LookAlike: Consistent Distractor Generation in Math MCQs

TL;DR

LookAlike is a novel method that enhances distractor generation for math MCQs by leveraging model inconsistencies and preference optimization, resulting in more accurate and consistent distractors compared to prior approaches.

Contribution

It introduces a scalable training approach using synthetic preference pairs from model inconsistencies and combines supervised fine-tuning with direct preference optimization.

Findings

Achieves 51.6% accuracy in distractor generation

Reaches 57.2% accuracy in error generation

Outperforms existing state-of-the-art methods

Abstract

Large language models (LLMs) are increasingly used to generate distractors for multiple-choice questions (MCQs), especially in domains like math education. However, existing approaches are limited in ensuring that the generated distractors are consistent with common student errors. We propose LookAlike, a method that improves error-distractor consistency via preference optimization. Our two main innovations are: (a) mining synthetic preference pairs from model inconsistencies, and (b) alternating supervised fine-tuning (SFT) with Direct Preference Optimization (DPO) to stabilize training. Unlike prior work that relies on heuristics or manually annotated preference data, LookAlike uses its own generation inconsistencies as dispreferred samples, thus enabling scalable and stable training. Evaluated on a real-world dataset of 1,400+ math MCQs, LookAlike achieves 51.6% accuracy in distractor generation and 57.2% in error generation under LLM-as-a-judge evaluation, outperforming an existing state-of-the-art method (45.6% / 47.7%). These improvements highlight the effectiveness of preference-based regularization and inconsistency mining for generating consistent math MCQ distractors at scale.