Forward-Backward Reasoning in Large Language Models for Mathematical Verification

TL;DR

This paper introduces FOBAR, a novel method combining forward and backward reasoning in large language models to improve mathematical verification, outperforming existing methods on multiple datasets.

Contribution

The paper proposes FOBAR, a new verification approach that combines forward and backward reasoning, significantly enhancing performance in mathematical tasks.

Findings

FOBAR achieves state-of-the-art results on six mathematical datasets.

Combining forward and backward reasoning outperforms self-consistency.

Backward reasoning with simple templates effectively verifies candidate answers.

Abstract

Self-Consistency samples diverse reasoning chains with answers and chooses the final answer by majority voting. It is based on forward reasoning and cannot further improve performance by sampling more reasoning chains when saturated. To further boost performance, we introduce backward reasoning to verify candidate answers. Specifically, for mathematical tasks, we mask a number in the question and ask the LLM to answer a backward question created by a simple template, i.e., to predict the masked number when a candidate answer is provided. Instead of using forward or backward reasoning alone, we propose FOBAR to combine FOrward and BAckward Reasoning for verification. Extensive experiments on six standard mathematical data sets and three LLMs show that FOBAR achieves state-of-the-art performance. In particular, FOBAR outperforms Self-Consistency, which uses forward reasoning alone, demonstrating that combining forward and forward reasoning is better. In addition, FOBAR performs better than existing verification methods, showing the effectiveness of the simple template used in backward reasoning and the proposed combination. Extensions to non-mathematical problems are also discussed and validated empirically.