# A Careful Examination of Large Language Model Performance on Grade School Arithmetic

arXiv: https://arxiv.org/abs/2405.00332 · HTML: https://mlsanity.com/paper/2405.00332/

## Key facts

- Cited by 191 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 76 references that are in the map.
- First posted on arXiv 1 May 2024.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://mlsanity.com/paper/2204.06745/) (2022)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Detecting Pretraining Data from Large Language Models](https://mlsanity.com/paper/2310.16789/) (2023)
- [NLP Evaluation in trouble: On the Need to Measure LLM Data Contamination for each Benchmark](https://mlsanity.com/paper/2310.18018/) (2023)
- [Data Contamination: From Memorization to Exploitation](https://mlsanity.com/paper/2203.08242/) (2022)
- [Leak, Cheat, Repeat: Data Contamination and Evaluation Malpractices in Closed-Source LLMs](https://mlsanity.com/paper/2402.03927/) (2024)
- [Stop Uploading Test Data in Plain Text: Practical Strategies for Mitigating Data Contamination by Evaluation Benchmarks](https://mlsanity.com/paper/2305.10160/) (2023)
- [Benchmarking Benchmark Leakage in Large Language Models](https://mlsanity.com/paper/2404.18824/) (2024)
- [Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap](https://mlsanity.com/paper/2402.19450/) (2024)

## Built on by (most cited first, 30 of 191)

- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [LMMs-Eval: Reality Check on the Evaluation of Large Multimodal Models](https://mlsanity.com/paper/2407.12772/) (2024)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [SWE-Bench Pro: Can AI Agents Solve Long-Horizon Software Engineering Tasks?](https://mlsanity.com/paper/2509.16941/) (2025)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [Lessons from the Trenches on Reproducible Evaluation of Language Models](https://mlsanity.com/paper/2405.14782/) (2024)
- [BRIGHT: A Realistic and Challenging Benchmark for Reasoning-Intensive Retrieval](https://mlsanity.com/paper/2407.12883/) (2024)
- [DynaMath: A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models](https://mlsanity.com/paper/2411.00836/) (2024)
- [Measuring what Matters: Construct Validity in Large Language Model Benchmarks](https://mlsanity.com/paper/2511.04703/) (2025)
- [On Memorization of Large Language Models in Logical Reasoning](https://mlsanity.com/paper/2410.23123/) (2024)
- [Small Language Models: Survey, Measurements, and Insights](https://mlsanity.com/paper/2409.15790/) (2024)
- [ForecastBench: A Dynamic Benchmark of AI Forecasting Capabilities](https://mlsanity.com/paper/2409.19839/) (2024)
- [Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process](https://mlsanity.com/paper/2407.20311/) (2024)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [INCLUDE: Evaluating Multilingual Language Understanding with Regional Knowledge](https://mlsanity.com/paper/2411.19799/) (2024)
- [A Systematic Survey and Critical Review on Evaluating Large Language Models: Challenges, Limitations, and Recommendations](https://mlsanity.com/paper/2407.04069/) (2024)
- [MixEval: Deriving Wisdom of the Crowd from LLM Benchmark Mixtures](https://mlsanity.com/paper/2406.06565/) (2024)
- [Parameters vs FLOPs: Scaling Laws for Optimal Sparsity for Mixture-of-Experts Language Models](https://mlsanity.com/paper/2501.12370/) (2025)
- [Is Your Model Really A Good Math Reasoner? Evaluating Mathematical Reasoning with Checklist](https://mlsanity.com/paper/2407.08733/) (2024)
- [UGPhysics: A Comprehensive Benchmark for Undergraduate Physics Reasoning with Large Language Models](https://mlsanity.com/paper/2502.00334/) (2025)
- [Toward an Evaluation Science for Generative AI Systems](https://mlsanity.com/paper/2503.05336/) (2025)
- [AntiLeakBench: Preventing Data Contamination by Automatically Constructing Benchmarks with Updated Real-World Knowledge](https://mlsanity.com/paper/2412.13670/) (2024)
- [Understand, Solve and Translate: Bridging the Multilingual Mathematical Reasoning Gap](https://mlsanity.com/paper/2501.02448/) (2025)
- [Agent-RLVR: Training Software Engineering Agents via Guidance and Environment Rewards](https://mlsanity.com/paper/2506.11425/) (2025)
- [MMLU-CF: A Contamination-free Multi-task Language Understanding Benchmark](https://mlsanity.com/paper/2412.15194/) (2024)
- [Adaptive In-conversation Team Building for Language Model Agents](https://mlsanity.com/paper/2405.19425/) (2024)
- [AI-Assisted Generation of Difficult Math Questions](https://mlsanity.com/paper/2407.21009/) (2024)

## Abstract (arXiv)

Large language models (LLMs) have achieved impressive success on many benchmarks for mathematical reasoning. However, there is growing concern that some of this performance actually reflects dataset contamination, where data closely resembling benchmark questions leaks into the training data, instead of true reasoning ability. To investigate this claim rigorously, we commission Grade School Math 1000 (GSM1k). GSM1k is designed to mirror the style and complexity of the established GSM8k benchmark, the gold standard for measuring elementary mathematical reasoning. We ensure that the two benchmarks are comparable across important metrics such as human solve rates, number of steps in solution, answer magnitude, and more. When evaluating leading open- and closed-source LLMs on GSM1k, we observe accuracy drops of up to 8%, with several families of models showing evidence of systematic overfitting across almost all model sizes. Further analysis suggests a positive relationship (Spearman's r^2 = 0.36) between a model's probability of generating an example from GSM8k and its performance gap between GSM8k and GSM1k, suggesting that some models may have partially memorized GSM8k. Nevertheless, many models, especially those on the frontier, show minimal signs of overfitting, and all models broadly demonstrate generalization to novel math problems guaranteed to not be in their training data.