Vector Quantization

Vector Quantization (VQ) is a compression technique that maps continuous high-dimensional vectors to a discrete set of representative vectors (called a codebook), reducing storage and enabling efficient similarity search in RAG systems.

How Vector Quantization Works

1. Training: Run clustering (K-means) on a training set of vectors to learn K representative vectors (centroids) — the codebook.
2. Encoding: Replace each vector with the index of its nearest codebook entry.
3. Storage: Store only the codebook indices (log₂(K) bits per vector) instead of full vectors.
4. Decoding: Reconstruct approximate vectors by looking up codebook entries.

Example

• Original: 768-dimensional float32 vector = 3,072 bytes.
• Codebook: 256 entries (8-bit indices).
• Compressed: 1 byte per vector (index into codebook).
• Compression: 3,072× (though codebook must be stored separately).

Types of Vector Quantization

• Scalar Quantization (SQ): Quantize each dimension independently (simple, less compression).
• Product Quantization (PQ): Split vector into sub-vectors, quantize each sub-vector separately (better compression-accuracy trade-off).
• Residual Quantization (RQ): Iteratively quantize the residual error (highest accuracy).

Advantages

• Compression: Dramatically reduces memory footprint for large vector collections.
• Fast Search: Distance computation can use lookup tables or specialized hardware.
• Scalability: Enables billion-scale vector search on limited hardware.

Disadvantages

• Lossy: Quantization introduces approximation error — may miss true nearest neighbors.
• Training Overhead: Requires clustering on representative data.
• Codebook Storage: Must store and load the codebook (typically small overhead).

Use in RAG

Vector quantization enables efficient semantic search over massive document collections:
- Coarse Search: Use quantized vectors for fast candidate retrieval.
- Reranking: Fetch full-precision vectors for top candidates and rerank.

Frameworks

• FAISS: Implements multiple VQ variants (IVF, PQ, SQ, RQ).
• ScaNN (Google): Optimized vector quantization for similarity search.
• Qdrant: Vector database with built-in quantization support.

Vector quantization is a fundamental technique for scaling RAG systems to billions of documents while maintaining sub-second query latency.