Are We Measuring Strategy or Phrasing? The Gap Between Surface- and Approach-Level Diversity in LLM Math Reasoning

Lee SangMook, minbeomkim, JeonghyeKim, Dohyung Kim, Sojeong Rhee, Kyomin Jung

Are We Measuring Strategy or Phrasing? The Gap Between Surface- and Approach-Level Diversity in LLM Math Reasoning: 11 upvotes on Hugging Face Daily Papers, #16 of 37 papers on 2026-07-01. Day-by-day upvote history. It lost 9 votes when the Hub removed votes in bulk.

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.

Paper page on Hugging Face · arXiv

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