Significant challenges remain in AI-driven educational systems in balancing privacy preservation with accurate cognitive diagnosis. To overcome this, we propose a federated inference framework in which several commercial LLM APIs collaborate without requiring access to raw student data or proprietary model internals. Using multiple federated entities, such as LLaMA-3.3-70B, GPT-4o-mini, and Claude-3-Haiku, our framework builds upon a heterogeneous multi-LLM architecture. The predictions generated by these entities are combined with epsilon-local differential privacy by adding Laplace noise locally to each entity's prediction output before aggregation, while residual-based aggregation mitigates model heterogeneity. Our approach is predicated on an honest-but-curious trust paradigm in which API providers are presumed not to abuse submitted queries, and our differential privacy mechanism shields the published diagnostic results from external inference. We conduct rigorous privacy-utility analysis showing strong privacy guarantees with minimal accuracy loss, and extensive real-world evaluations across three educational benchmarks confirm the framework's practical usability and cross-domain generalizability.
Q-matrices play a central role in cognitive diagnosis within educational data mining (EDM), specifying which latent skills each assessment item requires. Data-driven Q-matrix estimation remains challenging when assessments involve many correlated skills and when real response patterns depart from idealized generative assumptions. We introduce a novel quantum sparse autoencoder (QSAE) for Q-matrix estimation, which, to the best of our knowledge, is the first application of quantum machine learning (QML) to cognitive diagnosis. Overall, the QSAE embeds each student's binary response vector into a quantum circuit using an encoder, compresses it into a sparse latent representation, and maps that representation to the Q-matrix. We benchmark the QSAE against a classical autoencoder (CAE) across 60 simulated datasets and 9 real-world assessment datasets. The results reveal complementary strengths. Although the CAE partially achieves higher average accuracy under several simulation conditions, the QSAE is substantially more stable across replications, exhibiting lower variance in 49 of the 60 conditions. Moreover, on real assessment data, the QSAE outperforms the CAE on 6 of the 9 datasets. These findings suggest that the principal advancement of QML in this setting is not universal accuracy improvement, but enhanced robustness and capability to explore latent-structure complexity in real datasets.
The research proposes a multilayer Q-matrix-embedded neural network for cognitive diagnosis (M-QCDNet), which integrates the structural interpretability of cognitive diagnostic models (CDMs) with the deep learning neural network (NN). M-QCDNet structures the item-skill relationship using the Q-matrix as a structural prior, ensuring latent mastery profiles remain interpretable and consistent with cognitive theory, followed by the proposed loss function with an L2 penalty to penalize skills not aligned with the Q-matrix and to balance predictive performance and structural alignment. Corresponding evaluation matrices, the interpretable alignment-based metrics that quantify the degree to which predicted skill activations correspond to item-level skills, were further developed. M-QCDNet offers practical benefits for classroom practice, enabling early detection of learning difficulties and supporting mastery-based interventions. By embedding diagnostic validity into model design, M-QCDNet bridges psychometric transparency and neural flexibility, advancing interpretable, fair, and actionable AI for cognitive diagnostics.
Yawen Ma, Sahoko Ishida, Kate Cain +1cs.LG stat.AP
Digital learning environments record learners' responses to individual items, making it possible to study the development of specific skills rather than overall scores. Drawing conclusions about learning from these data requires a model that links responses to latent skills and tracks how mastery changes over time. When the skills measured by each item are unknown, the analyst must decide whether to estimate this structure, the Q-matrix, jointly with the learning process, or to establish it first and study learning afterwards. We show that this decision can change substantive conclusions about how learners develop. Using dynamic cognitive diagnostic models, we analyse data from two reading games measuring vocabulary and comprehension from Grade 2 to Grade 3, with item-text embeddings providing prior information for the unknown Q-matrix. A joint analysis and a bias-corrected stepwise analysis agree that most learners move toward mastering both skills, but disagree about how many remain only partially proficient at Grade 3, changing how reading progress would be reported. A simulation study identifies when the two analyses diverge and shows that joint analysis is more reliable when the item-skill structure is uncertain and the item pool changes between grades. We provide R code for both analyses.