The system outputs this IRT estimate of 0.421 as the final mastery level for subsequent learning path planning.

[0071] Example 2: IRT+DKT weighted fusion path (5 ≤ L < 10)

[0072] In another specific application example of this invention, a student has 7 answer records for the knowledge point of "quadratic function" (5 ≤ L=7 < 10). The DKT prediction value is 0.72, and the IRT estimate value is 0.58. alpha = 7 / 10 = 0.7.

[0073] Integration mastery = 0.7 × 0.72 + 0.3 × 0.58 = 0.504 + 0.174 = 0.678.

[0074] The fusion value falls between DKT and IRT—it's about 17% higher than the IRT estimate (0.58) because DKT captures the recent trend of correct answers (3 correct answers in the last 3 questions); however, due to insufficient data (only 7 data points), the DKT prediction (0.72) is not fully accepted, and the system retains 30% of the IRT weight as a "conservative estimate." This achieves a smooth transition from IRT to DKT, and the mastery estimate does not jump.

[0075] In another example, a student has 6 answer records (L=6), a DKT predicted value of 0.35, and an IRT estimated value of 0.45. alpha = 6 / 10 = 0.6. The integration mastery = 0.6 × 0.35 + 0.4 × 0.45 = 0.21 + 0.18 = 0.39. This student's accuracy rate on the last 6 questions is only 33% (2 / 6), and the integration mastery of 0.39 accurately reflects their below-average mastery level.

[0076] In another example, a student has 9 answer records (L=9), with a DKT prediction value of 0.88 and an IRT estimate of 0.72. alpha = 9 / 10 = 0.9. Fusion mastery = 0.9 × 0.88 + 0.1 × 0.72 = 0.792 + 0.072 = 0.864. With a data volume close to 10 records and a DKT weight as high as 90%, the system closely resembles a pure DKT model, reflecting the advantages of sequence learning when data is abundant.

[0077] Example 3: DKT dominant path (L ≥ 10)

[0078] In another specific application example of this invention, a student already has 15 answer records (L=15 ≥ 10) on the topic of "trigonometric functions," providing sufficient data. The system directly uses the DKT tracker for prediction.

[0079] The DKT tracker encodes each of the 15 interaction records into a one-hot vector sequence (vector length is twice the total number of knowledge points), and then inputs them sequentially into the MiniLSTM network. After 15 forward propagation steps, the hidden state of the last time step is mapped through the output layer and the softmax function, and the probability value corresponding to the target knowledge point "trigonometric function" is 0.81.

[0080] The DKT prediction value of 0.81 was used as the final mastery output. Due to the sufficient amount of data (≥10 data points), the system fully trusted the complex sequence pattern captured by DKT—the student had a 100% accuracy rate on the last 5 questions (all answers were correct), and the DKT model captured this upward trend, with a prediction value of 0.81 higher than its overall accuracy rate (11 out of 15 questions answered correctly, 73% accuracy), reflecting significant recent progress.

[0081] Example 3: IRT Tracker Estimation Process

[0082] The estimation process of the IRT tracker described in this invention includes a batch estimation mode and an online update mode.

[0083] Batch estimation mode (Newton-Raphson iterative method):

[0084] Step B01: Obtain the student's historical question-answering sequence for a certain knowledge point, including the question difficulty parameter b and discrimination parameter a for each record, as well as the answer result y (1 correct / 0 incorrect).

[0085] Step B02: Initialize potential capability parameters .

[0086] Step B03: Calculate the current Below, for the i-th question, what is the probability of being correct? .

[0087] Step B04: Calculate the first derivative (gradient) .

[0088] Step B05: Calculate the second derivative (information content) .

[0089] Step B06: Determine if |h| is less than the preset convergence precision ( If the result is less than 0, the iteration terminates and proceeds to step B09.

[0090] Step B07: Update θ = θ - g / h (equivalent to θ = θ + g / |h|, since h is negative).

[0091] Step B08: Determine if the update amount |g / h| is less than the preset update threshold. If it is, terminate the iteration; otherwise, return to step B03 to continue the iteration. The value range of θ is limited to the interval [-4.0, 4.0].

[0092] Step B09: Transform the final θ into mastery using the logistic function: Output the degree of mastery.

[0093] Online update mode (gradient descent):

[0094] Step B10: Receive the new answer result y, where the current θ is known.

[0095] Step B11: Calculate the correct probability at the current θ .

[0096] Step B12: Calculate the gradient grad = a × (y - P).

[0097] Step B13: Update .

[0098] Step B14: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] The output is transformed into a mastery level using a logistic function.

[0099] In a specific application example of this invention, a student answered a question correctly (y=1) with a difficulty level of b=0.5 and a discrimination index of a=1.0. Currently, θ=0.5. P = 0.5, grad = 1.0 × (1-0.5) = 0.5. After the update, the mastery level increased from 0.622 (corresponding to θ=0.5) to 0.634 (corresponding to θ=0.55).

[0100] Example 4: Forward Propagation Process of DKT Tracker

[0101] The DKT tracker described in this invention adopts a MiniLSTM network structure, and the forward propagation process includes the following steps:

[0102] Step C01: Obtain the interaction sequence, with a length of L and a total number of knowledge points of N.

[0103] Step C02: Encode each interaction sequence into a one-hot vector. The encoding rule is as follows: When answering correctly When answering incorrectly In a vector of length 2N containing only zeros, the index is... Set the position to 1.

[0104] For example, if the knowledge point number is 3, when the answer is correct, the offset = 3×2+1=7, and the 7th bit of the all-zero vector (counting from 0) is set to 1.

[0105] Step C03: Initialize hidden state The zero vector (32 dimensions) represents the cell state. It is a zero vector (32 dimensions).

[0106] Step C04: For the input vector at each time step t Calculate sequentially:

[0107] Forgotten Gate: ,in As part of the input to the hidden weight matrix, Forget gate bias (initialized to all 1s);

[0108] Input Gate: , Indicates the input gate weights. This represents the input gate bias vector;

[0109] Candidate memory units: , Indicates the weight of the candidate memory unit. Represents the bias vector of candidate memory cells;

[0110] Update cell status: ;

[0111] Output gate: , Indicates the output gate weight. This represents the output gate bias vector;

[0112] Hidden state: .

[0113] Step C05: Hidden state of the last time step After linear transformation by the output layer, the results are mapped to a probability vector of mastery for each knowledge point using the softmax function. .

[0114] Step C06: From The probability value corresponding to the target knowledge point is taken from the vector and output as the DKT prediction value.

[0115] In a specific application example of this invention, the total number of knowledge points N=50, the input dimension is 100, and the hidden dimension is 32. The length of a student's interaction sequence is 8. After forward propagation through MiniLSTM, the third component of the output vector p (corresponding to the "logarithmic function" knowledge point) is 0.72, which is the DKT prediction value.

[0116] Cold start rollback mechanism: When the length of the interaction sequence L < 5, the DKT tracker does not perform forward propagation, but directly returns the estimated value of the IRT tracker as the rollback output, thus avoiding overfitting of DKT under small sample conditions.

[0117] Example 5: Bayesian Update and Parameter Adaptation Process of BKT Tracker

[0118] The Bayesian update and parameter adaptation process of the BKT tracker 200 described in this invention includes the following steps:

[0119] Step D01: Initialize the four parameters—prior unknown probability P( The probability of learning transition is P(T) = 0.5, the probability of guessing is P(G) = 0.2, and the probability of error is P(S) = 0.1.

[0120] Step D02: Receive the new answer result, with the current mastery probability being P(L).

[0121] Step D03: Perform a Bayesian update. If the answer is correct (y=1), the posterior probability P(L|correct) = P(L)×(1-P(S)) / [P(L)×(1-P(S)) + (1-P(L))×P(G)]. If the answer is incorrect (y=0), the posterior probability P(L|wrong) = P(L)×P(S) / [P(L)×P(S) + (1-P(L))×(1-P(G))].

[0122] Step D04: Update the transition probability to a new posterior probability P(L_new) = P(L|y) + (1 - P(L|y)) × P(T) by learning the transition probability.

[0123] Step D05: Accumulate the number of observed data entries (count). If the count does not reach the preset trigger count of 20 entries, proceed to step D07.

[0124] Step D06 (Parameter Adaptation): Parameter adaptation is triggered when count reaches 20. Calculate the accuracy rate (acc) of the 20 historical answers. If acc > 0.8, decrease P(G) and P(S) by 0.05 each (lower limit 0.05); if acc < 0.3, increase P(G) and P(S) by 0.05 each (upper limit 0.35).

[0125] Step D07 (Forgetting Decay): Calculate the decay factor decay = 0.1^count. Final mastery = P(L_new) × (1-decay) + P( ) × decay.

[0126] Step D08: Output the final mastery level.

[0127] In a specific application example of the present invention, a student has 15 answer records for the knowledge point of "trigonometric functions", and the current P(L)=0.65, P(S)=0.1, P(G)=0.2.

[0128] After a student answers a question correctly:

[0129] P(L|correct)=0.65×0.9 / [0.65×0.9+0.35×0.2]=0.585 / (0.585+0.07)=0.893.

[0130] P(L_new) = 0.893 + (1 - 0.893) × 0.3 = 0.925. count = 16 < 20, parameter adaptation will not be triggered for now. Decay factor ≈ 1 × There is almost no attenuation. Final mastery ≈ 0.925.

[0131] In another application example, the student had only 3 answer records on the topic of "logarithmic functions," all of which were incorrect. P(L) = 0.4, P(S) = 0.1, P(G) = 0.2. Count = 3, decay factor decay = 0.1^3 = 0.001, the decay effect is negligible. After the student answered incorrectly, P(L|wrong) = 0.4 × 0.1 / [0.4 × 0.1 + 0.6 × 0.9] = 0.04 / (0.04 + 0.54) = 0.069. P(L_new) = 0.069 + (1 - 0.069) × 0.3 = 0.348. The final mastery level ≈ 0.348.

[0132] Example 6: Smooth transition of alpha-weighted fusion

[0133] This invention employs an alpha-weighted fusion strategy for sequences with lengths between 5 and 10, achieving a smooth transition from IRT to DKT.

[0134] When the sequence length L=5, alpha = 5 / 10 = 0.5, and the fusion mastery = 0.5×DKT + 0.5×IRT, with IRT and DKT each accounting for half of the weight.

[0135] When the sequence length L=7, alpha = 7 / 10 = 0.7, fusion mastery = 0.7×DKT + 0.3×IRT, and the DKT weight increases to 70%.

[0136] When the sequence length L=9, alpha = 9 / 10 = 0.9, fusion mastery = 0.9×DKT + 0.1×IRT, and DKT is absolutely dominant.

[0137] When the sequence length L=10, alpha = 1.0, fusion mastery = DKT, and the system is fully switched to DKT.

[0138] This fusion strategy ensures that the mastery estimate changes continuously with the amount of data, avoiding jumps in the estimate at switching boundaries (L=5 or L=10). For example, suppose a student's IRT estimate is 0.50 and DKT prediction is 0.70 at L=5, with a fused output of 0.60; at L=6, IRT=0.52 and DKT=0.72, with a fused output of 0.64; and at L=7, the fused output is 0.68. Mastery increases smoothly over time, rather than jumping from 0.50 to 0.70.

[0139] Example 7: Complete Knowledge Tracking Method Flow

[0140] The complete process of the knowledge tracking method based on multi-algorithm adaptive switching described in this invention includes the following steps:

[0141] Step S1: Obtain the student's historical question-answering interaction sequence on the target knowledge point.

[0142] In this embodiment, the target knowledge point is assumed to be "quadratic function". Student S001 has 8 answer records with an accuracy rate of 62.5%.

[0143] Step S2: Determine the sequence length L=8 of the interaction sequence.

[0144] Step S3: Since L=8 does not meet the condition L<5, skip the IRT standalone output path.

[0145] Step S4: Since 5 ≤ L=8 < 10, proceed to the fusion path. The DKT prediction value is 0.68, and the IRT estimate is 0.55. alpha = 8 / 10 = 0.8. Fusion mastery = 0.8×0.68 + 0.2×0.55 = 0.544 + 0.11 = 0.654.

[0146] Step S5: If the condition L≥10 is not met, skip the DKT dominant path.

[0147] Step S6: The BKT tracer runs independently and in parallel. The student's current score for the "quadratic function" knowledge point is P(L) = 0.60, with 7 previous records, and the answer was correct this time. After the Bayesian update, P(L_new) = 0.72, which is used as the BKT baseline output.

[0148] Step S7: The BKT tracker has accumulated 8 observations, which does not meet the trigger condition of 20 observations. Parameter adaptation will not be performed at this time. Forgetting decay factor decay = 1 × The attenuation is negligible.

[0149] Step S8: The unified API interface returns the outputs of three trackers—BKT: 0.72, DKT: 0.68, and IRT: 0.55. The caller (e.g., the intelligent question generation module) selects the appropriate tracker based on the current scenario: BKT for interpretability; DKT for sequence prediction accuracy; and IRT for fast estimation.

[0150] Example 8: Complete Triggering Process for BKT Parameter Adaptation

[0151] This embodiment demonstrates the complete triggering and execution process of the BKT tracker parameter adaptation mechanism.

[0152] A student continuously answers questions on the "Sequences" knowledge point, triggering parameter adaptation when the cumulative number of records reaches 20. The system calculates the historical accuracy rate of 20 records to be 0.85 (>0.8). Currently, P(G) = 0.20, P(S) = 0.10. Parameter adaptation is executed: P(G)_new = 0.20 - 0.05 = 0.15, P(S)_new = 0.10 - 0.05 = 0.05.

[0153] The adjusted parameters mean that the student has a low probability of guessing (15%) and a low probability of making a mistake (5%), which is consistent with the 85% accuracy rate – the student has indeed mastered the knowledge point, rather than answering correctly by guessing or by carelessness.

[0154] In another application example, a student's historical accuracy rate for 20 records in the "Permutations and Combinations" knowledge point is 0.25 (<0.3). P(G)_new = 0.20 + 0.05 = 0.25, P(S)_new = 0.10 + 0.05 = 0.15. The adjusted parameters reflect that the student's guess probability and error probability are both high, consistent with the low accuracy rate.

[0155] The parameter adjustment range is limited to the interval [0.05, 0.35] to prevent excessive parameter drift. Once the parameter has reached its boundary, subsequent adjustments will not exceed the boundary.

[0156] Example 9: The Effect of the Forgetting Decay Mechanism

[0157] This embodiment demonstrates the impact of the forgetting decay mechanism on mastery assessment.

[0158] A student achieved a mastery level of 0.90 in the "trigonometric functions" topic and then did not practice this topic for 60 consecutive days. The number of interaction records (count) is 60 (including previous practice records). The decay factor is 1× The value is almost zero, meaning that the level of knowledge almost completely decays to the prior probability of 0.5.

[0159] However, in practice, most of the 60 records likely come from early practice. If there are 40 early practice records, the increase in the number of records corresponding to the recent gap in practice is relatively small. A more precise decay mechanism should consider the time interval rather than the number of records. However, in scenarios that rely solely on answer records, using the number of records as a time proxy variable can achieve the basic effect of "mastery decays with prolonged inactivity."

[0160] For example, a student's current probability of mastering "trigonometric functions" is P(L_new) = 0.85, and the prior probability of not mastering it is P(L_new). =0.5, 20 records already exist. Attenuation factor The attenuation is negligible, and the final mastery is approximately 0.85.

[0161] If the student has only 5 records and the last record is a long time ago, the decay factor... , The decay rate is extremely small. This indicates that the decay effect is weak when the number of records is small, which differs from the actual cognitive pattern that "forgetting is faster when knowledge is first established." In practical applications, the calculation method of the decay factor can be optimized by introducing a timestamp dimension, making it more accurately reflect the impact of time intervals on forgetting.

[0162] Example 10: Collaborative Invocation of Multiple Algorithms Using a Unified API Interface

[0163] This embodiment demonstrates a multi-algorithm collaborative invocation method for the unified API interface 600.

[0164] The unified API interface 600 provides the following endpoints:

[0165] / bkt / query: Queries the mastery probability of the BKT tracker;

[0166] / dkt / query: Queries the mastery probability of the DKT tracker;

[0167] / irt / query: Queries the mastery probability of the IRT tracker;

[0168] / fusion / query: The degree of mastery of the fusion of the query algorithm adaptive switching module (main output);

[0169] / update: Submits new answer records and updates all three trackers simultaneously;

[0170] The caller (such as the intelligent question generation module) can select a tracker based on the characteristics of the question type:

[0171] Conceptual clarification questions: The BKT tracker is selected because its four parameters have good interpretability and can clearly determine whether students have conceptual confusion.

[0172] For computational word problems: the DKT tracker is used because it can capture the sequence dependency patterns between problem-solving steps and more accurately predict the mastery of complex problem types.

[0173] New knowledge point: Cold start: Choose the IRT tracker because it provides a stable capability estimate when the data is sparse;

[0174] Typical scenario: Select the fusion mastery level (main output) and automatically adapt to the data volume.

[0175] In a specific application example of this invention, a certain intelligent question-generating module needs to assess students' mastery of the "derivative" concept to determine the difficulty of the next question. This module calls the ` / fusion / query` endpoint of the unified API interface to obtain a fusion mastery score of 0.78 (sufficient data, DKT-driven), and simultaneously calls ` / bkt / query` to obtain a BKT baseline of 0.74 for reference. The question-generating module confirms the reliability of the assessment based on the consistency of the two scores (difference <0.05) and selects questions of medium to high difficulty to push to the next question.

[0176] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A knowledge tracking system based on multi-algorithm adaptive switching, characterized in that, include: The data acquisition module is used to acquire the student's historical answer interaction sequence on the target knowledge point. The interaction sequence contains several answer records, and each answer record includes a knowledge point identifier and a correctness indicator. The Bayesian knowledge tracker uses a four-parameter Bayesian model to track the mastery probability of each knowledge point. The four parameters include the prior non-mastery probability, learning transfer probability, guessing probability, and error probability. The Bayesian knowledge tracker updates the mastery probability in real time based on the student's answer results using the Bayesian update formula and runs independently in parallel with other trackers. The deep knowledge tracker uses a deep knowledge tracking model with a recurrent neural network structure to predict the mastery probability of each knowledge point using the interaction sequence as input. The Item Response Theory Tracker uses an ability assessment model based on Item Response Theory to estimate students' potential ability parameters through their answer performance and map them to the probability of mastering each knowledge point. The algorithm adaptive switching module automatically selects one or a combination of two of the deep knowledge tracker and the item response theory tracker for mastery estimation based on the sequence length of the interaction sequence, and outputs the tracking result of the Bayesian knowledge tracker as an independent baseline. When the sequence length is less than a first preset threshold, the algorithm adaptive switching module uses the estimation result of the project response theory tracker as the mastery output; When the sequence length is greater than or equal to the first preset threshold and less than the second preset threshold, the algorithm adaptive switching module performs a weighted fusion of the predicted value of the deep knowledge tracker and the estimated value of the project response theory tracker, and uses the fusion result as the mastery output. When the sequence length is greater than or equal to the second preset threshold, the algorithm adaptive switching module uses the prediction result of the deep knowledge tracker as the mastery output.

2. The knowledge tracking system based on multi-algorithm adaptive switching according to claim 1, characterized in that, The weighted fusion method of the algorithm adaptive switching module when the sequence length is greater than or equal to the first preset threshold and less than the second preset threshold is as follows: Calculate the fusion weight, which is equal to the sequence length divided by the second preset threshold; The degree of mastery is equal to the fusion weight multiplied by the predicted value of the deep knowledge tracker plus a first product, where the first product is 1 minus the fusion weight multiplied by the estimated value of the project response theory tracker.

3. The knowledge tracking system based on multi-algorithm adaptive switching according to claim 1, characterized in that, The project reaction theory tracker uses a two-parameter logistic model, which includes a discrimination parameter and a difficulty parameter. The batch estimation of the potential capability parameters adopts an iterative estimation method: the potential capability parameters are initialized with initial values, and the first and second derivatives are calculated in each iteration. The iteration is terminated when the absolute value of the second derivative is less than the preset convergence accuracy; otherwise, the potential capability parameters are updated by dividing the first derivative by the second derivative. The iteration convergence condition is that the absolute value of the update is less than the preset update threshold. The value range of the potential capability parameters is limited to the preset value range. The project response theory tracker also supports online gradient updates: calculate the correct probability under the current potential ability parameters, calculate the first difference, the first difference is the actual answer result minus the correct probability, the gradient is equal to the discrimination parameter multiplied by the first difference, the updated potential ability parameters are equal to the current potential ability parameters plus the preset learning rate multiplied by the gradient, and the mastery is obtained by transforming the potential ability parameters through the logistic function.

4. The knowledge tracking system based on multi-algorithm adaptive switching according to claim 1, characterized in that, The deep knowledge tracker adopts a long short-term memory network structure, with the input dimension being the number of knowledge points multiplied by a preset encoding multiple, and the hidden layer dimension being a preset hidden dimension value. The interactive encoding method is as follows: multiply the knowledge point number by the preset encoding multiple and add the correct flag bit as the offset. When the answer is correct, the correct flag bit is incremented by 1 and when the answer is incorrect, the correct flag bit is incremented by 0. Set the corresponding position to 1 in the all-zero vector with a length equal to the number of knowledge points multiplied by the preset encoding multiple to generate the one-hot encoding vector of the current interaction. The network weights are initialized using a preset method: the weight matrix input to the hidden weight matrix is ​​randomly sampled within the target interval. The lower limit of the target interval is a preset initialization constant divided by a first sum (where the lower limit is a negative square root of the target interval), and the upper limit of the target interval is the same preset initialization constant divided by the first sum (where the upper limit is a positive square root of the target interval). The first sum is the input dimension plus the hidden dimension. The weight matrix input to the hidden weight matrix is ​​randomly sampled within the second target interval. The lower limit of the second target interval is a preset initialization constant divided by a second sum (where the lower limit is a negative square root of the target interval), and the upper limit of the second target interval is the same preset initialization constant divided by the second sum (where the upper limit is a positive square root of the target interval). The second sum is the hidden dimension multiplied by a third preset constant. The forget gate bias is initialized to a first preset value, and the remaining biases are initialized to the second preset value. The forward propagation process sequentially calculates the input gate, forget gate, output gate, and candidate memory units. The output layer maps the hidden states to the mastery probability of each knowledge point through the softmax function.

5. The knowledge tracking system based on multi-algorithm adaptive switching according to claim 1, characterized in that, The deep knowledge tracker has a cold start rollback mechanism: When the length of the interaction sequence of the target knowledge point is less than the first preset threshold, the mastery estimate of the project response theory tracker is directly used as the backoff output of the deep knowledge tracker.

6. The knowledge tracking system based on multi-algorithm adaptive switching according to claim 1, characterized in that, The Bayesian update method is as follows: when a student answers correctly, the first product factor is calculated. The first product factor is the prior mastery probability multiplied by the first factor, and the first factor is 1 minus the error probability. Calculate the second product factor, which is 1 minus the prior knowledge probability and multiplied by the guess probability; the posterior knowledge probability is equal to the first product factor divided by the sum of the first product factor and the second product factor; When a student answers incorrectly, a third product factor is calculated, which is the prior knowledge probability multiplied by the error probability. Calculate a fourth product factor, which is 1 minus the prior mastery probability multiplied by a second factor, where the second factor is 1 minus the guess probability; the posterior mastery probability is equal to the third product factor divided by the sum of the third and fourth product factors; then update the posterior probability to a new one using the learning transition probability, where the new posterior probability is equal to the posterior probability plus a third factor, where the third factor is 1 minus the posterior probability multiplied by the learning transition probability.

7. The knowledge tracking system based on multi-algorithm adaptive switching according to claim 1, characterized in that, The Bayesian knowledge tracker also features a parameter adaptation mechanism and a forgetting decay mechanism: The parameter adaptive mechanism is as follows: when the number of observed data reaches the preset number of triggers, the guessing probability and the error probability are adjusted according to the historical answer accuracy. If the accuracy is greater than the first preset accuracy threshold, the guessing probability and the error probability are each reduced by a preset step size. If the accuracy is less than the second preset accuracy threshold, the guessing probability and the error probability are each increased by the preset step size. The adjustment range is limited to between the preset lower limit and the preset upper limit. The forgetting decay mechanism is as follows: the final mastery is equal to the current mastery probability multiplied by a first coefficient plus a fifth product factor, where the first coefficient is 1 minus the decay factor, the fifth product factor is the prior unmastered probability multiplied by the decay factor, and the decay factor is equal to the number of interaction records raised to the power of the preset decay rate.

8. The knowledge tracking system based on multi-algorithm adaptive switching according to claim 1, characterized in that, It also includes a unified API interface. The Bayesian knowledge tracker, the deep knowledge tracker, and the project response theory tracker all expose knowledge mastery query and update interfaces through the unified API interface. The caller selects to use the corresponding tracker results according to the question type.

9. A knowledge tracing method based on multi-algorithm adaptive switching, applied to the knowledge tracing system based on multi-algorithm adaptive switching as described in any one of claims 1-8, characterized in that, Includes the following steps: Step S1: Obtain the student's historical answer interaction sequence on the target knowledge point; Step S2: Determine the sequence length of the interaction sequence; Step S3: When the sequence length is less than the first preset threshold, the student's potential ability parameters are estimated using the item response theory tracker, and the potential ability parameters are mapped to the mastery probability through the logistic function, which is then used as the final mastery output. Step S4: When the sequence length is greater than or equal to the first preset threshold and less than the second preset threshold, start the deep knowledge tracker to perform forward propagation calculation on the interaction sequence, obtain the predicted value of the deep knowledge tracker, and at the same time obtain the estimated value of the item response theory tracker. Calculate the fusion weight, which is equal to the sequence length divided by the second preset threshold with an upper limit of 1.

0. The fusion mastery is equal to the fusion weight multiplied by the predicted value of the deep knowledge tracker plus a sixth product factor, which is 1 minus the fusion weight multiplied by the estimated value of the item response theory tracker. Output the fusion mastery as the final mastery. Step S5: When the sequence length is greater than or equal to the second preset threshold, start the deep knowledge tracker to perform a complete forward propagation calculation on the interaction sequence, and output the probability value of the corresponding knowledge point after the output layer is mapped by the softmax function as the final mastery output. Step S6: The Bayesian knowledge tracker runs independently of steps S3 to S5 in parallel. It performs Bayesian updates based on each answer result and outputs a structured knowledge point mastery probability as an independent baseline tracking result.

10. The knowledge tracking method based on multi-algorithm adaptive switching according to claim 9, characterized in that, It also includes step S7: When the Bayesian knowledge tracker observes data reaching a preset number of triggers, it triggers parameter adaptation: calculates the historical answer accuracy rate; if the accuracy rate is greater than the first preset accuracy rate threshold, it reduces the guess probability and the error probability by a preset step size; if the accuracy rate is less than the second preset accuracy rate threshold, it increases the guess probability and the error probability by the preset step size, and the adjustment range is limited to between the preset lower limit and the preset upper limit. The Bayesian knowledge tracker introduces forgetting decay when calculating mastery: the decay factor is equal to the number of interaction records raised to the power of the preset decay rate, and the final mastery is equal to the current mastery probability multiplied by the first coefficient plus the seventh product factor, where the first coefficient is 1 minus the decay factor, and the seventh product factor is the prior non-mastery probability multiplied by the decay factor.

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