Fact-inversion based online learning process truth inference method

Abstract

The application discloses an online learning process truth inference method based on fact inversion, comprising the following steps: uniformly modeling achievement data, behavior logs and question and teaching meta-information collected in a learning process, and constructing a standardized learning evidence sequence; defining a cognitive fact set to be inverted, configuring pre-fact conditions and corresponding supporting, counter-evidence and missing evidence rules for each type of cognitive fact; introducing a mixed memory kernel to model the cumulative influence of historical evidence in the learning process; generating learning observation results that should theoretically occur based on assumed cognitive fact trajectories and cognitive evolution constraints; introducing causal reachability constraints, structural stability constraints and minimum fact explanation constraints to solve the cognitive fact trajectory by inversion; calculating the occurrence confidence of each type of cognitive fact obtained by inversion; and triggering corresponding teaching intervention actions according to the cognitive fact type and fact trajectory jitter risk.

Description

Technical Field

[0001] This invention relates to the field of online learning technology, and in particular to a method for inferring the truth of an online learning process based on fact inversion. Background Technology

[0002] Online learning systems (including K-12 personalized homework systems, online question banks, intelligent assessment and adaptive practice systems, etc.) typically operate on an interactive chain of "learning task—answering—feedback—relearning," continuously collecting multi-source data from learners during each interaction to characterize the learning process and support teaching decisions. This multi-source data generally includes at least: performance data, such as the correctness of objective questions, scores, step-by-step scoring points, the accuracy of subjective question scoring details, and error categories; behavioral logs, such as answering time, pause duration, number of times hints / explanations were used, draft and modification history, number of times the question was reviewed, skipping questions, copying / pasting / window switching, and other abnormal clues; and question and teaching metadata, such as knowledge point tags, question structure, difficulty level, cognitive level, learning stage (pre-class / in-class / post-class, weekly / monthly tests, intensive review stage, etc.) and teaching objective constraints.

[0003] Based on the above data, existing learning diagnostic technologies typically employ two approaches: First, they model learners' learning states as continuous variables or probability parameters (such as knowledge mastery, proficiency, and forgetting rate), estimating them over time using a state update model. Second, they treat the learning process as sequential data, using sequential prediction models to predict the accuracy rate of the next question, future score trends, or learning risks, and based on this, provide personalized recommendations and teaching interventions (such as pushing exercises, arranging review sessions, providing hints and explanations, and conducting verification tests). These methods are widely used in engineering and constitute the basic capability modules of existing online learning systems. However, existing online learning diagnostic and analysis technologies generally suffer from the following defects and shortcomings in practical applications: First, performance-driven approaches carry a high risk of misjudgment: Existing methods typically use periodic achievements or short-term behavioral characteristics as the main basis for inferring or scoring learning status. This makes it difficult to distinguish between different learning situations such as "true mastery" and "superficial understanding" or "strategic coping." It is easy to misjudge occasional high scores, correct guesses, or perfunctory answers as effective learning, thus deviating from the true state of the learning process.

[0004] Second, diagnostic results are prone to fluctuations and repeated interventions: Most existing technologies lack constraints on the causal continuity and temporal consistency of the learning process, resulting in frequent changes in diagnostic conclusions between adjacent time steps, manifesting as repeated switching between mastery and non-mastery states. This diagnostic fluctuation easily triggers repeated question assignment, repeated verification, and frequent interventions, which not only increases the system burden but also reduces the learner's learning experience and teaching efficiency.

[0005] Third, diagnostic outputs are neither falsifiable nor auditable: Existing methods often use single scores, probabilities, or rank as outputs, lacking structured explanations of the judgment criteria. They cannot clearly indicate which observational evidence supports the diagnostic conclusion, which evidence contradicts the conclusion, or whether key evidence is missing. This "black box" output makes it difficult to support teacher review, teaching accountability, and system-level operational analysis.

[0006] Fourth, it fails to adequately characterize the historical memory patterns of the learning process: Existing technologies typically use simple time decay or Markov assumptions to describe changes in learning states, making it difficult to simultaneously characterize the mixed memory patterns of "short-term rapid forgetting" and "long-term lingering retention." It also lacks the ability to explain typical learning process phenomena such as delayed forgetting and transfer lag, affecting the stability and reliability of diagnostic results.

[0007] Therefore, there is an urgent need to propose a logically simple, accurate, and reliable method for inferring the truth of online learning processes based on fact inversion. Summary of the Invention

[0008] To address the aforementioned problems, the purpose of this invention is to provide a method for inferring the truth of an online learning process based on fact inversion. The technical solution adopted by this invention is as follows: The online learning process truth inference method based on fact inversion includes the following steps: The learning process involves collecting performance data, behavior logs, and question and teaching metadata, which are then used to create a unified model and construct a standardized sequence of learning evidence. Based on the learned evidence sequence, a set of cognitive facts to be inverted is defined, and each type of cognitive fact is configured with its preconditions and corresponding rules for supporting, contradictory and missing evidence, thus establishing a computable fact judgment framework. Based on the learned evidence sequence, a hybrid memory kernel is introduced to model the cumulative impact of historical evidence, and a cognitive state update constraint is constructed. Based on the cognitive state update constraints and the assumed cognitive fact trajectory, a theoretical observation evidence vector is generated. With the goal of minimizing the difference between the learned observation results and the actual observation evidence, under the historical accessibility constraint and the fact judgment framework, causal accessibility constraint, structural stability constraint and minimum fact explanation constraint are introduced to invert and solve the cognitive fact trajectory to obtain stable and interpretable cognitive fact judgment results. Based on the rules of supporting, counter-evidence, and missing evidence, the confidence level of the cognitive fact judgment result is calculated, and structured supporting evidence, counter-evidence, and explanation of missing evidence are output to achieve falsifiable and auditable diagnostic output. Based on the cognitive fact determination results and their occurrence confidence levels, a dynamic gating threshold is calculated in conjunction with the jitter risk of the fact trajectory. Teaching intervention is triggered under the condition that the confidence level requirement is met and the stability standard is met. Overdiagnosis and system oscillation are suppressed through a throttling mechanism, forming a stable and controllable teaching intervention closed loop.

[0009] Compared with the prior art, the present invention has the following beneficial effects: This invention uses discrete cognitive fact event trajectories as the inversion object to directly determine whether a certain type of cognitive fact actually occurs during the learning process. It fundamentally avoids simplifying the problem of "learning truth" into proficiency regression or performance prediction, and significantly reduces the risk of misjudgment caused by accidental high scores, correct guesses, or strategic coping.

[0010] This invention introduces a causal reachability constraint to explicitly bind the occurrence of a cognitive fact to the satisfaction rate of its preceding facts, preventing the inference of already occurred cognitive facts before key preconditions are met, effectively reducing arbitrary diagnosis and causal inconsistencies. Furthermore, this invention uses a structural stability constraint composed of jitter switching penalties and short-pulse penalties to suppress frequent flips and brief false triggers of cognitive facts between adjacent time steps, significantly reducing temporal jitter in diagnostic results and improving the stability of fact determination. Moreover, this invention employs segment-level complexity constraints to control the number of cognitive facts, prioritizing the selection of the fewest fact combinations that can explain the observational evidence, avoiding the decomposition of the same learning phenomenon into too many cognitive facts, thereby reducing system operational noise and the frequency of ineffective teaching interventions.

[0011] This invention simultaneously characterizes short-term rapid forgetting and long-term lingering effects by using a hybrid memory kernel, enabling the model to more accurately constrain typical learning process phenomena such as forgetting delay and transfer lag, and improving the ability to characterize the impact of learning history.

[0012] This invention not only outputs the confidence level of the occurrence of the perceived fact, but also simultaneously provides structured reconciliation results of supporting evidence, counter-evidence, and explanations of missing evidence, making the diagnostic conclusions falsifiable and auditable, facilitating teacher review and system-level analysis. By introducing a fact jitter index and a dynamic routing gating threshold, this invention establishes a feedback control mechanism between fact confidence and fact stability, effectively suppressing over-diagnosis and frequent intervention, forming a stable and controllable closed loop for online teaching intervention. Attached Figure Description

[0013] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope of protection. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a logic flowchart of the present invention. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of this application clearer, the present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments of the present invention include, but are not limited to, the following embodiments. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0016] like Figure 1 As shown, this embodiment provides a truth inference method for online learning processes based on fact inversion. It models the learning process as a unified inversion problem centered on discrete cognitive fact event trajectories, constrained by historically dependent cognitive evolution, and verified through observational consistency generation. Specifically: The first step is to uniformly model the performance data, behavior logs, and question and teaching metadata collected during the learning process to construct a standardized sequence of learning evidence.

[0017] (11) Construct a unified learning evidence vector for learner u based on the observation data at time index t. Its expression is: ; in, This represents the performance evidence vector of learner u at time index t, used to characterize the learner's answer results at time step t. Its elements may include, but are not limited to: correct / incorrect question identifier, score value, step-by-step score, hit rate of subjective question scoring items, error category code, etc. This represents the behavioral evidence vector of learner u at time index t, used to characterize the learner's learning behavior at time step t. Its elements may include, but are not limited to: answering time, pause duration, number of times hints or explanations are used, number of times questions are switched, number of times the question is reviewed, number of times the question is modified, and other interactive behavior indicators. This represents the metadata evidence vector for learner u at time index t, used to describe the questions and teaching attributes related to the current learning task. Its elements may include, but are not limited to: knowledge point identifiers, question type structure codes, difficulty levels, cognitive level identifiers, and learning stage codes. Here, t is a time step index, used to represent the temporal position in the learning process. The time step may correspond to a single response, a single learning session round, or a single independent learning task.

[0018] (12) The evidence from learner u throughout the learning process is arranged in chronological order to form a learning evidence sequence, the expression of which is: ; in, T represents the complete sequence of learning evidence for learner u; T represents the total number of time steps corresponding to the learning process, used to characterize the time span of the learning process.

[0019] The second step is to define a set of cognitive facts to be inverted based on the learned evidence sequence, and to configure the preconditions and corresponding rules for supporting, contradictory and missing evidence for each type of cognitive fact, thereby establishing a computable fact judgment framework.

[0020] (21) Let the set of cognitive fact categories be: ;in, This represents the k-th type of cognitive fact. K represents the total number of categories of cognitive facts.

[0021] (22) Introduce discrete fact event trajectory variables The trajectory of all cognitive facts of learner u throughout the entire learning process can be represented as: ; in, This represents the k-th type of cognitive fact for learner u at time index t. Is it in an established state? When Represents the k-th type of cognitive fact It has already occurred and is still valid at time index t; when Represents the k-th type of cognitive fact It did not occur or has expired at time index t.

[0022] (23) To ensure that the process of determining cognitive facts is calculable, falsifiable, and causally constrained, a corresponding fact template is constructed for any type of cognitive fact, the expression of which is: ; in, A structured fact template representing the k-th type of cognitive fact is used to characterize the conditions that the cognitive fact must satisfy to be valid during the learning process and its evidence judgment rules. The set of antecedent facts for the k-th type of cognitive fact is used to limit the causal accessibility of the cognitive fact, that is, when the antecedent facts are not satisfied, the cognitive fact is not allowed to be determined as having occurred; This represents the set of support rules for the k-th type of cognitive fact, used to describe which learning evidence patterns provide positive support for the validity of this cognitive fact; This represents the set of rules for refuting the k-th type of cognitive fact, used to describe which patterns of learned evidence contradict the validity of that cognitive fact; This represents the set of rules for determining the absence of the k-th type of cognitive fact, used to determine whether the current evidence is insufficient to support or refute the cognitive fact, thus introducing uncertainty constraints.

[0023] (24) Establish a computable fact-determination framework, the expression of which is: ; in, This represents the k-th type of cognitive fact at time index t. The trigger strength of the r-th rule on a given sequence of evidence can be expressed as a threshold function, a piecewise linear function, or a normalized scoring function. A larger output value indicates that the corresponding rule is more relevant to the cognitive facts. The stronger the supporting or counter-evidence; Represents the k-th type of cognitive fact The corresponding evidence window length, from the evidence sequence Interval Fragments of evidence within.

[0024] The third step involves modeling the cumulative impact of historical evidence on the learned evidence sequence using a hybrid memory kernel, thereby constructing constraints for updating the cognitive state. Here, to characterize the influence of historical evidence on the current cognitive state and the occurrence of cognitive facts during the learning process, this embodiment introduces a history-dependent cognitive evolution constraint with a hybrid memory kernel to limit the historical accessibility of cognitive fact retrieval.

[0025] (41) Let the learner u's cognitive state vector at time index t be: ;in, The cognitive state dimension is used to represent the joint state of multiple cognitive sub-dimensions, which may include, but are not limited to, the degree of concept mastery, knowledge transfer ability, information extraction ability, and cognitive load level.

[0026] (42) To reflect the cumulative impact of historical learning evidence on the current cognitive state, a historical memory convergence vector is constructed, the expression of which is: ; ; in, This represents the historical memory convergence vector of learner u at time index t, used to characterize the weighted cumulative result of all historical evidence before time step t; Representing time index t and historical time index The time interval between; This represents the evidence embedding function, used to learn evidence vectors. Mapped to the memory aggregation space, its output dimension is the same as Maintain consistency; This represents a hybrid memory kernel function, used to describe the weights of historical evidence on the current state at different time intervals; This represents the memory kernel parameter vector, used to determine the specific shape of the hybrid memory kernel.

[0027] (43) To simultaneously characterize the short-term rapid forgetting effect and the long-term lingering effect, the expression for the hybrid memory kernel function in this embodiment is as follows: ; in, This represents the short-term memory weighting parameter, used to balance the contributions of short-term and long-term memory; This represents the exponential decay rate parameter, used to describe the rapid decay characteristics of short-term memory; This represents the power-law tail strength parameter, used to describe the slow decay characteristics of long-term memory; Indicates a time interval variable; This represents the natural exponential function.

[0028] (44) Under the constraint of the historical memory aggregation term, construct the cognitive state update constraint, the expression of which is: ; in, This represents the cognitive state vector of learner u at time index t+1; This represents the cognitive state update function, used to describe the evolution of cognitive states under the combined influence of the current state, learned actions, and historical memories. This represents the learning action performed by learner u at time index t. It is used to represent the learning action performed by learner at time step t. Its elements may include the encoding of actions such as practice, quizzes, reviews, hints, and explanations. This represents the parameter vector of the state update function.

[0029] The fourth step involves generating a theoretical observation evidence vector based on the cognitive state update constraints and the hypothesized cognitive fact trajectory. This embodiment constructs a forward consistency generator based on the cognitive state evolution constraints. This generator maps the hypothesized cognitive fact trajectory to the cognitive state as theoretically expected observations, thus providing a consistency constraint basis for subsequent fact-inversion optimization.

[0030] The expression for the theoretical observational evidence vector is: ; in, The vector of theoretical observation evidence for learner u at time index t is used to represent the theoretically expected performance and behavioral observations of learner u at time step t, given the cognitive state and cognitive fact trajectory. This represents the forward consistency generation function, used to describe the joint mapping relationship between cognitive states and cognitive facts to observable learning evidence; This represents the parameter vector of the forward consistency generation function; This represents the cognitive state vector of learner u at time index t. The corresponding historical trajectory of cognitive facts.

[0031] The fifth step, with the goal of minimizing the difference between the learned observation results and the actual observation evidence, introduces causal accessibility constraints, structural stability constraints, and minimum fact explanation constraints under the historical accessibility constraints and the fact judgment framework, and performs inversion solution on the cognitive fact trajectory to obtain stable and interpretable cognitive fact judgment results.

[0032] (51) Construct the learning evidence vector of learner u at time index t The theoretical observation evidence vector of learner u at time index t The difference measurement function between them is expressed as follows: ; This represents the difference measurement function.

[0033] (52) The observation consistency loss is obtained, and its expression is: ; in, This represents the entire cognitive fact trajectory of learner u throughout the learning process. The observation consistency loss value.

[0034] (53) To avoid problems such as no prior triggering, frequent reversals or uncontrolled number of facts during the fact reversal process, causal accessibility constraints, structural stability constraints and minimum fact interpretation constraints are introduced.

[0035] (531) The expression for the causal reachability constraint is: ; ; in, This represents the j-th type of cognitive fact for learner u at time index t. The success rate (preliminary satisfaction rate) within its prior assessment window. Represents the j-th type of cognitive fact The length of the pre-evaluation window is used to calculate the cognitive fact within a historical time interval. The condition within the range; s represents the time index variable in the summation, used to iterate through the time interval. Each historical time step within; This represents the state of learner u’s cognitive fact at time step s. If it is true, the value is 1; otherwise, the value is 0. Represents the k-th type of cognitive fact The prerequisite threshold parameter is used to determine the minimum prerequisite satisfaction level for whether the cognitive fact has causal accessibility.

[0036] (532) To suppress frequent reversals and brief false triggers of the fact trajectory, a structural stability constraint is introduced, the expression of which is: ; ; ; in, This represents the jitter switching penalty term, used to characterize the number of state transitions for the same cognitive fact between adjacent time steps; This indicates a short-pulse penalty term, used to penalize cognitive fact segments that are too short in duration; This represents the jitter switching penalty coefficient, used to control the degree of impact of state switching on the total loss; This represents the short pulse penalty coefficient, used to control the penalty intensity for short-duration fact segments; This represents the entire cognitive fact trajectory of learner u throughout the learning process. The set of continuous segments with a value of 1; any continuous segment It can be represented as a time index interval The condition is satisfied for all time steps t within this interval. And satisfy outside the interval boundary (or )as well as (or ); Indicates a continuous segment The time step length is defined as: ; Represents the k-th type of cognitive fact The shortest duration steps; This represents the learner u's cognitive fact of type k at time index t-1. Is it in an established state?

[0037] (533) To avoid breaking down the same learning phenomenon into too many cognitive facts, a minimum fact explanation constraint is introduced, the expression of which is: ; in, Represents the k-th type of cognitive fact The segment cost weight is used to control the complexity penalty strength for the frequency of occurrence of this type of fact; Represents the k-th type of cognitive fact The number of consecutive fact segments formed throughout the learning process.

[0038] (54) Construct the overall optimization objective of fact inversion, the expression of which is: ; in, Indicates the weight of causal reachability constraints; Indicates the structural stability constraint weights; Indicates the minimum factual interpretation constraint weight; This represents a causal reachability constraint term; Represents structural stability constraints; This indicates the principle of least fact interpretation.

[0039] (55) To support the implementation of the project, the original binary fact variables are continuously relaxed. ， The above objective function is solved using an alternating optimization strategy: under a fixed fact trajectory Under these conditions, update the cognitive state according to the third step. And through the fourth step, the corresponding theoretical observations are calculated. In a fixed cognitive state Under these conditions, the trajectory of facts Perform local updates to reduce the overall objective function value. These local updates may include a fact-by-fact category or time-step coordinate descent method, or a dynamic programming approximation method within a finite time window. Repeat steps one and two until the decrease in the objective function is less than a preset threshold. ， in, The iteration threshold for the objective function. Iterative optimization of the overall optimization objective of fact inversion yields the threshold for determining the transformation from continuous variables to binary variables. And recover the discrete cognitive fact trajectory. ;in, This represents the k-th type of cognitive fact for learner u at time index t. Restore discrete cognitive fact trajectory variables.

[0040] The sixth step involves calculating the confidence level of the cognitive fact determination result based on the rules of supporting, counter-evidence, and missing evidence, and outputting structured supporting evidence, counter-evidence, and explanations of missing evidence to achieve falsifiable and auditable diagnostic output.

[0041] (61) Calculate the k-th cognitive fact of learner u at time index t. Support points And learner u at time index t, the kth type of cognitive fact Contrast proof Its expression is: ; ; in, This indicates that the r-th rule of contradiction applies to the k-th type of cognitive fact. Support rule weights (positive contributions); This indicates that the r-th supporting rule applies to the k-th type of cognitive fact. The weight of the proof by contradiction rule (negative contribution).

[0042] (62) To characterize the uncertainty in the judgment due to insufficient key evidence, the missing penalty term is calculated, and its expression is: ; in, This represents the k-th type of cognitive fact for learner u at time index t. The historical memory convergence vector; This indicates the weight of the missing rule, used to quantify the degree to which missing evidence weakens the reliability of fact-finding.

[0043] (63) Calculate the confidence level of the cognitive fact judgment result, the expression of which is: ; in, This represents the k-th type of cognitive fact for learner u at time index t. The confidence level of occurrence; Represents the Sigmoid function; Represents the k-th type of cognitive fact The missing evidence penalty strength parameter is used to control the degree to which missing evidence inhibits the confidence of the fact.

[0044] The evidence reconciliation output content is tailored to each type of cognitive fact. This method outputs a structured evidence statement, which includes at least: a set of triggered supporting rule indexes and corresponding evidence descriptions; a set of triggered counter-evidence rule indexes and corresponding evidence descriptions; a set of triggered missing rule indexes and corresponding descriptions of the reasons for the missing rules; and the confidence level of the fact occurrence at the corresponding time step. .

[0045] The seventh step involves calculating a dynamic gating threshold based on the cognitive fact determination results and their occurrence confidence levels, combined with the jitter risk of the fact trajectory. Under the condition that the confidence level requirement is met and the stability is up to standard, teaching intervention is triggered, and overdiagnosis and system oscillation are suppressed through a throttling mechanism, forming a stable and controllable teaching intervention closed loop.

[0046] (71) To quantify the degree of change in the cognitive fact trajectory between adjacent time steps, the fact jitter index is obtained, and its expression is: ; in, This represents the learner u's cognitive fact of type k at time index t-1. Restore discrete cognitive fact trajectory variables; This represents the overall fact jitter intensity of learner u at time index t. The larger the value, the more cognitive facts that have undergone state switching within adjacent time steps.

[0047] (72) Construct the dynamic routing gating threshold, the expression of which is: ; in, This represents the dynamic intervention gating value of learner u under time index t. The larger the value, the stronger the system's inhibition of intervention triggers. This represents the basic routing gating threshold, used to characterize the default gating level that the system allows to trigger interventions under conditions of no significant jitter; This represents the jitter gain factor, which maps the actual jitter intensity to an additional gating lift.

[0048] (73) Construct the intervention trigger condition, the expression of which is: ;in, Represents the k-th type of cognitive fact The confidence threshold is the minimum confidence level required to determine that the fact has reached the point of "executable intervention". This indicates the maximum allowed gating threshold.

[0049] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any changes made based on the design principles of the present invention, or any non-creative modifications made thereon, shall fall within the scope of protection of the present invention.

Claims

1. A method for inferring the truth of an online learning process based on fact inversion, characterized in that, Includes the following steps: The learning process involves collecting performance data, behavior logs, and question and teaching metadata, which are then used to create a unified model and construct a standardized sequence of learning evidence. Based on the learned evidence sequence, a set of cognitive facts to be inverted is defined, and each type of cognitive fact is configured with its preconditions and corresponding rules for supporting, contradictory and missing evidence, thus establishing a computable fact judgment framework. Based on the learned evidence sequence, a hybrid memory kernel is introduced to model the cumulative impact of historical evidence, and a cognitive state update constraint is constructed. Based on the cognitive fact trajectory of the cognitive state update constraints and assumptions, a theoretical observation evidence vector is generated. With the goal of minimizing the difference between the learned observation results and the actual observation evidence, under the historical accessibility constraint and the fact judgment framework, causal accessibility constraint, structural stability constraint and minimum fact explanation constraint are introduced to invert and solve the cognitive fact trajectory to obtain stable and interpretable cognitive fact judgment results. Based on the rules of supporting, counter-evidence, and missing evidence, the confidence level of the cognitive fact judgment result is calculated, and structured supporting evidence, counter-evidence, and explanation of missing evidence are output to achieve falsifiable and auditable diagnostic output. Based on the cognitive fact determination results and their occurrence confidence levels, a dynamic gating threshold is calculated in conjunction with the jitter risk of the fact trajectory. Teaching intervention is triggered under the condition that the confidence level requirement is met and the stability standard is met. Overdiagnosis and system oscillation are suppressed through a throttling mechanism, forming a stable and controllable teaching intervention closed loop.

2. The method for inferring the truth of an online learning process based on fact inversion as described in claim 1, characterized in that, A unified model is used to construct a standardized sequence of learning evidence, including: (The model is based on) the collected performance data, behavior logs, and question and teaching metadata collected during the learning process. Construct a unified learning evidence vector from the observation data of learner u at time index t. Its expression is: ； in, This represents the evidence vector of learner u's performance at time index t; This represents the behavioral evidence vector of learner u at time index t; This represents the meta-information evidence vector of learner u at time index t; The evidence provided by learner u throughout the learning process is arranged in chronological order to form a sequence of learning evidence, expressed as: ； in, T represents the complete sequence of learning evidence for learner u; T represents the total number of time steps corresponding to the learning process.

3. The method for inferring the truth of an online learning process based on fact inversion according to claim 2, characterized in that, Based on the learned evidence sequence, a set of cognitive facts to be inverted is defined, and for each type of cognitive fact, its preconditions and corresponding rules for supporting, contradictory, and missing evidence are configured, establishing a computable fact-determination framework, including: Let the set of cognitive fact categories be: ;in, This represents the k-th type of cognitive fact. K represents the total number of categories of cognitive facts; Introducing discrete fact event trajectory variables The trajectory of all cognitive facts of learner u throughout the entire learning process can be represented as: ； in, This represents the k-th type of cognitive fact for learner u at time index t. Is it in an established state? When Represents the k-th type of cognitive fact It has already occurred and is still valid at time index t; when Represents the k-th type of cognitive fact It did not occur or has expired at time index t; To construct a corresponding fact template for any type of cognitive fact, its expression is: ； in, A structured fact template representing the k-th type of cognitive fact; This represents the set of antecedent facts for the k-th type of cognitive fact; This represents the set of support rules for the k-th type of cognitive fact; Represents the set of rules for refuting the k-th type of cognitive fact; Represents the set of rules for determining the absence of the k-th type of cognitive fact; Establish a computable fact-determination framework, the expression of which is: ； in, This represents the k-th type of cognitive fact at time index t. The trigger strength of the r-th rule on a given sequence of evidence; Represents the k-th type of cognitive fact The corresponding evidence window length.

4. The method for inferring the truth of an online learning process based on fact inversion as described in claim 3, characterized in that, Based on the learned evidence sequence, a hybrid memory kernel is introduced to model the cumulative impact of historical evidence, and cognitive state update constraints are constructed, including: Let learner u's cognitive state vector at time index t be: ;in, Represents the dimensions of cognitive state; Construct a historical memory convergence vector, the expression of which is: ； ； in, This represents the convergence vector of learner u's historical memory at time index t; Representing time index t and historical time index The time interval between; Indicates the evidence embedding function; Represents a hybrid memory kernel function; Represents the memory kernel parameter vector; The expression for the hybrid memory kernel function is: ； in, This represents the short-term memory weighting parameter; This represents the parameter indicating the exponential decay rate. Indicates the power-law tail intensity parameter; Indicates a time interval variable; Represents the natural exponential function; The cognitive state update constraint is constructed as follows: ； in, This represents the cognitive state vector of learner u at time index t+1. This represents the cognitive state update function; This represents the learning action performed by learner u at time index t; This represents the parameter vector of the state update function.

5. The method for inferring the truth of an online learning process based on fact inversion according to claim 4, characterized in that, Based on the cognitive fact trajectory of the cognitive state update constraints and assumptions, a theoretical observation evidence vector is generated, the expression of which is: ； in, This represents the vector of theoretical observational evidence for learner u at time index t; This represents the forward consistency generation function; This represents the parameter vector of the forward consistency generation function; This represents the cognitive state vector of learner u at time index t. The corresponding historical trajectory of cognitive facts.

6. The method for inferring the truth of an online learning process based on fact inversion as described in claim 5, characterized in that, With the objective of minimizing the difference between the learned observation results and the actual observation evidence, under the historical accessibility constraint and the fact judgment framework, causal accessibility constraint, structural stability constraint, and minimum fact explanation constraint are introduced to invert and solve the cognitive fact trajectory, obtaining stable and interpretable cognitive fact judgment results, including: Construct the learning evidence vector of learner u at time index t The theoretical observation evidence vector of learner u at time index t The difference measurement function between them is expressed as follows: ; Represents the difference measurement function; The observation consistency loss is calculated as follows: ； in, This represents the entire cognitive fact trajectory of learner u throughout the learning process. The observation consistency loss value; By introducing causal reachability constraints, structural stability constraints, and minimum fact interpretation constraints, and constructing the overall optimization objective for fact inversion, its expression is as follows: ； in, Indicates the weight of causal reachability constraints; Indicates the structural stability constraint weights; Indicates the minimum factual interpretation constraint weight; This represents a causal reachability constraint term; Represents structural stability constraints; This indicates the principle of interpretation based on the minimum facts; Preset iteration threshold of the objective function The overall optimization objective of fact inversion is iteratively optimized to obtain the threshold for the transformation of continuous variables into binary variables. And recover the discrete cognitive fact trajectory. ;in, This represents the k-th type of cognitive fact for learner u at time index t. Restore discrete cognitive fact trajectory variables.

7. The method for inferring the truth of an online learning process based on fact inversion as described in claim 6, characterized in that, Introducing causal reachability constraints, structural stability constraints, and minimum fact explanation constraints, including: The expression for the causal reachability constraint is: ； ； in, This represents the j-th type of cognitive fact for learner u at time index t. The success rate within its pre-assessment window; Represents the j-th type of cognitive fact The length of the pre-evaluation window; s represents the time index variable in the summation; This represents the state of learner u’s cognitive fact at time step s. If it is true, the value is 1; otherwise, the value is 0. Represents the k-th type of cognitive fact Pre-threshold parameters; The expression for the structural stability constraint is: ； ； ； in, This indicates the penalty for jitter switching; Indicates a short-pulse penalty term; This represents the jitter handover penalty coefficient; Indicates the short pulse penalty coefficient; This represents the entire cognitive fact trajectory of learner u throughout the learning process. A set of continuous segments with a value of 1; Indicates continuous segment Time step length; Represents the k-th type of cognitive fact The shortest duration steps; This represents the learner u's cognitive fact of type k at time index t-1. Whether it is in a valid state; if valid, the value is 1, otherwise the value is 0. The expression for the minimum fact interpretation constraint is: ； in, Represents the k-th type of cognitive fact Segment cost weight; Represents the k-th type of cognitive fact The number of consecutive fact segments formed throughout the learning process.

8. The method for inferring the truth of an online learning process based on fact inversion according to claim 7, characterized in that, Based on the aforementioned rules of supporting, counter-evidence, and missing evidence, the confidence level of the cognitive fact determination result is calculated, and structured supporting evidence, counter-evidence, and explanations of missing evidence are output, achieving falsifiable and auditable diagnostic output, including: Calculate the cognitive facts of learner u at time index t for class k. Support points And learner u at time index t, the kth type of cognitive fact Contrast proof Its expression is: ； ； in, This indicates that the r-th rule of contradiction applies to the k-th type of cognitive fact. Support rule weights; This indicates that the r-th supporting rule applies to the k-th type of cognitive fact. The weight of the proof by contradiction rule; The expression for calculating the missing penalty term is: ； in, This represents the k-th type of cognitive fact for learner u at time index t. The historical memory convergence vector; Indicates the weight of the missing rule; The confidence level of the cognitive fact determination result is calculated, and its expression is: ； in, This represents the k-th type of cognitive fact for learner u at time index t. The confidence level of occurrence; Represents the Sigmoid function; Represents the k-th type of cognitive fact The missing penalty intensity parameter.

9. The method for inferring the truth of an online learning process based on fact inversion as described in claim 8, characterized in that, Based on the cognitive fact determination results and their occurrence confidence levels, a dynamic gating threshold is calculated in conjunction with the jitter risk of the fact trajectory. Teaching intervention is triggered under conditions that meet the confidence requirements and stability standards, and over-diagnosis and systemic oscillations are suppressed through a throttling mechanism, forming a stable and controllable teaching intervention closed loop, including: The fact jitter index is obtained by the following expression: ； in, This represents the learner u's cognitive fact of type k at time index t-1. Restore discrete cognitive fact trajectory variables; This represents the overall fact jitter intensity for learner u at time index t; The dynamic routing gating threshold is constructed using the following expression: ； in, This represents the dynamic intervention gating quantity for learner u under time index t; Indicates the basic routing gating threshold; This represents the jitter gain coefficient; The intervention trigger condition is constructed, and its expression is: ;in, Represents the k-th type of cognitive fact The confidence threshold for triggering; This indicates the maximum allowed gating threshold.

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