| title | Are We Measuring Strategy or Phrasing? The Gap Between Surface- and Approach-Level Diversity in LLM Math Reasoning |
|---|---|
| authors | Sangmook Lee, Minbeom Kim, Jeonghye Kim, Dohyung Kim, Sojeong Rhee, Kyomin Jung |
| date | 2026-06-29 |
| venue | arXiv (preprint, not peer reviewed) |
| id | arXiv:2606.29985 |
| affiliation | Seoul National University |
| upvotes | 11 (Hugging Face Daily Papers, 2026-11-01) |
| links | abs pdf hf |
| abstract | Diversity in LLM mathematical reasoning is critical for exploration, but common diversity metrics mostly capture surface-level variation rather than differences in how a problem is solved. We address this gap by introducing approach-level diversity: variation in strategies across correct solutions to the same problem. Using a human-calibrated LLM judge framework, we show that prior diversity measures are unreliable proxies for approach-level diversity, and this mismatch carries over to diversity-aware RLVR, where target metrics are preserved while approach-level diversity declines. Investigating when approach-level diversity helps and whether it can be directly induced, we find that approach-diverse candidate sets improve test-time scaling. However, optimizing an LLM judge diversity reward during training causes the policy to exploit judge-specific preferences rather than broaden its approaches, leaving direct optimization of approach-level diversity as an open problem. Together, our work introduces the notion of approach-level diversity and uncovers a systematic divergence between surface- and approach-level signals, marking a step toward LLMs that reason in genuinely diverse, human-like ways. |
cite
@misc{lee2026are,
title={Are We Measuring Strategy or Phrasing? The Gap Between Surface- and Approach-Level Diversity in LLM Math Reasoning},
author={Sangmook Lee and Minbeom Kim and Jeonghye Kim and Dohyung Kim and Sojeong Rhee and Kyomin Jung},
year={2026},
eprint={2606.29985},
archivePrefix={arXiv},
url={https://arxiv.org/abs/2606.29985}
}