From 5b167a9e397ccda0803420232b7e5398bdf337ae Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Sat, 25 Jul 2026 09:04:55 +0200 Subject: [PATCH] [DMDB] Finished vector search --- semester4/dmdb/assets/filter-agnosticism.png | Bin 0 -> 140924 bytes .../dmdb/data-modelling-databases-summary.pdf | Bin 1109114 -> 1261891 bytes semester4/dmdb/glossary/acronyms.tex | 2 + .../parts/05_vector-search/01_hsnw-index.tex | 35 ++++++++ .../parts/05_vector-search/02_hash-index.tex | 16 ++++ .../03_filtered-vector-search.tex | 78 ++++++++++++++++++ .../dmdb/parts/05_vector-search/main.tex | 2 + 7 files changed, 133 insertions(+) create mode 100644 semester4/dmdb/assets/filter-agnosticism.png create mode 100644 semester4/dmdb/parts/05_vector-search/02_hash-index.tex create mode 100644 semester4/dmdb/parts/05_vector-search/03_filtered-vector-search.tex diff --git a/semester4/dmdb/assets/filter-agnosticism.png b/semester4/dmdb/assets/filter-agnosticism.png new file mode 100644 index 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zU-YXzo;^oWb+|PqDgwF+0@sS}`^D0H*}t~Nak7hQO;na3^xpNM4mN#TYJI=5oI8?h z04hsv^jS-^r#!fEpKvB K$ and thus $\sigma(K') < K$, then we have low recall. +\end{itemize} + +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. + +Sounds too good to be true? That's because it is. There are still some issues, namely if filtered out nodes don't participate in the navigation. +In that case, the search stops if we reach such a filtered node, but there would be nodes that are closer to the query behind this node, +which due to the removal of the filtered out node are now no longer accessible. + +This means that we need to have the filtered nodes participate in the navigation, which increases the cost by increasing the number of needed distance computations. + +Thus, \textit{filters increase the search effort and difficulty of tuning search parameters}. +Selective filters make it harder to find valid nodes. + +This is where the \texttt{Value-Vector-Correlation} comes in. It captures the relationship between the \bi{probability of satisfying the filters} +and the \bi{distance from the query vector}. +It doesn't however always correlate positively and the correlation depends on the query. +For instance, a query like ``Item like a blue T-Shirt and price > \$10K'' is negatively correlated. + + +\subsubsection{Hash-Tree Index} +If we use a Hash-Tree instead of the HNSW index, with filtering the internal node navigation does not change, as the data vectors are only in the leaves, +so we simply filter there. + + +\subsubsection{Performance Challenges} +The cost of a vector search is given by $f(n_d \cdot c_d, n_f \cdot c_f)$, where $n_d$ is the number of distance computations, $n_f$ is the number of filter evaluations +and $c_i$ and $c_f$ are the associated costs. + +Depending on the query, the cost very much differs, in that for 20\% selectivity, filtering first is faster, while for 50\% selectivity, doing the NNS first is faster. + +Since the distance computation and associated access costs are relative to the vector size, +we could use Principal Component Analysis (PCA) or others to reduce the dimension of the vectors. +Alternatively, we can quantize some values, with the drawback of reducing precision. +Trees offer more residualization, so the best of both worlds is to score fast with quantized vectors, then re-score with the full precision on just a subset. + +A further optimization is to change how much of the set we re-score vs how much of it we score. + +Not all dataset and query combinations are equally easy, and filters also change the difficulty. + + +\subsubsection{Filter agnosticism} +Filter agnosticism isn't just a single type, it's a spectrum. + +\begin{figure}[h!] + \begin{center} + \includegraphics[width=0.8\textwidth]{assets/filter-agnosticism.png} + \end{center} + \caption{Spectrum of filter agnosticism + (Figure from lecture slides 18, slide 65)} +\end{figure} + +Ideally, we would build an index per filter, but there are issues: +\begin{itemize} + \item Footprint is too high because of duplicated nodes + \item Not enough data to build an index on the small partitions +\end{itemize} +We can emulate this partitioning with efficient footprint using a monolithic graph with pruning. + +\inlinedefinition[Value-induced neighbourhood] We can build a new index based on attributes and embedding similarity (embedding distance) + +\inlinedefinition[Predicate Traversal] Alternatively we can reuse unfiltered indexes and use inline filtering to discover filter-passing nodes, +then light up the right neighbourhood at search time. + +\inlinedefinition[Densified Predicate Traversal] We also add edges to alleviate connectivity issues and proceed as with the predicate traversal diff --git a/semester4/dmdb/parts/05_vector-search/main.tex b/semester4/dmdb/parts/05_vector-search/main.tex index dedff59..8774e64 100644 --- a/semester4/dmdb/parts/05_vector-search/main.tex +++ b/semester4/dmdb/parts/05_vector-search/main.tex @@ -1,4 +1,6 @@ \section{Vector Search} \input{parts/05_vector-search/00_intro-trees-clustering.tex} \input{parts/05_vector-search/01_hsnw-index.tex} +\input{parts/05_vector-search/02_hash-index.tex} +\input{parts/05_vector-search/03_filtered-vector-search.tex} % \input{parts/05_vector-search/}

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