# Exploring the Mystery of Influential Data for Mathematical Reasoning

arXiv: https://arxiv.org/abs/2404.01067 · HTML: https://mlsanity.com/paper/2404.01067/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 60 references that are in the map.
- First posted on arXiv 1 Apr 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 25 of 25)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [How Abilities in Large Language Models are Affected by Supervised Fine-tuning Data Composition](https://mlsanity.com/paper/2310.05492/) (2023)
- [Why Can GPT Learn In-Context? Language Models Implicitly Perform Gradient Descent as Meta-Optimizers](https://mlsanity.com/paper/2212.10559/) (2022)
- [Platypus: Quick, Cheap, and Powerful Refinement of LLMs](https://mlsanity.com/paper/2308.07317/) (2023)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset](https://mlsanity.com/paper/2402.10176/) (2024)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (2024)
- [#InsTag: Instruction Tagging for Analyzing Supervised Fine-tuning of Large Language Models](https://mlsanity.com/paper/2308.07074/) (2023)
- [MoDS: Model-oriented Data Selection for Instruction Tuning](https://mlsanity.com/paper/2311.15653/) (2023)
- [Solving Math Word Problems via Cooperative Reasoning induced Language Models](https://mlsanity.com/paper/2210.16257/) (2022)
- [Augmenting Math Word Problems via Iterative Question Composing](https://mlsanity.com/paper/2401.09003/) (2024)
- [Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning](https://mlsanity.com/paper/2403.02333/) (2024)
- [Self-Evolved Diverse Data Sampling for Efficient Instruction Tuning](https://mlsanity.com/paper/2311.08182/) (2023)
- [Do Emergent Abilities Exist in Quantized Large Language Models: An Empirical Study](https://mlsanity.com/paper/2307.08072/) (2023)
- [One-Shot Learning as Instruction Data Prospector for Large Language Models](https://mlsanity.com/paper/2312.10302/) (2023)

## Built on by (most cited first, 13 of 13)

- [Rho-1: Not All Tokens Are What You Need](https://mlsanity.com/paper/2404.07965/) (2024)
- [What is Wrong with Perplexity for Long-context Language Modeling?](https://mlsanity.com/paper/2410.23771/) (2024)
- [Unlocking Multimodal Mathematical Reasoning via Process Reward Model](https://mlsanity.com/paper/2501.04686/) (2025)
- [JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models](https://mlsanity.com/paper/2405.14365/) (2024)
- [Prismatic Synthesis: Gradient-based Data Diversification Boosts Generalization in LLM Reasoning](https://mlsanity.com/paper/2505.20161/) (2025)
- [Skywork-Math: Data Scaling Laws for Mathematical Reasoning in Large Language Models -- The Story Goes On](https://mlsanity.com/paper/2407.08348/) (2024)
- [CodeACT: Code Adaptive Compute-efficient Tuning Framework for Code LLMs](https://mlsanity.com/paper/2408.02193/) (2024)
- [How Do Your Code LLMs Perform? Empowering Code Instruction Tuning with High-Quality Data](https://mlsanity.com/paper/2409.03810/) (2024)
- [Skill-Targeted Adaptive Training](https://mlsanity.com/paper/2510.10023/) (2025)
- [Your Language Model May Think Too Rigidly: Achieving Reasoning Consistency with Symmetry-Enhanced Training](https://mlsanity.com/paper/2502.17800/) (2025)
- [Rethinking Personalization in Large Language Models at the Token Level](https://mlsanity.com/paper/2603.06595/) (2026)
- [Mind the Gap: Bridging Thought Leap for Improved Chain-of-Thought Tuning](https://mlsanity.com/paper/2505.14684/) (2025)
- [On Representation Redundancy in Large-Scale Instruction Tuning Data Selection](https://mlsanity.com/paper/2602.13773/) (2026)

## Abstract (arXiv)

Selecting influential data for fine-tuning on downstream tasks is a key factor for both performance and computation efficiency. Recent works have shown that training with only limited data can show a superior performance on general tasks. However, the feasibility on mathematical reasoning tasks has not been validated. To go further, there exist two open questions for mathematical reasoning: how to select influential data and what is an influential data composition. For the former one, we propose a Quality-aware Diverse Selection (QaDS) strategy adaptable for mathematical reasoning. A comparison with other selection strategies validates the superiority of QaDS. For the latter one, we first enlarge our setting and explore the influential data composition. We conduct a series of experiments and highlight: scaling up reasoning data, and training with general data selected by QaDS is helpful. Then, we define our optimal mixture as OpenMathMix, an influential data mixture with open-source data selected by QaDS. With OpenMathMix, we achieve a state-of-the-art 48.8% accuracy on MATH with 7B base model. Additionally, we showcase the use of QaDS in creating efficient fine-tuning mixtures with various selection ratios, and analyze the quality of a wide range of open-source datasets, which can perform as a reference for future works on mathematical reasoning tasks.