# MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations

arXiv: https://arxiv.org/abs/2502.06453 · HTML: https://mlsanity.com/paper/2502.06453/

## Key facts

- Cited by 89 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 48 of its 59 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Placed in

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

## Builds on (most cited first, 30 of 48)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Deduplicating Training Data Makes Language Models Better](https://mlsanity.com/paper/2107.06499/) (2021)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Scalable Extraction of Training Data from (Production) Language Models](https://mlsanity.com/paper/2311.17035/) (2023)
- [Detecting Pretraining Data from Large Language Models](https://mlsanity.com/paper/2310.16789/) (2023)
- [Reasoning or Reciting? Exploring the Capabilities and Limitations of Language Models Through Counterfactual Tasks](https://mlsanity.com/paper/2307.02477/) (2023)

## Built on by (most cited first, 30 of 89)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [CostBench: Evaluating Multi-Turn Cost-Optimal Planning and Adaptation in Dynamic Environments for LLM Tool-Use Agents](https://mlsanity.com/paper/2511.02734/) (2025)
- [Reasoning on a Budget: A Survey of Adaptive and Controllable Test-Time Compute in LLMs](https://mlsanity.com/paper/2507.02076/) (2025)
- [A Comprehensive Survey on Trustworthiness in Reasoning with Large Language Models](https://mlsanity.com/paper/2509.03871/) (2025)
- [Cats Confuse Reasoning LLM: Query Agnostic Adversarial Triggers for Reasoning Models](https://mlsanity.com/paper/2503.01781/) (2025)
- [Large Language Model Reasoning Failures](https://mlsanity.com/paper/2602.06176/) (2026)
- [Mathematical Proof as a Litmus Test: Revealing Failure Modes of Advanced Large Reasoning Models](https://mlsanity.com/paper/2506.17114/) (2025)
- [Stepwise Guided Policy Optimization: Coloring your Incorrect Reasoning in GRPO](https://mlsanity.com/paper/2505.11595/) (2025)
- [Recitation over Reasoning: How Cutting-Edge Language Models Can Fail on Elementary School-Level Reasoning Problems?](https://mlsanity.com/paper/2504.00509/) (2025)
- [Exposing Numeracy Gaps: A Benchmark to Evaluate Fundamental Numerical Abilities in Large Language Models](https://mlsanity.com/paper/2502.11075/) (2025)
- [Patterns Over Principles: The Fragility of Inductive Reasoning in LLMs under Noisy Observations](https://mlsanity.com/paper/2502.16169/) (2025)
- [EngiBench: A Benchmark for Evaluating Large Language Models on Engineering Problem Solving](https://mlsanity.com/paper/2509.17677/) (2025)
- [Can LLMs Explain Themselves Counterfactually?](https://mlsanity.com/paper/2502.18156/) (2025)
- [The Landscape of Memorization in LLMs: Mechanisms, Measurement, and Mitigation](https://mlsanity.com/paper/2507.05578/) (2025)
- [Can Theoretical Physics Research Benefit from Language Agents?](https://mlsanity.com/paper/2506.06214/) (2025)
- [An Investigation of Robustness of LLMs in Mathematical Reasoning: Benchmarking with Mathematically-Equivalent Transformation of Advanced Mathematical Problems](https://mlsanity.com/paper/2508.08833/) (2025)
- [Debunk the Myth of SFT Generalization](https://mlsanity.com/paper/2510.00237/) (2025)
- [Toward Scientific Reasoning in LLMs: Training from Expert Discussions via Reinforcement Learning](https://mlsanity.com/paper/2505.19501/) (2025)
- [None of the Others: a General Technique to Distinguish Reasoning from Memorization in Multiple-Choice LLM Evaluation Benchmarks](https://mlsanity.com/paper/2502.12896/) (2025)
- [Benford's Curse: Tracing Digit Bias to Numerical Hallucination in LLMs](https://mlsanity.com/paper/2506.01734/) (2025)
- [Toward Automated Robustness Evaluation of Mathematical Reasoning](https://mlsanity.com/paper/2506.05038/) (2025)
- [Skill-Targeted Adaptive Training](https://mlsanity.com/paper/2510.10023/) (2025)
- [How Well Do Large Reasoning Models Translate? A Comprehensive Evaluation for Multi-Domain Machine Translation](https://mlsanity.com/paper/2505.19987/) (2025)
- [ASyMOB: Algebraic Symbolic Mathematical Operations Benchmark](https://mlsanity.com/paper/2505.23851/) (2025)
- [Decoupling Knowledge and Reasoning in LLMs: An Exploration Using Cognitive Dual-System Theory](https://mlsanity.com/paper/2507.18178/) (2025)
- [In Good GRACEs: Principled Teacher Selection for Knowledge Distillation](https://mlsanity.com/paper/2511.02833/) (2025)
- [OPT-Engine: Benchmarking the Limits of LLMs in Optimization Modeling via Complexity Scaling](https://mlsanity.com/paper/2601.19924/) (2026)

## Abstract (arXiv)

Large language models have demonstrated impressive performance on challenging mathematical reasoning tasks, which has triggered the discussion of whether the performance is achieved by true reasoning capability or memorization. To investigate this question, prior work has constructed mathematical benchmarks when questions undergo simple perturbations -- modifications that still preserve the underlying reasoning patterns of the solutions. However, no work has explored hard perturbations, which fundamentally change the nature of the problem so that the original solution steps do not apply. To bridge the gap, we construct MATH-P-Simple and MATH-P-Hard via simple perturbation and hard perturbation, respectively. Each consists of 279 perturbed math problems derived from level-5 (hardest) problems in the MATH dataset (Hendrycksmath et. al., 2021). We observe significant performance drops on MATH-P-Hard across various models, including o1-mini (-16.49%) and gemini-2.0-flash-thinking (-12.9%). We also raise concerns about a novel form of memorization where models blindly apply learned problem-solving skills without assessing their applicability to modified contexts. This issue is amplified when using original problems for in-context learning. We call for research efforts to address this challenge, which is critical for developing more robust and reliable reasoning models.