Product quantisation budget arithmetic

NumericalBeginner⏱ 30 minRAGproduct quantisationcompressionmemorycodebook

Problem

For $d = 768$ float32 vectors, $N = 10^8$ documents:

Compute the raw storage.
Compute the storage with product quantisation at $m = 16$ subvectors and $b = 8$ bits each, and the compression ratio.
Compute the number of representable points and the codebook size.
Estimate the cost of one asymmetric distance computation.

Compute the requested quantities and say what they mean. A number without an interpretation is not an answer.

Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.

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