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