Knowledge tracing method for enhancing problem representation based on adaptive concept relation discovery and structure-semantic collaborative optimization

Abstract

The application belongs to the technical field of knowledge tracing, and discloses a knowledge tracing method based on adaptive concept relationship discovery and structure-semantic collaborative optimization enhanced problem representation, wherein a concept discovery module learns a directed acyclic graph of concept relationships, and then encodes through heterogeneous graph convolution to generate structure-enhanced problem embedding. In addition, a semantic enhancement module adopts multi-head attention to capture internal problem-concept association, and uses a topological concept difficulty metric as a cognitive scaling factor to adjust the offset vector of each problem, so as to realize accurate cognitive load modeling. Then, through contrastive learning, the structure and semantic representations are aligned to reduce redundancy, and high-differentiation embedding is provided for knowledge state modeling. Experiments on five public datasets show that the method is 1.39% better than the SOTA baseline on average in ACC, and 1.42% better than the SOTA baseline on average in AUC, thereby verifying the effectiveness of the adaptive concept relationship discovery and structure-semantic collaborative optimization framework.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of knowledge tracing technology, and particularly relates to a knowledge tracing method based on adaptive concept relationship discovery and structure-semantic co-optimization to enhance problem representation. Background Technology

[0002] The proliferation of digital learning platforms has generated massive amounts of student interaction data, offering unprecedented opportunities for personalized education (Yinetal. 2023). A key challenge in realizing this potential lies in knowledge tracking (KT), a task that infers a student's evolving state of knowledge from their answer history. Accurate KT enables intelligent tutoring systems to identify conceptual difficulties and provide timely, targeted interventions, such as recommending supplementary exercises or review materials (Liuetal. 2025).

[0003] Knowledge tracing (KT) is typically formulated as a supervised sequence learning task aimed at predicting future learner performance based on historical interaction trajectories. To capture the underlying semantics, existing literature generally employs two main paradigms to enhance question representations. The first paradigm incorporates external auxiliary features, including textual descriptions (e.g., EERNN (Sue et al. 2018), RKT (Pandey and Srivastava 2020)), exam templates (Wu and Ling 2023), answer behavior (Xue et al. 2023), or question type metadata (Liue et al. 2020). However, relying on such rich auxiliary information incurs high annotation costs and limits generalization ability. Therefore, developing a general representation mechanism that relies entirely on basic interaction tuples (i.e., question, concept, and answer) is more practical and scalable. The second paradigm focuses on mining the underlying semantic relationships within these basic interactions. To address the complex mapping between questions and concepts, previous research has often employed simplification strategies such as concept merging (Xionget et al. 2016) or temporal decomposition (Ghoshe et al. 2020). However, both methods exhibit serious drawbacks: the composite concepts generated by merging not only blur the clear semantic boundaries of each concept, but also cause combinatorial explosion in large-scale scenarios; conversely, decomposition artificially fragments a single answer event into multi-step sequential input, disrupting the student's answering trajectory and injecting temporal noise.

[0004] Recent advances have attempted to move beyond simple bipartite mappings by constructing higher-order problem graphs through shared concepts (e.g., QCKT (Shenetal. 2025)) or by utilizing diffusion denoising in the latent space (e.g., DiffuQKT (Yuetal. 2025)). Despite these improvements, such methods still primarily treat knowledge concepts as parallel, isolated entities, ignoring their inherent structural dependencies. Based on constructivist learning theory (Jonassen 1991), the human knowledge architecture is fundamentally an interdependent network, where mastering a new concept largely depends on the understanding of preconditions. Existing representation frameworks fail to integrate this logical cognitive progression into the feature space. By limiting models to superficial relationships between isolated entities (which deviates significantly from objective cognitive laws), these methods fundamentally limit the ability of models to construct deep problem semantics and accurately diagnose complex knowledge states.

[0005] Currently, methods for obtaining conceptual relationships can be broadly categorized into three paradigms. First, manual annotation by domain experts (e.g., CMKT (Luetal.2022), (Kimetal.2023)) ensures high fidelity but is extremely time-consuming and laborious, making it unscalable to massive question banks. Second, statistical methods (e.g., APGKT (Zhangetal.2022), CRKT (Parketal.2024)) derive dependencies through co-occurrence frequencies or transition probabilities; however, they are inherently dataset-specific, thus impairing generalization ability. Third, while large language models (LLMs) are increasingly used to generate these structural relationships (e.g., TransKT (Hanetal.2025), CEKT (Sunetal.2025)), synthesized relationships often lack domain-specific granularity and require manual verification to ensure pedagogical accuracy. More importantly, relationships derived from expert priors or LLMs inherently embody an idealized disciplinary logic. In real-world online education environments, students' experiential learning trajectories often deviate from these theoretical constructs due to the significant moderating effects of diverse course structures, algorithmic recommendations, and individual cognitive differences. Therefore, static conceptual relationships cannot accurately capture the dynamics of underlying relationships embedded in actual interaction logs. Furthermore, while statistical methods extract relationships directly from empirical data, they rely on shallow indicators (such as co-occurrence frequency and transition probability), making them highly susceptible to data sparsity.

[0006] Therefore, to effectively introduce conceptual relationships to enhance problem representation, two key challenges must be addressed: First, the adaptive acquisition of experiential conceptual relationships. How can we dynamically acquire conceptual relationship structures that truly reflect real-world interaction patterns? Static priors struggle to adapt to dynamic response distributions, while shallow statistical inference is easily affected by sparse interactions. Developing a mechanism that adapts to dynamic cognitive trajectories and is robust to data sparsity to capture these authentic conceptual relationships remains a critical hurdle. Second, micro-semantic representation based on conceptual difficulty. Given conceptual relationships, how can we further depict the micro-differences between different problems? Based on cognitive load theory (Sweller 1988), the inherent complexity of learning materials imposes varying degrees of intrinsic cognitive load on learners. In real-world scenarios, not only do problems targeting different concepts carry different cognitive loads, but different problems examining the same concept also exhibit different levels of complexity (e.g., basic questions versus complex variations). Accurately modeling this fundamental conceptual difficulty and utilizing it to adjust for micro-semantic variations in individual questions is crucial for generating discriminative problem semantics and refining overall representations.

[0007] Knowledge Tracking: Early knowledge tracking models relied primarily on statistical methods and factor analysis. Bayesian Knowledge Tracking (BKT) (Corbett and Anderson 1994) and Item Response Theory (IRT) (Wilsone et al. 2016) used probabilistic processes and item parameters to approximate students' proficiency. However, they inherently struggle to capture complex multi-concept interactions and the sequential nature of learning. Factor analysis models such as LFA (Cene et al. 2006) and PFA (Pavlik et al. 2009) improve interpretability by incorporating explicit macro and micro variables. Nevertheless, these traditional methods remain fundamentally limited by linear assumptions and a heavy reliance on artificial feature engineering.

[0008] The emergence of deep learning has propelled knowledge tracing into the era of data-driven sequence modeling. Early neural methods used recurrent neural networks (represented by DKT (Pieche et al. 2015)) and memory-enhancing networks (such as DKVMN (Zhang et al. 2017)) to encode interaction history and dynamically track concept mastery end-to-end. Subsequently, attention mechanisms and Transformers revolutionized the field. Researchers have evolved from basic self-attention architectures (including SAKT (Pandey and Karypis 2019) and SAINT (Choie et al. 2020)) to complex variants that explicitly simulate cognitive mechanisms. Notable examples include context-aware forgetting mechanisms in AKT (Ghoshe et al. 2020) and hierarchical cross-session decay in HiTSKT (Keet et al. 2024).

[0009] Meanwhile, graph neural networks have significantly enhanced the representation of complex knowledge structures. While early frameworks (such as GKT (Nakagawa et al. 2019) and HGKT (Tongetal. 2022)) propagated knowledge states over static or heterogeneous topologies, recent advances have focused on capturing complex, high-order, and dynamic relationships. To model high-order interactions, researchers have explored hypergraphs combining knowledge distillation (DGEKT (Cuietal. 2024)) or hyperbolic spaces combining contrastive clustering (DisenKT (Lietal. 2025)). Furthermore, to address temporal complexity, continuous-time dynamic graph learning in DyGKT (Cheng et al. 2024) and bidirectional feedback frameworks such as BDGKT (Ouetal. 2026) have been introduced, successfully adapting to irregular learning intervals and capturing the overall interaction between learners and potential problem attributes.

[0010] Problem Representation in Knowledge Tracing: The effectiveness of knowledge tracing fundamentally depends on a representation that accurately reflects the inherent characteristics of the original problem. Early methods, including EERNN (Sue et al. 2018), EKT (Liue et al. 2019), and RKT (Pandey and Srivastava 2020), utilize word embeddings to encode textual descriptions; however, their applicability is severely hampered by the sparse or missing metadata in real-world scenarios. Therefore, graph-based representations have become the mainstream paradigm. Researchers have progressed from modeling basic problem-concept bipartite graphs (as proposed by GIKT (Yang et al. 2020)) to constructing complex isomorphic or heterogeneous structures to capture broader context (as demonstrated by Bi-CLKT (Song et al. 2022) and S2-HHN (Wu and Ling 2023)). Recent advances have further utilized higher-order relation graphs (e.g., QCKT (Shenetal. 2025)) and generative diffusion models (including DiffuQKT (Yuetal. 2025)) to synthesize high-quality embeddings. Despite these advances, existing methods primarily model static binary associations or direct connections between questions. They fundamentally fail to integrate the inherent structured relationships between deep knowledge concepts into the representation learning process. This critical omission limits the ability of current models to describe the internal logic of human cognitive architecture, thus hindering the extraction of deep, cognitively consistent question semantics.

[0011] Conceptual Relationships in Knowledge Tracing: Revealing the underlying dependencies between concepts is crucial for deciphering deep knowledge structures. Early methods (such as CMKT (Luetal.2022) and related research (Kimetal.2023)) largely relied on manual annotation by domain experts. However, this approach incurs extremely high manual costs and inherently lacks scalability to massive question banks. To mitigate these limitations, statistical methods have been widely adopted. For example, CSKVMN (Maoetal.2024) assumes that the concurrent occurrence of concepts in a single question implies an intrinsic relationship, while APGKT (Zhangetal.2022) uses co-occurrence frequency to quantify the strength of the relationship. Extending static metrics, LCKT (Laietal.2024) derives dependencies based on the temporal ordering of concepts in empirical interaction logs. Similarly, CRKT (Parketal.2024) constructs a performance-based accuracy matrix to calculate transition probabilities, thereby inferring the hierarchy of prerequisites.

[0012] Recently, the rapid proliferation of large-scale language models has introduced generative paradigms for establishing skill dependencies. Methods including CEKT (Sunetal. 2025) utilize these state-of-the-art models to autonomously synthesize subject-specific concepts and their corresponding dependency graphs. Furthermore, TransKT (Hanetal. 2025) successfully facilitates broader knowledge transfer by processing cross-domain question-concept pairs through language models to establish implicit cross-domain connections. Despite these diverse innovations, relationships derived from static statistical or generative models often reflect an idealized subject-specific logic, making it difficult to dynamically adapt to the complex and sparse characteristics of real-world student response distributions.

[0013] Knowledge tracing (KT) aims to model students' evolving knowledge states based on their historical learning interactions, a fundamental task in intelligent education systems. The quality of the question representation is a key factor determining the performance of a KT model. However, existing methods that incorporate concept relationships into question encoding face two key limitations: First, static concept relationship graphs generated by experts or large language models cannot capture students' dynamic cognitive trajectories, and shallow statistical methods are highly susceptible to data sparsity and interaction noise; second, fine-grained feature descriptions of question semantics remain insufficient, primarily lacking the integration of concept difficulty to accurately simulate the cognitive load of individual questions.

[0014] Based on the above analysis, the urgent technical problems that need to be solved in the existing technology are:

[0015] (1) Static concept relationship diagrams generated by experts or large language models cannot capture students’ dynamic cognitive trajectories, while shallow statistical methods are easily affected by data sparsity and interactive noise.

[0016] (2) The fine-grained feature description of problem semantics is still insufficient, mainly due to the lack of integration of conceptual difficulty to accurately simulate the cognitive load of individual problems. Summary of the Invention

[0017] To address the problems existing in the prior art, this invention provides a knowledge tracking method based on adaptive concept relationship discovery and structure-semantic co-optimization to enhance problem representation.

[0018] This invention is implemented as follows: A knowledge tracking method based on adaptive concept relationship discovery and structure-semantic co-optimization to enhance problem representation includes:

[0019] Step 1: The concept discovery module learns a directed acyclic graph of concept relationships and encodes them through heterogeneous graph convolution to generate structure-enhanced question embeddings.

[0020] Step 2: The semantic enhancement module uses multi-head attention to capture the inherent problem-concept associations and uses the topological concept difficulty metric as a cognitive scaling factor to adjust the offset vector of each problem, thereby achieving accurate cognitive load modeling.

[0021] Step 3 involves aligning these structural and semantic representations through contrastive learning to reduce redundancy and provide highly discriminative embeddings for knowledge state modeling.

[0022] Furthermore, the concept discovery module:

[0023] Define a learnable relational adjacency matrix:

[0024]

[0025] in It is a learnable parameter matrix of potential cognitive relationships; It maps the intensity to The Sigmoid activation function; Represents the Hadamard product; It is the identity matrix; its elements Intuitively reflects the mastery of concepts Learning concepts Basic support provided;

[0026] Introduce DAGMA continuous constraint loss:

[0027]

[0028] in It is a conceptual quantity. Control the strength of the constraint;

[0029] First, set a cognitive threshold. (To be discussed in later experiments) This filters out weak ties, generating a binary cognitive map. :

[0030]

[0031] in It is an indicator function;

[0032] ;

[0033] Following the principle that cognition flows from basic to comprehensive, we cut off the noisy edges pointing from the sink node to the source node to create the final DAG mask. :

[0034]

[0035] Finally, this mask is applied to the original dependency strength to obtain the denoised relation matrix. :

[0036] .

[0037] Furthermore, the aforementioned topological concept:

[0038] The extracted concept relationship graph is fused with the basic concept-question mapping matrix to construct a heterogeneous graph:

[0039]

[0040] in Including problem nodes and concept nodes Directed edge set The conceptual progression path was preserved. And explicitly decouple the original relation into bidirectional edges: Indicates the route of investigation. Indicates the instantiation path;

[0041] Given an initial node feature matrix , The aggregation of layers is as follows:

[0042]

[0043] in and These are the learnable weight matrices for specific relation flows and self-loops, respectively. It is a degree-normalized sparse adjacency matrix;

[0044] The model aggregates features through slicing. Break it down into problem representations and concept representation Then, it depends on the node type. Independently apply Dropout, residual connections, and layer normalization:

[0045]

[0046] By stacking two layers of heterogeneous graph convolutions, a problem representation rich in structural priors was obtained. :

[0047] .

[0048] Furthermore, the semantic enhancement module:

[0049] Using multi-head attention mechanisms to identify problem characteristics and conceptual features Perform cross alignment:

[0050]

[0051]

[0052] in ,and , , It is a learnable projection matrix, where And there are Size; The matrix masks irrelevant conceptual noise (if) Investigation If it is 1, then set it to 1; otherwise, set it to 0.

[0053] All concepts are initialized to Then, accumulate depth along the topology:

[0054]

[0055] These values ​​constitute the global depth vector. The in-degree centrality of prerequisite nodes is calculated as follows:

[0056]

[0057] These constitute the central vector To eliminate dimensional differences, depth was normalized to... A learnable parameter Adaptively fuse depth and centrality to achieve comprehensive difficulty. :

[0058]

[0059] Passed this difficulty level. Mapping to the problem to obtain the concept-driven basic problem difficulty ,in It is a row-normalized relation matrix used to average the difficulty in problems containing multiple concepts;

[0060] Finally, to guide micro-level changes, we move towards basic semantic features. Introduce a directional offset:

[0061]

[0062] in It is a learnable offset matrix used to capture the direction of inherent complexity; Guiding individual differences in semantic space, while conceptual difficulty As a scaling scalar that determines the magnitude.

[0063] Another objective of this invention is to provide a knowledge tracking system based on adaptive concept relationship discovery and structure-semantic co-optimization to enhance problem representation, comprising:

[0064] The concept discovery module learns directed acyclic graphs of concept relationships, which are encoded through heterogeneous graph convolutions to generate structure-enhanced question embeddings.

[0065] The semantic enhancement module is used to capture the inherent problem-concept associations by employing multi-head attention and to adjust the offset vector of each problem by using a topological concept difficulty metric as a cognitive scaling factor, thereby achieving accurate cognitive load modeling.

[0066] The contrastive learning module is used to align these structural and semantic representations through contrastive learning to reduce redundancy and provide highly discriminative embeddings for knowledge state modeling.

[0067] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the knowledge tracking method based on adaptive concept relationship discovery and structure-semantic co-optimization enhancement problem representation.

[0068] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the knowledge tracking method based on adaptive concept relationship discovery and structure-semantic co-optimization enhancement problem representation.

[0069] Another objective of this invention is to provide an information data processing terminal, which includes the knowledge tracking system based on adaptive concept relationship discovery and structure-semantic co-optimization to enhance problem representation.

[0070] Combining the above-mentioned technical solutions and the technical problems solved, the technical solution to be protected by this invention possesses significant advancements and unexpected effects:

[0071] First, this invention proposes a novel knowledge tracing framework centered on concept relation discovery and structure-semantic co-optimization. The proposed method reveals latent concept dependencies in a purely data-driven manner and utilizes concept difficulty to guide the generation of semantic features. By jointly optimizing the structural associations and semantic representations of the problem, the model significantly enhances problem embedding and improves the diagnostic accuracy of complex student knowledge states. Specifically, a concept relation discovery and aggregation module is designed. Unlike static priors or shallow statistical strategies that decouple dependencies from downstream targets, this module introduces an end-to-end paradigm, synchronizing latent relation mining with the core response prediction task. By utilizing prediction errors as direct feedback signals to capture the impact of concept associations on student performance, this mechanism effectively outlines latent cognitive dependencies. Therefore, it avoids the over-reliance on co-occurrence density and transition probability in traditional statistical methods and successfully extracts robust concept relations dynamically aligned with empirical response distributions.

[0072] Furthermore, to accurately depict the true cognitive load embedded in individual questions, a concept difficulty-guided semantic enhancement module is proposed. Based on classical cognitive load theory (Sweller 1994), the problem-solving process inherently imposes varying degrees of intrinsic cognitive load on learners. The main determinant of this load is the interactivity of information elements, primarily stemming from two levels. The first level comprises the base load established by the inherent complexity of concepts within the knowledge network. The second level involves the problem-specific intrinsic load generated by different test formats and necessary solution steps. Guided by this theoretical framework, the model utilizes the extracted concept topology to calculate concept difficulty, serving as a baseline measure of cognitive load across different concepts. To further address the micro-semantic variations between different questions targeting the same concept, a trainable question offset vector is introduced. The model uses the calculated concept difficulty as an adaptive scaling factor to adjust the magnitude of this offset. By fusing concept difficulty and specific question offsets, this framework successfully captures macro-level differences in cognitive load between different concepts while accurately characterizing micro-level variations between questions sharing the same concept, thereby generating highly discriminative question representations.

[0073] The main contributions of this invention are summarized as follows:

[0074] Based on continuous optimization for latent concept relationship discovery, a continuous acyclic constraint algorithm is introduced to establish an adaptive concept relationship mining mechanism. Through a purely data-driven approach, this mechanism dynamically extracts the directed acyclic structure of concept relationships directly from student answer interaction records. This method successfully overcomes the inherent limitations of traditional methods (which often ignore the actual answer paths or are affected by sparse data), thus providing a priori concept structures that conform to the actual cognitive progression patterns.

[0075] Combining Conceptual Prior Difficulty-Guided Semantic Enhancement: A semantic enhancement module guided by conceptual difficulty is designed. This module initially employs multi-head attention to extract the fundamental semantic mapping between questions and concepts. Crucially, it innovatively quantifies the inherent conceptual difficulty by leveraging topological depth and in-degree centrality. By modulating the question offset vector using this computed difficulty as a cognitive load scaling factor, the proposed mechanism effectively captures fine-grained cognitive load variations across different questions, enhancing the discriminative power of question representations.

[0076] A dual-perspective representation framework with structure-semantic co-optimization is constructed: a dual-perspective framework is built with topological aggregation and difficulty-guided semantics as its core. To ensure consistency between structure and semantics, a contrastive learning mechanism is introduced to co-align the structural and semantic features of the problem, effectively reducing representation redundancy. Extensive experiments on five public knowledge tracing datasets demonstrate that the proposed method significantly outperforms existing mainstream baseline models in both accuracy (ACC) and area under the curve (AUC) metrics for question prediction tasks.

[0077] This invention proposes a problem representation learning framework based on concept relationship discovery and structure-semantic co-optimization, overcoming the limitations of existing knowledge tracking methods, such as static graphs detached from real cognitive trajectories, shallow statistical methods interfered with by interaction noise, and insufficient fine-grained semantic feature description. Methodologically, the model introduces a continuous acyclic constraint algorithm to adaptively mine potential concept relationships directly from the answer data. It includes a concept relationship discovery and aggregation module and a concept difficulty-guided semantic enhancement module. By contrastive learning to co-align dual-view problem features to eliminate redundancy, it utilizes a long short-term memory network to represent students' dynamic knowledge states. Experiments on five public educational datasets show that in the prediction answer task, this invention improves the average ACC and AUC by 1.39% and 1.42%, respectively, compared to the suboptimal baseline. Analysis confirms that, compared to traditional static priors, this data-driven concept relationship discovery mechanism better reflects the real cognitive progression path, and the combination of difficulty-aware semantic enhancement strategy accurately depicts the micro-cognitive load differences between questions. In summary, the proposed framework effectively compensates for the shortcomings of existing models in terms of deep cognitive structure and fine-grained semantic representation, and provides a reliable representation optimization scheme for accurately assessing students' knowledge status.

[0078] Secondly, as supporting evidence of the inventiveness of this invention, it is also reflected in the following important aspects:

[0079] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0080] The core value of the knowledge tracking framework proposed in this invention lies in its ability to achieve high-precision diagnosis of students' knowledge status solely based on the most basic question-concept-answer triplet, without requiring any additional manual annotation (such as expert-defined conceptual relationships, test question text descriptions, or question type metadata). This characteristic gives it strong scalability and commercial application potential.

[0081] The expected benefits are as follows: This invention can be directly integrated into the backend engines of various online education platforms (such as intelligent tutoring systems, MOOCs, and adaptive learning apps). By accurately predicting students' answer performance and potential cognitive weaknesses, the platform can achieve personalized learning path planning and exercise recommendations tailored to each student, thereby significantly improving students' learning efficiency, engagement, and retention rates.

[0082] The commercial value is: Empowering B-end educational institutions: As a core algorithm service, it can provide API interfaces to K-12 schools and vocational education institutions, charging authorization or licensing fees; Enhancing the competitiveness of C-end products: Compared to existing competitors that can only provide generalized recommendations, this solution can provide more scientific and detailed cognitive diagnostic reports, which can be used as an advanced paid feature to create direct value-added revenue; Reduced operating costs: Since it does not rely on expensive expert annotation and text processing, this technical solution can significantly reduce the platform's operating costs during content cold start and question bank updates, giving it a significant cost advantage in market competition.

[0083] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally:

[0084] This invention fills a technological gap in the field of knowledge tracing by deeply co-optimizing data-driven adaptive concept relationship mining with fine-grained semantic enhancement guided by cognitive load theory. Existing technologies, when introducing concept relationships, either rely on static expert knowledge or LLM generation logic that may deviate from the actual learning path, or use shallow statistical indicators that are highly susceptible to data noise. This invention proposes for the first time an end-to-end concept relationship discovery paradigm that uses DAG constraints and prediction errors as feedback signals to directly mine concept structures that conform to the actual cognitive progression from interaction logs. Simultaneously, this invention also, for the first time, uses topological depth and centrality as quantifiable indicators of cognitive load and successfully applies them to modulate the micro-semantic shift of problems, achieving a unified modeling of macro-conceptual difficulty and micro-question variation. This structure-semantic dual-perspective co-optimization approach has not been disclosed in existing published literature and patents.

[0085] (3) The technical solution of the present invention solves a technical problem that people have long wanted to solve but have never been able to solve successfully:

[0086] This invention solves two core problems that the field of knowledge tracing has long sought to address:

[0087] Firstly, how to adaptively and robustly acquire conceptual relationships that truly reflect students' cognitive trajectories. For a long time, those skilled in the art have generally anticipated a technical solution capable of autonomously perceiving and modeling students' cognitive development trajectories. That is, enabling the system to automatically infer objectively existing dependencies between knowledge points that conform to the actual laws of cognitive progression by observing and analyzing learners' historical answer performance. However, traditional graph structure search is an NP-hard problem, while statistical methods are too fragile. This invention cleverly solves this contradiction by introducing a two-stage strategy of continuous acyclic constraints and discrete topological filtering, achieving stable and adaptive discovery of conceptual dependencies on large-scale, high-noise data.

[0088] Secondly, how to assign differentiated semantic representations to different questions. There has always been a desire for models to perceive the differences in cognitive load between basic and variant questions, but effective quantification methods have been lacking. This invention, based on constructivist cognitive theory, creatively transforms the depth and in-degree of concepts in a dependency graph into a measure of cognitive load, and uses this as a scaling factor to control the offset direction and magnitude of question embedding, successfully solving this challenge of micro-level semantic modeling.

[0089] (4) The technical solution of the present invention overcomes technical bias:

[0090] For a long time, there has been a prevailing technological bias in this field, namely that obtaining high-quality conceptual relationships requires reliance on external knowledge sources, such as:

[0091] Expert experience is the only reliable source: this has led to a large number of studies relying on time-consuming and laborious manual annotation.

[0092] The knowledge graphs generated by LLM are advanced, leading recent research to overlook the problem that the LLM generation logic may be out of sync with the actual student experience trajectory.

[0093] Concepts are isolated, and their relationships are static: this leads traditional graphical models to model only simple dichotomous relationships between problems and concepts.

[0094] This invention overcomes all the aforementioned biases. It abandons the reliance on external priors and demonstrates that, driven solely by pure data, by combining relation mining with main task prediction, it can uncover directed acyclic conceptual structures that more closely resemble the dynamics of real learning. Attached Figure Description

[0095] Figure 1 This is a flowchart of a knowledge tracking method based on adaptive concept relationship discovery and structure-semantic co-optimization to enhance problem representation, provided by an embodiment of the present invention.

[0096] Figure 2 This is a block diagram of a knowledge tracking system based on adaptive concept relationship discovery and structure-semantic co-optimization enhancement problem representation provided in an embodiment of the present invention.

[0097] Figure 3 This is a simplified diagram of knowledge tracking provided in an embodiment of the present invention.

[0098] Figure 4 This is an overall architecture framework diagram of SSCKT provided in the embodiments of the present invention.

[0099] Figure 5 This is a graph comparing the prediction performance of different concept relationship construction methods provided in the embodiments of the present invention (on the Edi dataset).

[0100] Figure 6This is a diagram showing the influence of different τ values ​​on our model, provided by an embodiment of the present invention.

[0101] Figure 7 This is an average performance graph provided by the embodiments of the present invention under different thresholds τ.

[0102] Figure 8 This is a t-SNE visualization dimensionality reduction diagram of the feature embeddings of outputs at different stages, provided by an embodiment of the present invention. Detailed Implementation

[0103] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0104]

[0105] like Figure 1 As shown, the knowledge tracking method based on adaptive concept relationship discovery and structure-semantic co-optimization to enhance problem representation provided by this embodiment of the invention includes the following steps:

[0106] S101, the concept discovery module learns a directed acyclic graph of concept relationships, which is encoded through heterogeneous graph convolution to generate structure-enhanced question embeddings;

[0107] S102, the semantic enhancement module uses multi-head attention to capture the inherent problem-concept associations and uses the topological concept difficulty metric as a cognitive scaling factor to adjust the offset vector of each problem, thereby achieving accurate cognitive load modeling;

[0108] S103 uses contrastive learning to align these structural and semantic representations to reduce redundancy, providing highly discriminative embeddings for knowledge state modeling.

[0109] The concept discovery module provided in this embodiment of the invention:

[0110] Define a learnable relational adjacency matrix:

[0111]

[0112] in It is a learnable parameter matrix of potential cognitive relationships; It maps the intensity to The Sigmoid activation function; Represents the Hadamard product; It is the identity matrix; its elements Intuitively reflects the mastery of concepts Learning concepts Basic support provided;

[0113] Introduce DAGMA continuous constraint loss:

[0114]

[0115] in It is a conceptual quantity. Control the strength of the constraint;

[0116] First, set a cognitive threshold. (To be discussed in later experiments) This filters out weak ties, generating a binary cognitive map. :

[0117]

[0118] in It is an indicator function;

[0119] ;

[0120] Following the principle that cognition flows from basic to comprehensive, we cut off the noisy edges pointing from the sink node to the source node to create the final DAG mask. :

[0121]

[0122] Finally, this mask is applied to the original dependency strength to obtain the denoised relation matrix. :

[0123] .

[0124] The topology concept provided in the embodiments of this invention:

[0125] The extracted concept relationship graph is fused with the basic concept-question mapping matrix to construct a heterogeneous graph:

[0126]

[0127] in Including problem nodes and concept nodes Directed edge set The conceptual progression path was preserved. And explicitly decouple the original relation into bidirectional edges: Indicates the route of investigation. Indicates the instantiation path;

[0128] Given an initial node feature matrix , The aggregation of layers is as follows:

[0129]

[0130] in and These are the learnable weight matrices for specific relation flows and self-loops, respectively. It is a degree-normalized sparse adjacency matrix;

[0131] The model aggregates features through slicing. Break it down into problem representations and concept representation Then, it depends on the node type. Independently apply Dropout, residual connections, and layer normalization:

[0132]

[0133] By stacking two layers of heterogeneous graph convolutions, a problem representation rich in structural priors was obtained. :

[0134] .

[0135] The semantic enhancement module provided in this embodiment of the invention:

[0136] Using multi-head attention mechanisms to identify problem characteristics and conceptual features Perform cross alignment:

[0137]

[0138]

[0139] in ,and , , It is a learnable projection matrix, where And there are Size; The matrix masks irrelevant conceptual noise (if) Investigation If it is 1, then set it to 1; otherwise, set it to 0.

[0140] All concepts are initialized to Then, accumulate depth along the topology:

[0141]

[0142] These values ​​constitute the global depth vector. The in-degree centrality of prerequisite nodes is calculated as follows:

[0143]

[0144] These constitute the central vector To eliminate dimensional differences, depth was normalized to... A learnable parameter Adaptively fuse depth and centrality to achieve comprehensive difficulty. :

[0145]

[0146] Passed this difficulty level. Mapping to the problem to obtain the concept-driven basic problem difficulty ,in It is a row-normalized relation matrix used to average the difficulty in problems containing multiple concepts;

[0147] Finally, to guide micro-level changes, we move towards basic semantic features. Introduce a directional offset:

[0148]

[0149] in It is a learnable offset matrix used to capture the direction of inherent complexity; Guiding individual differences in semantic space, while conceptual difficulty As a scaling scalar that determines the magnitude.

[0150] like Figure 2 As shown, an embodiment of the present invention provides a knowledge tracking system based on adaptive concept relationship discovery and structure-semantic co-optimization to enhance problem representation, comprising:

[0151] The concept discovery module learns directed acyclic graphs of concept relationships, which are encoded through heterogeneous graph convolutions to generate structure-enhanced question embeddings.

[0152] The semantic enhancement module is used to capture the inherent problem-concept associations by employing multi-head attention and to adjust the offset vector of each problem by using a topological concept difficulty metric as a cognitive scaling factor, thereby achieving accurate cognitive load modeling.

[0153] The contrastive learning module is used to align these structural and semantic representations through contrastive learning to reduce redundancy and provide highly discriminative embeddings for knowledge state modeling.

[0154] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the knowledge tracking method based on adaptive concept relationship discovery and structure-semantic co-optimization enhancement problem representation.

[0155] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the knowledge tracking method based on adaptive concept relationship discovery and structure-semantic co-optimization enhancement problem representation.

[0156] Another objective of this invention is to provide an information data processing terminal, which includes the knowledge tracking system based on adaptive concept relationship discovery and structure-semantic co-optimization to enhance problem representation.

[0157] Specific implementation of the present invention:

[0158] 1. This invention provides SSCKT, a KT framework that adaptively extracts concept relationships from interactive data and achieves structure-semantic co-optimization of question representations. Specifically, the concept discovery module learns a directed acyclic graph of concept relationships and then encodes them through heterogeneous graph convolution to generate structure-enhanced question embeddings. Furthermore, the semantic enhancement module employs multi-head attention to capture inherent question-concept associations and utilizes a topological concept difficulty metric as a cognitive scaling factor to adjust the offset vector of each question for accurate cognitive load modeling. Then, contrastive learning is used to align these structural and semantic representations to reduce redundancy, providing highly discriminative embeddings for knowledge state modeling. Experiments on five public datasets show that the method outperforms the state-of-the-art baseline by an average of 1.39% on ACC and 1.42% on AUC, validating the effectiveness of the adaptive concept relationship discovery and structure-semantic co-optimization framework. Figure 3 A simplified illustration of knowledge tracing: This model predicts students' answers to future concept-related questions based on their learning sequence and simulates changes in their knowledge state for each concept. Knowledge tracing (KT) is often formulated as a supervised sequence learning task (such as... Figure 3 (As shown)

[0159] 2. This invention proposes a novel knowledge tracing framework centered on concept relation discovery and structure-semantic co-optimization. The proposed method reveals latent concept dependencies in a purely data-driven manner and uses concept difficulty to guide the generation of semantic features. By jointly optimizing structural associations and semantic representations, the model significantly enhances question embedding and improves the diagnostic accuracy of complex student knowledge states. Specifically, a concept relation discovery and aggregation module is designed. Unlike static priors or shallow statistical strategies that decouple dependencies from downstream targets, this module introduces an end-to-end paradigm that synchronizes latent relation mining with the core response prediction task. By utilizing prediction errors as direct feedback signals to capture the impact of concept associations on student performance, this mechanism effectively outlines latent cognitive dependencies. Therefore, it avoids the over-reliance on co-occurrence density and transition probability in traditional statistical methods and successfully extracts robust concept relations dynamically aligned with empirical response distributions.

[0160] 3 Method Framework

[0161] like Figure 4 As shown, the framework consists of two main functional modules and a feature alignment and prediction part. The concept relationship discovery and aggregation module mines potential concept relationships in a data-driven manner, constructs a heterogeneous directed graph containing concept relationships and explicit mappings between questions and concepts, and aggregates them through a heterogeneous graph convolutional network to output question embeddings rich in structure priors. The concept difficulty-guided semantic enhancement module uses the basic question-concept relationship extracted through multi-head attention as a baseline, introduces concept difficulty as a scaling factor, and combines it with question mutation vectors to generate semantic feature encodings. Finally, the feature alignment and prediction parts use contrastive learning to co-align the two embeddings, constrain redundancy, and feed cascaded features into the prediction network to track the knowledge state.

[0162] 3.1 Problem Definition

[0163] The knowledge tracing task is defined as follows: given a student's historical interaction sequence ,in Indicates the time of the student Questions that need to be answered Indicates and Related set of concepts The correctness is indicated by 0 (0 for incorrect, 1 for correct). The goal is to model students' knowledge state based on their interaction history and predict whether they will answer correctly. .

[0164] This method utilizes the three most fundamental elements of knowledge tracing: questions, concepts, and responses. These elements are independently embedded into three matrices: the question embedding matrix... Concept Embedding Matrix and response embedding matrix .here, Indicates the number of questions. Indicates the quantity of concepts. Indicates the size of the embedding dimension. Used respectively. , and Representation matrix , and Specific row vectors in the matrix. These matrices use a uniform distribution. Random initialization is performed. For ease of reading and formula derivation, the core mathematical symbols used in this invention are defined in Table 1.

[0165] Figure 4 This is the overall architecture framework for SSCKT. The concept relation discovery and aggregation module adaptively mines concept relations and outputs question features rich in concept structure through heterogeneous graph convolution. The concept difficulty-guided semantic enhancement module captures basic semantic relations using multi-head attention and outputs semantic features scaled by concept difficulty and question mutation vectors. The feature alignment part uses BarlowTwins loss to align these two feature types. Finally, an LSTM captures the student's knowledge state to predict the outcome.

[0166] 3.2 Concept Relationship Discovery and Aggregation Module

[0167] This module injects conceptual relationships mined from student question-answering interactions into the question representation. The process includes two steps: first, adaptively discovering directed acyclic conceptual relationships to construct a question-concept heterogeneous graph; second, aggregating neighbor information on the topological structure of this graph to obtain a structurally enhanced question representation.

[0168] 3.2.1 Discovery of Latent Conceptual Relationships

[0169] In real educational settings, the learning process inherently follows the fundamental laws of cognitive progression. For example, mastering a linear equation in one variable is a strict prerequisite for understanding a quadratic equation. This hierarchical dependency collectively constructs the underlying cognitive framework of any particular subject. However, traditional methods for establishing these explicit relationships are highly labor-intensive and lack the necessary flexibility to adapt to different teaching systems. Therefore, the proposed module aims to adaptively mine and construct latent conceptual relationships directly from historical response trajectories of experience. This purely data-driven approach ensures that the derived relational structures can dynamically capture the underlying, authentic cognitive progression logic within real learning behaviors.

[0170] To quantify the strength of potential relationships between concepts, a learnable relational adjacency matrix is ​​defined:

[0171]

[0172] in It is a learnable parameter matrix of potential cognitive relationships; It maps the intensity to The Sigmoid activation function; Represents the Hadamard product; It is the identity matrix; and Element-wise multiplication explicitly eliminates self-loops (a concept cannot be a prerequisite for itself). Elements It intuitively reflects the mastery of concepts. Learning concepts Basic support provided.

[0173] Because the acquisition of knowledge follows a strict directionality, if the concept yes The prerequisite, then It can't be A prerequisite is that the learned graph must be a strictly directed acyclic graph (DAG). Since performing discrete graph structure search in deep networks is an NP-hard problem, the DAGMA continuous constraint loss is introduced (Bello et al. 2022):

[0174]

[0175] in It is a conceptual quantity. Control the strength of the constraints. This unidirectional progression of learning is transformed into a mathematical penalty for continuously differentiable non-DAG structures. If in If a cyclic relationship appears, this function will incur a positive penalty. Minimizing this loss allows the model to automatically avoid cyclic paths and evolve globally reasonable relationships.

[0176] While continuity constraints drive matrices toward a DAG, real sequences contain noise from guesses or errors, leaving weak spurious cyclic connections. To ensure mathematical legitimacy and educational rigor, discrete topological filtering is applied to extract the cognitive backbone.

[0177] First, set a cognitive threshold. (To be discussed in later experiments) This filters out weak ties, generating a binary cognitive map. :

[0178]

[0179] in It is an indicator function. To remove symmetric bidirectional edges caused by noise, a node scoring mechanism based on topological in-degree and out-degree is introduced:

[0180]

[0181] This score reflects the concept's position within the knowledge system: higher scores indicate foundational concepts as source nodes, while lower scores indicate comprehensive concepts as sink nodes. Following the cognitive flow from foundational to comprehensive, we cut off noisy edges pointing from sink nodes to source nodes to create the final DAG mask. :

[0182]

[0183] Finally, this mask is applied to the original dependency strength to obtain the denoised relation matrix. :

[0184]

[0185] Since the indicator functions in formulas [f1] and [f2] cause gradient truncation (derivatives are zero), a pass-through estimator (STE (Bengio et al. 2013)) is introduced for end-to-end training. Forward propagation uses a binarized graph. To maintain a sparse skeleton, backpropagation truncates the gradient, approximating it as an identity mapping, allowing for error gradient updates. This balances discrete constraints with continuous optimization.

[0186] Through this two-stage mechanism of continuous evolution and discrete purification, the module overcomes the limitations of static priors and shallow statistical methods. It adaptively learns latent DAG relationships directly from interactive data, providing data-driven priors without human intervention.

[0187] 3.2.2 Problem Representation of Topology Enhancement

[0188] Problem-concept interaction is described as a basic bipartite graph. While problems sharing specific concepts can indirectly exchange information, this structural paradigm inherently assumes that all knowledge concepts exist as parallel and isolated entities. Therefore, the flow of semantic information across different concepts is severely hampered. For example, under this paradigm, semantic information about addition problems cannot be effectively propagated to enrich the representation of multiplication problems.

[0189] To overcome these limitations, this module fuses the extracted concept relationship graph with the basic concept-question mapping matrix to construct a heterogeneous graph:

[0190]

[0191] in Including problem nodes and concept nodes Directed edge set The conceptual progression path was preserved. And explicitly decouple the original relation into bidirectional edges: This indicates the examination path (showing that a question examines a concept). This represents the instantiation path (meaning a concept is instantiated as a problem). This decoupling allows GNNs to distinguish between two different educational information flows: knowledge sourcing and knowledge application.

[0192] To integrate the conceptual structure into the problem representation, a heterogeneous graph convolutional network is used. Since the graph contains three different transition logics, an independent parameter matrix is ​​assigned to each directed edge type. Given an initial node feature matrix... , The aggregation of layers is as follows:

[0193]

[0194] in and These are the learnable weight matrices for specific relation flows and self-loops, respectively. It is a degree-normalized sparse adjacency matrix.

[0195] Next, the model will aggregate the features by slicing. Break it down into problem representations and concept representation Then, it depends on the node type. Independently apply Dropout, residual connections, and layer normalization:

[0196]

[0197] By stacking two layers of heterogeneous graph convolutions, a problem representation rich in structural priors was obtained. :

[0198]

[0199] therefore, It retains the inherent characteristics of the questions while effectively integrating a macro-conceptual topology driven by real-world response data.

[0200] 3.3 Semantic Enhancement Module Guided by Conceptual Difficulty

[0201] While the preceding stages integrate structural priors through topological aggregation, the true cognitive load of an individual question is simultaneously determined by both macroscopic conceptual difficulty and microscopic problem complexity. To accurately distinguish these cognitive differences, the proposed modules characterize their respective functions. Specifically, the inherent complexity of a question determines the precise directional deviation of its feature representation from the underlying concepts in the latent semantic space. Simultaneously, conceptual difficulty acts as a global scaling factor to modulate the overall magnitude of this semantic shift. Building upon the extraction of underlying conceptual semantics through a multi-head attention mechanism, the module uses the topological properties of the constructed relational graph to quantify conceptual difficulty. By adaptively scaling the question offset vector using this metric, the proposed mechanism successfully decouples semantically similar questions, thereby achieving deep semantic representation enhancement.

[0202] First, in order to capture multifaceted semantic relationships, a multi-head attention mechanism is used to analyze the problem features. and conceptual features Perform cross alignment:

[0203]

[0204]

[0205] in ,and , , It is a learnable projection matrix, where And there are Size. The matrix masks irrelevant conceptual noise (if) Investigation If the value is 1, then set it to 1; otherwise, set it to 0. This allows the model to learn test preferences across different subspaces and generate features. This reflects the core semantic mapping.

[0206] Next, in order to establish a cognitive load baseline, this module uses a relational matrix. Quantifying conceptual difficulty from a network structure perspective. The deeper a concept is (topological depth) and the more supporting nodes it has (in-degree), the higher its accumulated cognitive load. For depth, all concepts are initialized as follows: Then, the depth is accumulated along the topology:

[0207]

[0208] These values ​​constitute the global depth vector. The in-degree centrality of prerequisite nodes is calculated as follows:

[0209]

[0210] These constitute the centrality vector. To eliminate dimensional differences, depth was normalized to... A learnable parameter Adaptively fuse depth and centrality to achieve comprehensive difficulty. :

[0211]

[0212] Passed this difficulty level. Mapping to the problem to obtain the concept-driven basic problem difficulty ,in It is a row-normalized relation matrix used to average the difficulty in problems containing multiple concepts.

[0213] Finally, to guide micro-level changes, we move towards basic semantic features. Introduce a directional offset:

[0214]

[0215] in It is a learnable offset matrix used to capture the direction of inherent complexity (e.g., computational steps, variant problems). Here, Guiding individual differences in semantic space, while conceptual difficulty As a scaling scalar that determines the magnitude, the problem will shift proportionally to the fundamental difficulty of the concept along its direction of change, thus producing a highly discriminative semantic representation. .

[0216] 3.4 Dual-view alignment and sequence modeling

[0217] This section will discuss macroscopic topological features. and micro-semantic features Alignment and fusion are performed. By co-optimizing these two perspectives, the model obtains a robust and discriminative integrated embedding to drive the sequential modeling of knowledge states.

[0218] 3.4.1 Collaborative Alignment of Problem Features from Two Perspectives

[0219] although and The problem is represented in different spaces, but they characterize the underlying educational properties of the same problem. To maintain internal consistency and avoid schema collapse or redundancy, BarlowTwins loss is introduced.

[0220]

[0221] in This is a question index. It is a dimensional index. yes The peacekeeping The The cross-correlation coefficient between dimensions. The BarlowTwins loss is:

[0222]

[0223] Invariant terms are forced to have a diagonal term of 1 (indicating high correlation on the same dimension), while redundant terms are forced to have an off-diagonal term of 0. This extracts a representative cognitive kernel.

[0224] The aligned features are fused into the final embedding via a linear mapping. middle:

[0225]

[0226] in This indicates a cascading splicing operation. This is the issue index.

[0227] 3.4.2 Dynamic Knowledge State Modeling

[0228] To model the cognitive feedback of correct / incorrect answers, a response embedding matrix is ​​introduced. In time Interactive representation for:

[0229]

[0230] in Indicates the answer result. yes The corresponding row vectors in the middle, It is a learnable projection matrix, and This indicates cascading splicing.

[0231] Since students' knowledge evolves dynamically, a Long Short-Term Memory (LSTM) network is used to model the interaction trajectory. Utilizing a built-in gating mechanism, the LSTM adaptively retains historical records, accurately modeling knowledge acquisition and forgetting, thereby generating dynamic states. :

[0232]

[0233] in This is the current interaction representation. It is a historical state.

[0234] 3.5 Joint Loss Function and Model Training

[0235] Based on dynamic state The fusion representation of the next question Construct a prediction layer to calculate the probability of a correct answer:

[0236]

[0237] in It is the Sigmoid function. It is a cascaded splicing. ,in and For the first layer weights and biases, and This is the second layer. Cross-entropy loss is used to optimize the prediction:

[0238]

[0239] in , This is the total number of time steps. The total loss is:

[0240]

[0241] in and The adaptive weights are dynamically optimized during training to balance the three loss components. To clearly outline the proposed framework, the complete forward propagation and structure-semantic co-optimization process is summarized in Algorithm 1. This process begins with establishing basic parameter initialization before each iterative training cycle (line 1). The main full-process training loop fundamentally integrates four key phases within each complete epoch (lines 2–17). First, the model systematically constructs a heterogeneous concept relation graph to aggregate structural priors (lines 3–5). Simultaneously, it performs a semantic enhancement module, extracting basic question-concept associations and generating semantic representations strictly modulated by concept difficulty (lines 6–9). Furthermore, these specific iterations co-align complementary representations through contrastive learning to update the dynamic knowledge state (lines 10–12). Finally, the framework predicts future cognitive states and explicitly optimizes all learnable parameters via gradient descent based on the joint loss function (lines 13–16). Ultimately, the algorithm outputs fully optimized model parameters after completing all training epochs (line 18).

[0242]

[0243] 4 Experiments

[0244] In this section, extensive experiments were conducted to answer the following questions:

[0245] RQ1: How does the proposed model perform overall on the question prediction task compared to existing mainstream and state-of-the-art (SOTA) baselines?

[0246] RQ2: What are the specific impacts of different core components on overall prediction performance?

[0247] RQ3: Does the data-driven adaptive approach demonstrate superiority over concept relations based on statistics, expert annotation, and large language models?

[0248] RQ4: Cognitive Threshold in the Conceptual Relationship Module How does it affect final performance?

[0249] RQ5: What is the quality of the question embeddings generated after structural-semantic co-optimization?

[0250] 4.1 Dataset

[0251] The model was evaluated on five public datasets: ASSIST09, ASSIST12, ASSIST17, EdNet, and Eedi.

[0252] ASSIST09: Collected from the ASSISTments platform (2009-2010).

[0253] ASSIST12: Collected from the ASSISTments platform (2012-2013).

[0254] ASSIST17: Collected from the ASSISTments platform in 2017.

[0255] EdNet: Collected by the Santa platform (2017-2019).

[0256] Eedi: Collected from the Eedi platform (2018-2020).

[0257] Statistics on the processed dataset.

[0258] Number of students 6371 27145 1708 5000 5000 Number of questions 13539 50988 3162 12115 27081 Number of concepts 139 208 102 188 388 Interaction Log 432236 2630080 942814 6223532 667324

[0259] For the ASSIST dataset, following previous research (Ghoshetal. 2020), records lacking concept annotations were removed. Due to the large size of the EdNet and Eedi datasets and limited computational resources, 5,000 students were randomly selected from each dataset. Dataset statistics are shown in Table 2.

[0260] 4.2 Baseline Model

[0261] The following widely accepted state-of-the-art (SOTA) models were selected as the baseline:

[0262] DKT (Piechetal.2015): Introduces Recurrent Neural Networks (LSTM) into knowledge tracing, enabling end-to-end modeling of sequences and achieving significant performance improvements.

[0263] DKVMN (Zhang et al. 2017): Introduced a dynamic key-value memory network, which uses a memory matrix to store and update concept mastery levels, enhancing interpretability.

[0264] SAKT (Pandey and Karypis 2019): The first to apply self-attention mechanism to knowledge tracing, achieving efficient modeling by focusing on historical interactions related to the current problem.

[0265] SAINT (Choietal.2020): Based entirely on the Transformer architecture, it encodes questions and answers separately to make full use of sequence information.

[0266] AKT (Ghoshetal.2020): proposed a context-aware attention mechanism that combines problem and concept relationships, and explicitly models forgetting behavior to improve robustness.

[0267] CL4KT (Leeetal.2022): Constructs a contrastive learning task through data augmentation to learn a robust student knowledge state representation.

[0268] QCKT (Shenetal.2025): It constructs a high-order relation graph by leveraging the concept of shared information between problems, and aggregates neighbor information through graph convolution to enhance problem representation.

[0269] DiffuQKT (Yuetal.2025): Introduces a diffusion model to semantically enhance embeddings, generating discriminative representations through diffusion and denoising in the latent space.

[0270] BDGKT (Ouetal.2026): Construct a bidirectional dynamic graph based on a homogeneous student population to capture bidirectional information flow for collaborative modeling of knowledge state and feature evolution.

[0271] For DKT, the raw output provides the probabilities of all questions, which is not suitable for large datasets. Therefore, the output layer of DKT was modified so that it only predicts the probability of the next question.

[0272] 4.3 Experimental Setup

[0273] For each dataset, the training, validation, and test sets are divided in a 7:1.5:1.5 ratio. (Embedding dimension) The set value is 512, the batch size is 16, the learning rate is 0.05, and the weight decay is [missing value]. Due to the varying lengths of the input sequences, the maximum sequence length was set to 200 (Shenetal.2025). Sequences shorter than 3 characters were filtered out because excessively short sequences lacked meaningful context. To prevent overfitting, Dropout was set to 0.2, gradient clipping to 15.0, and the patience value for early stopping was set to 10. For latent concept relationship discovery, the scaling parameter... The value is 1, and the numerical stability constant is The largest eigenvalue of the matrix exponent is 10, and the threshold is... The value was 0.01. The experiment was repeated three times and the average results were taken. The Adam optimizer was used, with a maximum of 300 training epochs. The model was trained on a Linux server equipped with an Intel Xeon Gold 6230 R CPU, an NVIDIA A100 GPU, and CUDA 12.4. ACC and AUC were used as evaluation metrics.

[0274] 4.4 Comparative Experiment (RQ1)

[0275] As shown in Table 3, the proposed method achieved state-of-the-art performance on all datasets. On ASSIST09 and ASSIST12, its ACC / AUC was 1.10% / 1.32% and 1.08% / 1.69% higher than the second-best baseline, respectively. It improved performance by 2.46% / 2.43% on ASSIST17 and maintained a stable lead on EdNet and Edi. This advantage stems from three core designs: explicitly modeling directed relationships between concepts, overcoming the limitations of isolated entities; introducing semantic enhancement guided by concept difficulty, effectively distinguishing the differences in cognitive load between different questions examining the same concept; and eliminating feature redundancy through dual-view contrastive learning, improving representation quality. The improvement on EdNet was relatively small (0.31% / 0.93%), which may be due to the high interaction noise in this dataset. These results validate the effectiveness of integrating cognitive recursion and fine-grained difficulty perception, providing a new modeling paradigm for knowledge tracing.

[0276]

[0277] 4.5 Impact Analysis of Different Components (RQ2)

[0278] To verify the specific contribution of each core component, ablation experiments were conducted. Three variants were built: removing the concept relationship discovery and aggregation modules (w / o). Remove the semantic enhancement module guided by concept difficulty (w / o) ), and retaining dual-view feature fusion but removing contrastive learning alignment (w / o) The results are shown in Table 4. Removing any enhancement features reduces ACC and AUC by: w / o Average decrease of 0.18% / 0.19%, w / o Decreased by 0.15% / 0.13%, w / o A decrease of 0.20% / 0.24% indicates that the complete model is optimal. This shows that: Topological aggregation injects structural priors; without it, the model loses cross-concept context, leading to a significant drop in performance. Conceptual difficulty scaling addresses problem offsets; without it, even with structural information preserved, the model struggles to represent cognitive load gradients between problems. Contrastive learning decouples dual-view features; direct concatenation introduces redundancy, leading to the most significant performance degradation. These results reveal a progressive dependency: topological aggregation provides a baseline for difficulty perception, difficulty perception refines discriminative power, and contrastive learning collaboratively fuses them to minimize representational redundancy.

[0279]

[0280] 4.6 Comparative Analysis of Conceptual Relationship Methods (RQ3)

[0281] Figure 5 Different methods for constructing concept relationships were compared. The statistical-based method achieved ACC / AUC of 0.7294 / 0.7833, the manual-based method 0.7296 / 0.7838, and the LLM-based method 0.7297 / 0.7839, while the adaptive discovery mechanism achieved the best results (0.7301 / 0.7849). The performance differences were very small; this may be due to the high density of question-concept mappings in the Edi dataset, which diluted the impact of inter-concept dependencies on question representation. The results show that static priors from experts and LLM perform similarly because they both rely on inherent subject logic; statistical methods are highly susceptible to interaction noise, leading to a slight performance decrease; the method achieved leadership through adaptive joint optimization and acyclic constraint noise filtering, validating the effectiveness of the adaptive mechanism.

[0282] 4.7 Sensitivity Analysis of Key Parameters (RQ4)

[0283] In the concept relationship discovery and aggregation module, the threshold It discretizes and filters the evolving relation matrix. To explore its impact, it was evaluated on five datasets. Values Performance at time ( Figure 6 For specific analysis of thresholds. The impact of this is considered, focusing on the average performance for each parameter value. Figure 7 The average ACC and AUC are displayed. At that time, the average performance reached its peak (AUC). ACC ).when Too low ( ) or too high ( When ), performance degrades significantly: At that time, AUC dropped to ACC dropped to ;exist At that time, AUC dropped to ACC dropped to This indicates It controls the sparsity of the relationship graph. When Too small (e.g.) When [the graph is] dense, many weak relationships are preserved, leading to an overly dense graph, introducing noise, and limiting discriminative power. At that time, the model achieved a balance between preserving valid relationships and eliminating noise. Too large ( When this happens, the actual cognitive connection is severed, blocking the flow of information across concepts and reducing performance. Therefore, a moderate... ( It effectively strips away false relationships while retaining the core cognitive framework, maximizing the discriminative power of representation.

[0284] 4.8 Qualitative Analysis of Problem Representation (RQ5)

[0285] To intuitively explore the optimization process of the dual-view feature fusion framework, t-SNE visualization dimensionality reduction was performed on the feature embeddings output at different stages using nine highly related concepts from ASSIST12. Figure 8 ).exist Figure 8 In (a), the initial embedding forms a uniformly mixed cluster where data points are completely intertwined and lack any discriminative power. Figure 8 In (b), topological aggregation features This evolves into multiple branching streams, concepts separate, and data points within a class extend along the cognitive gradient. Figure 8 In (c), semantic enhancement features This forms compact clusters, expanding the space between conceptual clusters and maintaining strong intra-cluster cohesion around their respective geometric centers. Figure 8In (d), the final fused embeddings form a smooth, curved ribbon-like manifold with clear inter-class boundaries and a continuous, well-structured intra-class distribution, achieving the dual goals of inter-class isolation and intra-class manifold preservation. This evolution reveals that topological aggregation establishes a progressive direction through DAG dependencies, along the preceding... Subsequent gradient stretching features; the difficulty-aware mechanism clusters questions of the same concept toward their base and generates isotropic scattering through offset vectors; contrastive learning further decouples redundancy and reconstructs clusters into a banded manifold, thereby generating question embeddings with high discriminative power.

[0286] A visualization of t-SNE for question embeddings. Nodes represent individual questions and are color-coded according to their corresponding knowledge concepts. This figure illustrates the evolution of representations from initial random initialization to the final fused semantics generated by the model.

[0287] Evidence related to the technical effects obtained by the embodiments of the present invention.

[0288] Evidence 1: Significant improvement in overall performance (corresponding to RQ1)

[0289] Comparative experiments on five public datasets (ASSIST09, ASSIST12, ASSIST17, EdNet, Eedi) demonstrate that our invention (SSCKT) achieves the best performance among all baseline models. As shown in Table 3, on average, compared to the second-best baseline model, our invention improves ACC by 1.39% and AUC by 1.42%. Particularly on the ASSIST17 dataset, ACC and AUC are improved by 2.46% and 2.43%, respectively. This fully demonstrates the effectiveness and superiority of the proposed structure-semantic co-optimization framework. Detailed comparative data are shown in Table 3.

[0290] Evidence 2: Indispensability of core components (corresponding to RQ2) The results of the ablation experiment (Table 4) prove that each core module designed in this invention makes a positive contribution to the final performance.

[0291] After removing the structural enhancement features (w / o FQ1), the model's average ACC decreased by 0.18% and AUC decreased by 0.19%, indicating that the structural prior injected by topological aggregation is the basis for the model to perceive the dependencies between concepts.

[0292] When the semantic enhancement features (without FQ2) were removed, the model's average ACC decreased by 0.15% and AUC decreased by 0.13%, demonstrating that the concept difficulty-guided offset mechanism is crucial for distinguishing fine-grained cognitive load.

[0293] The most significant performance degradation occurred after removing contrastive learning alignment (w / o CL), with ACC decreasing by 0.20% and AUC decreasing by 0.24%, indicating that contrastive learning can effectively eliminate the redundancy of dual-view features and is the key to achieving collaborative optimization.

[0294] Evidence 3: The superiority of the adaptive concept relationship discovery mechanism (corresponding to RQ3)

[0295] like Figure 5 As shown, on the Edi dataset, the adaptive relation discovery mechanism proposed in this invention outperforms relation construction methods based on statistics, expert annotation, and LLM in both ACC and AUC. This confirms that the adaptive mechanism of this invention can better filter interaction noise and extract robust concept structures that are more consistent with the actual learning dynamics.

[0296] Evidence 4: Validity and robustness of key parameters (corresponding to RQ4)

[0297] By analyzing the impact of the cognitive threshold τ on model performance ( Figure 6 , Figure 7 We found that the model performance peaks when τ=0.01. This result demonstrates that the relation discovery module of this invention can effectively balance the preservation of effective information and the removal of noise in the relation graph by adjusting a hyperparameter, thereby maximizing the discriminative power of the representation while preserving the core cognitive backbone, proving the robustness of the model.

[0298] Evidence 5: Visual verification of the quality of the problem statement (corresponding to RQ5)

[0299] Visualization of the t-SNE of the problem embedding ( Figure 8 We have visually verified the optimization process of this invention. From Figure 8 (a) initial random mixing, to Figure 8 The features in (b) and (c) gradually separate, and then... Figure 8 (d) ultimately forms a banded manifold with clear inter-class boundaries and structured intra-class distribution, which strongly demonstrates that the final problem embedding generated by this invention has extremely high discriminative power and semantic richness.

[0300] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0301] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A knowledge tracing method based on adaptive concept relationship discovery and structure-semantic co-optimization to enhance problem representation, characterized in that, include: The structural enhancement step involves obtaining a concept relationship matrix by adaptively learning the directed acyclic dependencies between concepts, and constructing a heterogeneous graph containing problem nodes and concept nodes based on the concept relationship matrix and the concept-problem association. The structural enhancement problem embedding is then generated via heterogeneous graph convolutional encoding. The semantic enhancement step involves cross-aligning the problem features and concept features through a multi-head attention mechanism to obtain basic semantic features. The cognitive difficulty of each concept is determined based on its topological position in the directed acyclic dependency relationship. The cognitive difficulty is used as a scaling factor to scale the learnable problem offset vector. The scaled offset vector is then superimposed on the basic semantic features to obtain the semantically enhanced problem representation. The alignment step maximizes the consistency between the structure-enhanced question embedding and the semantically enhanced question representation of the same problem through contrastive learning, and outputs the final question representation for knowledge state modeling. Causal attribution and interpretable path generation: Based on the learned directed acyclic graph and attention weights, weak concept dependency chains are derived in reverse, and a visualized cognitive diagnostic path is output, providing a highly reliable basis for teaching intervention. Personalized cognitive difficulty calibration: By using feedback from students' historical performance, the topological difficulty metric is dynamically adjusted, combining the static graph structure difficulty with individual learning trajectories to achieve a personalized problem representation shift for each student. End-to-end joint prediction optimization: The problem representation learning and downstream knowledge tracking prediction tasks are fully jointly trained, so that the loss of answer accuracy directly guides the adaptive discovery of concept relationship graphs, forming a closed-loop learning framework.

2. The method according to claim 1, characterized in that, The directed acyclic dependencies between the adaptively learned concepts are used to obtain a concept relationship matrix, including: A learnable relation strength matrix is ​​constructed, whose elements represent the cognitive support strength between concepts. After the relation strength matrix is ​​nonlinearly activated and mapped to a preset numerical range, it is multiplied element-wise with a mask matrix that excludes self-loops to eliminate concept self-dependency. The directed acyclic graph constraint loss is calculated based on the processed relation strength matrix to constrain the acyclicity of the graph structure corresponding to the relation strength matrix; Based on a preset cognitive threshold, elements in the processed relation strength matrix that are greater than or equal to the threshold are set to a first value, and the remaining elements are set to a second value, thus obtaining a binarized cognitive map. Based on the difference between the out-degree and in-degree of each concept node in the binary cognitive graph, the cognitive level score of each concept node is determined. A directed acyclic graph mask is constructed based on the cognitive level score. The value of the direction from the source concept to the target concept in the mask is the first value only when the cognitive level score of the source concept is higher than that of the target concept and the corresponding position in the binarized cognitive graph is the first value. The directed acyclic graph mask is multiplied element-wise with the processed relation strength matrix to obtain the denoised concept relation matrix.

3. The method according to claim 1, characterized in that, The generation of the structure enhancement problem embedding via heterogeneous graph convolutional encoding includes: The concept relationship matrix is ​​fused with the preset concept-problem association matrix to construct a heterogeneous graph containing problem nodes and concept nodes. The heterogeneous graph contains a first type of directed edge pointing from a concept node to a concept node, a second type of directed edge pointing from a problem node to a concept node, and a third type of directed edge pointing from a concept node to a problem node. Obtain the initial feature vectors of each node and construct the initial feature matrix; In each layer of the heterogeneous graph convolution, based on the adjacency relationships corresponding to the first type of directed edges, the second type of directed edges, and the third type of directed edges, a learnable linear transformation and aggregation are performed on the features of the current layer nodes, and the result is added to the result of the self-loop transformation of the features of the current layer nodes to generate an aggregated feature matrix. The aggregated feature matrix is ​​split into problem aggregated features and concept aggregated features according to node type. Random deactivation, residual connection with the corresponding current layer node features, and layer normalization are performed on the aggregated features of each type of node in sequence to obtain the problem node features and concept node features of the next layer. After stacking multiple heterogeneous graph convolutions, the final problem node features are used as the structure-enhanced problem embedding.

4. The method according to claim 1, characterized in that, The method of cross-aligning problem features and concept features through a multi-head attention mechanism to obtain basic semantic features includes: The problem feature matrix is ​​projected through the query projection matrix of each attention head, and the concept feature matrix is ​​projected through the key projection matrix and value projection matrix of each attention head. For each attention head, the scaled dot product attention of the query projection and the key projection is calculated, and the attention weights corresponding to the unexamined concepts are reset to masked values ​​using a mask matrix to obtain the concept-question association weights for that attention head. The value projection is weighted and aggregated using the concept-problem association weights, and the outputs of each attention head are concatenated along the feature dimension and then transformed by the output projection matrix to obtain the basic semantic features.

5. The method according to claim 1, characterized in that, Determining the cognitive difficulty of each concept based on its topological position in the directed acyclic dependency includes: Set the initial depth value of all concept nodes to 1, update the depth value of each concept node one by one along the topological order of the directed acyclic dependency relationship, and the updated depth value of each concept node is equal to the maximum value of the previous depth value of all its predecessor concept nodes plus 1 to obtain the global depth vector. Calculate the ratio of the in-degree of each concept node in the directed acyclic dependency relationship to the total number of concepts minus 1, and use it as the centrality vector; The global depth vector is normalized by dividing it by its maximum value to obtain a normalized depth vector; The normalized depth vector and the centrality vector are weighted and summed using learnable fusion parameters to obtain a comprehensive difficulty vector. The comprehensive difficulty vector is mapped to the problem space via a row-normalized concept-problem correlation matrix to obtain the basic difficulty scalar of each problem.

6. The method according to claim 5, characterized in that, The process of scaling the learnable question offset vector using the cognitive difficulty as a scaling factor, and then superimposing the scaled offset vector onto the basic semantic features to obtain a semantically enhanced question representation includes: Obtain a learnable offset matrix, where each row of the offset matrix corresponds to a directional offset vector of a problem in the representation space; The basic difficulty scalar of each problem is used as a scaling factor and multiplied by the directional offset vector of the corresponding row in the offset matrix to obtain the adjustment offset vector of each problem. The basic semantic features are added to the adjusted offset vector to obtain the semantic enhancement problem representation.

7. A knowledge tracking system based on adaptive concept relationship discovery and structure-semantic co-optimization to enhance problem representation, characterized in that, include: The concept discovery module is used to adaptively learn the directed acyclic dependencies between concepts, generate a concept relationship matrix, and construct a heterogeneous graph based on the concept relationship matrix and the concept-question association relationship. The heterogeneous graph convolutional encoding is used to generate structure-enhanced question embeddings. The semantic enhancement module is used to cross-align the problem features and concept features through a multi-head attention mechanism to obtain basic semantic features, and to determine the cognitive difficulty of the concept based on the topological position of the concept in the directed acyclic dependency relationship. The cognitive difficulty is used as a scaling factor to scale the learnable problem offset vector, and the scaled offset vector is superimposed on the basic semantic features to obtain the semantically enhanced problem representation. The contrastive learning module is used to maximize the consistency between the structure-enhanced question embedding and the semantically enhanced question representation of the same problem through contrastive learning, and outputs the final question representation for knowledge state modeling.

8. The system according to claim 7, characterized in that, The concept discovery module includes: The relation strength construction unit is used to construct a learnable relation strength matrix, whose elements represent the cognitive support strength between concepts. After performing a nonlinear activation mapping on the relation strength matrix, it is multiplied element-wise with a mask matrix that excludes self-loops to eliminate self-dependencies. Directed acyclic constraint unit is used to calculate the constraint loss of a directed acyclic graph based on the relation strength matrix after relation strength construction unit processing, so as to constrain the acyclicity of the corresponding graph structure; The binarization processing unit is used to binarize the processed relationship strength matrix according to a preset cognitive threshold to obtain a binarized cognitive map. The hierarchical scoring calculation unit is used to determine the cognitive hierarchical score of each concept node based on the difference between the out-degree and in-degree of each concept node in the binary cognitive graph. A mask generation unit is used to construct a directed acyclic graph mask based on the cognitive level score, wherein only edges that point from high cognitive level concepts to low cognitive level concepts and are connected in the binary cognitive graph are retained. The denoised relation output unit is used to perform element-wise multiplication of the directed acyclic graph mask with the processed relation strength matrix to obtain the denoised concept relation matrix.

9. The system according to claim 7, characterized in that, The concept discovery module also includes a heterogeneous graph convolutional coding unit, used for: The concept relationship matrix is ​​fused with the preset concept-problem association matrix to construct a heterogeneous graph containing problem nodes and concept nodes. The heterogeneous graph contains a first type of directed edge pointing from a concept node to a concept node, a second type of directed edge pointing from a problem node to a concept node, and a third type of directed edge pointing from a concept node to a problem node. Obtain the initial feature vectors of each node and construct the initial feature matrix; In each layer of the heterogeneous graph convolution, the node features are transformed and aggregated using the adjacency relationships corresponding to the three types of directed edges, and then added to the self-loop transformation result to generate an aggregated feature matrix. The aggregated feature matrix is ​​split into problem aggregated features and concept aggregated features according to node type. For each type of node aggregated feature, random deactivation, residual connection with the current layer node features, and layer normalization are performed in sequence to obtain the problem node features and concept node features of the next layer. After stacking multiple heterogeneous graph convolutions, the final problem node features are used as the structure-enhanced problem embedding.

10. The system according to claim 7, characterized in that, The semantic enhancement module includes: The cross-alignment unit is used to project the problem feature matrix through the query of each attention head, project the concept feature matrix through the key and value of each attention head, calculate the scaled dot product attention and mask the unexamined concepts to obtain the attention weights, weight the value projections, concatenate the multi-head outputs and project them through the output to obtain the basic semantic features. The topology difficulty calculation unit is used to set the initial depth of all concept nodes to 1, update the depth of each concept node along the topological order of the directed acyclic dependency relationship to the maximum depth of its predecessor node plus 1, and obtain a global depth vector; calculate the in-degree centrality of each concept node; normalize the global depth vector to its maximum value, and then sum the normalized depth vector and the centrality vector with weights using learnable fusion parameters to obtain a comprehensive difficulty vector; map the comprehensive difficulty vector to the problem space through a row-normalized concept-problem association matrix to obtain the basic difficulty scalar of each problem. The offset adjustment unit is used to obtain a learnable direction offset matrix, scale the direction offset vector of the corresponding problem using the basic difficulty scalar of each problem as a scaling factor, and superimpose the scaled offset vector onto the basic semantic features to obtain the semantically enhanced problem representation.

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