Cumulative Reasoning with Large Language Models

August 2, 2025 · View on GitHub

This is the official implementation for the paper "Cumulative Reasoning with Large Language Models", published in Transactions on Machine Learning Research (TMLR).

Cumulative Reasoning (CR) is 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, validate intermediate steps, and compose them into a final solution.

🚀 Key Achievements

CR demonstrates state-of-the-art performance across multiple complex reasoning benchmarks:

Game of 24: Achieves 98% accuracy, a +24% absolute improvement over Tree-of-Thoughts (ToT).
MATH Dataset (No Code Interpreter): Attains 58% accuracy with GPT-4, outperforming Progressive-Hint Prompting (PHP) by +4.2%.
MATH Dataset (Hardest Problems): Shows a 43% relative improvement on Level 5 problems (from 22.4% to 32.1%).
MATH Dataset (with Code Interpreter): The CR Agent reaches 72.2% accuracy, surpassing PAL (PoT) by +20.2%. On Level 5 problems, this represents a 66.8% relative improvement over PAL.

🔧 Installation

To get started, clone the repository and set up the environment:

# Clone the repository
git clone https://github.com/iiis-ai/cumulative-reasoning.git
cd cumulative-reasoning

# Create and activate a conda environment
conda create -n cr python=3.10
conda activate cr

# Install the required packages
pip install -r requirements.txt

For detailed instructions on specific experiments, please refer to the README.md files within each subdirectory.

🤖 CR Agent: Solving MATH with a Code Environment

The CR-Agent directory contains our implementation for solving the MATH dataset using a code interpreter. This agent demonstrates how CR can be integrated with external tools for robust, semi-symbolic reasoning.

Experimental Results

Our CR Agent, using GPT-4-1106-preview, significantly outperforms previous methods. The agent uses a minimalist setup, accumulating context as a simple string without complex frameworks.

Performance on MATH by Category

Method	Algebra	Counting & Prob.	Geometry	Interm. Algebra	Num. Theory	Prealgebra	Precalculus	Overall
PAL (PoT)	65.3	57.9	31.7	30.9	66.1	73.2	23.2	52.0
ToRA	71.8	68.4	48.8	49.5	66.1	67.1	44.6	60.8
CR Agent	86.3	71.1	53.7	51.5	88.7	86.6	51.8	72.2

Performance on MATH by Difficulty

Method	Level 1	Level 2	Level 3	Level 4	Level 5
PAL (PoT)	88.4	65.6	60.0	45.3	31.3
ToRA	74.4	75.6	69.5	53.9	46.3
CR Agent	90.7	90.0	81.9	66.4	52.2

✨ CR Agent Assistant & Meta Prompting

We also explore a simplified implementation of the CR Agent using the OpenAI Assistants API, guided by the principles of Meta Prompting.

Demo: Try the CR Agent v0.1 on the GPT Store.
Implementation: See the minimalist prompt structure in ./CR-Agent-Assistant/cr-agent-assistant-v0.1.md.

Meta Prompting is a technique that emphasizes the structure and syntax of prompts, providing a scaffold for the LLM to generate complex, structured outputs. Learn more at the meta-prompting repository.

@article{zhang2023cumulative,
  title={Cumulative Reasoning With Large Language Models},
  author={Zhang, Yifan and Yang, Jingqin and Yuan, Yang and Yao, Andrew Chi-Chih},
  journal={Transactions on Machine Learning Research; arXiv preprint arXiv:2308.04371},
  year={2023}
}