How to fine-tune RVQ-based quantization with custom codebooks

 Fine-tuning Residual Vector Quantization (RVQ) with custom codebooks can be an advanced and effective technique for quantizing large models, especially when you need a highly compressed representation while retaining as much model accuracy as possible. The goal is to optimize the codebooks alongside the model weights in a way that minimizes the quantization error.

Overview of Fine-Tuning RVQ with Custom Codebooks

When you fine-tune RVQ-based quantization with custom codebooks, you essentially aim to:

1. Train the model with quantized embeddings or weights that are represented by custom codebooks.
2. Optimize both the codebooks and the model so that the reconstruction error between the quantized and original weights or embeddings is minimized.
3. Use Quantization-Aware Training (QAT) to adjust the model during fine-tuning, so it can learn to adjust its weights for a lower-precision, quantized representation.

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Step-by-Step Guide to Fine-Tuning RVQ-Based Quantization

1. Initialize Model and Tokenizer

We'll start by loading a pre-trained model and tokenizer. For simplicity, let’s use a model like BERT, but you can apply the same steps to any Hugging Face Transformer.

from transformers import AutoModelForSequenceClassification, AutoTokenizer
import torch

# Load pre-trained model
model_name = "bert-base-uncased"
tokenizer = AutoTokenizer.from_pretrained(model_name)
model = AutoModelForSequenceClassification.from_pretrained(model_name)

# Example input text
text = "Fine-tuning RVQ-based quantization in Hugging Face."

# Tokenize input text
inputs = tokenizer(text, return_tensors="pt")

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2. Create Custom Codebooks

In RVQ, the key idea is to quantize the model’s embeddings or weights using codebooks. We'll create codebooks with random initialization and later fine-tune them.

def create_codebooks(embed_dim, codebook_size, num_stages):
    return [torch.randn(codebook_size, embed_dim, requires_grad=True) for _ in range(num_stages)]

# Example: embedding dimension of 768, 256 codebook vectors, 4 stages
codebooks = create_codebooks(768, 256, 4)

In this example:

• embed_dim is the size of the embedding (e.g., 768 for BERT).
• codebook_size is the number of codebook vectors per stage.
• num_stages represents how many residual quantization steps to perform.

Each codebook is initialized with random values, and it’s set to require gradients so that it can be fine-tuned.

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3. Apply RVQ Quantization to Embeddings

Next, we’ll define a function to quantize the embeddings using the RVQ process.

def rvq_quantize(embedding, codebooks):
    residual = embedding.clone()
    indices = []
    
    for stage in range(len(codebooks)):
        codebook = codebooks[stage]
        distances = torch.cdist(residual.unsqueeze(0), codebook.unsqueeze(0)).squeeze(0)
        closest_idx = torch.argmin(distances, dim=0)
        indices.append(closest_idx)
        residual -= codebook[closest_idx]
    
    return indices

This function takes in an embedding (e.g., word embeddings) and applies RVQ quantization using the codebooks.

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4. Reconstruct the Quantized Embeddings

To reconstruct the quantized embeddings from the codebook indices, we need to use the indices to pull the vectors from the codebooks and combine them.

def reconstruct_embeddings(codebooks, indices):
    reconstructed = torch.zeros_like(codebooks[0][0])
    for stage, idx in enumerate(indices):
        reconstructed += codebooks[stage][idx]
    return reconstructed

This function reconstructs the quantized embeddings by adding the corresponding codebook vectors.

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5. Forward Pass with RVQ Quantized Embeddings

Now, instead of using the original model embeddings, we'll pass the RVQ-quantized embeddings into the model.

# Forward pass using RVQ quantized embeddings
with torch.no_grad():
    # Extract original embeddings
    original_embedding = model.embeddings.word_embeddings(inputs['input_ids'])
    
    # Quantize the embeddings using RVQ
    quantized_indices = rvq_quantize(original_embedding, codebooks)
    
    # Reconstruct embeddings from quantized indices
    reconstructed_embedding = reconstruct_embeddings(codebooks, quantized_indices)
    
    # Replace original embeddings with reconstructed embeddings
    model.embeddings.word_embeddings.weight.data = reconstructed_embedding

In this code:

• We first obtain the embeddings from the pre-trained model.
• We then quantize these embeddings using RVQ and reconstruct them.
• Finally, we replace the original embeddings in the model with the reconstructed ones for inference.

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6. Fine-Tuning the Model with Codebook Adjustment

To fine-tune both the model and the codebooks, we need to use an optimizer that will adjust both. During fine-tuning, you want to minimize the loss and the quantization error between the original and reconstructed embeddings.

from torch.optim import AdamW

# Fine-tune the model
optimizer = AdamW(model.parameters(), lr=1e-5)

# Define the loss function (cross-entropy for classification)
loss_fn = torch.nn.CrossEntropyLoss()

# Sample labels for fine-tuning (for a classification task)
labels = torch.tensor([1])  # Example label

# Forward pass, compute loss, and backward pass
model.train()
optimizer.zero_grad()

# Get original embeddings
original_embedding = model.embeddings.word_embeddings(inputs['input_ids'])

# Quantize and reconstruct embeddings
quantized_indices = rvq_quantize(original_embedding, codebooks)
reconstructed_embedding = reconstruct_embeddings(codebooks, quantized_indices)

# Replace embeddings with reconstructed embeddings
model.embeddings.word_embeddings.weight.data = reconstructed_embedding

# Forward pass through the model with modified embeddings
outputs = model(**inputs)
loss = loss_fn(outputs.logits, labels)

# Backward pass and optimization step
loss.backward()
optimizer.step()

print(f"Loss: {loss.item()}")

In this code:

• The optimizer adjusts both the model weights and the codebooks during training.
• We compute the loss for the task (classification in this case), and then propagate gradients back to both the model and codebooks.
• The codebooks are fine-tuned based on the task's gradients, helping the model learn to optimize its performance with the quantized representation.

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7. Evaluate the Model

After fine-tuning, you can evaluate the model on a downstream task (e.g., classification, question answering) and compare the performance with the original, unquantized model.

# Evaluation using fine-tuned model
model.eval()
with torch.no_grad():
    outputs = model(**inputs)
    print(outputs.logits)

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Conclusion: Fine-Tuning RVQ-Based Quantization

• RVQ-based quantization is useful when you need highly efficient embedding or weight compression while minimizing accuracy loss.
• By using custom codebooks, you can ensure the quantization is specifically tailored to the model's needs.
• Fine-tuning the model along with the codebooks ensures that the model adapts to quantized weights and embeddings while maintaining good performance.
• This process involves using quantization-aware training (QAT) to adjust both model parameters and the quantized representation during training.

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