Neuro-Symbolic Data Generation for Math Reasoning

TL;DR

This paper introduces a neuro-symbolic method for generating high-quality mathematical datasets to improve LLM reasoning, showing that realigning models with this data enhances their performance.

Contribution

The paper presents a novel neuro-symbolic framework for automated math data generation that improves LLM reasoning capabilities by augmenting training data.

Findings

Generated datasets are high-quality and diverse.

Realigned LLMs outperform state-of-the-art models.

Method effectively combines informalization and symbolic reasoning.

Abstract

A critical question about Large Language Models (LLMs) is whether their apparent deficiency in mathematical reasoning is inherent, or merely a result of insufficient exposure to high-quality mathematical data. To explore this, we developed an automated method for generating high-quality, supervised mathematical datasets. The method carefully mutates existing math problems, ensuring both diversity and validity of the newly generated problems. This is achieved by a neuro-symbolic data generation framework combining the intuitive informalization strengths of LLMs, and the precise symbolic reasoning of math solvers along with projected Markov chain Monte Carlo sampling in the highly-irregular symbolic space. Empirical experiments demonstrate the high quality of data generated by the proposed method, and that the LLMs, specifically LLaMA-2 and Mistral, when realigned with the generated data, surpass their state-of-the-art counterparts.