LearnOpt reveals hidden exam skill structures with knowledge graphs and optimization

Researchers Joy Bose and Om Thomas have released LearnOpt, a novel framework that uses knowledge graphs and constrained optimization to recover the latent cognitive structure of standardized examinations. The system treats exams as adversarial systems with stable but hidden skill distributions, diverging from official syllabi. LearnOpt was applied to 1,496 NEET (Indian medical entrance) questions from 2016-2024. It first builds an exam knowledge graph by tagging questions with LLMs, then extracts a five-category latent skill distribution using Bayesian Knowledge Tracing. Study planning is formulated as a knapsack-variant optimization over prerequisite-aware subgraphs, producing personalized, time-bounded study plans.

The key finding is that NEET's latent skill distribution is piecewise stable: within a syllabus regime (2016-2021) consecutive-year KL divergence ranged from 0.004 to 0.032 (non-significant), but a significant shift occurred after NCERT's 2023 syllabus rationalization (KL=0.040, p=0.0005), with Elimination/Negation questions rising from ~20-29% to ~31-35%. Applying the same pipeline to JEE Advanced revealed a profile dominated by Multi-concept Integration (80.9% vs 33.3% for NEET), with an overall exam divergence (KL=0.505) exceeding NEET's largest cross-subject divergence. This demonstrates that exam tier shapes cognitive structure more than subject, which in turn shapes it more than time within a regime. The code, knowledge graph, and annotated datasets are publicly available on GitHub and HuggingFace.