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

Sangmook Lee, Minbeom Kim, Jeonghye Kim, Dohyung Kim, Sojeong Rhee, Kyomin Jung · Jun 29, 2026 · Citations: 0

Math Pairwise Preference
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How to use this page

Low trust

Use this as background context only. Do not make protocol decisions from this page alone.

Best use

Background context only

What to verify

Read the full paper before copying any benchmark, metric, or protocol choices.

Evidence quality

Low

Derived from extracted protocol signals and abstract evidence.

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.

Low-signal caution for protocol decisions

Use this page for context, then validate protocol choices against stronger HFEPX references before implementation decisions.

  • The available metadata is too thin to trust this as a primary source.
  • The abstract does not clearly describe the evaluation setup.
  • The abstract does not clearly name benchmarks or metrics.
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Should You Rely On This Paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

Background context only.

Main weakness

The available metadata is too thin to trust this as a primary source.

Trust level

Low

Usefulness score

40/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Detected

Evaluation Signal

Weak / implicit signal

Usefulness for eval research

Adjacent candidate

Extraction confidence 45%

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

What We Could Verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

partial

Pairwise Preference

Directly usable for protocol triage.

"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."

Evaluation Modes

missing

None explicit

Validate eval design from full paper text.

"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."

Quality Controls

missing

Not reported

No explicit QC controls found.

"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."

Benchmarks / Datasets

missing

Not extracted

No benchmark anchors detected.

"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."

Reported Metrics

missing

Not extracted

No metric anchors detected.

"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."

Human Feedback Details

  • Uses human feedback: Yes
  • Feedback types: Pairwise Preference
  • Rater population: Not reported
  • Expertise required: Math

Evaluation Details

  • Evaluation modes:
  • Agentic eval: None
  • Quality controls: Not reported
  • Evidence quality: Low
  • Use this page as: Background context only

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

No metric terms were extracted from the available abstract.

Research Brief

Metadata summary

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.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

  • 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.

Researcher Actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Check the full text for explicit evaluation design choices (raters, protocol, and metrics).
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

Research Summary

Contribution Summary

  • 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…
  • 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.

Why It Matters For Eval

  • 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…
  • 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.

Researcher Checklist

  • Pass: Human feedback protocol is explicit

    Detected: Pairwise Preference

  • Gap: Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Gap: Metric reporting is present

    No metric terms extracted.

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