What is vector quantization in embeddings?

Vector quantization in embeddings is a technique used to reduce the computational and storage costs of high-dimensional vectors by mapping them to a finite set of representative vectors, called a “codebook.” This codebook contains a smaller number of vectors (or “codewords”) that approximate the original data. Each high-dimensional embedding is replaced by the index of the closest codeword in the codebook, effectively compressing the data. For example, a 1024-dimensional embedding might be represented as a single integer pointing to a codeword in a codebook of 256 entries, drastically reducing memory usage.

The process typically involves two steps: creating the codebook and assigning embeddings to codewords. Codebooks are often generated using clustering algorithms like k-means, where the cluster centers become the codewords. Once the codebook is built, each original embedding is compared to all codewords (e.g., using Euclidean distance or cosine similarity) and replaced by the index of the nearest match. For instance, in a recommendation system, user and item embeddings could be quantized into a shared codebook, enabling faster similarity searches by comparing indices instead of raw vectors. Libraries like FAISS (Facebook AI Similarity Search) use vector quantization to accelerate nearest-neighbor queries in large datasets.

The trade-offs of vector quantization revolve around accuracy versus efficiency. While it reduces memory and speeds up computations, quantization introduces approximation errors because embeddings are replaced with codewords. Techniques like product quantization mitigate this by splitting vectors into subvectors and quantizing each separately, balancing accuracy and compression. For example, a 128-dimensional vector could be divided into eight 16-dimensional subvectors, each quantized into 256 codewords, resulting in 8 indices (8 bytes total) instead of 128 floating-point numbers (512 bytes). This is especially useful in applications like real-time recommendation engines or mobile devices with limited resources, where fast, memory-efficient operations are critical, even if some precision is lost.