@inproceedings{lee-etal-2026-measuring-strategy,
title = "Are We Measuring Strategy or Phrasing? The Gap Between Surface- and Approach-Level Diversity in {LLM} Math Reasoning",
author = "Lee, Sangmook and
Kim, Minbeom and
Kim, Jeonghye and
Kim, Dohyung and
Rhee, Sojeong and
Jung, Kyomin",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.2332/",
pages = "52966--52996",
ISBN = "979-8-89176-459-0",
abstract = "Diversity in LLM mathematical reasoning is critical for exploration, but common diversity metrics mostly capture \textit{surface-level variation} rather than differences in how a problem is solved. We address this gap by introducing \textbf{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."
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<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.</abstract>
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%0 Conference Proceedings
%T Are We Measuring Strategy or Phrasing? The Gap Between Surface- and Approach-Level Diversity in LLM Math Reasoning
%A Lee, Sangmook
%A Kim, Minbeom
%A Kim, Jeonghye
%A Kim, Dohyung
%A Rhee, Sojeong
%A Jung, Kyomin
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F lee-etal-2026-measuring-strategy
%X 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.
%U https://aclanthology.org/2026.emnlp-main.2332/
%P 52966-52996
Markdown (Informal)
[Are We Measuring Strategy or Phrasing? The Gap Between Surface- and Approach-Level Diversity in LLM Math Reasoning](https://aclanthology.org/2026.emnlp-main.2332/) (Lee et al., EMNLP 2026)
ACL