# MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoning

arXiv: https://arxiv.org/abs/2310.05506 · HTML: https://mlsanity.com/paper/2310.05506/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 34 of its 40 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Placed in

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

## Builds on (most cited first, 30 of 34)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only](https://mlsanity.com/paper/2306.01116/) (2023)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [WizardCoder: Empowering Code Large Language Models with Evol-Instruct](https://mlsanity.com/paper/2306.08568/) (2023)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [A Survey of Data Augmentation Approaches for NLP](https://mlsanity.com/paper/2105.03075/) (2021)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Environment Inference for Invariant Learning](https://mlsanity.com/paper/2010.07249/) (2020)
- [Platypus: Quick, Cheap, and Powerful Refinement of LLMs](https://mlsanity.com/paper/2308.07317/) (2023)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [Solving Math Word Problems via Cooperative Reasoning induced Language Models](https://mlsanity.com/paper/2210.16257/) (2022)

## Built on by (most cited first, 30 of 45)

- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (2024)
- [Common 7B Language Models Already Possess Strong Math Capabilities](https://mlsanity.com/paper/2403.04706/) (2024)
- [Learning From Mistakes Makes LLM Better Reasoner](https://mlsanity.com/paper/2310.20689/) (2023)
- [OVM, Outcome-supervised Value Models for Planning in Mathematical Reasoning](https://mlsanity.com/paper/2311.09724/) (2023)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [Exploring the Limit of Outcome Reward for Learning Mathematical Reasoning](https://mlsanity.com/paper/2502.06781/) (2025)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [MathFusion: Enhancing Mathematical Problem-solving of LLM through Instruction Fusion](https://mlsanity.com/paper/2503.16212/) (2025)
- [Self-Training with Direct Preference Optimization Improves Chain-of-Thought Reasoning](https://mlsanity.com/paper/2407.18248/) (2024)
- [Revisit Input Perturbation Problems for LLMs: A Unified Robustness Evaluation Framework for Noisy Slot Filling Task](https://mlsanity.com/paper/2310.06504/) (2023)
- [MuMath-Code: Combining Tool-Use Large Language Models with Multi-perspective Data Augmentation for Mathematical Reasoning](https://mlsanity.com/paper/2405.07551/) (2024)
- [LEMMA: Learning from Errors for MatheMatical Advancement in LLMs](https://mlsanity.com/paper/2503.17439/) (2025)
- [Mid-Training of Large Language Models: A Survey](https://mlsanity.com/paper/2510.06826/) (2025)
- [DotaMath: Decomposition of Thought with Code Assistance and Self-correction for Mathematical Reasoning](https://mlsanity.com/paper/2407.04078/) (2024)
- [Harder Is Better: Boosting Mathematical Reasoning via Difficulty-Aware GRPO and Multi-Aspect Question Reformulation](https://mlsanity.com/paper/2601.20614/) (2026)
- [Learn Beyond The Answer: Training Language Models with Reflection for Mathematical Reasoning](https://mlsanity.com/paper/2406.12050/) (2024)
- [BEATS: Optimizing LLM Mathematical Capabilities with BackVerify and Adaptive Disambiguate based Efficient Tree Search](https://mlsanity.com/paper/2409.17972/) (2024)
- [Toward General Instruction-Following Alignment for Retrieval-Augmented Generation](https://mlsanity.com/paper/2410.09584/) (2024)
- [A Strategic Coordination Framework of Small LLMs Matches Large LLMs in Data Synthesis](https://mlsanity.com/paper/2504.12322/) (2025)
- [An Empirical Study of Data Ability Boundary in LLMs' Math Reasoning](https://mlsanity.com/paper/2403.00799/) (2024)
- [TreeSynth: Synthesizing Diverse Data from Scratch via Tree-Guided Subspace Partitioning](https://mlsanity.com/paper/2503.17195/) (2025)
- [SPARQ: Synthetic Problem Generation for Reasoning via Quality-Diversity Algorithms](https://mlsanity.com/paper/2506.06499/) (2025)
- [VCSearch: Bridging the Gap Between Well-Defined and Ill-Defined Problems in Mathematical Reasoning](https://mlsanity.com/paper/2406.05055/) (2024)
- [ScaleDiff: Scaling Difficult Problems for Advanced Mathematical Reasoning](https://mlsanity.com/paper/2509.21070/) (2025)
- [Long-Chain Reasoning Distillation via Adaptive Prefix Alignment](https://mlsanity.com/paper/2601.10064/) (2026)
- [Data Science and Technology Towards AGI Part I: Tiered Data Management](https://mlsanity.com/paper/2602.09003/) (2026)

## Abstract (arXiv)

In math reasoning with large language models (LLMs), fine-tuning data augmentation by query evolution and diverse reasoning paths is empirically verified effective, profoundly narrowing the gap between open-sourced LLMs and cutting-edge proprietary LLMs. In this paper, we conduct an investigation for such data augmentation in math reasoning and are intended to answer: (1) What strategies of data augmentation are more effective; (2) What is the scaling relationship between the amount of augmented data and model performance; and (3) Can data augmentation incentivize generalization to out-of-domain mathematical reasoning tasks? To this end, we create two new dataset AugGSM8K and AugMATH, by complicating and diversifying the queries and sampling multiple reasoning paths from GSM8K and MATH. We obtained a series of LLMs called MuggleMath by fine-tuning LLaMA models on AugGSM8K and AugMATH. MuggleMath substantially achieves new state-of-the-art on GSM8K and MATH. A log-linear relationship and a segmented log-linear are presented between MuggleMath's performance and the amount of augmented data on GSM8K and MATH, respectively. We also find that it is weak in out-of-domain math reasoning generalization from AugGSM8K to MATH and from AugMATH to GSM8K, which suggests that augmenting queries that cover a broader range of subjects is more beneficial for generalization. We release our codes and augmented data in https://github.com/OFA-Sys/gsm8k-ScRel.