  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.
