# Dual Instruction Tuning with Large Language Models for Mathematical Reasoning

arXiv: https://arxiv.org/abs/2403.18295 · HTML: https://mlsanity.com/paper/2403.18295/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 42 references that are in the map.
- First posted on arXiv 27 Mar 2024.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [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)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [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)
- [Baichuan 2: Open Large-scale Language Models](https://mlsanity.com/paper/2309.10305/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [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)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2310.03731/) (2023)
- [Active Prompting with Chain-of-Thought for Large Language Models](https://mlsanity.com/paper/2302.12246/) (2023)
- [Cumulative Reasoning with Large Language Models](https://mlsanity.com/paper/2308.04371/) (2023)

## Built on by (most cited first, 10 of 10)

- [An Intelligent Agentic System for Complex Image Restoration Problems](https://mlsanity.com/paper/2410.17809/) (2024)
- [Brains vs. Bytes: Evaluating LLM Proficiency in Olympiad Mathematics](https://mlsanity.com/paper/2504.01995/) (2025)
- [IPO: Your Language Model is Secretly a Preference Classifier](https://mlsanity.com/paper/2502.16182/) (2025)
- [Grokking in LLM Pretraining? Monitor Memorization-to-Generalization without Test](https://mlsanity.com/paper/2506.21551/) (2025)
- [PuzzleWorld: A Benchmark for Multimodal, Open-Ended Reasoning in Puzzlehunts](https://mlsanity.com/paper/2506.06211/) (2025)
- [Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structures](https://mlsanity.com/paper/2411.16260/) (2024)
- [RefGrader: Automated Grading of Mathematical Competition Proofs using Agentic Workflows](https://mlsanity.com/paper/2510.09021/) (2025)
- [AirQA: A Comprehensive QA Dataset for AI Research with Instance-Level Evaluation](https://mlsanity.com/paper/2509.16952/) (2025)
- [FRoG: Evaluating Fuzzy Reasoning of Generalized Quantifiers in Large Language Models](https://mlsanity.com/paper/2407.01046/) (2024)
- [REAMS: Reasoning Enhanced Algorithm for Maths Solving](https://mlsanity.com/paper/2509.16241/) (2025)

## Abstract (arXiv)

Recent advancements highlight the success of instruction tuning with large language models (LLMs) utilizing Chain-of-Thought (CoT) data for mathematical reasoning tasks. Despite the fine-tuned LLMs, challenges persist, such as incorrect, missing, and redundant steps in CoT generation leading to inaccuracies in answer predictions. To alleviate this problem, we propose a dual instruction tuning strategy to meticulously model mathematical reasoning from both forward and reverse directions. This involves introducing the Intermediate Reasoning State Prediction task (forward reasoning) and the Instruction Reconstruction task (reverse reasoning) to enhance the LLMs' understanding and execution of instructions. Training instances for these tasks are constructed based on existing mathematical instruction tuning datasets. Subsequently, LLMs undergo multi-task fine-tuning using both existing mathematical instructions and the newly created data. Comprehensive experiments validate the effectiveness and domain generalization of the dual instruction tuning strategy across various mathematical reasoning tasks.