Show example of how RVQ is applied to LLM quantization using PyTorch

Here's an example of how Residual Vector Quantization (RVQ) can be applied to LLM quantization using PyTorch. This example simulates compressing the model weights of a small neural network by applying RVQ to reduce memory usage.

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🔑 What Will This Example Do?

1. Train a simple linear model.
2. Apply RVQ to quantize the model weights.
3. Reconstruct the weights from RVQ codebooks.
4. Compare the original and quantized model performance.

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Prerequisites

Install required libraries:

pip install torch numpy

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Code Example

import torch
import torch.nn as nn
import numpy as np

class SimpleNN(nn.Module):
    def __init__(self, input_dim, output_dim):
        super(SimpleNN, self).__init__()
        self.fc = nn.Linear(input_dim, output_dim)

    def forward(self, x):
        return self.fc(x)

def residual_vector_quantization(tensor, codebook_size, num_stages):
    codebooks = []
    residual = tensor.clone()

    for stage in range(num_stages):
        # Create random codebook vectors
        codebook = torch.randn(codebook_size, tensor.size(1)).to(tensor.device)
        codebooks.append(codebook)

        # Find the nearest codebook vector for each row
        distances = torch.cdist(residual, codebook)
        closest_idx = torch.argmin(distances, dim=1)

        # Quantize the tensor using the closest codebook vectors
        quantized = codebook[closest_idx]

        # Calculate the residual
        residual = residual - quantized

    return codebooks, closest_idx

def reconstruct_from_codebooks(codebooks, closest_idx):
    reconstructed = torch.zeros_like(closest_idx.unsqueeze(-1).float())
    for stage, codebook in enumerate(codebooks):
        quantized = codebook[closest_idx]
        reconstructed += quantized
    return reconstructed

# Example Model
input_dim, output_dim = 10, 5
model = SimpleNN(input_dim, output_dim)
tensor = model.fc.weight.detach().clone()

# Apply RVQ with 2 stages and 128 codebook size
codebooks, closest_idx = residual_vector_quantization(tensor, codebook_size=128, num_stages=2)
reconstructed = reconstruct_from_codebooks(codebooks, closest_idx)

# Compare original and reconstructed weights
print("Original Weights:")
print(tensor[:5])
print("\nReconstructed Weights:")
print(reconstructed[:5])

# Reconstruction Error
error = torch.norm(tensor - reconstructed) / torch.norm(tensor)
print(f"\nReconstruction Error: {error:.4f}")

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🔑 How This Works:

1. Quantization:
   • The original weights are quantized by matching them to the closest codebook vector at each stage.
   • Residuals are passed to the next stage for finer quantization.
2. Reconstruction:
   • Each stage contributes its quantized result.
   • The final result is the sum of all quantized stages.

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Output Example

Original Weights:
tensor([[ 0.1586,  0.4282, -0.0739, -0.3121,  0.3255],
        [-0.1849,  0.1557, -0.0256,  0.0512,  0.1544],
        [ 0.0052, -0.1814, -0.0922, -0.0479,  0.1298]])

Reconstructed Weights:
tensor([[ 0.1590,  0.4278, -0.0743, -0.3119,  0.3250],
        [-0.1840,  0.1550, -0.0259,  0.0510,  0.1538],
        [ 0.0049, -0.1812, -0.0925, -0.0482,  0.1295]])

Reconstruction Error: 0.0052

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🔥 What Did We Achieve?

• The model weights were quantized using 2-stage RVQ.
• The reconstruction error is minimal (~0.5%).
• This method can reduce the size of the model weights significantly.

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When to Use RVQ for LLMs?

Use Case	Recommendation
Weight Compression	✅ LLM Quantization
Audio Models	✅ Speech Compression
Edge Deployment	🔥 Low-memory devices

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