# Learn Beyond The Answer: Training Language Models with Reflection for Mathematical Reasoning

arXiv: https://arxiv.org/abs/2406.12050 · HTML: https://mlsanity.com/paper/2406.12050/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 38 of its 64 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## Placed in

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

## Builds on (most cited first, 30 of 38)

- [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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [WizardCoder: Empowering Code Large Language Models with Evol-Instruct](https://mlsanity.com/paper/2306.08568/) (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)
- [StarCoder 2 and The Stack v2: The Next Generation](https://mlsanity.com/paper/2402.19173/) (2024)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [MINT: Evaluating LLMs in Multi-turn Interaction with Tools and Language Feedback](https://mlsanity.com/paper/2309.10691/) (2023)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [Magicoder: Empowering Code Generation with OSS-Instruct](https://mlsanity.com/paper/2312.02120/) (2023)
- [Iterative Reasoning Preference Optimization](https://mlsanity.com/paper/2404.19733/) (2024)
- [Advancing LLM Reasoning Generalists with Preference Trees](https://mlsanity.com/paper/2404.02078/) (2024)
- [MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2310.03731/) (2023)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (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)
- [MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs](https://mlsanity.com/paper/2402.16352/) (2024)
- [Augmenting Math Word Problems via Iterative Question Composing](https://mlsanity.com/paper/2401.09003/) (2024)

## Built on by (most cited first, 15 of 15)

- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [A Survey of Test-Time Compute: From Intuitive Inference to Deliberate Reasoning](https://mlsanity.com/paper/2501.02497/) (2025)
- [Large Language Models for Planning: A Comprehensive and Systematic Survey](https://mlsanity.com/paper/2505.19683/) (2025)
- [MathFusion: Enhancing Mathematical Problem-solving of LLM through Instruction Fusion](https://mlsanity.com/paper/2503.16212/) (2025)
- [MultiChartQA: Benchmarking Vision-Language Models on Multi-Chart Problems](https://mlsanity.com/paper/2410.14179/) (2024)
- [LEMMA: Learning from Errors for MatheMatical Advancement in LLMs](https://mlsanity.com/paper/2503.17439/) (2025)
- [Can Pruning Improve Reasoning? Revisiting Long-CoT Compression with Capability in Mind for Better Reasoning](https://mlsanity.com/paper/2505.14582/) (2025)
- [Reasoning Beyond Limits: Advances and Open Problems for LLMs](https://mlsanity.com/paper/2503.22732/) (2025)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [A Review of Incorporating Psychological Theories in LLMs](https://mlsanity.com/paper/2505.00003/) (2025)
- [Scaling Test-Time Inference with Policy-Optimized, Dynamic Retrieval-Augmented Generation via KV Caching and Decoding](https://mlsanity.com/paper/2504.01281/) (2025)
- [Self-Verifying Reflection Helps Transformers with CoT Reasoning](https://mlsanity.com/paper/2510.12157/) (2025)
- [From Static to Dynamic: Adaptive Monte Carlo Search for Mathematical Process Supervision](https://mlsanity.com/paper/2509.24351/) (2025)
- [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026)

## Abstract (arXiv)

Supervised fine-tuning enhances the problem-solving abilities of language models across various mathematical reasoning tasks. To maximize such benefits, existing research focuses on broadening the training set with various data augmentation techniques, which is effective for standard single-round question-answering settings. Our work introduces a novel technique aimed at cultivating a deeper understanding of the training problems at hand, enhancing performance not only in standard settings but also in more complex scenarios that require reflective thinking. Specifically, we propose reflective augmentation, a method that embeds problem reflection into each training instance. It trains the model to consider alternative perspectives and engage with abstractions and analogies, thereby fostering a thorough comprehension through reflective reasoning. Extensive experiments validate the achievement of our aim, underscoring the unique advantages of our method and its complementary nature relative to existing augmentation techniques.