mlsanityData to 7 Oct 2026

From Calculation to Adjudication: Examining LLM judges on Mathematical Reasoning Tasks

arXiv 2409.04168 ↗First posted 6 Sep 2024cs.CL cs.AIcited by 22

On the map: LLM reasoning → Reasoning benchmarks and evaluation

Abstract (arXiv)

To reduce the need for human annotations, large language models (LLMs) have been proposed as judges of the quality of other candidate models. The performance of LLM judges is typically evaluated by measuring the correlation with human judgments on generative tasks such as summarization or machine translation. In contrast, we study LLM judges on mathematical reasoning tasks. These tasks require multi-step reasoning, and the correctness of their solutions is verifiable, enabling a more objective evaluation. We perform a detailed performance analysis and find that easy samples are easy to judge, and difficult samples are difficult to judge. Our analysis uncovers a strong correlation between judgment performance and the candidate model task performance, indicating that judges tend to favor higher-quality models even if their answer is incorrect. As a consequence, we test whether we can predict the behavior of LLM judges using simple features such as part-of-speech tags and find that we can correctly predict 70%-75% of judgments. We conclude this study by analyzing practical use cases, showing that LLM judges consistently detect the on-average better model but largely fail if we use them to improve task performance.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 18 of its 42 references that are in the map. First posted on arXiv 6 Sep 2024.

Builds on

18 of 42 references.

References · 18

  1. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  2. 2023Mistral 7Bcited by 3,065
  3. 2022Constitutional AI: Harmlessness from AI Feedbackcited by 2,950
  4. 2024Qwen2 Technical Reportcited by 2,076
  5. 2024Mixtral of Expertscited by 1,785
  6. 2024Gemma: Open Models Based on Gemini Research and Technologycited by 889
  7. 2024Yi: Open Foundation Models by 01.AIcited by 706
  8. 2024Self-Rewarding Language Modelscited by 654
  9. 2024LLM Evaluators Recognize and Favor Their Own Generationscited by 651
  10. 2024LLMs instead of Human Judges? A Large Scale Empirical Study across 20 NLP Evaluation Taskscited by 236
  11. 2024HelpSteer2: Open-source dataset for training top-performing reward modelscited by 232
  12. 2024Meta-Rewarding Language Models: Self-Improving Alignment with LLM-as-a-Meta-Judgecited by 202
6 more
  1. 2024Large Language Models for Data Annotation and Synthesis: A Surveycited by 201
  2. 2023Benchmarking Cognitive Biases in Large Language Models as Evaluatorscited by 147
  3. 2024Is LLM-as-a-Judge Robust? Investigating Universal Adversarial Attacks on Zero-shot LLM Assessmentcited by 117
  4. 2024Pride and Prejudice: LLM Amplifies Self-Bias in Self-Refinementcited by 111
  5. 2024The BiGGen Bench: A Principled Benchmark for Fine-grained Evaluation of Language Models with Language Modelscited by 89
  6. 2023LLMs as Narcissistic Evaluators: When Ego Inflates Evaluation Scorescited by 88

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 11; 2026: 8.

22 papers.

Sort:

By area:

  1. 2024LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methodscited by 451
  2. 2024U-MATH: A University-Level Benchmark for Evaluating Mathematical Skills in LLMscited by 24
  3. 2025Brains vs. Bytes: Evaluating LLM Proficiency in Olympiad Mathematicscited by 22
  4. 2024A Systematic Assessment of OpenAI o1-Preview for Higher Order Thinking in Educationcited by 16
  5. 2025Theorem Prover as a Judge for Synthetic Data Generationcited by 13
  6. 2025DualVLA: Building a Generalizable Embodied Agent via Partial Decoupling of Reasoning and Actioncited by 11
  7. 2025Improving Preference Extraction In LLMs By Identifying Latent Knowledge Through Classifying Probescited by 9
  8. 2025Can You Trick the Grader? Adversarial Persuasion of LLM Judgescited by 9
  9. 2025UPME: An Unsupervised Peer Review Framework for Multimodal Large Language Model Evaluationcited by 7
  10. 2025EarthSE: A Benchmark for Evaluating Earth Scientific Exploration Capability of LLMscited by 7
  11. 2026Who Endorsed It? Measuring Authority Bias Across Expertise Levels in Language Modelscited by 7
  12. 2025RefGrader: Automated Grading of Mathematical Competition Proofs using Agentic Workflowscited by 3
10 more
  1. 2025A Matter of Interest: Understanding Interestingness of Math Problems in Humans and Language Modelscited by 3
  2. 2026Judging Against the Reference: Uncovering Knowledge-Driven Failures in LLM-Judges on QA Evaluationcited by 3
  3. 2026Rethinking Math Reasoning Evaluation: A Robust LLM-as-a-Judge Framework Beyond Symbolic Rigiditycited by 3
  4. 2026LLM Judges Can Be Too Generous When There Is No Reference Answercited by 3
  5. 2026Reject, Resample, Repeat: Understanding Parallel Reasoning in Language Model Inferencecited by 2
  6. 2025Improving Multilingual Math Reasoning for African Languagescited by 1
  7. 2025Evaluating Implicit Biases in LLM Reasoning through Logic Grid Puzzlescited by 1
  8. 2026TAMTRL: Teacher-Aligned Reward Reshaping for Multi-Turn Reinforcement Learning in Long-Context Compressioncited by 1
  9. 2026How Hypocritical Is Your LLM judge? Listener-Speaker Asymmetries in the Pragmatic Competence of Large Language Modelscited by 1
  10. 2026Right Answer, Wrong Method: Shortcut Hacking Misleads the Evaluation of LLM Reasoning on Frontier Science Benchmarkscited by 1

Similar, not cited

Close in wording, no citation either way

  1. 2026SLMJury: Can Small Language Models Judge as Well as Large Ones?
  2. 2026Can LLM Reasoning Be Trusted? A Comparative Study: Using Human Benchmarking on Statistical Tasks
  3. 2024JudgeBench: A Benchmark for Evaluating LLM-based Judges
  4. 2025Do LLMs Overthink Basic Math Reasoning? Benchmarking the Accuracy-Efficiency Tradeoff in Language Models
  5. 2026When Consistency Does Not Mean Reliability: Evaluating Local LLM Judges Against Human Ratings
  6. 2024Judging the Judges: Evaluating Alignment and Vulnerabilities in LLMs-as-Judges
  7. 2025Evaluating Judges as Evaluators: The JETTS Benchmark of LLM-as-Judges as Test-Time Scaling Evaluators
  8. 2025Leveraging LLMs as Meta-Judges: A Multi-Agent Framework for Evaluating LLM Judgments