x0root/math-hq-10k

---
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}}
}
```