# Can Large Reasoning Models Improve Accuracy on Mathematical Tasks Using Flawed Thinking?

arXiv: https://arxiv.org/abs/2512.17079 · HTML: https://mlsanity.com/paper/2512.17079/

## 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 15 of its 18 references that are in the map.
- First posted on arXiv 18 Dec 2025.

## Placed in

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

## Builds on (most cited first, 15 of 15)

- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Learning From Mistakes Makes LLM Better Reasoner](https://mlsanity.com/paper/2310.20689/) (2023)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)
- [Lean-STaR: Learning to Interleave Thinking and Proving](https://mlsanity.com/paper/2407.10040/) (2024)
- [LLMs can Find Mathematical Reasoning Mistakes by Pedagogical Chain-of-Thought](https://mlsanity.com/paper/2405.06705/) (2024)
- [MuMath-Code: Combining Tool-Use Large Language Models with Multi-perspective Data Augmentation for Mathematical Reasoning](https://mlsanity.com/paper/2405.07551/) (2024)
- [S^3cMath: Spontaneous Step-level Self-correction Makes Large Language Models Better Mathematical Reasoners](https://mlsanity.com/paper/2409.01524/) (2024)
- [CoMAT: Chain of Mathematically Annotated Thought Improves Mathematical Reasoning](https://mlsanity.com/paper/2410.10336/) (2024)
- [Large Reasoning Models Learn Better Alignment from Flawed Thinking](https://mlsanity.com/paper/2510.00938/) (2025)

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

- [Better Eyes, Better Thoughts: Why Vision Chain-of-Thought Fails in Medicine](https://mlsanity.com/paper/2603.06665/) (2026)
- [The Fragility of Chain-of-Thought Monitoring Across Typologically Diverse Languages](https://mlsanity.com/paper/2605.27901/) (2026)

## Abstract (arXiv)

Chain-of-thought (CoT) prompting has become central to mathematical reasoning in large language models, yet models remain brittle to early errors: a single arithmetic slip or unjustified inference typically propagates uncorrected to an incorrect final answer. We investigate whether training on intentionally flawed reasoning traces can teach models to detect and recover from such errors without degrading standard problem-solving ability. Using competition-level problems from MATH-lighteval, we generate CoT prefixes containing exactly one controlled error, either a calculation error (sign flips, dropped terms) or a reasoning error (misapplied rules, unjustified logical steps), and fine-tune Qwen3-4B with GRPO using a binary final-answer reward. Our Mixed-CoT-RL model matches standard RL on clean problems (41% vs 41%) while substantially outperforming it on problems prefilled with flawed reasoning (24% vs 19%). Notably, clean-only RL fine-tuning degrades robustness below the untuned baseline 19% vs. 20%), indicating that conventional training increases susceptibility to misleading prefills. Among error types, training on reasoning errors yields greater robustness gains than calculation errors alone, with mixed training performing best. These findings demonstrate that exposure to flawed traces during training can improve error-recovery behavior without sacrificing accuracy, suggesting a path toward more robust mathematical reasoning in LLMs.