🟦 Cumulative Reasoning Prompting

What is Cumulative Reasoning?

Large Language Models (LLMs) have made remarkable advances in a variety of applications, including language translation, problem-solving, etc., but they still struggle to provide stable and accurate answers for complex tasks. For instance, LLMs frequently make errors when solving high school maths problems.

An instance where an LLM fails to correctly predict the answer^{1Yifan Zhang. (2023). Cumulative Reasoning with Large Language Models. https://arxiv.org/abs/2308.04371}

LLMs are fast and intuitive thinkers and lack the ability to slower more deliberate thought processes. Chain-of-Thought (CoT)^{2Jason Wei. (2022). Chain-of-Thought Prompting Elicits Reasoning in Large Language Models.} Prompting and Tree-of-Thought^{3Shunyu Yao. (2023). Tree of Thoughts: Deliberate Problem Solving with Large Language Models.} (ToT) Prompting help guide LLM through a more structured reasoning process. Still, they can't instill the ability to dynamically store and leverage intermediate results.

Cumulative Reasoning (CR) Prompting^{1Yifan Zhang. (2023). Cumulative Reasoning with Large Language Models. https://arxiv.org/abs/2308.04371} uses three key roles: the proposer, verifier(s), and reporter. They work together to suggest, check, and compile the reasoning steps into a complete solution.

1. Proposer: Initiates the reasoning by suggesting potential steps based on the current context.
2. Verifier: Critically evaluates the proposer's suggestions.
3. Reporter: Decides when to wrap up the reasoning process

How to Use Cumulative Reasoning?

In CR prompting, the proposer initiates the reasoning process by suggesting actions to take. The verifier evaluates them and decides whether or not the proposer's suggestion will lead to a valid conclusion. If the verifier thinks the proposer's suggestions do not lead to a valid conclusion, the proposer provides new suggestions. The process continues till the verifier thinks that the proposer's suggestions can lead to a valid conclusion. At this point, the report combines the reasoning steps to come up with a final solution.

Let's use CR to solve the Game of 24. In this game, the goal is to use basic math operations and the given four numbers to get 24 as the final result. For this example, let's take 4, 9, 10, and 13 as the four input numbers.

1. First, ask the proposer model to choose two numbers and manipulate them using one of the basic operations and report the remaining numbers.

2. Using the verifier, check if the intermediate step is correct or not.

3. Using the verifier again, check if it is possible to reach the number by combining the remaining numbers using basic maths operations.

4. Since the verifier thinks it is possible to reach the final solution, combine all previous steps into a final solution using the reporter.

What Are Cumulative Reasoning Results?

• In the Game of 24, CR achieves 98% accuracy, 24% higher than the previous state-of-the-art.

CR's accuracy in Game of 24 compared to other models^{1Yifan Zhang. (2023). Cumulative Reasoning with Large Language Models. https://arxiv.org/abs/2308.04371}

• In the MATH dataset, CR sets new state-of-the-art, achieving 4.2% over the previous one.
• After removing the problematic instances from the FOLIO wiki dataset, CR achieves an accuracy of 98.04%.

CR's accuracy in the FOLIO wiki dataset^{1Yifan Zhang. (2023). Cumulative Reasoning with Large Language Models. https://arxiv.org/abs/2308.04371}

Conclusion

Cumulative Reasoning mimics humans' deliberate thought processes when solving complex tasks. By using a proposer, verifier(s), and reporter, CR decomposes the complex problem into smaller, easy-to-solve tasks and combines individual solutions into a comprehensive solution, demonstrating CR's potential to advance LLM's capabilities for solving complex tasks.