README.md

metadata

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.

{
  "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:

@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}}
}