# LLM Reasoning Engine: Specialized Training for Enhanced Mathematical Reasoning

arXiv: https://arxiv.org/abs/2412.20227 · HTML: https://mlsanity.com/paper/2412.20227/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 28 Dec 2024.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [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)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [No Language Left Behind: Scaling Human-Centered Machine Translation](https://mlsanity.com/paper/2207.04672/) (2022)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [MEDITRON-70B: Scaling Medical Pretraining for Large Language Models](https://mlsanity.com/paper/2311.16079/) (2023)
- [SeamlessM4T: Massively Multilingual & Multimodal Machine Translation](https://mlsanity.com/paper/2308.11596/) (2023)
- [Mixture-of-Experts Meets Instruction Tuning:A Winning Combination for Large Language Models](https://mlsanity.com/paper/2305.14705/) (2023)
- [Improving Large Language Model Fine-tuning for Solving Math Problems](https://mlsanity.com/paper/2310.10047/) (2023)
- [Practice Makes a Solver Perfect: Data Augmentation for Math Word Problem Solvers](https://mlsanity.com/paper/2205.00177/) (2022)

## Built on by (most cited first, 2 of 2)

- [Improved LLM Agents for Financial Document Question Answering](https://mlsanity.com/paper/2506.08726/) (2025)
- [Exploring Solution Divergence and Its Effect on Large Language Model Problem Solving](https://mlsanity.com/paper/2509.22480/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical reasoning skills. Existing approaches to address this challenge often rely on ensemble methods and suffer from the problem of data scarcity in target domains. In this work, we present a novel method to enhance LLMs' capabilities in mathematical reasoning tasks. Motivated by the need to bridge this gap, our approach incorporates a question paraphrase strategy, which aims at diversifying the linguistic forms of mathematical questions to improve generalization. Additionally, specialized training objectives are employed to guide the model's learning process, focusing on enhancing its understanding of mathematical concepts and reasoning processes. We conduct experiments on four datasets using different LLMs, and demonstrate the effectiveness of our approach in improving LLMs' performance on mathematical reasoning tasks. Our findings underscore the significance of our methodology in the advancement of large language models and its potential implications for real-world applications that require mathematical reasoning abilities.