Test Time Compute Guide

# test-time-compute-guide

## Description
Master test-time compute and chain-of-thought reasoning techniques for LLMs. Learn how to effectively use "thinking time" to improve model performance through parallel sampling, sequential revision, and process reward models.

## Implementation

Test-time compute (TTC) and Chain-of-Thought (CoT) have led to significant improvements in LLM performance. The core idea is enabling models to "think" longer before producing final answers, similar to human System 2 thinking.

### Key Concepts:
- **Parallel Sampling**: Generate multiple outputs simultaneously and select the best using verifiers or process reward models
- **Sequential Revision**: Iteratively refine responses by asking the model to reflect on and correct mistakes  
- **Process Reward Models (PRM)**: Guide beam search candidate selection during decoding
- **Self-Consistency**: Use majority voting among multiple CoT rollouts when ground truth isn't available

### When to Use Each Approach:
- **Easier questions**: Benefit from purely sequential test-time compute
- **Harder questions**: Perform best with optimal ratio of sequential to parallel compute

## Code Examples

### Example 1: Basic Chain-of-Thought Prompting
```python
def cot_prompt(problem):
    """Generate chain-of-thought prompt for math problems"""
    return f"""Solve this step by step:

Problem: {problem}

Let's think step by step:
"""

# Usage
problem = "What is 12345 times 56789?"
prompt = cot_prompt(problem)
```

### Example 2: Best-of-N Sampling
```python
import random

def best_of_n_sampling(model, prompt, n=5, scorer=None):
    """Generate N samples and return the highest scoring one"""
    samples = []
    for _ in range(n):
        sample = model.generate(prompt, temperature=random.uniform(0.7, 1.2))
        score = scorer(sample) if scorer else len(sample)  # Simple length-based scoring
        samples.append((sample, score))
    
    return max(samples, key=lambda x: x[1])[0]
```

### Example 3: Beam Search with Process Reward
```python
def beam_search_with_prm(model, prm_model, prompt, beam_width=5, max_steps=10):
    """Beam search guided by process reward model"""
    beams = [(prompt, 0.0)]  # (sequence, cumulative_reward)
    
    for step in range(max_steps):
        candidates = []
        for seq, reward in beams:
            # Generate next tokens
            next_tokens = model.generate_next_tokens(seq, top_k=beam_width)
            for token in next_tokens:
                new_seq = seq + token
                # Get process reward for this step
                step_reward = prm_model.evaluate(new_seq)
                candidates.append((new_seq, reward + step_reward))
        
        # Keep top beam_width candidates
        beams = sorted(candidates, key=lambda x: x[1], reverse=True)[:beam_width]
    
    return beams[0][0]  # Return highest reward sequence
```

## Dependencies
- Python 3.8+
- Transformers library (for LLM integration)
- Custom process reward model implementation