Compare scalar quantization, product quantization, and binary quantization in Qdrant in terms of compression ratio and accuracy impact.

Qdrant's original quantization trio sits at three different points on the compression-vs-accuracy curve. Scalar quantization (SQ) maps each float32 dimension to an int8 value using a linear scale, typically clipped at a quantile to handle outliers. It gives a fixed 4x compression, and because 256 levels per dimension is a fairly fine grid, the accuracy loss is small - often under one point of recall@10 on real embeddings. It is the safe default and the first thing to try. Product quantization (PQ) splits the vector into subspaces, runs k-means on each subspace to learn a codebook of centroids, and stores the centroid index for each subspace instead of the raw values. Compression depends on the number of subspaces and the codebook size: with 8-bit codes and 96 subspaces on a 768-dim vector, you get roughly 32x compression. The accuracy loss is larger because the codebook is a coarse approximation, but PQ can be tuned via the number of subspaces and centroids to land anywhere on the curve. Binary quantization (BQ) reduces each dimension to a single bit - essentially the sign - giving 32x compression. It is the most aggressive and the most lossy, and it is only viable with oversampling and rescoring to recover accuracy.

The mechanism behind the accuracy differences is how much information each scheme preserves about the relative geometry. SQ preserves the ordering of values along each dimension but loses magnitude precision; distances between quantized vectors are close to the true distances because the error per dimension is small and roughly unbiased. PQ preserves the cluster membership in each subspace but loses the position within the cluster; distances are approximated by the distance between centroids, which is a coarser approximation but still captures the dominant structure. BQ preserves only the sign, which is enough to capture the direction of the vector but throws away all magnitude information. For cosine similarity on normalized vectors, BQ is surprisingly effective because direction is what matters, which is why it works well on high-dimensional embeddings. For Euclidean distance on unnormalized vectors, BQ is much weaker. The other dimension of difference is the interaction with HNSW: SQ and PQ quantized vectors are typically used for the distance computations during graph traversal, while full-precision vectors are kept for rescoring. BQ almost always requires rescoring because the binary distance alone is too noisy to rank a candidate set reliably.