Paraphrase and Solve: Exploring and Exploiting the Impact of Surface Form on Mathematical Reasoning in Large Language Models
On the map: LLM reasoning → Mathematical reasoning
Abstract (arXiv)
This paper studies the relationship between the surface form of a mathematical problem and its solvability by large language models. We find that subtle alterations in the surface form can significantly impact the answer distribution and the solve rate, exposing the language model's lack of robustness and sensitivity to the surface form in reasoning through complex problems. To improve mathematical reasoning performance, we propose Self-Consistency-over-Paraphrases (SCoP), which diversifies reasoning paths from specific surface forms of the problem. We evaluate our approach on four mathematics reasoning benchmarks over three large language models and show that SCoP improves mathematical reasoning performance over vanilla self-consistency, particularly for problems initially deemed unsolvable. Finally, we provide additional experiments and discussion regarding problem difficulty and surface forms, including cross-model difficulty agreement and paraphrasing transferability, and Variance of Variations (VOV) for language model evaluation.
Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 16 of its 28 references that are in the map. First posted on arXiv 17 Apr 2024.
Builds on
16 of 28 references.
References · 16
- 2023GPT-4 Technical Reportcited by 18,396
- 2022Training language models to follow instructions with human feedbackcited by 15,971
- 2023Llama 2: Open Foundation and Fine-Tuned Chat Modelscited by 13,028
- 2021Training Verifiers to Solve Math Word Problemscited by 10,109
- 2022Large Language Models are Zero-Shot Reasonerscited by 4,374
- 2023Let's Verify Step by Stepcited by 3,789
- 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Modelscited by 3,211
- 2021Scaling Language Models: Methods, Analysis & Insights from Training Gophercited by 1,202
- 2022Large Language Models Are Human-Level Prompt Engineerscited by 1,045
- 2023Graph of Thoughts: Solving Elaborate Problems with Large Language Modelscited by 886
- 2023Chameleon: Plug-and-Play Compositional Reasoning with Large Language Modelscited by 356
- 2022Reasoning with Language Model Prompting: A Surveycited by 252
4 more
- 2020AutoPrompt: Eliciting Knowledge from Language Models with Automatically Generated Promptscited by 249
- 2022Demystifying Prompts in Language Models via Perplexity Estimationcited by 216
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Citing papers per year: 2025: 6; 2026: 8.
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- 2026LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signalscited by 24
- 2025Self-Harmony: Learning to Harmonize Self-Supervision and Self-Play in Test-Time Reinforcement Learningcited by 10
- 2025Bridging Language Models and Financial Analysiscited by 4
- 2025Uncertainty Profiles for LLMs: Uncertainty Source Decomposition and Adaptive Model-Metric Selectioncited by 4
- 2025AbstRaL: Augmenting LLMs' Reasoning by Reinforcing Abstract Thinkingcited by 4
- 2025Your Language Model May Think Too Rigidly: Achieving Reasoning Consistency with Symmetry-Enhanced Trainingcited by 3
- 2025Clarification as Supervision: Reinforcement Learning for Vision-Language Interfacescited by 2
- 2026Finding the Cracks: Improving LLMs Reasoning with Paraphrastic Probing and Consistency Verificationcited by 2
- 2026Are We Evaluating Knowledge or Phrasing? Mitigating MCQA Sensitivity with ParaEvalcited by 1
- 2026Same Question, Different Answers: Evaluating LLM Reliability Beyond Accuracycited by 1
- 2026StoryCoder: Narrative Reformulation for Structured Reasoning in LLM Code Generationcited by 0
- 2026When to Vote, When to Rewrite: Disagreement-Guided Strategy Routing for Test-Time Scalingcited by 0
- 2026Test-Time Augmentation for LLMs: When Input Diversity Beats Output Diversity at Matched Compute10 Aug 2026
- 2026Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving8 Jul 2026
- 2026Are We Evaluating Knowledge or Phrasing? Mitigating MCQA Sensitivity with ParaEval9 Jun 2026
- 2026Same Question, Different Answers: Evaluating LLM Reliability Beyond Accuracy18 May 2026
- 2026When to Vote, When to Rewrite: Disagreement-Guided Strategy Routing for Test-Time Scaling29 Apr 2026
- 2026StoryCoder: Narrative Reformulation for Structured Reasoning in LLM Code Generation16 Apr 2026
- 2026LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals7 Apr 2026
- 2026Finding the Cracks: Improving LLMs Reasoning with Paraphrastic Probing and Consistency Verification11 Feb 2026
- 2025Self-Harmony: Learning to Harmonize Self-Supervision and Self-Play in Test-Time Reinforcement Learning3 Nov 2025
- 2025Clarification as Supervision: Reinforcement Learning for Vision-Language Interfaces30 Sep 2025
- 2025AbstRaL: Augmenting LLMs' Reasoning by Reinforcing Abstract Thinking9 Jun 2025
- 2025Uncertainty Profiles for LLMs: Uncertainty Source Decomposition and Adaptive Model-Metric Selection12 May 2025
- 2026LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signalscited by 24
- 2025AbstRaL: Augmenting LLMs' Reasoning by Reinforcing Abstract Thinkingcited by 4
- 2025Your Language Model May Think Too Rigidly: Achieving Reasoning Consistency with Symmetry-Enhanced Trainingcited by 3
- 2025Clarification as Supervision: Reinforcement Learning for Vision-Language Interfacescited by 2
- 2026Finding the Cracks: Improving LLMs Reasoning with Paraphrastic Probing and Consistency Verificationcited by 2
- 2026StoryCoder: Narrative Reformulation for Structured Reasoning in LLM Code Generationcited by 0
- 2026When to Vote, When to Rewrite: Disagreement-Guided Strategy Routing for Test-Time Scalingcited by 0
- 2026Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solvingcited by 0
- 2026Test-Time Augmentation for LLMs: When Input Diversity Beats Output Diversity at Matched Computecited by 0
- 2026Test-Time Augmentation for LLMs: When Input Diversity Beats Output Diversity at Matched Compute10 Aug 2026
- 2026Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving8 Jul 2026
- 2026When to Vote, When to Rewrite: Disagreement-Guided Strategy Routing for Test-Time Scaling29 Apr 2026
- 2026StoryCoder: Narrative Reformulation for Structured Reasoning in LLM Code Generation16 Apr 2026
- 2026LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals7 Apr 2026
- 2026Finding the Cracks: Improving LLMs Reasoning with Paraphrastic Probing and Consistency Verification11 Feb 2026
- 2025Clarification as Supervision: Reinforcement Learning for Vision-Language Interfaces30 Sep 2025
- 2025AbstRaL: Augmenting LLMs' Reasoning by Reinforcing Abstract Thinking9 Jun 2025
- 2025Your Language Model May Think Too Rigidly: Achieving Reasoning Consistency with Symmetry-Enhanced Training25 Feb 2025
- 2025Bridging Language Models and Financial Analysiscited by 4
- 2025Uncertainty Profiles for LLMs: Uncertainty Source Decomposition and Adaptive Model-Metric Selectioncited by 4
- 2026Are We Evaluating Knowledge or Phrasing? Mitigating MCQA Sensitivity with ParaEvalcited by 1
- 2026Same Question, Different Answers: Evaluating LLM Reliability Beyond Accuracycited by 1
- 2026Are We Evaluating Knowledge or Phrasing? Mitigating MCQA Sensitivity with ParaEval9 Jun 2026
- 2026Same Question, Different Answers: Evaluating LLM Reliability Beyond Accuracy18 May 2026
- 2025Uncertainty Profiles for LLMs: Uncertainty Source Decomposition and Adaptive Model-Metric Selection12 May 2025
- 2025Bridging Language Models and Financial Analysis14 Mar 2025
Similar, not cited
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- 2023Reasoning in Large Language Models Through Symbolic Math Word Problems
- 2024Large Language Models Struggle with Unreasonability in Math Problems
- 2025Putnam-AXIOM: A Functional and Static Benchmark for Measuring Higher Level Mathematical Reasoning in LLMs
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