# Numerical Sensitivity and Robustness: Exploring the Flaws of Mathematical Reasoning in Large Language Models

arXiv: https://arxiv.org/abs/2511.08022 · HTML: https://mlsanity.com/paper/2511.08022/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 27 of its 39 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap](https://mlsanity.com/paper/2402.19450/) (2024)
- [A Peek into Token Bias: Large Language Models Are Not Yet Genuine Reasoners](https://mlsanity.com/paper/2406.11050/) (2024)
- [Apple Intelligence Foundation Language Models](https://mlsanity.com/paper/2407.21075/) (2024)
- [Mathematical Reasoning in Large Language Models: Assessing Logical and Arithmetic Errors across Wide Numerical Ranges](https://mlsanity.com/paper/2502.08680/) (2025)
- [Recitation over Reasoning: How Cutting-Edge Language Models Can Fail on Elementary School-Level Reasoning Problems?](https://mlsanity.com/paper/2504.00509/) (2025)

## Built on by (most cited first, 3 of 3)

- [Robust Reasoning Benchmark](https://mlsanity.com/paper/2604.08571/) (2026)
- [Measuring Stability and Failure Behavior in Language Models Under Structured Perturbations](https://mlsanity.com/paper/2608.22138/) (2026)
- [Beyond the Answer Key: Robustness Evaluation of Large Language Models for Step-Level Mathematical Verification](https://mlsanity.com/paper/2608.28725/) (2026)

## Abstract (arXiv)

LLMs have made significant progress in the field of mathematical reasoning, but whether they have true the mathematical understanding ability is still controversial. To explore this issue, we propose a new perturbation framework to evaluate LLMs' reasoning ability in complex environments by injecting additional semantically irrelevant perturbation sentences and gradually increasing the perturbation intensity. At the same time, we use an additional perturbation method: core questioning instruction missing, to further analyze the LLMs' problem-solving mechanism. The experimental results show that LLMs perform stably when facing perturbation sentences without numbers, but there is also a robustness boundary. As the perturbation intensity increases, the performance exhibits varying degrees of decline; when facing perturbation sentences with numbers, the performance decreases more significantly, most open source models with smaller parameters decrease by nearly or even more than 10%, and further increasing with the enhancement of perturbation intensity, with the maximum decrease reaching 51.55%. Even the most advanced commercial LLMs have seen a 3%-10% performance drop. By analyzing the reasoning process of LLMs in detail, We find that models are more sensitive to perturbations with numerical information and are more likely to give incorrect answers when disturbed by irrelevant numerical information. The higher the perturbation intensity, the more obvious these defects are. At the same time, in the absence of core questioning instruction, models can still maintain an accuracy of 20%-40%, indicating that LLMs may rely on memory templates or pattern matching to complete the task, rather than logical reasoning. In general, our work reveals the shortcomings and limitations of current LLMs in their reasoning capabilities, which is of great significance for the further development of LLMs.