LearnOpt: Recovering the Latent Cognitive Structure of Standardized Examinations via Knowledge Graphs and Constrained Optimization

Standardized examinations are typically treated as uniform syllabus coverage problems. LearnOpt recovers stable latent cognitive structures diverging systematically from official syllabi, using LLM-tagged questions and constrained optimization. Applied to 9 years of NEET questions (n=1,496) and JEE Advanced questions. Finds NEET latent skill distribution is stable within syllabus regimes (KL 0.004-0.032) but shifts significantly after syllabus rationalization (KL=0.040, p=0.0005). JEE Advanced is dominated by multi-concept integration (80.9%). Formulates study planning as a knapsack-variant optimization with Bayesian Knowledge Tracing.

Key Findings

Standardized exams have recoverable latent cognitive structures; multi-concept integration dominates higher-tier exams (JEE: 80.9%).

LearnOpt builds an exam knowledge graph from LLM-tagged questions and extracts a five-category latent skill distribution, applied to nine years of NEET questions (2016–2024, n=1,496).

NEET's latent skill distribution is stable within a syllabus regime (consecutive-year KL divergence 0.004–0.032 for 2016–2021, non-significant under permutation testing) but shifts significantly with NCERT's 2023 syllabus rationalization (pooling 2016–2021 vs 2023–2024 gives KL=0.040, p=0.0005), with Elimination/Negation questions rising from roughly 20–29% to 31–35%.

Within either regime, subject predicts skill profile more strongly than year; exam tier shapes latent cognitive structure more than subject, which shapes it more than time within a regime.

Study planning is formulated as a knapsack-variant optimization over prerequisite-aware subgraphs with Bayesian Knowledge Tracing; evaluation with one real and two synthetic mastery profiles shows the skill-weighted objective produces a modest but real reordering of recommended topics over a mastery-conditioned frequency baseline.

The JEE Advanced profile is dominated by Multi-concept Integration (80.9% vs. 33.3% for NEET), with a JEE-vs-NEET divergence (KL=0.505) exceeding NEET's largest cross-subject divergence.

Study Design & Method

LearnOpt treats standardized examinations not as uniform syllabus coverage problems but as adversarial systems with stable latent cognitive structures that diverge systematically from official syllabi. The pipeline tags historical questions with LLMs, assembles a knowledge graph, extracts skill distributions, and optimizes time-bounded study plans. The JEE analysis uses the single-correct MCQ subset of JEEBench (110 of 515 problems, 2016–2023) because only that response type is structurally comparable to NEET's single-correct format. Code, knowledge graph, and annotated dataset are released publicly.

Implications for AI in Education

The piecewise-stable latent structure means exam preparation can be modeled as skill acquisition over an inferred structure rather than uniform syllabus coverage, supporting personalized study planning for high-stakes exams such as NEET and JEE. The LLM-tagging pipeline also shows a practical use of generative models for exam analytics, while the optimization framework connects exam data to Knowledge Tracing-style mastery estimation and adaptive study recommendations.

Connected Concepts

Self Regulated Learning

Personalized Learning

Adaptive Learning

Formative Assessment

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Citation

Joy Bose, Om Thomas (2026). LearnOpt: Recovering the Latent Cognitive Structure of Standardized Examinations via Knowledge Graphs and Constrained Optimization. arXiv:2606.15349. arXiv preprint.