A time series analysis method for learning weakness identification

Abstract

The present application relates to the field of artificial intelligence and education data mining technology, especially to a learning weak link identification time sequence analysis method, comprising: extracting the time difference of the answer data, the test question code and the error identification, combining the knowledge graph dependence feature fusion and mapping to the Riemann manifold to obtain the initial feature tensor; projecting the previous time hidden state to the tangent space to perform time decay calculation, and projecting back to the Riemann manifold to obtain the decayed hidden state; inputting the two into the evolution model trained by the composite loss function to update the current time hidden state; calculating the distance between the hidden state and the graph anchor point to output the state tensor containing the mastery probability; when the mastery probability is lower than the preset threshold, it is determined as a weak link, and the associated remedial module is extracted on the Riemann manifold to perform distribution. The present application guarantees the topological conservation of time sequence evolution, avoids the geometric distortion and weak point positioning error caused by traditional space calculation.

Description

Technical Field

[0001] This invention relates to the fields of artificial intelligence and educational data mining technology, and in particular to a time-series analysis method for identifying learning weaknesses. Background Technology

[0002] In adaptive online education scenarios for science subjects, the system typically needs to extract irregular temporal response data generated by students and combine it with the pre-dependent knowledge graph associated with the test questions to dynamically track students' cognitive status in order to identify their weaknesses.

[0003] Most existing temporal knowledge tracing models are forced to operate within a flat Euclidean space, directly applying linear time decay penalties and hidden state update calculations to feature tensors containing complex hierarchical dependencies. Since the geometric capacity of a flat space cannot support a tree-like knowledge graph structure with exponential node expansion, this forced dimensionality reduction mapping and scalar operations, which violate the natural non-Euclidean geometry of the graph, lead to severe geometric distortions and topological tearing of the model's underlying hidden states during long-term evolution. Once the model's underlying spatial data overlaps and becomes topologically entangled, the system cannot effectively separate behavioral deviations caused by temporal anomalies from actual cognitive chain breaks. Ultimately, this results in the system being unable to accurately trace and locate the student's truly missing pre-existing weaknesses within the complex hierarchical network. Summary of the Invention

[0004] To overcome the above shortcomings, this invention provides a temporal analysis method for identifying learning weaknesses, aiming to improve the problem that traditional knowledge tracing mostly uses flat Euclidean space, which cannot support the expansion properties of knowledge networks and causes geometric distortion, thus resulting in inaccurate location of weaknesses.

[0005] This invention provides the following technical solution: a time-series analysis method for identifying learning weaknesses, comprising the following steps:

[0006] S1. Extract the question code, error identifier, and timestamp of the current moment from the time-series answer data, and calculate the time difference based on the timestamp; extract the dependency features of the question code from the preset knowledge graph, and fuse the dependency features, the question code, and the error identifier and map them to a Riemannian manifold to obtain the initial feature tensor;

[0007] S2. Project the hidden state of the previous time step onto the tangent space to obtain the tangent vector, perform attenuation calculation on the tangent vector based on the time difference, and project the attenuated tangent vector back onto the Riemann manifold to obtain the attenuated hidden state.

[0008] S3. Input the initial feature tensor and the decayed hidden state into the evolution model to obtain the hidden state at the current time.

[0009] S4. Calculate the distance between the current hidden state and the anchor point in the preset knowledge graph, and output the state tensor; the evolution model is trained based on a composite loss function, which consists of a base loss based on the error identifier and the state tensor, and a penalty term calculated based on the preset knowledge graph for the current hidden state; the state tensor contains the mastery probability of the corresponding knowledge point.

[0010] S5. If the mastery probability of knowledge points in the state tensor is lower than a preset threshold, the knowledge point is determined to be a weak link.

[0011] S6. Extract and distribute the remedial modules associated with the weak link on the Riemannian manifold.

[0012] By adopting the above technical solution, the answer data and graph features are mapped to a Riemannian manifold and time decay is performed in the tangent space, thereby ensuring the topological conservation of state evolution. This improves the problem that traditional knowledge tracing mostly uses flat Euclidean space, which cannot bear the geometric distortion caused by the expansion properties of knowledge networks, thus causing inaccurate location of weak links.

[0013] The present invention has the following beneficial effects:

[0014] 1. In this invention, by mapping the answer data and graph features to a Riemannian manifold and performing time decay in the tangent space, the topological conservation of state evolution is guaranteed. This improves the problem that traditional knowledge tracing mostly uses flat Euclidean space, which cannot bear the geometric distortion caused by the expansion properties of the knowledge network, thus causing inaccurate location of weak links.

[0015] 2. In this invention, by dividing the time difference by the baseline time consumption to construct the decay factor and performing scaling in the Euclidean tangent space, a time forgetting penalty with physical dimension consistency is achieved, thereby improving the problem that traditional time series analysis mostly uses direct scalar calculation, which causes distortion of state representation due to the destruction of the curvature continuity of non-Euclidean geometry.

[0016] 3. In this invention, by using the operator matrix of the preset knowledge graph to perform topological constraints on the hidden state sequence, the model parameters are forced to be optimized along the knowledge graph skeleton. This improves the problem that traditional knowledge models mostly use a single error function, which leads to the divergence and entanglement of the hidden state evolution trajectory due to the lack of spatial geometric constraints.

[0017] 4. In this invention, by extracting teaching modules along the geodesic direction on the Riemannian manifold surface and comparing the difficulty level attributes, the most suitable resources that best address the learning weaknesses are accurately identified. This improves upon the problem that traditional recommendation and distribution methods, which mostly use inner product metrics and deviate from the inherent hierarchical depth of the graph, often result in the mispromotion of invalid resources across levels. Attached Figure Description

[0018] Figure 1 This is a flowchart of a time-series analysis method for identifying learning weaknesses proposed in this invention;

[0019] Figure 2 This is a flowchart of the feature mapping and temporal decay process for a temporal analysis method for identifying learning weaknesses proposed in this invention.

[0020] Figure 3 This is a flowchart illustrating the state evolution and composite loss constraints of a time-series analysis method for identifying learning weaknesses proposed in this invention. Detailed Implementation

[0021] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Example 1:

[0023] In a first embodiment of the present invention, the present invention provides a time-series analysis method for identifying learning weaknesses, such as... Figures 1-3 As shown, it includes the following steps:

[0024] S1. Extract the question code, error identifier, and timestamp of the current moment from the time-series answer data, and calculate the time difference based on the timestamp; extract the dependency features of the question code in the preset knowledge graph, fuse the dependency features, question code, and error identifier, and map them to a Riemannian manifold to obtain the initial feature tensor;

[0025] Furthermore, in S1, the dependency features, test item codes, and error labels are fused and mapped onto a Riemannian manifold to obtain the initial feature tensor, which includes:

[0026] The test item codes are processed by word embedding mapping to obtain feature word vectors, and error identifiers are converted into discrete feature vectors;

[0027] The feature word vectors, discrete feature vectors and dependent features are concatenated and aggregated in the spatial dimension to construct a high-dimensional joint feature vector;

[0028] The high-dimensional joint eigenvectors are nonlinearly transformed using the Poincaré sphere hyperbolic embedding algorithm. The high-dimensional joint eigenvectors in Euclidean space are projected into a Riemann space with negative curvature to generate an initial feature tensor on the Riemann manifold.

[0029] Specifically, the input data includes the test question codes, error identifiers, and timestamps generated by the student, as well as the dependency features of the test question codes retrieved from the pre-defined knowledge graph. The output data is the initial feature tensor generated in a negative curvature space after manifold space transformation.

[0030] The system receives test question codes, transforms them using a word embedding model to generate feature word vectors, and extracts error identifiers, converting them into binary discrete feature vectors. The system then concatenates and aggregates the feature word vectors, discrete feature vectors, and dependent features in a spatial dimension to construct a high-dimensional joint feature vector in a conventional flat space. The constructed high-dimensional joint feature vector is defined as... .

[0031] To overcome the limitations of representation in flat spaces, the system employs the Poincaré sphere hyperbolic embedding algorithm to perform high-dimensional joint feature vector processing. Perform spatial projection. Define the manifold space of the Poincaré sphere as... The manifold space is confined to The interior of the unit open sphere in the real number field. The system uses a nonlinear mapping operator to combine high-dimensional joint eigenvectors. Projection as manifold space Mapping points on For manifold spaces Any two points within With point The specific formula for calculating hyperbolic distance is set as follows:

[0032] ;

[0033] in Set as a point With point The distance between true hyperbolic geodesics on a negative curvature Riemannian space surface. It is set as an inverse hyperbolic cosine function operator. It is set to the standard Euclidean norm and used to calculate the distance in the vector space. Set as a point With point Square linear distance under Euclidean geometric projection. and Set as points respectively and points The squared Euclidean distance from the origin of the manifold. The system is forcibly constrained according to the geometric boundary constraints of the unit open sphere. Strictly less than the value 1 and The value must be strictly less than 1 to ensure that all projected points are within the effective boundary of the manifold.

[0034] Through the aforementioned Poincaré sphere hyperbolic embedding calculation, the system transforms the Euclidean vector that incorporates multimodal information into the coordinates of a point set on a non-Euclidean manifold, generating the initial feature tensor.

[0035] Current mainstream data processing methods directly analyze temporal features within a conventional Euclidean space. The pre-defined knowledge graph involved in this invention contains knowledge point dependencies with a tree-like hierarchical expansion property. The geometric capacity of Euclidean space increases only polynomially with its radius; its actual spatial structure cannot accommodate tree-like network data with exponential node expansion. Forced dimensionality reduction mapping would cause irreversible geometric distortion.

[0036] This embodiment utilizes the Poincaré sphere hyperbolic embedding algorithm to project a high-dimensional joint feature vector, integrating question attributes, correct / incorrect answers, and the topology of the knowledge graph network, onto a Riemannian space with negative constant curvature. The volume of a negative constant curvature manifold increases exponentially with its radius, mathematically perfectly matching the node divergence and expansion characteristics of a dendritic graph. This feature projection process ensures the geometric consistency between the multidimensional answer behavior features and the knowledge point topology network from the perspective of the underlying data structure, eliminating the spatial compression and feature distortion problems caused by forced dimensionality reduction in conventional Euclidean space. It directly provides a distance-preserving and topology-conserving underlying tensor foundation for subsequent spatiotemporal analysis of the model in the continuous time domain.

[0037] S2. Project the hidden state of the previous time step onto the tangent space to obtain the tangent vector. Perform decay calculation on the tangent vector based on the time difference, and project the decayed tangent vector back onto the Riemann manifold to obtain the decayed hidden state.

[0038] Furthermore, in S2, projecting the hidden state from the previous time step onto the tangent space to obtain the tangent vector includes:

[0039] Using the geometric center origin of the Riemannian manifold as the reference projection base point, construct a flat Euclidean space tangent to the Riemannian manifold;

[0040] Extract the manifold space coordinates of the previous hidden state on the Riemannian manifold, and calculate the vector norm corresponding to the previous hidden state;

[0041] By using the logarithmic mapping function and the inverse hyperbolic tangent function, combined with the vector norm, the coordinates of the manifold space are analytically processed. The previous time-latent hidden state of the Riemannian manifold is expanded into a flat Euclidean space to obtain the tangent vector.

[0042] In S2, the attenuation calculation based on the time difference on the tangent vector includes:

[0043] Extract the baseline time attribute corresponding to the question type of the question code in the preset database;

[0044] The time difference is normalized by dividing it by the baseline time consumption attribute to obtain the time deviation.

[0045] The time deviation is multiplied by the preset curvature forgetting coefficient to construct the exponential time decay factor;

[0046] In a flat Euclidean space, the tangent vector is scaled by scalar multiplication using an exponential time decay factor to obtain the scaled and decayed tangent vector.

[0047] In S2, projecting the decayed tangent vector back onto the Riemannian manifold yields the decayed hidden states, including:

[0048] Extract the Euclidean norm of the decayed tangent vector in a flat Euclidean space;

[0049] Scale compression calculation of Euclidean vector norm is performed using the exponential mapping function and the hyperbolic tangent function;

[0050] The product operation is performed on the direction vector of the attenuated tangent vector using the results of the scale compression calculation. The direction vector after the operation is remapped from the flat Euclidean space to the negative curvature space, generating the attenuated hidden state.

[0051] Specifically, the input data includes the previous hidden state extracted from the temporal knowledge state evolution model, the time difference calculated based on the answer timestamp, the baseline time consumption attribute corresponding to the question code in the preset database, and the preset curvature forgetting coefficient. The output data is the decayed hidden state that has been reduced, scaled, and upgraded back to a negative curvature Riemannian manifold.

[0052] The system extracts the previous time-series hidden state on the Riemannian manifold and calculates the vector norm of that hidden state. A flat Euclidean tangent space is constructed with the origin of the manifold's geometric center as the reference. Dimensionality reduction is performed using the inverse hyperbolic tangent function and logarithmic mapping, expanding the manifold coordinates into a flat Euclidean space to form tangent vectors. The specific mapping calculation formula is set as follows:

[0053] ;

[0054] in It is set as the tangent vector expanded into a flat Euclidean space. It is set to the hidden state of the previous moment on the Riemannian manifold. It is set to the vector norm corresponding to the hidden state at the previous time step. It is set as the inverse hyperbolic tangent function operator.

[0055] The system normalizes the time difference by dividing it by the baseline time consumption attribute to obtain a time deviation degree characterizing the degree of time consumption anomaly. The system constructs an exponential time decay factor by multiplying the time deviation degree by the curvature forgetting coefficient. In a flat Euclidean space, the direction vector of the tangent vector is scaled using scalar multiplication using this decay factor. The specific calculation formula for decay scaling is set as follows:

[0056] ;

[0057] in Set as the decayed tangent vector generated after the scaling operation. Set to the time difference calculated based on the timestamp. Set as the baseline time attribute corresponding to the question type to which the question code belongs. Set to the system's preset curvature forgetting coefficient. Set to the natural exponential operator.

[0058] After obtaining the decayed tangent vector, the system extracts its Euclidean vector norm and performs a scaling operation using the hyperbolic tangent function and exponential mapping to remap the direction vector to a Riemannian manifold with negative curvature. The specific calculation formula for the dimensionality upscaling is set as follows:

[0059] ;

[0060] in It is set as a decayed hidden state generated by remapping up to negative curvature space. Set as the Euclidean vector norm of the decayed tangent vector. It is set as the hyperbolic tangent function operator.

[0061] Conventional time series analysis networks, upon receiving time interval features, typically apply a time decay penalty directly to the data representation. However, non-Euclidean geometric manifolds possess inherent negative constant curvature structures, and directly performing vector scalar multiplication decay operations on the manifold surface severely disrupts the curvature continuity of the geometric space. This embodiment constructs a cross-space mapping decay mechanism, relying on logarithmic mapping to reduce the dimension of the manifold's hidden state and project it to a flat Euclidean tangent space tangent to the origin. The flat Euclidean tangent space is a standard linear geometric space, supporting scalar multiplication scaling of vectors within it without causing geometric distortion.

[0062] Within the linear tangent space, the system scales the tangent vector based on the normalized temporal deviation of student answers. Then, it uses exponential mapping to precisely upscale the decayed tangent vector back to the negative curvature manifold space. This process, in the underlying calculation of the learning behavior's forgetting penalty logic, strictly maintains the topological conservation properties of the pre-dependencies of knowledge points within the manifold space, avoiding the manifold geometric distortion caused by directly performing linear temporal penalty calculations in non-Euclidean space. This provides a mathematical foundation for the subsequent evolution model to extract accurate spatial state features.

[0063] S3. Input the initial feature tensor and the decayed hidden state into the evolution model to obtain the hidden state at the current time.

[0064] Furthermore, in S3, the initial feature tensor and the decayed hidden state are input into the evolution model to obtain the hidden state at the current time step, which includes:

[0065] In the negative curvature space of the Riemannian manifold, the Möbius addition operator is invoked to perform tensor aggregation operations on the initial feature tensor and the decayed hidden state;

[0066] The feature tensor after aggregation is fed as an input signal into the hyperbolic gated loop unit built into the evolution model;

[0067] The reset and update gates of the hyperbolic gated loop unit are used to update the state characteristics of the input signal and output the hidden state at the current time.

[0068] Specifically, the data input / output process is as follows. Input data includes the initial feature tensor generated by the system in the pre-calculation steps, and the decayed hidden state generated after time decay calculation. Output data is the current hidden state obtained after spatial aggregation calculation and network gating update.

[0069] The system extracts the initial feature tensor and decayed hidden states within a Riemannian manifold space with negative constant curvature. Non-Euclidean geometry does not support direct addition of vectors as in linear algebra, as this would cause the computational results to deviate from the manifold surface. Therefore, the system invokes the Möbius addition operator to perform tensor aggregation operations. The specific formula for the Möbius addition operation is defined as follows:

[0070] ;

[0071] in Set as the initial feature tensor after multi-feature fusion mapping at the current time. It is set to a hidden state after decay from the previous moment, subject to time penalty. It is set as the Möbius addition operator corresponding to the absolute value of spatial curvature. It is set to the absolute value of the negative constant curvature of the Riemannian manifold. It is set to a standard Euclidean inner product operation between two input tensors. Set to the standard Euclidean vector norm of the corresponding tensor.

[0072] After obtaining the feature tensor after aggregation, the system feeds it as a low-level signal into the hyperbolic gated loop unit set inside the evolution model. The hyperbolic gated loop unit is configured with a reset gate and an update gate. The system uses the reset gate to remove redundant knowledge states from the historical time series that are irrelevant to the current test item's encoding prerequisites, and relies on the update gate to determine the proportion of features in the decayed hidden states that need to be retained up to the current time step. Based on this, it performs a state feature update operation, calculates and outputs the current hidden state. The final calculation formula for the hyperbolic update gate-controlled state combination is set as follows:

[0073] ;

[0074] in This is set to the current hidden state of the network's final output after feature filtering and feature accumulation. It is set as the control weight tensor output by the update gate inside the hyperbolic gated loop unit. Set as a Möbius scalar multiplication operator that matches the absolute value of the manifold curvature. It is set as the hidden state of the candidate manifold generated within the network at the current moment. It is set as the inverse feature tensor of the hidden state after decay within the negative curvature space.

[0075] For knowledge graph data with complex pre-dependent topologies, conventional tensor addition and network-gated updates in Euclidean space can lead to spatial congestion in feature dimensions and breakage of the topological structure. This embodiment employs the Möbius addition operator to directly perform nonlinear aggregation operations on multimodal features within negative curvature space, avoiding the technical drawback of tensor addition exceeding the effective geometric boundaries of the manifold. By combining hyperbolic gated cyclic units with conventional cyclic network structures, it ensures that the knowledge tracing sequence perfectly conforms to the surface geometry of the Poincaré sphere throughout the entire time evolution cycle. Executing this underlying logic ensures consistent spatial curvature when the model captures long-term dependencies of knowledge points, preventing network topology overlap and geometric dimension collapse during sequence transmission of the underlying data state.

[0076] S4. Calculate the distance between the current hidden state and the anchor point in the preset knowledge graph, and output the state tensor. The evolution model is trained based on the composite loss function. The composite loss function consists of the basic loss based on the error label and the state tensor, and the penalty term calculated based on the preset knowledge graph for the current hidden state. The state tensor contains the mastery probability of the corresponding knowledge point.

[0077] Furthermore, in S4, the distance between the hidden state at the current time and the anchor point in the preset knowledge graph is calculated, and the output state tensor includes:

[0078] Extract the manifold space coordinates corresponding to each knowledge point in the preset knowledge graph as anchor points;

[0079] Calculate the hyperbolic geodesic distances between the current hidden state and each anchor point on the surface of the Riemannian manifold;

[0080] The Fermi-Dirac distribution function is called to perform activation mapping on the hyperbolic geodesic distance to obtain the mastery probability of each knowledge point corresponding to a continuous interval between zero and one, and the set is used to generate a state tensor.

[0081] In S4, the composite loss function consists of a base loss based on error identification and state tensor, and a penalty term calculated based on the hidden state at the current time step using a pre-defined knowledge graph.

[0082] The basic loss is obtained by calculating the binary cross-entropy between the mastery probability and the error label in the state tensor.

[0083] Extract the association boundary matrix of the preset knowledge graph, perform transpose multiplication to construct the Hodge Laplace operator matrix, and use the Hodge Laplace operator matrix to perform trace operation on the sequence matrix composed of the hidden states at the current time to generate a penalty term;

[0084] The penalty term is weighted and then added to the base loss to generate a composite loss function for optimizing network weight parameters.

[0085] Specifically, the input data includes the current hidden state obtained from the forward computation of the hyperbolic gated recurrent unit, the association boundary matrix of the pre-defined knowledge graph, and error markers recorded in real historical interactions. The output data consists of the state tensor generated after the forward inference is completed, and the composite loss function used for gradient updates during the backpropagation phase.

[0086] The system extracts the manifold spatial coordinates corresponding to each knowledge point within a pre-defined knowledge graph as spatial anchor points. On the Riemannian manifold surface, the system calculates the hyperbolic geodesic distance between the current hidden state and each anchor point. Since conventional activation functions cannot directly handle non-Euclidean features with spatial metric properties, the system here calls the Fermi-Dirac distribution function to perform a nonlinear probability mapping on the hyperbolic geodesic distance. The mapping calculation formula is set as follows:

[0087] ;

[0088] in It is set as the mastery probability corresponding to a specific knowledge point, and its numerical range is between 0 and 1. Set as the hidden state of the current time in the network output. It is set as the anchor point of the manifold space corresponding to a specific knowledge point in the preset knowledge graph. The hyperbolic geodesic distance is set to be calculated on a Riemannian manifold surface. It is set as a margin parameter to characterize the mastery state boundary. A temperature coefficient is set to control the smoothness of the probability distribution, and the system restricts its value to be strictly greater than 0. The system collects the mastery probability values ​​corresponding to all knowledge point nodes and constructs the final state tensor.

[0089] After entering the network training phase, the system calculates the binary cross-entropy value for the mastery probability and true error label in the state tensor, establishing it as the basic loss. To constrain the parameter update trajectory, the system extracts the association boundary matrix from the preset knowledge graph. The association boundary matrix is ​​set as follows: The system performs a transpose-multiplication operation on it to construct the Hodge Laplace operator matrix, and the algebraic relation is set as follows. .

[0090] The system summarizes all hidden states at the current time step within the sequence period to construct a global sequence matrix. The constructed Hodge Laplacian operator matrix is ​​used to perform a trace operation on the global sequence matrix to generate a penalty term. The operation formula is set as follows:

[0091] ;

[0092] in Set as a penalty term for smoothness constraints in manifold space. Set as the global sequence matrix composed of the hidden states at the current time. Set as the transpose of the global sequence matrix. Set as the constructed Hodge Laplace operator matrix. It is set to the matrix trace operator in linear algebra.

[0093] The system introduces a preset topology penalty weight. The generated penalty term is then multiplied and weighted, and then combined with the binary cross-entropy base loss. Perform the addition operation to generate the composite loss function:

[0094] ;

[0095] in It is set as the composite loss function ultimately used for optimizing network weight parameters.

[0096] Conventional knowledge tracing networks rely solely on binary right-or-wrong feedback to establish errors and perform gradient descent. When dealing with complex knowledge networks containing pre-existing dependencies, the single error backpropagation mechanism is prone to disordered drift of its underlying state vectors within the manifold space, thereby disrupting the original knowledge point topology.

[0097] This technical solution employs the Fermi-Dirac distribution function at the network output, accurately mapping the hyperbolic distance in non-Euclidean space to continuous probabilities that conform to cognitive patterns. In the underlying mechanism of model training, the system introduces a Hodge Laplace operator matrix to construct a manifold topological constraint penalty term. The mathematical essence of matrix trace operation is equivalent to minimizing the geometric distance between adjacent nodes in the knowledge graph within the manifold space. This constraint penalty term forces the parameter update trajectory of the evolving model to strictly conform to the skeleton topology set by the knowledge graph. This forward-backward joint mathematical constraint mechanism avoids the risk of spatial geometric distortion caused by long-term sequential training, maintains the absolute structural conservation of the hidden state evolution trajectory in negative curvature space, and provides unbiased numerical evidence for the system to accurately identify weak points.

[0098] S5. If the mastery probability of knowledge points in the state tensor is lower than the preset threshold, the knowledge points are determined to be weak links.

[0099] Furthermore, in S5, if the mastery probability of a knowledge point in the state tensor is lower than a preset threshold, the knowledge point is determined to be a weak link, including:

[0100] Analyze the state tensor and extract the scalar values ​​of the mastery probability of knowledge points within a continuous interval;

[0101] Obtain the preset threshold values ​​that represent the security perception boundary of the system;

[0102] Perform a numerical comparison operation. When the probability scalar value is strictly less than a preset threshold, generate a weak identifier and identify the knowledge points associated with the weak identifier as weak links.

[0103] Specifically, the input data includes the state tensor mapped out by the forward inference computation stage, and the preset threshold representing the security awareness boundary configured in the system backend. The output data consists of weakness identifiers generated after low-level numerical comparison operations, and target knowledge points identified by the system as weaknesses.

[0104] After receiving the state tensor, the system executes a parsing instruction, traversing the data dimensions of the tensor to extract the mastery probability scalar value for each knowledge point within a continuous interval. The system synchronously reads the preset thresholds configured in the underlying runtime environment. For each extracted mastery probability scalar value, the system's computational unit performs a rigorous numerical comparison logic. This judgment logic, along with the mathematical calculation expression generated by the identifier, is set as follows:

[0105] ;

[0106] in This is a weakness identifier generated by the system for specific knowledge points. When the identifier is calculated to a value of one, it indicates that the associated knowledge point is considered a weak point; when it is calculated to a value of zero, it indicates that the associated knowledge point is already mastered. It is set as the scalar value of the mastery probability of a specific knowledge point, which is extracted by the system from the state tensor. Its numerical range is strictly distributed between 0 and 1. A preset threshold is set to characterize the boundary of safe cognitive understanding. This preset threshold is predetermined based on the achievement requirements of specific educational scenarios. In general application scenarios, the system sets the value of this preset threshold to 0.6. When performing numerical comparison operations, once the system identifies a mastery probability scalar value that is strictly less than this preset threshold, the underlying business logic determines that the student's cognitive level of that knowledge point has not reached the safety boundary. The system then triggers an identifier generation program, outputting a weakness identifier with a value of 1, and binds this weakness identifier to the feature code of the current knowledge point, thereby establishing that knowledge point as a weak link.

[0107] Conventional knowledge tracing systems often use hard classification labels directly in their terminal outputs, keeping the internal probability determination process a black box to the outside world. When faced with knowledge network nodes whose predicted probabilities hover on the edge of classification, conventional systems are highly susceptible to misjudgments and frequent state transitions during periods of numerical oscillation.

[0108] This technical embodiment independently constructs a scalar parsing and comparison layer with rigid constraints between the non-Euclidean manifold evolution network and the downstream resource distribution service module. The system forcibly extracts the mastery probability scalar value with continuous numerical characteristics and performs a forced hard alignment with a static preset threshold representing the bottom line of security cognition. The abstract tensor features output from the high-dimensional non-Euclidean space are thoroughly reduced in dimensionality by this comparison logic, transforming them into deterministic Boolean control instructions that can be directly parsed and recognized by the downstream service processing module. This underlying execution logic effectively shields the numerical ambiguity fluctuations at the probability boundary output of the evolution model, accurately anchoring the abstract inference results in the preceding manifold space as a definite service trigger switch. This ensures that the downstream terminal has an absolutely clear target when calling the matching and distribution system, eliminating the underlying risk of missing hidden weak knowledge points in complex graph networks.

[0109] S6. Extract and distribute remedial modules associated with weak links on the Riemannian manifold;

[0110] Furthermore, in S6, remedial modules associated with weak points are extracted and distributed on the Riemannian manifold, including:

[0111] In the negative curvature space of the Riemannian manifold, the anchor point corresponding to the knowledge point that is determined to be a weak link is used as the retrieval origin;

[0112] Perform a search along the geodesic direction of the manifold surface to extract candidate teaching modules corresponding to the distance between adjacent hyperbolic geodesics;

[0113] By comparing the preset difficulty level attributes, candidate teaching modules that match the difficulty level attributes are pushed to the student's end as remedial modules.

[0114] Specifically, the input / output data flow is defined as follows: Input data includes the spatial anchor coordinates of the weak knowledge points identified by the system, the set of candidate teaching module coordinates stored in the underlying database of the knowledge graph, and the difficulty level attribute of each module. Output data is a remedial module data package generated after spatial geodesic comparison and attribute filtering.

[0115] The specific execution logic of the retrieval and distribution mechanism is as follows. The system locates the retrieval origin in the negative curvature space of the Riemannian manifold. This origin is determined by the coordinates of the anchor points corresponding to the knowledge points identified as weak points. The system extends the retrieval outward along the geodesic direction of the manifold surface. A geodesic represents the shortest physical path between two points in the negative curvature geometric space. The system calculates the hyperbolic geodesic distance between the retrieval origin and the anchor points of each candidate teaching module. The specific formula for calculating the hyperbolic geodesic distance is set as follows:

[0116] ;

[0117] in It is set as the true hyperbolic geodesic distance on the Riemannian manifold surface between the search origin and the anchor point of a specific candidate teaching module. Set as the spatial coordinate vector of the retrieval origin corresponding to the knowledge point of the weak link. Set as the manifold space coordinate vector corresponding to a specific candidate teaching module. It is set as an inverse hyperbolic cosine mapping operator. It is set as the square straight-line distance between the two spatial coordinate vectors in the sense of flat geometry. United It is set as the square Euclidean vector norm of the distance between the corresponding coordinate vector and the geometric center of the manifold.

[0118] The system filters candidate teaching modules based on calculated hyperbolic geodesic distances, identifying those within adjacent preset threshold ranges. After extraction, the system reads the preset difficulty level attributes associated with these candidate modules. The system then compares these difficulty level attributes with the associated target difficulty level. Candidate teaching modules whose difficulty level attributes match are confirmed by the system backend as the final remedial modules. The underlying distribution port receives the confirmation command and pushes the remedial module to the student's end as a data stream.

[0119] Conventional educational recommendation architectures often rely on cosine distance or inner product to perform content retrieval in a flat Euclidean space. Euclidean metric mechanisms deviate from the inherent hierarchical tree-like topology of knowledge points, easily returning irrelevant knowledge points with vastly different hierarchical spans but similar literal features as recommendation results. This embodiment forces the system to perform searches along the geodesic direction on the Riemannian manifold surface. Hyperbolic geodesic distance mathematically and accurately recreates the objective paths of pre-dependent dependencies within the knowledge graph. The system uses this non-Euclidean geometric metric to extract teaching modules within adjacent distances, ensuring that the extracted content necessarily belongs to the direct pre-existing foundation of weak knowledge points or closely parallel concepts. The hard comparison rules of the subsequent difficulty level attribute directly intercept ineffective educational resources that are too difficult or too easy. This retrieval and distribution architecture, purely based on the geometric metric properties of manifold space and the combination of difficulty attributes, eliminates the underlying logical risk of mis-proposing knowledge resources across levels, accurately achieving the technical goal of targeted compensation for knowledge gaps.

[0120] Example 2:

[0121] In a large-scale online education platform providing adaptive practice for science subjects, students engage in frequent, cross-chapter practice during intensive pre-exam review, generating massive amounts of interactive data with highly irregular time spans. The knowledge network of this subject possesses an extremely strict tree-like hierarchical structure of pre-dependencies. When the system encounters extreme interactive behaviors with extremely high temporal variance, such as students quickly guessing to complete tasks or idling for extended periods when facing difficult problems, existing temporal knowledge tracking models reveal underlying computational flaws. Traditional models force linear time decay penalties and hidden state updates directly onto feature tensors containing complex hierarchical dependencies within a flat Euclidean space. Since the geometric capacity of a flat space cannot support the exponentially expanding knowledge graph nodes, this forced computation, violating the natural non-Euclidean property of the graph, leads to severe geometric distortions and topological tearing of the model's underlying hidden states during temporal evolution. The underlying spatial data exhibits overlapping and topological entanglement, failing to effectively separate behavioral deviations caused by temporal anomalies from actual cognitive chain breaks. Ultimately, this results in the platform's inability to accurately trace and locate the truly missing pre-dependencies within the complex hierarchical network. To address the aforementioned problems, this invention provides a time-series analysis method for identifying learning weaknesses, the structure of which is as follows: Figure 1 As shown. The specific implementation process of this method is as follows:

[0122] The system extracts the time difference and error markers of the question-answering interaction, and maps them uniformly to a negative curvature Riemannian manifold by combining the pre-dependency features of the knowledge graph, constructing an initial feature tensor that naturally fits the hierarchical expansion structure of the knowledge network. To address the spatial curvature destruction problem caused by conventional temporal computation, the system projects the previous hidden state into Euclidean space in reduced dimensions, performs a time-difference-based decay operation, and then projects it back into the Riemannian manifold in increased dimensions, completing the temporal forgetting penalty of the state while maintaining curvature continuity. The decayed hidden state and the initial feature tensor are input into the evolution model to update and generate the current hidden state. The system calculates the distance between this state and each knowledge point anchor point on the manifold surface to map the mastery probability. In its underlying training stage, a topological constraint penalty term is constructed based on the knowledge graph and incorporated into a composite loss function, forcing the parameter update trajectory to conform to the graph skeleton, thus avoiding geometric distortion and topological entanglement of the state vector under long-term computation. Finally, the business layer compares the preset thresholds to accurately identify weak links, and extracts nearby remedial modules along the geodesic lines of the manifold surface to perform targeted distribution. This pure manifold geometric measurement opens up a technical closed loop from the analysis of underlying temporal features to the intervention of top-level cognitive shortcomings.

[0123] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A time-series analysis method for identifying learning weaknesses, characterized in that, Includes the following steps: S1. Extract the question code, error identifier, and timestamp of the current moment from the time-series answer data, and calculate the time difference based on the timestamp; Extract the dependency features of the test question codes from the preset knowledge graph, fuse the dependency features, the test question codes and the error identifiers and map them to a Riemannian manifold to obtain the initial feature tensor; S2. Project the hidden state of the previous time step onto the tangent space to obtain the tangent vector, perform attenuation calculation on the tangent vector based on the time difference, and project the attenuated tangent vector back onto the Riemann manifold to obtain the attenuated hidden state. S3. Input the initial feature tensor and the decayed hidden state into the evolution model to obtain the hidden state at the current time. S4. Calculate the distance between the current hidden state and the anchor point in the preset knowledge graph, and output the state tensor; The evolution model is trained based on a composite loss function, which consists of a base loss based on the error identifier and the state tensor, and a penalty term calculated based on the hidden state at the current time based on the preset knowledge graph. The state tensor contains the mastery probability of the corresponding knowledge point. S5. If the mastery probability of knowledge points in the state tensor is lower than a preset threshold, the knowledge point is determined to be a weak link. S6. Extract and distribute the remedial modules associated with the weak link on the Riemannian manifold.

2. The time-series analysis method for identifying learning weaknesses according to claim 1, characterized in that, In S1, fusing the dependency features, the test item codes, and the error identifiers and mapping them to a Riemannian manifold to obtain the initial feature tensor includes: The test question code is processed by word embedding mapping to obtain feature word vectors, and the error identifier is converted into a discrete feature vector; The feature word vectors, the discrete feature vectors, and the dependent features are concatenated and aggregated in the spatial dimension to construct a high-dimensional joint feature vector. The high-dimensional joint feature vector is nonlinearly transformed using the Poincaré sphere hyperbolic embedding algorithm, projecting the high-dimensional joint feature vector in Euclidean space onto a Riemann space with negative curvature, thereby generating the initial feature tensor located on the Riemann manifold.

3. The time-series analysis method for identifying learning weaknesses according to claim 1, characterized in that, In S2, the step of projecting the hidden state from the previous time step onto the tangent space to obtain the tangent vector includes: Using the origin of the geometric center of the Riemannian manifold as the reference projection point, a flat Euclidean space tangent to the Riemannian manifold is constructed. Extract the manifold space coordinates of the previous hidden state located on the Riemannian manifold, and calculate the vector norm corresponding to the previous hidden state; By using the logarithmic mapping function and the inverse hyperbolic tangent function, combined with the vector norm, the coordinates of the manifold space are analyzed, and the previous hidden state of the Riemannian manifold is expanded into the flat Euclidean space to obtain the tangent vector.

4. The time-series analysis method for identifying learning weaknesses according to claim 3, characterized in that, In S2, performing attenuation calculation on the tangent vector based on the time difference includes: Extract the baseline time consumption attribute corresponding to the question type to which the question code belongs in the preset database; The time difference is divided by the baseline time consumption attribute and then normalized to obtain the time deviation. The time deviation is multiplied by a preset curvature forgetting coefficient to construct an exponential time decay factor; In the flat Euclidean space, the tangent vector is scaled by scalar multiplication using the exponential time decay factor to obtain the scaled decayed tangent vector.

5. The time-series analysis method for identifying learning weaknesses according to claim 4, characterized in that, In S2, projecting the attenuated tangent vector back onto the Riemannian manifold to obtain the attenuated hidden state includes: Extract the Euclidean norm of the decayed tangent vector in the flat Euclidean space; The Euclidean vector norm is scaled using the exponential mapping function and the hyperbolic tangent function. The direction vector of the attenuated tangent vector is multiplied by the result of the scale compression calculation, and the calculated direction vector is remapped from the flat Euclidean space to the negative curvature space to generate the attenuated hidden state.

6. The time-series analysis method for identifying learning weaknesses according to claim 1, characterized in that, In S3, the step of inputting the initial feature tensor and the decayed hidden state into the evolution model to obtain the hidden state at the current time includes: Within the negative curvature space of the Riemannian manifold, the Möbius addition operator is invoked to perform tensor aggregation operations on the initial feature tensor and the decayed hidden state; The feature tensor after aggregation is fed as an input signal into the hyperbolic gated loop unit built into the evolution model; The input signal is updated by using the reset and update gates of the hyperbolic gated loop unit to output the current hidden state.

7. The time-series analysis method for identifying learning weaknesses according to claim 1, characterized in that, In S4, calculating the distance between the current hidden state and the anchor point in the preset knowledge graph, and outputting the state tensor includes: Extract the manifold space coordinates corresponding to each knowledge point in the preset knowledge graph as the anchor point; Calculate the hyperbolic geodesic distance between the current hidden state and each of the anchor points on the Riemannian manifold surface; The Fermi-Dirac distribution function is invoked to perform activation mapping on the hyperbolic geodesic distance to obtain the mastery probability of each knowledge point corresponding to a continuous interval between zero and one, and the set is used to generate the state tensor.

8. The time-series analysis method for identifying learning weaknesses according to claim 1, characterized in that, In S4, the composite loss function consists of a base loss based on the error identifier and the state tensor, and a penalty term calculated based on the hidden state at the current time based on the preset knowledge graph, including: The base loss is obtained by calculating the binary cross-entropy between the mastery probability in the state tensor and the error flag. Extract the association boundary matrix of the preset knowledge graph, perform transpose multiplication to construct the Hodge Laplace operator matrix, and use the Hodge Laplace operator matrix to perform trace operation on the sequence matrix composed of the hidden states at the current time to generate the penalty term; The penalty term is weighted and then added to the basic loss to generate the composite loss function used for optimizing network weight parameters.

9. The time-series analysis method for identifying learning weaknesses according to claim 1, characterized in that, In S5, determining that a knowledge point is a weak point if the mastery probability of the knowledge point in the state tensor is lower than a preset threshold includes: Analyze the state tensor and extract the mastery probability scalar value of the knowledge point within a continuous interval; Obtain the preset threshold value that represents the boundary of security cognition set by the system; A numerical comparison operation is performed. When the mastery probability scalar value is strictly less than the preset threshold, a weakness identifier is generated, and the knowledge point associated with the weakness identifier is identified as the weakness.

10. The time-series analysis method for identifying learning weaknesses according to claim 1, characterized in that, In S6, the step of extracting and distributing the remedial module associated with the weak link on the Riemannian manifold includes: In the negative curvature space of the Riemannian manifold, the anchor point corresponding to the knowledge point that is determined to be the weak link is used as the retrieval origin; Perform a search along the geodesic direction of the manifold surface to extract candidate teaching modules corresponding to the distance between adjacent hyperbolic geodesics; By comparing the preset difficulty level attributes, the candidate teaching modules that match the difficulty level attributes are pushed to the student's end as the remedial modules.

Images