MINT: Multi-Vector Search Index Tuning

TL;DR

Mint tackles the problem of tuning indexes for multi-vector search workloads by decomposing it into a Query Planning problem and a Configuration Searching problem, both shown to be NP-hard. It introduces estimators and dynamic programming- and beam-search-based algorithms to find near-optimal plans and configurations using multi-column indexes, notably supporting HNSW and DiskANN. The framework achieves substantial latency reductions (2.1×–8.3×) over per-column baselines while adhering to recall and storage constraints, demonstrated on semi-synthetic and real datasets. Mint’s modular design enables plug-and-play estimators and index types, offering practical scalability and guidance for deploying multi-vector search systems in real-world settings.

Abstract

Vector search plays a crucial role in many real-world applications. In addition to single-vector search, multi-vector search becomes important for multi-modal and multi-feature scenarios today. In a multi-vector database, each row is an item, each column represents a feature of items, and each cell is a high-dimensional vector. In multi-vector databases, the choice of indexes can have a significant impact on performance. Although index tuning for relational databases has been extensively studied, index tuning for multi-vector search remains unclear and challenging. In this paper, we define multi-vector search index tuning and propose a framework to solve it. Specifically, given a multi-vector search workload, we develop algorithms to find indexes that minimize latency and meet storage and recall constraints. Compared to the baseline, our latency achieves 2.1X to 8.3X speedup.

Figures (14)

• Figure 1: Overview of Mint. The Configuration Searcher searches for the workload's best configuration by interacting with the Query Planner and the Storage Estimator. The Query Planner finds each individual query's best plan using the Cost Estimator and the Recall Estimator.
• Figure 2: An example query plan retrieves $k^1$ and $k^3$ items from $x^1$ and $x^3$ and then re-rank.
• Figure 3: Example HNSW index with one layer for $\mathscr{n}=3$. IDs $\{1, 2, 3\} = \mathscr{U}$ in Problem \ref{['problem:SetCover']}, while $\text{IDs}\geq91$ are dummy IDs. When $1 \leq ek_i\leq \mathscr{n}-1 = 2$, $\mathscr{n}=3$ items in the first row are scanned. When $ek_i=\mathscr{n}=3$, $(2\mathscr{n}+1)=7$ items in the first and seconds rows are scanned. When $ek_i \geq \mathscr{n}+1$ = 4, all items in the database are scanned.
• Figure 4: Example of relevant $ek$. The number of each relevant $ek$ is limited to $k=3$. The search space of $ek^1$ and $ek^3$ is $\{0, 6, 31, 183\} \times \{0, 8, 116, 230\}$, which has $(k+1)(k+1)=16$ combinations. A possible plan is $ek^1=31$ and $ek^3=8$, which covers $r_1$, $r_2$, and $r_3$.
• Figure 5: Observed $numDist(q,x_i,ek_i)$ using (a) HNSW and (b) DiskANN indexes on four example datasets can be represented by linear models.

Theorems & Definitions (8)

• Definition 1: Multi-Vector Search Query
• Example 1
• Example 2
• Example 3
• Theorem 1
• Example 4
• Example 5
• Theorem 2