# Token-by-Token Regeneration and Domain Biases: A Benchmark of LLMs on Advanced Mathematical Problem-Solving

arXiv: https://arxiv.org/abs/2501.17084 · HTML: https://mlsanity.com/paper/2501.17084/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 28 Jan 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 7 of 7)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [A Comprehensive Survey of Hallucination Mitigation Techniques in Large Language Models](https://mlsanity.com/paper/2401.01313/) (2024)
- [Can Language Models Rival Mathematics Students? Evaluating Mathematical Reasoning through Textual Manipulation and Human Experiments](https://mlsanity.com/paper/2412.11908/) (2024)

## Built on by (most cited first, 2 of 2)

- [Token-Hungry, Yet Precise: DeepSeek R1 Highlights the Need for Multi-Step Reasoning Over Speed in MATH](https://mlsanity.com/paper/2501.18576/) (2025)
- [The Prompt Engineering Report Distilled: Quick Start Guide for Life Sciences](https://mlsanity.com/paper/2509.11295/) (2025)

## Abstract (arXiv)

Large language models (LLMs) excel in many natural language tasks, yet they struggle with complex mathemat-ical problem-solving, particularly in symbolic reasoning and maintaining consistent output. This study evalu-ates 10 LLMs with 7 to 8 billion parameters using 945 competition-level problems from the MATH dataset. The focus is on their ability to generate executable Python code as a step in their reasoning process, involving over 9,450 code executions. The research introduces an evaluation framework using mistral-large-2411 to rate answers on a 5-point scale, which helps address inconsistencies in mathematical notation. It also examines the impact of regenerating output token-by-token on refining results. The findings reveal a significant 34.5% per-formance gap between the top commercial model (gpt-4o-mini, scoring 83.7%) and the least effective open-source model (open-codestral-mamba:v0.1, scoring 49.2%). This disparity is especially noticeable in complex areas like Number Theory. While token-by-token regeneration slightly improved accuracy (+0.8%) for the model llama3.1:8b, it also reduced code execution time by 36.7%, highlighting a trade-off between efficiency and precision. The study also noted a consistent trend where harder problems correlated with lower accuracy across all models. Despite using controlled execution environments, less than 1% of the generated code was unsafe, and 3.17% of problems remained unsolved after 10 attempts, suggesting that hybrid reasoning methods may be beneficial.