Cumulative Reasoning with Large Language Models

• URL: http://arxiv.org/abs/2308.04371v6
• Date: Tue, 2 Apr 2024 03:37:39 GMT
• Title: Cumulative Reasoning with Large Language Models
• Authors: Yifan Zhang, Jingqin Yang, Yang Yuan, Andrew Chi-Chih Yao,
• Abstract summary: Cumulative Reasoning (CR) is a novel approach that utilizes language models cumulatively and iteratively. We demonstrate CR's superiority through several complex reasoning tasks. CR sets new state-of-the-art on the MATH dataset.
• Score: 12.267474250936123
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Despite the recent advancements in language models (LMs), their ability to solve complex problems remains limited. This paper introduces Cumulative Reasoning (CR), a novel approach that utilizes LMs cumulatively and iteratively, mirroring human thought processes for problem-solving. CR decomposes tasks into smaller, manageable components and leverages previous propositions for effective composition, significantly enhancing problem-solving capabilities. We demonstrate CR's superiority through several complex reasoning tasks: it outperforms existing methods in logical inference tasks with up to a 9.3% improvement, achieving 98.04% accuracy on the curated FOLIO wiki dataset. In the Game of 24, it achieves 98% accuracy, marking a 24% improvement over the prior state-of-the-art. Additionally, CR sets new state-of-the-art on the MATH dataset, achieving a 4.2% increase from previous methods and a 43% relative improvement in the most challenging problems. By extending CR to incorporate a code environment without external aids like retrieval or web browsing, we further harness the computational and logical reasoning capabilities of LMs, achieving a remarkable 72.2% accuracy on the MATH dataset and outperforming the PAL/PoT method by 38.8%. Our work not only sets new state-of-the-art but also paves the way toward more sophisticated AI reasoning methods. The code is available at https://github.com/iiis-ai/cumulative-reasoning.

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