---
title: "Cumulative Reasoning with Large Language Models (2023)"
description: "The authors propose Cumulative Reasoning (CR), which uses role-specific… 98.04% accuracy. 72 references, cited by 62 papers here."
authors: ["Yifan Zhang", "Jingqin Yang", "Yang Yuan", "Andrew Chi-Chih Yao"]
year: 2023
venue: "arXiv:2308.04371"
source: "https://arxiv.org/abs/2308.04371"
doi: "10.48550/arxiv.2308.04371"
arxiv: "2308.04371"
licence: "arXiv — non-exclusive license to distribute"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/zhang-2023-cumulative-reasoning-large-language-models/"
---
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# Cumulative Reasoning with Large Language Models

**Authors:** [Yifan Zhang](https://md.research.elamur.ai/free/en/authors/yifan-zhang/), Jingqin Yang, Yang Yuan and [Andrew Chi-Chih Yao](https://md.research.elamur.ai/free/en/authors/andrew-chi-chih-yao/) · **Year:** 2023 · **Venue:** arXiv:2308.04371 · **Licence:** [arXiv — non-exclusive license to distribute](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2308.04371) · [PDF](https://arxiv.org/pdf/2308.04371) · [DOI 10.48550/arxiv.2308.04371](https://doi.org/10.48550/arxiv.2308.04371) · [arXiv 2308.04371](https://arxiv.org/abs/2308.04371) · [OpenAlex](https://openalex.org/W4385774107)

**Citations:** 12 citations (OpenAlex, 2026-10-14) · [62](https://md.research.elamur.ai/free/en/papers/zhang-2023-cumulative-reasoning-large-language-models/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Large language models still struggle with tasks that require long, rigorous, multi-step deduction. Existing prompting schemes such as Chain-of-Thought and Tree-of-Thought either follow one fragile path or explore separate branches without combining everything they have confirmed. The authors propose Cumulative Reasoning (CR), which uses role-specific prompts to give an LLM three jobs. A Proposer suggests the next intermediate statement. One or more Verifiers accept or reject it, using either another LLM call or a tool such as a Python interpreter or a theorem prover. A Reporter judges when enough has been established to produce the answer. Each accepted statement becomes a node in a directed acyclic graph (DAG), so a new step can build on any combination of earlier verified facts. CR was tested on logical inference (FOLIO wiki, AutoTNLI), the Game of 24 and the MATH benchmark, and it outperformed earlier prompting methods on all of them. The work matters because separating generation from checking, while pooling verified knowledge, improves LLM reasoning without any extra training.

## Key points
- On logical inference, CR gains up to 9.3% over prior methods and reaches 98.04% accuracy on a curated version of FOLIO wiki.
- In the Game of 24, CR solves 98% of puzzles. That is 24% better than Tree-of-Thought (ToT), while visiting only about a quarter as many search states.
- On MATH without external tools, CR improves on Complex CoT and Progressive-Hint Prompting by 4.2%. On the hardest level 5 problems, accuracy rises from 22.4% to 32.1%, a 43% relative gain.
- With a Python code environment as the Verifier and no retrieval, CR reaches 72.2% on MATH. This is a 38.8% relative improvement over Program of Thought (PoT) and PAL.
- Code and prompts are available at github.com/iiis-ai/cumulative-reasoning. The paper is published in Transactions on Machine Learning Research.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Tsinghua University](https://md.research.elamur.ai/free/en/universities/tsinghua-university/) — University, Beijing, China · 415 works · 94,028 citations
- [Shanghai Qi Zhi Institute](https://md.research.elamur.ai/free/en/labs/shanghai-qi-zhi-institute/) — Research institute, Shanghai, China · 7 works · 3,082 citations

📚 Shelves (4): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 18,614 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 17,965 works · [🎭 Arts and Humanities](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/) · 17,450 works · [🗣️ Language and Linguistics](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/language-and-linguistics/) · 17,296 works

🧭 Topics (1): [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,685 works

## Cite

Cite as: Yifan Zhang, Jingqin Yang, Yang Yuan and Andrew Chi-Chih Yao. 2023. Cumulative Reasoning with Large Language Models. arXiv:2308.04371.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{zhang2023cumulative,
  title = {{Cumulative Reasoning with Large Language Models}},
  author = {Yifan Zhang, Jingqin Yang, Yang Yuan and Andrew Chi-Chih Yao},
  year = {2023},
  doi = {10.48550/arxiv.2308.04371},
  eprint = {2308.04371},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2308.04371}
}
```

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*Updated 2 November 2026*