A Framework for Human-AI Q-Matrix Refinement: A NeuralCDM Evaluation

The evaluation of large language models (LLMs) relies heavily on human-designed assessments, implicitly assuming that AI and humans employ similar underlying cognitive constructs. Challenging this assumption, we investigate whether the latent factors governing LLM performance carry the same substantive, human-interpretable meaning as the cognitive constructs governing human learners. Using responses from humans and six LLMs across quantitative reasoning and chemistry assessments, we conducted Exploratory Factor Analysis (EFA) separately for both groups. Subject-Matter Experts (SMEs) then blindly evaluated the resulting factor graphs to ascribe pedagogical meaning to the emerged constructs. SMEs successfully interpreted most of the human-derived factors. Conversely, they could not ascribe meaning to any LLM-derived factors in quantitative reasoning and interpreted only half of the LLM factors in chemistry. By combining data-driven EFA with blind expert interpretation, this framework shows that LLMs frequently operate on statistically opaque mechanisms distinct from human reasoning.

The rapid development and growing deployment of large language models (LLMs) have made it increasingly important to understand their capabilities. A common approach is to evaluate LLMs using assessment instruments originally designed to measure skills and competencies in humans, such as standardized exams, and to use performance on these instruments as evidence for generalizable claims about LLMs' underlying abilities on the same skills the assessments are intended to measure in humans. However, from a validity perspective, such inferences require that the relationship between observed performance and underlying constructs established for humans also holds for LLMs. In particular, a necessary condition for transferring score interpretations is similarity in the latent structure of responses to the assessment. In this study, we examine whether this condition holds in two educational contexts: high-school chemistry and a quantitative reasoning section of a university entrance exam. Using a case study design, we compare human response data with responses generated by six multimodal LLMs. Our analytical approach combines exploratory factor analysis, factor congruence, and resampling to assess latent structure similarity across human learners and LLMs. Across both instruments, we find systematic differences between human and LLM factor structures, showing evidence that the analyzed assessments may not measure the same constructs for humans and LLMs. These findings call into question the validity of evaluation practices that use educational assessments to make claims about AI capabilities.

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.