# From Mastery Profile to Simulated Response: Stochastic Student Knowledge Graphs (SSKG) for Faithful LLM Student Simulation

arXiv: https://arxiv.org/abs/2608.21668 · HTML: https://mlsanity.com/paper/2608.21668/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Unifying Large Language Models and Knowledge Graphs: A Roadmap](https://mlsanity.com/paper/2306.08302/) (2023)
- [Deep Knowledge Tracing](https://mlsanity.com/paper/1506.05908/) (2015)
- [Generative Students: Using LLM-Simulated Student Profiles to Support Question Item Evaluation](https://mlsanity.com/paper/2405.11591/) (2024)
- [Embedding Uncertain Knowledge Graphs](https://mlsanity.com/paper/1811.10667/) (2018)
- [CLST: Cold-Start Mitigation in Knowledge Tracing by Aligning a Generative Language Model as a Students' Knowledge Tracer](https://mlsanity.com/paper/2406.10296/) (2024)
- [Do LLMs Give Psychometrically Plausible Responses in Educational Assessments?](https://mlsanity.com/paper/2506.09796/) (2025)
- [System 2 thinking in OpenAI's o1-preview model: Near-perfect performance on a mathematics exam](https://mlsanity.com/paper/2410.07114/) (2024)
- [Take Out Your Calculators: Estimating the Real Difficulty of Question Items with LLM Student Simulations](https://mlsanity.com/paper/2601.09953/) (2026)
- [Can LLMs Reliably Simulate Real Students' Abilities in Mathematics and Reading Comprehension?](https://mlsanity.com/paper/2507.08232/) (2025)
- [Rate-Distortion Guided Knowledge Graph Construction from Lecture Notes Using Gromov-Wasserstein Optimal Transport](https://mlsanity.com/paper/2511.14595/) (2025)
- [PS2: Parameterized Control for Fine-Grained Student Proficiency Simulation](https://mlsanity.com/paper/2602.00850/) (2026)
- [BEAGLE: Behavior-Enforced Agent for Grounded Learner Emulation](https://mlsanity.com/paper/2602.13280/) (2026)
- [Simulating Learners' Task-Selection Strategies and System Constraints in Mastery Learning](https://mlsanity.com/paper/2605.21613/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used to simulate students at different mastery levels to generate synthetic training data and stress-test tutoring systems. Existing approaches primarily leverage an LLM to answer questions or perform tests while instructing it to simulate various skill levels. However, LLMs tend to execute at their full built-in capability regardless of target skill levels. We demonstrate this limitation on SAT questions across five mastery levels, where three LLMs consistently achieve 96.8-100% accuracy. To faithfully simulate student behavior, we propose a Stochastic Student Knowledge Graph (SSKG)-based approach that leverages the strengths of LLM in different ways. Using human-in-the-loop workflows, LLMs extract a Curriculum Knowledge Graph (CKG) from course materials, decompose solution paths into CKG triples, and map incorrect distractors. A student's mastery profile is represented as an SSKG, assigning mastery probabilities to CKG triples. When solving a problem, the SSKG is sampled to determine the outcome, after which an LLM generates a rationale consistent with the sampled result. Compared to seven baselines which fail to separate profiles and maintain 86.5-100% accuracy, our SSKG-based approach achieves 44.1-85.2% accuracy from low to high-mastery profiles, creating a clear monotonic gradient. An ablation study demonstrates that taxonomy awareness contributes most significantly to these fidelity gains, particularly for lower-mastery profiles.