| --- |
| license: mit |
| task_categories: |
| - text-generation |
| - question-answering |
| language: |
| - en |
| tags: |
| - math |
| - synthetic |
| - programmatic |
| - sympy |
| - reasoning |
| - instruction-tuning |
| - error-correction |
| - self-verification |
| - latex |
| - word-problems |
| pretty_name: Math-HQ-10k |
| --- |
| |
| # Dataset Card for Math-HQ-10k |
|
|
| ## Dataset Description |
|
|
| **Math-HQ-10k** is a high-quality, synthetic, programmatic math instruction dataset designed to train large language models on mathematical reasoning, problem solving, and self-correction. |
|
|
| The dataset mixes symbolic/LaTeX-style math problems and plain-language word problems. Ground-truth computations were generated and verified programmatically with SymPy (`v1.14.0`) to reduce arithmetic and algebraic errors in the targets. |
|
|
| - **Curated by:** x0root |
| - **Language(s):** English |
| - **License:** MIT |
| - **Format:** JSONL |
| - **Total Examples:** 10,000 |
| - **Unique problem IDs:** 4,995 |
|
|
| ## Dataset Structure |
|
|
| ### Data Instances |
|
|
| Each row in the dataset corresponds to a specific instruction style applied to a mathematical problem. |
|
|
| ```json |
| { |
| "id": "5073fa55b1444226", |
| "problem_id": "14378efbde3f5230", |
| "style": "concise", |
| "instruction": "Solve with minimal but sufficient steps, then provide the final answer.", |
| "input": "Solve the quadratic equation over the real numbers:\n$x^{2} + \\frac{7 x}{3} - 2$ = 0.", |
| "output": "Identify coefficients a, b, c in ax^2+bx+c=0.\nHere a=$1$, b=$\\frac{7}{3}$, c=$-2$.\nCompute the discriminant Δ=b^2−4ac.\nFinal answer: $x \\in \\{\\frac{2}{3}, -3\\}$", |
| "final_answer": "x \\in \\{\\frac{2}{3}, -3\\}", |
| "metadata": { |
| "format": "symbolic", |
| "domain": "algebra", |
| "topic": "quadratic_equation", |
| "difficulty": 3, |
| "verified": true, |
| "source": "synthetic_v3_open", |
| "sympy_version": "1.14.0" |
| } |
| } |
| ``` |
|
|
| ### Data Fields |
|
|
| * `id` *(string)*: Identifier for the prompt-completion pair. In this raw export, some `id` values repeat because there are repeated rows. |
| * `problem_id` *(string)*: Shared identifier for the base mathematical problem. Use this to group style variants of the same problem. |
| * `style` *(string)*: The response style requested, such as `tutor`, `concise`, `verifier`, `answer_only`, or `verifier_negative`. |
| * `instruction` *(string)*: The instruction that defines the desired response behavior. |
| * `input` *(string)*: The math problem, either in LaTeX-heavy form or plain-language word-problem form. |
| * `output` *(string)*: The target response. |
| * `final_answer` *(string)*: The answer extracted for evaluation. |
| * `metadata` *(dictionary)*: |
| * `format`: Output format type, currently `symbolic` or `word`. |
| * `domain`: Broad mathematical field such as `algebra`, `calculus`, `arithmetic`, `discrete`, or `probability`. |
| * `topic`: More specific problem type, such as `quadratic_equation`, `derivative`, or `mixture`. |
| * `difficulty`: Integer from 1 to 5. |
| * `verified`: Boolean indicating deterministic verification. |
| * `source`: Generator source. |
| * `sympy_version`: SymPy version used for validation. |
|
|
| ## Key Features & Supported Tasks |
|
|
| ### 1. Error Localization (`verifier_negative`) |
| The dataset includes negative examples where a model must identify the first incorrect step in a flawed solution, explain the error, and give the corrected reasoning. |
| |
| ### 2. Multi-Style Instruction Tuning |
| The same base problem is represented with multiple response styles: |
| * `tutor`: detailed, pedagogical solutions |
| * `concise`: minimal but sufficient derivations |
| * `verifier`: solutions with explicit checks |
| * `answer_only`: final-answer-focused responses |
| * `verifier_negative`: critique and correction examples |
|
|
| ### 3. Curriculum Learning Metadata |
| Every row includes `domain`, `topic`, and `difficulty`, which makes the dataset useful for curriculum learning and difficulty-based sampling. |
|
|
| ## Dataset Creation |
|
|
| The data was generated using a structured synthetic pipeline (`synthetic_v3_open`). Problems and target solutions were derived and verified programmatically with SymPy to reduce hallucinated arithmetic and algebraic mistakes. |
|
|
| ## Considerations for Using the Data |
|
|
| * The raw export contains repeated rows, so deduplication is recommended before training or evaluation if you need strict uniqueness. |
| * Split train/test sets by `problem_id` to avoid leakage across different style variants of the same problem. |
| * The dataset contains both symbolic/LaTeX-style inputs and plain-language word problems, so the tokenizer and preprocessing pipeline should handle both. |
|
|
| ## Citation |
|
|
| If you use this dataset in your research or for training models, please cite: |
|
|
| ```bibtex |
| @misc{MathHQ10k, |
| author = {x0root}, |
| title = {Math-HQ-10k: Programmatic Math Instruction Dataset}, |
| year = {2026}, |
| publisher = {Hugging Face}, |
| journal = {Hugging Face repository}, |
| howpublished = {\url{https://huggingface.co/datasets/x0root/math-hq-10k}} |
| } |
| ``` |
