# MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipeline

arXiv: https://arxiv.org/abs/2401.08190 · HTML: https://mlsanity.com/paper/2401.08190/

## Key facts

- Cited by 81 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 35 of its 42 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Placed in

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

## Builds on (most cited first, 30 of 35)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [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)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (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)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [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)
- [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)
- [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)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [ZeRO-Infinity: Breaking the GPU Memory Wall for Extreme Scale Deep Learning](https://mlsanity.com/paper/2104.07857/) (2021)
- [Specializing Smaller Language Models towards Multi-Step Reasoning](https://mlsanity.com/paper/2301.12726/) (2023)
- [Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification](https://mlsanity.com/paper/2308.07921/) (2023)

## Built on by (most cited first, 30 of 81)

- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [ToolRL: Reward is All Tool Learning Needs](https://mlsanity.com/paper/2504.13958/) (2025)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [ToRL: Scaling Tool-Integrated RL](https://mlsanity.com/paper/2503.23383/) (2025)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)
- [OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset](https://mlsanity.com/paper/2402.10176/) (2024)
- [Reward-Guided Speculative Decoding for Efficient LLM Reasoning](https://mlsanity.com/paper/2501.19324/) (2025)
- [DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving](https://mlsanity.com/paper/2407.13690/) (2024)
- [LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning](https://mlsanity.com/paper/2410.02884/) (2024)
- [AceMath: Advancing Frontier Math Reasoning with Post-Training and Reward Modeling](https://mlsanity.com/paper/2412.15084/) (2024)
- [Step-level Value Preference Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2406.10858/) (2024)
- [Ego-R1: Chain-of-Tool-Thought for Ultra-Long Egocentric Video Reasoning](https://mlsanity.com/paper/2506.13654/) (2025)
- [ReasonFlux: Hierarchical LLM Reasoning via Scaling Thought Templates](https://mlsanity.com/paper/2502.06772/) (2025)
- [Visual Agentic Reinforcement Fine-Tuning](https://mlsanity.com/paper/2505.14246/) (2025)
- [Code to Think, Think to Code: A Survey on Code-Enhanced Reasoning and Reasoning-Driven Code Intelligence in LLMs](https://mlsanity.com/paper/2502.19411/) (2025)
- [Scaling Laws of Synthetic Data for Language Models](https://mlsanity.com/paper/2503.19551/) (2025)
- [JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models](https://mlsanity.com/paper/2405.14365/) (2024)
- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [MathCoder2: Better Math Reasoning from Continued Pretraining on Model-translated Mathematical Code](https://mlsanity.com/paper/2410.08196/) (2024)
- [S2R: Teaching LLMs to Self-verify and Self-correct via Reinforcement Learning](https://mlsanity.com/paper/2502.12853/) (2025)
- [Demystifying Reinforcement Learning in Agentic Reasoning](https://mlsanity.com/paper/2510.11701/) (2025)
- [To Code or not to Code? Adaptive Tool Integration for Math Language Models via Expectation-Maximization](https://mlsanity.com/paper/2502.00691/) (2025)
- [Process-based Self-Rewarding Language Models](https://mlsanity.com/paper/2503.03746/) (2025)
- [An LLM Agent for Automatic Geospatial Data Analysis](https://mlsanity.com/paper/2410.18792/) (2024)
- [SCRIBE: Structured Mid-Level Supervision for Tool-Using Language Models](https://mlsanity.com/paper/2601.03555/) (2026)
- [Markov Chain of Thought for Efficient Mathematical Reasoning](https://mlsanity.com/paper/2410.17635/) (2024)

## Abstract (arXiv)

Large language models (LLMs) have seen considerable advancements in natural language understanding tasks, yet there remains a gap to bridge before attaining true artificial general intelligence, especially concerning shortcomings in mathematical reasoning capabilities. We postulate that the inherent nature of LLM training, which focuses on predicting probabilities of next token, presents challenges in effectively modeling mathematical reasoning that demands exact calculations, both from data-driven and theoretical standpoints. In this paper, we address this challenge by enriching the data landscape and introducing a novel math dataset, enhanced with a capability to utilize a Python code interpreter. This dataset is derived from GSM8K and MATH and has been further refined through a combination of GPT-4 annotations, human review, and self-training processes, where the errors in the original GSM8K training set have been fixed. Additionally, we propose a tentative, easily replicable protocol for the fine-tuning of math-specific LLMs, which has led to a significant improvement in the performance of a 7B-parameter LLM on the GSM8K and MATH datasets. We are committed to advancing the field of mathematical reasoning in LLMs and, to that end, we have made source code for data generation / training / inference, and the model checkpoints publicly available at urlhttps://github.com/MARIO-Math-Reasoning/MARIO. We hope this will facilitate further research and development within the community.