ClozeMath: Improving Mathematical Reasoning in Language Models by Learning to Fill Equations

TL;DR

ClozeMath is a novel fine-tuning method for large language models that enhances mathematical reasoning by training on a text-infilling task involving masked equations, inspired by human learning techniques.

Contribution

It introduces a new ClozeMath approach that improves mathematical reasoning in LLMs through a text-infilling task, outperforming previous methods on multiple benchmarks.

Findings

ClozeMath outperforms Masked Thought in accuracy and robustness.

The approach benefits from test-time decoding algorithms like Beam Search and Chain-of-Thought.

Ablation studies reveal key architectural choices impacting performance.

Abstract

The capabilities of large language models (LLMs) have been enhanced by training on data that reflects human thought processes, such as the Chain-of-Thought format. However, evidence suggests that the conventional scheme of next-word prediction may not fully capture how humans learn to think. Inspired by how humans generalize mathematical reasoning, we propose a new approach named ClozeMath to fine-tune LLMs for mathematical reasoning. Our ClozeMath involves a text-infilling task that predicts masked equations from a given solution, analogous to cloze exercises used in human learning. Experiments on GSM8K, MATH, and GSM-Symbolic show that ClozeMath surpasses the strong baseline Masked Thought in performance and robustness, with two test-time scaling decoding algorithms, Beam Search and Chain-of-Thought decoding. Additionally, we conduct an ablation study to analyze the effects of various architectural and implementation choices on our approach.