# SMART: Simulated Students Aligned with Item Response Theory for Question Difficulty Prediction

arXiv: https://arxiv.org/abs/2507.05129 · HTML: https://mlsanity.com/paper/2507.05129/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Placed in Process reward models for reasoning, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 26 of its 71 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 26 of 26)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Smarter, Better, Faster, Longer: A Modern Bidirectional Encoder for Fast, Memory Efficient, and Long Context Finetuning and Inference](https://mlsanity.com/paper/2412.13663/) (2024)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [Large Language Model as Attributed Training Data Generator: A Tale of Diversity and Bias](https://mlsanity.com/paper/2306.15895/) (2023)
- [Synthetic Text Generation with Differential Privacy: A Simple and Practical Recipe](https://mlsanity.com/paper/2210.14348/) (2022)
- [Exploring Knowledge Tracing in Tutor-Student Dialogues using LLMs](https://mlsanity.com/paper/2409.16490/) (2024)
- [Conditional Language Policy: A General Framework for Steerable Multi-Objective Finetuning](https://mlsanity.com/paper/2407.15762/) (2024)
- [Training LLM-based Tutors to Improve Student Learning Outcomes in Dialogues](https://mlsanity.com/paper/2503.06424/) (2025)
- [The continuous Bernoulli: fixing a pervasive error in variational autoencoders](https://mlsanity.com/paper/1907.06845/) (2019)
- [Learning Latent Parameters without Human Response Patterns: Item Response Theory with Artificial Crowds](https://mlsanity.com/paper/1908.11421/) (2019)
- [Leveraging LLM-Respondents for Item Evaluation: a Psychometric Analysis](https://mlsanity.com/paper/2407.10899/) (2024)
- [Mixture-of-Personas Language Models for Population Simulation](https://mlsanity.com/paper/2504.05019/) (2025)
- [Embracing Imperfection: Simulating Students with Diverse Cognitive Levels Using LLM-based Agents](https://mlsanity.com/paper/2505.19997/) (2025)
- [Psychometric Alignment: Capturing Human Knowledge Distributions via Language Models](https://mlsanity.com/paper/2407.15645/) (2024)
- [Generating and Evaluating Tests for K-12 Students with Language Model Simulations: A Case Study on Sentence Reading Efficiency](https://mlsanity.com/paper/2310.06837/) (2023)
- [Reasoning and Sampling-Augmented MCQ Difficulty Prediction via LLMs](https://mlsanity.com/paper/2503.08551/) (2025)
- [A quantitative study of NLP approaches to question difficulty estimation](https://mlsanity.com/paper/2305.10236/) (2023)
- [Improving Reading Comprehension Question Generation with Data Augmentation and Overgenerate-and-rank](https://mlsanity.com/paper/2306.08847/) (2023)
- [LookAlike: Consistent Distractor Generation in Math MCQs](https://mlsanity.com/paper/2505.01903/) (2025)
- [Student Data Paradox and Curious Case of Single Student-Tutor Model: Regressive Side Effects of Training LLMs for Personalized Learning](https://mlsanity.com/paper/2404.15156/) (2024)
- [Prediction of Item Difficulty for Reading Comprehension Items by Creation of Annotated Item Repository](https://mlsanity.com/paper/2502.20663/) (2025)
- [Cyborg Data: Merging Human with AI Generated Training Data](https://mlsanity.com/paper/2503.22736/) (2025)

## Built on by (most cited first, 23 of 23)

- [Simulated Students in Tutoring Dialogues: Substance or Illusion?](https://mlsanity.com/paper/2601.04025/) (2026)
- [Towards Valid Student Simulation with Large Language Models](https://mlsanity.com/paper/2601.05473/) (2026)
- [KASER: Knowledge-Aligned Student Error Simulator for Open-Ended Coding Tasks](https://mlsanity.com/paper/2601.06633/) (2026)
- [RADAR: Reasoning-Ability and Difficulty-Aware Routing for Reasoning LLMs](https://mlsanity.com/paper/2509.25426/) (2025)
- [BRIDGE: Predicting Human Task Completion Time From Model Performance](https://mlsanity.com/paper/2602.07267/) (2026)
- [Take Out Your Calculators: Estimating the Real Difficulty of Question Items with LLM Student Simulations](https://mlsanity.com/paper/2601.09953/) (2026)
- [FoundationalASSIST: An Educational Dataset for Foundational Knowledge Tracing and Pedagogical Grounding of LLMs](https://mlsanity.com/paper/2602.00070/) (2026)
- [Interpretable Difficulty-Aware Knowledge Tracing in Tutor-Student Dialogues](https://mlsanity.com/paper/2605.01097/) (2026)
- [PsyScore: A Psychometrically-Aware Framework for Trait-Adaptive Essay Scoring and ZPD-Scaffolded Feedback](https://mlsanity.com/paper/2606.20287/) (2026)
- [RIDE: Difficulty Evolving Perturbation with Item Response Theory for Mathematical Reasoning](https://mlsanity.com/paper/2511.04120/) (2025)
- [Reconstructing Item Characteristic Curves using Fine-Tuned Large Language Models](https://mlsanity.com/paper/2601.02580/) (2026)
- [VDAR-Router: Adaptive LLMs Routing via Verbalized Query Difficulty Analysis Retrieval](https://mlsanity.com/paper/2607.18098/) (2026)
- [SWIM: Student Writing Simulation via Proficiency-Conditioned Generation](https://mlsanity.com/paper/2609.03215/) (2026)
- [CodeGENCAT: Generative Computerized Adaptive Testing for Open-ended Coding Problems](https://mlsanity.com/paper/2602.20020/) (2026)
- [Estimating LLM Grading Ability and Response Difficulty in Automatic Short Answer Grading via Item Response Theory](https://mlsanity.com/paper/2605.00238/) (2026)
- [MCQ Difficulty Prediction via Modeling Learner Heterogeneity Using Data-Driven Cognitive Profiling](https://mlsanity.com/paper/2605.16290/) (2026)
- [Aligning LLM-Simulated and Human Examinees for Psychometric Calibration: A Cognitive Diagnostic Profiling Approach](https://mlsanity.com/paper/2607.26317/) (2026)
- [Automated item evaluation: Predicting item acceptance and rejection using LLM-generated critiques](https://mlsanity.com/paper/2608.06609/) (2026)
- [Multimodal Item Parameter Estimation using Simulated Response Probabilitie](https://mlsanity.com/paper/2608.10154/) (2026)
- [A Dataset for Modeling Iterative Problem-Solving](https://mlsanity.com/paper/2609.00940/) (2026)
- [From Learner Behavior to Reusable Skills for Effective and Efficient Learner Simulation](https://mlsanity.com/paper/2609.37157/) (2026)
- [Do LLM Tutors Actually Teach? A Process-Centered Synthesis of the Tutoring Loop](https://mlsanity.com/paper/2610.15692/) (2026)
- [A Unified Response Framework for Questions and Tutoring Dialogues](https://mlsanity.com/paper/2610.19532/) (2026)

## Abstract (arXiv)

Item (question) difficulties play a crucial role in educational assessments, enabling accurate and efficient assessment of student abilities and personalization to maximize learning outcomes. Traditionally, estimating item difficulties can be costly, requiring real students to respond to items, followed by fitting an item response theory (IRT) model to get difficulty estimates. This approach cannot be applied to the cold-start setting for previously unseen items either. In this work, we present SMART (Simulated Students Aligned with IRT), a novel method for aligning simulated students with instructed ability, which can then be used in simulations to predict the difficulty of open-ended items. We achieve this alignment using direct preference optimization (DPO), where we form preference pairs based on how likely responses are under a ground-truth IRT model. We perform a simulation by generating thousands of responses, evaluating them with a large language model (LLM)-based scoring model, and fit the resulting data to an IRT model to obtain item difficulty estimates. Through extensive experiments on two real-world student response datasets, we show that SMART outperforms other item difficulty prediction methods by leveraging its improved ability alignment.