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One way around this issue is to apply an \textit{inline filter}, i.e. during \acrshort{ann} search, we do vector search, evaluate the stopping condition and apply the filter. This gives us $K$ rows directly and a handy performance uplift to go along with it. @@ -52,6 +53,15 @@ A further optimization is to change how much of the set we re-score vs how much Not all dataset and query combinations are equally easy, and filters also change the difficulty. +\subsubsection{Quantization} +The total storage usage of course is always $N \cdot c$, where $N$ is the number of vectors and $c$ is the cost per vector, computed as follows: +\begin{itemize} + \item \bi{Scalar-Quantization} (SQ): $c = i + d \cdot m$, where $d$ is the number of dimensions of the vector and $m$ is the byte count per dim. + \item \bi{Product Quantization} (PQ): $c = i + q$, with $i$ the cost of the vector ID and $q = m \ceil{\log_2(k) / 8}$ bytes, with $m$ the number of subvectors, + and $k$ the codebook entry count. Remember that we divide by 8 to get bytes, as the $\log_2(k)$ gives us the number of bits. +\end{itemize} + + \subsubsection{Filter agnosticism} Filter agnosticism isn't just a single type, it's a spectrum.