# MatheMagic: Generating Dynamic Mathematics Benchmarks Robust to Memorization

arXiv: https://arxiv.org/abs/2510.05962 · HTML: https://mlsanity.com/paper/2510.05962/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 19 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Builds on (most cited first, 16 of 16)

- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [NLP Evaluation in trouble: On the Need to Measure LLM Data Contamination for each Benchmark](https://mlsanity.com/paper/2310.18018/) (2023)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [Phenomenal Yet Puzzling: Testing Inductive Reasoning Capabilities of Language Models with Hypothesis Refinement](https://mlsanity.com/paper/2310.08559/) (2023)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contamination](https://mlsanity.com/paper/2507.10532/) (2025)
- [AntiLeakBench: Preventing Data Contamination by Automatically Constructing Benchmarks with Updated Real-World Knowledge](https://mlsanity.com/paper/2412.13670/) (2024)
- [MathHay: An Automated Benchmark for Long-Context Mathematical Reasoning in LLMs](https://mlsanity.com/paper/2410.04698/) (2024)
- [Data Laundering: Artificially Boosting Benchmark Results through Knowledge Distillation](https://mlsanity.com/paper/2412.15255/) (2024)

## Built on by (most cited first, 1 of 1)

- [Automatically Generating Hard Math Problems from Hypothesis-Driven Error Analysis](https://mlsanity.com/paper/2604.04386/) (2026)

## Abstract (arXiv)

Conducting contamination-free evaluation of mathematical capabilities can be difficult for two reasons: models may memorize a test set once it is made public, and current mathematical benchmarks are prone to overfitting due to having limited diversity of symbols and rules, coupled with closed-ended answers. This paper proposes a method to leverage these shortcomings as useful features to a construct dynamic, counterfactual benchmark, which can be used to both reveal overfitting and measure true reasoning. We demonstrate this via MatheMagic, which generates math test instances with the interpretations of numbers and operators altered, yet has automatically verifiable answers. Test instances are randomly seeded and constructed at test time to evaluate a model's induction or deduction capability, offering stability, extensibility, comparability, and robustness to overfitting. Our experiments find that models solve deduction more easily than induction, but they revert to standard math. Further analysis reveals that math-adapted models fail to exhibit a general "skill" of reasoning, and fine-tuning on induction tasks generalizes poorly.