Cumulative Reasoning with Large Language Models

Yifan Zhang; Jingqin Yang; Yang Yuan; Andrew Chi-Chih Yao

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arXiv · 2308.04371

Cumulative Reasoning with Large Language Models

Yifan Zhang·Jingqin Yang·Yang Yuan·Andrew Chi-Chih Yao

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Abstract

Recent advancements in large language models (LLMs) have shown remarkable progress, yet their ability to solve complex problems remains limited. In this work, we introduce Cumulative Reasoning (CR), a structured framework that enhances LLM problem-solving by emulating human-like iterative and cumulative thought processes. CR orchestrates LLMs in three distinct roles: Proposer, Verifier(s), and Reporter, to systematically decompose tasks, generate and validate intermediate reasoning steps, and compose them into a solution by building a dynamic Directed Acyclic Graph (DAG) of verified propositions. This approach substantially enhances problem-solving capabilities. We demonstrate CR's advantage 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 previous methods. In solving MATH problems, CR achieves a 4.2% increase from previous methods and a 43% relative improvement in the most challenging level 5 problems. When incorporating a code environment with CR, we further harness LLMs' reasoning capabilities and outperform the Program of Thought (PoT) method by 38.8%.

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Yifan Zhang, Jingqin Yang, Yang Yuan, Andrew Chi-Chih Yao. 2023-08-08. Cumulative Reasoning with Large Language Models. https://arxiv.org/abs/2308.04371

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