🟦 Plan-and-Solve Prompting

What is Plan-and-Solve Prompting?

Zero-Shot Chain-of-Thought (CoT) Prompting improves the reasoning and accuracy of Large Language Models (LLMs) by enabling them to generate intermediate reasoning steps before predicting the final answer. While this improves the performance in multi-step reasoning tasks, the experiments show that Zero-Shot CoT has three pitfalls:

• Calculation errors
• Missing Step errors
• Semantic misunderstanding

Plan-and-Solve (PS) prompting aims to solve the issue of missing step errors in Zero-Shot CoT Prompting. To achieve its goal, PS prompting replaces the phrase "Let's think step by step" used in Zero-Shot CoT with "Let's first understand the problem and devise a plan to solve the problem. Then, let's carry out the plan and solve the problem step by step". The example below shows the difference between Zero-Shot CoT and PS prompting.

• Zero-Shot CoT Prompting

• Plan-and-Solve (PS) Prompting

From the example, it is clear that for complex problems, the reasoning steps generated using the Zero-Shot CoT prompt: "Let's think step by step" may still yield incorrect reasoning steps. Asking the LLM first to devise the plan and then carry it out - PS prompting - can help minimize the missing steps errors.

It is important to note that the Zero-Shot prompt in PS prompting can be anything as long as it satisfies the following conditions:

• It triggers the LLM to determine subtasks and accomplish the subtasks.
• It guides the LLM to pay more attention to calculation and intermediate results to ensure a correct response

How to Use Plan-and-Solve Prompting?

Implementing PS prompting is a two-step process. It includes:

• inference, and
• answer extraction

Step 1: Inference

Feed the prompt to the LLM in the first step; this generates the reasoning step and the answer.

Step 2: Answer Extraction

Next, pass the initial prompt and the generated answer to the LLM to extract the final answer. To extract the answer, you can append a phrase like "Therefore, the answer (arabic numerals) is" at the end of the prompt.

What is PS+ Prompting?

While PS prompting helps minimize the missing steps error, PS+ prompting, an extension of PS prompting, aims to reduce calculation errors of Zero-Shot-CoT along with improving the generated reasoning steps. PS+ prompt extends the PS prompt with additional details instructing the LLM to compute intermediate results and pay more attention to calculation and common sense.

PS+ Prompting Example

Given a math word problem, Grace weighs 125 pounds. Alex weighs 2 pounds less than 4 times what Grace weighs. What are their combined weights in pounds?, let's solve it using both PS and PS+ prompting.

First, let's try with PS prompting:

You can clearly see that PS fails to correctly evaluate the expression 125 + (4 * 125 - 2) resulting in an incorrect answer. Now, let's employ PS+ prompting.

• Inference

• Answer extraction

The only difference between PS and PS+ prompting is that in PS+ prompting, the prompt emphasizes the LLM to pay attention to calculation and intermediate steps. As a result, PS+ prompting reduces calculation and the missing steps error.

What Are Plan-and-Solve Prompting Results?

• PS+ prompting outperforms Zero-Shot CoT in symbolic reasoning datasets like last letters, commonsense reasoning datasets (CSQA, StrategyQA), and math reasoning datasets.
• PS+ prompting reduces the missing steps error and semantic understanding error compared to Zero-Shot CoT.

Limitations of Plan-and-Solve Prompting

There are two major limitations to the PS prompting approach:

• Models like GPT-3 are sensitive to expressions in the prompt hence, designing the prompt to guide LLMs in generating correct reasoning steps takes considerable effort.
• PS prompting addresses calculation and missing-reasoning-step errors but doesn't pacify semantic misunderstanding errors.

Conclusion

Plan-and-Solve prompting techniques (PS and PS+) help reduce the missing steps error and calculation errors by carefully crafting prompts and making the model think and plan before solving the problem. The approach has proven effective in various tasks: math reasoning, common sense reasoning, and symbolic reasoning. However, the approach heavily relies on the trigger sentence in the prompt. As such, coming up with the best trigger sentence or prompt may prove challenging as it is manual.

Bhuwan Bhatt

Bhuwan Bhatt, a Machine Learning Engineer with over 5 years of industry experience, is passionate about solving complex challenges at the intersection of machine learning and Python programming. Bhuwan has contributed his expertise to leading companies, driving innovation in AI/ML projects. Beyond his professional endeavors, Bhuwan is deeply committed to sharing his knowledge and experiences with others in the field. He firmly believes in continuous improvement, striving to grow by 1% each day in both his technical skills and personal development.

Footnotes

1. Jason Wei. (2022). Chain-of-Thought Prompting Elicits Reasoning in Large Language Models. ↩

2. Lei Wang. (2023). Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models. ↩ ↩²