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Training and Evaluating Language Models with Template-based Data Generation

Yifan Zhang

TL;DR

The paper tackles the data scarcity hindering mathematical reasoning in large language models by introducing Template-based Data Generation (TDG), which uses GPT-4 to author meta-templates and automatically instantiate verifiable problems and solutions. It proposes a robust pipeline where problems are generated, programmatically verified through sandboxed code execution, and rewarded via Reinforcement Learning with Verifiable Rewards (RLVR). The authors present TemplateGSM, a massive dataset of over 7 million math problems with code-based and natural-language solutions, publicly available for training, evaluation, and alignment research. This approach provides a scalable, objective pathway to improve reasoning capabilities and offers a generalizable blueprint for applying template-based data generation and verification to other reasoning-intensive domains.

Abstract

The rapid advancement of large language models (LLMs) such as GPT-3, PaLM, and Llama has significantly transformed natural language processing, showcasing remarkable capabilities in understanding and generating language. However, a fundamental bottleneck persists: these models often struggle with tasks requiring complex, multi-step reasoning, particularly in mathematical problem-solving. This deficiency stems from the critical scarcity of large-scale, high-quality, domain-specific datasets necessary for cultivating sophisticated reasoning abilities. To overcome this challenge, we introduce Template-based Data Generation (TDG), a novel and scalable paradigm that harnesses frontier LLMs (GPT-4) to automatically generate parameterized meta-templates, which in turn synthesize a virtually infinite stream of high-quality problems and solutions. Using this paradigm, we create TemplateMath Part I: TemplateGSM, a foundational dataset of over 7 million synthetically generated grade school math problems. Each problem is accompanied by a programmatically verifiable solution, offering an unprecedented level of quality at scale. This resource not only resolves the data scarcity issue for supervised fine-tuning but also provides a robust mechanism for model alignment through Reinforcement Learning with Verifiable Rewards (RLVR). Our approach elevates data augmentation by leveraging GPT-4 to generate meta-templates, ensuring diverse and complex problem structures. By providing a scalable solution to the data and verification bottleneck, TDG and TemplateGSM pave the way for a new generation of LLMs with powerful, reliable reasoning skills. Project Page: https://github.com/iiis-ai/TemplateMath

Training and Evaluating Language Models with Template-based Data Generation

TL;DR

The paper tackles the data scarcity hindering mathematical reasoning in large language models by introducing Template-based Data Generation (TDG), which uses GPT-4 to author meta-templates and automatically instantiate verifiable problems and solutions. It proposes a robust pipeline where problems are generated, programmatically verified through sandboxed code execution, and rewarded via Reinforcement Learning with Verifiable Rewards (RLVR). The authors present TemplateGSM, a massive dataset of over 7 million math problems with code-based and natural-language solutions, publicly available for training, evaluation, and alignment research. This approach provides a scalable, objective pathway to improve reasoning capabilities and offers a generalizable blueprint for applying template-based data generation and verification to other reasoning-intensive domains.

Abstract

The rapid advancement of large language models (LLMs) such as GPT-3, PaLM, and Llama has significantly transformed natural language processing, showcasing remarkable capabilities in understanding and generating language. However, a fundamental bottleneck persists: these models often struggle with tasks requiring complex, multi-step reasoning, particularly in mathematical problem-solving. This deficiency stems from the critical scarcity of large-scale, high-quality, domain-specific datasets necessary for cultivating sophisticated reasoning abilities. To overcome this challenge, we introduce Template-based Data Generation (TDG), a novel and scalable paradigm that harnesses frontier LLMs (GPT-4) to automatically generate parameterized meta-templates, which in turn synthesize a virtually infinite stream of high-quality problems and solutions. Using this paradigm, we create TemplateMath Part I: TemplateGSM, a foundational dataset of over 7 million synthetically generated grade school math problems. Each problem is accompanied by a programmatically verifiable solution, offering an unprecedented level of quality at scale. This resource not only resolves the data scarcity issue for supervised fine-tuning but also provides a robust mechanism for model alignment through Reinforcement Learning with Verifiable Rewards (RLVR). Our approach elevates data augmentation by leveraging GPT-4 to generate meta-templates, ensuring diverse and complex problem structures. By providing a scalable solution to the data and verification bottleneck, TDG and TemplateGSM pave the way for a new generation of LLMs with powerful, reliable reasoning skills. Project Page: https://github.com/iiis-ai/TemplateMath

Paper Structure

This paper contains 18 sections, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Template-based Data Generation
  3. Methodology
  4. Generation of Meta-Templates with LLMs
  5. Generation with Integrated Verification and Verifiable Rewards
  6. Process Flowchart
  7. Code Implementation Example
  8. Generated Problem and Solution Example
  9. Advantages of TDG
  10. TemplateMath Part I: TemplateGSM Dataset
  11. Dataset Construction
  12. Dataset Statistics
  13. Dataset Availability
  14. Related Work
  15. Mathematical Datasets.
  16. ...and 3 more sections

Figures (2)

  • Figure 1: Flowchart illustrating the Template-based Data Generation (TDG) process. An LLM generates meta-templates, which are instantiated into Q&A pairs. These pairs undergo programmatic verification. The binary outcome (pass/fail) serves as both a quality filter and a verifiable reward signal.
  • Figure 2: An example of our TDG method. The code demonstrates how variable parameters are used to generate unique problem statements and corresponding solutions based on GPT-4-generated meta-templates, with integrated verification via code execution.