| --- |
| pretty_name: MATH (RLVR format) |
| license: mit |
| language: |
| - en |
| task_categories: |
| - text-generation |
| - question-answering |
| tags: |
| - math |
| - reasoning |
| - rlvr |
| - reinforcement-learning |
| - verl |
| size_categories: |
| - 10K<n<100K |
| configs: |
| - config_name: default |
| data_files: |
| - split: train |
| path: train.parquet |
| - split: test |
| path: test.parquet |
| --- |
| |
| # MATH (RLVR format) |
|
|
| This is the MATH competition-mathematics dataset ([Hendrycks et al., 2021](https://arxiv.org/abs/2103.03874)) in the verl-style RLVR (reinforcement learning with verifiable rewards) format. We used it to train and evaluate **A-NSR** and **CW-NSR** in our paper *Adaptive Negative Reinforcement for LLM Reasoning: Dynamically Balancing Correction and Diversity in RLVR*. |
|
|
| The files are an unmodified copy of the preprocessed MATH data released by Zhu et al. with *The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning* (NeurIPS 2025). The `data_source` field is `TianHongZXY/MATH`. We re-host the data so that our experiments can be reproduced with exactly the same files. |
|
|
| ## Dataset summary |
|
|
| | Split | Problems | Use in our paper | |
| |-------|---------:|------------------| |
| | `train` | 7,500 | RLVR training (10 epochs, prompt batch size 128) | |
| | `test` | 5,000 | Evaluation (Pass@k, k = 1 … 256) | |
|
|
| Each problem has a difficulty level (1–5), one of seven subjects, a reference step-by-step solution, and a final answer (`target`). The final answer is used for rule-based reward checking. |
|
|
| ### Subject distribution |
|
|
| | Subject | Train | Test | |
| |---------|------:|-----:| |
| | Algebra | 1,744 | 1,187 | |
| | Counting & Probability | 771 | 474 | |
| | Geometry | 870 | 479 | |
| | Intermediate Algebra | 1,295 | 903 | |
| | Number Theory | 869 | 540 | |
| | Prealgebra | 1,205 | 871 | |
| | Precalculus | 746 | 546 | |
|
|
| ### Difficulty distribution |
|
|
| | Level | Train | Test | |
| |-------|------:|-----:| |
| | Level 1 | 564 | 437 | |
| | Level 2 | 1,348 | 894 | |
| | Level 3 | 1,592 | 1,131 | |
| | Level 4 | 1,690 | 1,214 | |
| | Level 5 | 2,304 | 1,324 | |
| | `Level ?` (unlabeled in the original data) | 2 | 0 | |
|
|
| ## Data fields |
|
|
| | Field | Type | Description | |
| |-------|------|-------------| |
| | `level` | string | Difficulty, `"Level 1"` … `"Level 5"` | |
| | `type` | string | Subject (see table above) | |
| | `data_source` | string | Always `"TianHongZXY/MATH"` | |
| | `prompt` | list of `{role, content}` | Chat-format prompt: one `user` message containing the problem statement | |
| | `ability` | string | Always `"math"` | |
| | `reward_model.style` | string | Always `"rule"` (rule-based verifiable reward) | |
| | `reward_model.ground_truth.question` | string | Problem statement | |
| | `reward_model.ground_truth.solution` | string | Reference solution from MATH, with the answer in `\boxed{}` | |
| | `reward_model.ground_truth.target` | string | Final answer used for reward computation | |
| | `extra_info.index` | int | Index within the split | |
| | `extra_info.split` | string | `"train"` or `"test"` | |
|
|
| ### Example |
|
|
| ```json |
| { |
| "level": "Level 3", |
| "type": "Algebra", |
| "data_source": "TianHongZXY/MATH", |
| "prompt": [{"role": "user", "content": "How many vertical asymptotes does the graph of $y=\\frac{2}{x^2+x-6}$ have?"}], |
| "ability": "math", |
| "reward_model": { |
| "style": "rule", |
| "ground_truth": { |
| "question": "How many vertical asymptotes does the graph of $y=\\frac{2}{x^2+x-6}$ have?", |
| "solution": "The denominator of the rational function factors into $x^2+x-6=(x-2)(x+3)$. ... Therefore, the graph has $\\boxed{2}$ vertical asymptotes.", |
| "target": "2" |
| } |
| }, |
| "extra_info": {"index": 0, "split": "test"} |
| } |
| ``` |
|
|
| ## Usage |
|
|
| ```python |
| from datasets import load_dataset |
| |
| ds = load_dataset("<your-username>/MATH-RLVR") |
| print(ds["train"][0]["prompt"][0]["content"]) |
| print(ds["train"][0]["reward_model"]["ground_truth"]["target"]) |
| ``` |
|
|
| The `prompt` field holds only the raw problem. In our experiments with `Qwen2.5-Math-1.5B`, it was wrapped in the following chat template, which is the same as in Zhu et al. and SimpleRL-Zoo: |
|
|
| ``` |
| <|im_start|>system |
| You are a helpful assistant.<|im_end|> |
| <|im_start|>user |
| {input} |
| Please reason step by step, and put your final answer |
| within \boxed{}.<|im_end|> |
| <|im_start|>assistant |
| ``` |
|
|
| The reward is binary: a response is correct if the answer in its final `\boxed{}` matches `target` under a math-equivalence check, and incorrect otherwise. |
|
|
| ## Source and license |
|
|
| - **Original dataset:** MATH, by Hendrycks et al. (2021), released under the MIT License: <https://github.com/hendrycks/math>. |
| - **Preprocessing:** Zhu et al. (2025), <https://github.com/TianHongZXY/RLVR-Decomposed>. |
| - The MATH problems come from competitions such as AMC 10, AMC 12, and AIME, via the Art of Problem Solving. |
|
|
| ## Citation |
|
|
| If you use this dataset, please cite the original MATH paper and the work whose preprocessing we reuse: |
|
|
| ```bibtex |
| @inproceedings{hendrycks2021math, |
| title = {Measuring Mathematical Problem Solving With the {MATH} Dataset}, |
| author = {Hendrycks, Dan and Burns, Collin and Kadavath, Saurav and Arora, Akul and Basart, Steven and Tang, Eric and Song, Dawn and Steinhardt, Jacob}, |
| booktitle = {NeurIPS Datasets and Benchmarks}, |
| year = {2021} |
| } |
| |
| @inproceedings{zhu2025nsr, |
| title = {The Surprising Effectiveness of Negative Reinforcement in {LLM} Reasoning}, |
| author = {Zhu, Xinyu and Xia, Mengzhou and Wei, Zhepei and Chen, Wei-Lin and Chen, Danqi and Meng, Yu}, |
| booktitle = {NeurIPS}, |
| year = {2025} |
| } |
| ``` |
|
|
| Our paper: |
|
|
| <!-- Replace with the final citation once the paper is published. --> |
| ```bibtex |
| @article{ingle2026adaptive, |
| title = {Adaptive Negative Reinforcement for {LLM} Reasoning: Dynamically Balancing Correction and Diversity in {RLVR}}, |
| author = {Ingle, Yash and Chauhan, Jaival and Yadav, Ankit and Mishra, Sudhakar}, |
| year = {2026} |
| } |
| ``` |
|
|
| Code: [A-NSR](https://github.com/Jaival111/Adaptive-Negative-Reinforcement) · [CW-NSR](https://github.com/Jaival111/Confidence-Weighted-NSR) |
|
|
