# RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library

arXiv: https://arxiv.org/abs/2504.20426 · HTML: https://mlsanity.com/paper/2504.20426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 30 of its 33 references that are in the map.
- First posted on arXiv 29 Apr 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

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

- [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)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (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)
- [MAmmoTH2: Scaling Instructions from the Web](https://mlsanity.com/paper/2405.03548/) (2024)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset](https://mlsanity.com/paper/2402.10176/) (2024)
- [Common 7B Language Models Already Possess Strong Math Capabilities](https://mlsanity.com/paper/2403.04706/) (2024)
- [Synthetic Data (Almost) from Scratch: Generalized Instruction Tuning for Language Models](https://mlsanity.com/paper/2402.13064/) (2024)
- [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)
- [Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning](https://mlsanity.com/paper/2403.02333/) (2024)
- [MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoning](https://mlsanity.com/paper/2310.05506/) (2023)
- [JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models](https://mlsanity.com/paper/2405.14365/) (2024)
- [MUSTARD: Mastering Uniform Synthesis of Theorem and Proof Data](https://mlsanity.com/paper/2402.08957/) (2024)
- [AI-Assisted Generation of Difficult Math Questions](https://mlsanity.com/paper/2407.21009/) (2024)
- [Unlocking Reasoning Potential in Large Langauge Models by Scaling Code-form Planning](https://mlsanity.com/paper/2409.12452/) (2024)
- [From Good to Great: Improving Math Reasoning with Tool-Augmented Interleaf Prompting](https://mlsanity.com/paper/2401.05384/) (2023)
- [ControlMath: Controllable Data Generation Promotes Math Generalist Models](https://mlsanity.com/paper/2409.15376/) (2024)

## Built on by (most cited first, 1 of 1)

- [DESIGNER: Design-Logic-Guided Multidisciplinary Data Synthesis for LLM Reasoning](https://mlsanity.com/paper/2508.12726/) (2025)

## Abstract (arXiv)

The advancement of reasoning capabilities in Large Language Models (LLMs) requires substantial amounts of high-quality reasoning data, particularly in mathematics. Existing data synthesis methods, such as data augmentation from annotated training sets or direct question generation based on relevant knowledge points and documents, have expanded datasets but face challenges in mastering the inner logic of the problem during generation and ensuring the verifiability of the solutions. To address these issues, we propose RV-Syn, a novel Rational and Verifiable mathematical Synthesis approach. RV-Syn constructs a structured mathematical operation function library based on initial seed problems and generates computational graphs as solutions by combining Python-formatted functions from this library. These graphs are then back-translated into complex problems. Based on the constructed computation graph, we achieve solution-guided logic-aware problem generation. Furthermore, the executability of the computational graph ensures the verifiability of the solving process. Experimental results show that RV-Syn surpasses existing synthesis methods, including those involving human-generated problems, achieving greater efficient data scaling. This approach provides a scalable framework for generating high-quality reasoning datasets.