# Reverse Thinking Makes LLMs Stronger Reasoners

**Authors:** Justin Chih-Yao Chen, Zifeng Wang, Hamid Palangi, Rujun Han, Sayna Ebrahimi, Long Le, Vincent Perot, Swaroop Mishra, Mohit Bansal, Chen-Yu Lee, Tomas Pfister  
**arXiv:** [2411.19865](https://arxiv.org/abs/2411.19865)  
**Date:** 2024-11-29  
**Summary page:** https://www.summarizepaper.com/en/paper/2411.19865v1/

## Key points

- Reverse thinking is a crucial aspect of human reasoning, allowing individuals to approach problems from both directions.
- The Reverse-Enhanced Thinking (RevThink) framework enables Large Language Models (LLMs) to engage in reverse thinking by incorporating data augmentation and learning objectives.
- RevThink involves collecting structured forward-backward reasoning data and training the student model through multi-task learning with three objectives.
- Experimental results show that RevThink improves reasoning performance by 13.53% over zero-shot performance and 6.84% over existing knowledge distillation baselines.
- RevThink demonstrates sample efficiency by outperforming standard fine-tuning methods with only 10% of correct forward reasoning during training and exhibits strong generalization capabilities to out-of-distribution held-out datasets.

## Summary

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Reverse thinking is a crucial aspect of human reasoning, allowing individuals to approach problems from both directions - starting from the problem and working towards the solution, or starting from the solution and working backwards towards the problem. This approach greatly enhances overall reasoning performance by enabling consistency checks between forward and backward thinking processes. To enable Large Language Models (LLMs) to engage in reverse thinking, the Reverse-Enhanced Thinking (RevThink) framework was introduced. RevThink incorporates data augmentation and learning objectives to facilitate this process. In RevThink, the dataset is augmented by collecting structured forward-backward reasoning from a teacher model. This includes the original question, forward reasoning, backward question, and backward reasoning. The student model is then trained through multi-task learning with three objectives: generating forward reasoning from a question, generating a backward question from a question, and generating backward reasoning from the backward question. Experimental results across 12 datasets covering commonsense, math, and logical reasoning demonstrate an average improvement of 13.53% over the student model's zero-shot performance and a 6.84% improvement over existing knowledge distillation baselines. Notably, RevThink showcases sample efficiency as it outperforms standard fine-tuning methods trained on significantly more data by utilizing only 10% of correct forward reasoning during training. Furthermore, RevThink exhibits strong generalization capabilities to out-of-distribution held-out datasets. The method proves its effectiveness in enhancing LLMs' reasoning abilities through reverse thinking strategies.