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

2026-06-13

AI Summary

Standardized examinations are often mistakenly assumed to faithfully reflect official curricula, yet they harbor stable but implicit cognitive structural biases. This work proposes the first formalization of such exams as adversarial systems with piecewise-stable latent structures. By constructing knowledge graphs from historical test items and integrating large language model–based annotation, Bayesian knowledge tracing, and knapsack optimization under prerequisite constraints, the study generates personalized, time-bound study plans. It further introduces a mechanism to detect structural shifts attributable to curriculum reforms. Empirical validation on NEET and JEE Advanced datasets confirms both the stability of these latent structures and their variation across educational levels, with the proposed approach significantly outperforming frequency-based baselines. The code, knowledge graphs, and annotated datasets are publicly released.

Abstract

Standardized examinations are typically treated as uniform syllabus coverage problems. We argue they are better understood as adversarial systems with stable latent cognitive structures diverging systematically from official syllabi. We introduce LearnOpt, which recovers this structure from historical question papers and generates personalized, time-bounded study plans. Applied to nine years of NEET questions (2016-2024, n=1,496), LearnOpt builds an exam knowledge graph from LLM-tagged questions, extracts a five-category latent skill distribution, and formulates study planning as a knapsack-variant optimization over prerequisite-aware subgraphs with Bayesian Knowledge Tracing. Central finding: 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 (n=1,072) vs 2023-2024 (n=392) gives KL=0.040 (p=0.0005), with Elimination/Negation questions rising from ~20-29% to ~31-35%. Latent structure, while not permanently stationary, is piecewise stable, with shifts detectable and attributable to curricular events. Within either regime, subject predicts skill profile more strongly than year. An optimization evaluation, using 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. Applying the pipeline to JEE Advanced reveals a profile 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: exam tier shapes latent cognitive structure more than subject, which shapes it more than time within a regime. Code, knowledge graph, and annotated dataset are released publicly.

Problem

• standardized examinations
• latent cognitive structure
• knowledge graphs
• syllabus divergence
• exam analysis

Innovation

• knowledge graph
• constrained optimization
• latent cognitive structure
• Bayesian Knowledge Tracing
• syllabus rationalization