Active-Prompt

Chain-of-thought (CoT) methods rely on a fixed set of human-annotated exemplars. The problem? Those exemplars might not be the most effective ones for different tasks. To address this, Diao et al. (2023) proposed Active-Prompt, a new approach that adapts LLMs to different task-specific example prompts (annotated with human-designed CoT reasoning).

Here's the method illustrated. Step one: query the LLM with or without a few CoT examples. Generate k possible answers for a set of training questions. Compute an uncertainty metric based on those k answers (using disagreement). Select the most uncertain questions for human annotation. Then use the new annotated exemplars for inference on each question.

Image source: Diao et al. (2023)

Core Idea

The problem with traditional CoT: all tasks share the same set of hand-annotated examples, but different tasks have different hard parts. Fixed examples can't cover every scenario. Active-Prompt's key insight: let the model tell you which questions are hardest, then prioritize annotating those as examples.

This borrows from active learning -- instead of randomly picking training samples, you pick the ones the model is most "confused" about. Minimum annotation effort, maximum performance gain.

Four-Step Process

Step 1: Uncertainty Estimation

First, use the LLM to generate k answers for each training question (e.g., k=5). Multiple samples let you observe how consistent the model is on each question.

Question: If 3 times a number minus 7 equals 20, what is the number?

Sample 1: 3x - 7 = 20, 3x = 27, x = 9 → Answer: 9
Sample 2: 3x - 7 = 20, 3x = 27, x = 9 → Answer: 9
Sample 3: 20 + 7 = 27, 27 / 3 = 9 → Answer: 9
Sample 4: 3x = 20 + 7 = 27, x = 9 → Answer: 9
Sample 5: 3x - 7 = 20, x = 9 → Answer: 9
→ Disagreement: 0 (all answers agree, model is confident)

Question: A train takes 3 hours from station A to B. From B to C, the speed is 1.5x
         and the distance is 2x. How many hours total from A to C?

Sample 1: AB 3hrs, BC = 2d/(1.5v) = 4hrs, total 7hrs → Answer: 7
Sample 2: BC speed 1.5x distance 2x, time = 2/1.5 × 3 = 4hrs, total 7 → Answer: 7
Sample 3: BC = 2 × distance, speed 1.5×, time = 2d/1.5v = 2/(1.5) × 3 = 4, → Answer: 7
Sample 4: 1.5x speed for 2x distance, needs 2/1.5 = 1.33x time = 4hrs, total 5 → Answer: 5
Sample 5: 3 + (2 × 3)/(1.5) = 3 + 4 = 7 → Answer: 7
→ Disagreement: 0.2 (one answer disagrees, model isn't fully confident)

Step 2: Select the Most Uncertain Questions

Rank by uncertainty (disagreement) from high to low. Pick the top n questions. These are the ones the model struggles with most -- and they're the most valuable to annotate.

The paper uses several uncertainty metrics:

• Disagreement: proportion of different answers among k samples
• Entropy: information entropy of the answer distribution
• Variance: for numerical answers, the variance across answers

Step 3: Human Annotation

For the selected most-uncertain questions, human annotators provide detailed CoT reasoning. Since you only need to annotate a small number of high-value questions (typically 4-8), the annotation cost is much lower than annotating everything.

Step 4: Inference

Use the newly annotated exemplars as few-shot examples for inference on all questions. Because these examples are "hand-picked" based on model weaknesses, they typically deliver better results.

Experimental Results

Active-Prompt achieved significant improvements across multiple reasoning benchmarks:

Note: Results based on code-davinci-002. See the original paper for exact numbers.

Key findings:

• Uncertainty-selected examples consistently outperformed randomly selected ones
• Even with a tiny annotation budget (4-8 examples), Active-Prompt delivered significant gains
• Different uncertainty metrics (disagreement vs. entropy) performed similarly -- disagreement is the simplest and most effective choice

Practical Application Guide

When to Use Active-Prompt?

Active-Prompt works best when:

1. Annotation budget is limited: You can only annotate a few examples and need each one to count
2. Tasks are highly specific: Generic examples don't work well, you need domain-specific customization
3. There's a clear distribution of hard problems: Certain question types consistently trip up the model

Simplified Practice Workflow

You don't need to implement the full paper pipeline for daily use. Here's a simplified approach:

Step 1: Test your LLM on your question set, find questions it frequently gets wrong
Step 2: Write detailed CoT examples for these "error-prone" questions
Step 3: Put those examples into your few-shot prompt
Step 4: Verify the new prompt's performance on the full test set

Comparison with Other Methods

Self-Check Checklist

• Did you do sufficient uncertainty estimation (at least k=5 samples)?
• Do the selected annotation questions cover the main error types?
• Is the annotated CoT reasoning detailed and logically clear?
• Did you confirm the improvement on a validation set?

References

• Active Prompting with Chain-of-Thought for Large Language Models (Diao et al., 2023)
• Chain-of-Thought Prompting Elicits Reasoning in Large Language Models (Wei et al., 2022)