Low-Selectivity Filtered ANNS Strategies

Updated 10 January 2026

Low-selectivity filtered ANNS is defined as approximate nearest neighbor search in high-dimensional space with attribute filters matching <1% of data, creating unique connectivity and performance challenges.
Innovative methods like FusedANN, Curator, PathFinder, UNIFY/HSIG, and VecFlow employ geometric penalties, dual-index schemes, and unified range filtering to enhance recall and throughput.
Dynamic index selection and filter-aware routing, guided by rigorous empirical tuning, enable robust and cost-effective search solutions under extreme low-selectivity conditions.

Low-selectivity filtered Approximate Nearest Neighbor Search (ANNS) refers to the problem of retrieving approximate nearest neighbors in a high-dimensional vector space, given queries that include attribute-based filters where the filter matches a very small fraction (often <1%) of the dataset. This regime presents significant algorithmic and system design challenges due to the potential breakdown in index connectivity, excessive search overheads, and degraded recall or throughput of classical ANNS approaches. Recent research introduces new methodologies and indexing architectures to address these challenges, with particular emphasis on geometric relaxation, hybrid and dual-index systems, graph and partition structures, search-time optimization, and empirical tuning for the low-selectivity regime.

1. Formal Problem Definition and Challenges

Low-selectivity filtered ANNS is defined over a dataset $X = \{v_x, a_x\}_{x=1}^N$ , where $v_x \in \mathbb{R}^d$ is the content embedding and $a_x$ is an m-dimensional attribute vector or label set. The search objective is, given a query $(v_q, a_q)$ (vector and attribute(s)), to find the $k$ approximate nearest vectors by a similarity metric $\rho(v_q, v_x)$ , but restricted to those $x$ where $g(a_x, a_q) = 0$ for some filter function $g$ (e.g., matching or range condition). The filter selectivity $\alpha$ is the fraction of dataset entries satisfying the filter, typically $\alpha \ll 1$ in the low-selectivity setting.

Key challenges in this regime include:

Connectivity breakdown in graph indexes: For graph-based indexes with average out-degree $M$ , after filtering only $\alpha N$ nodes typically remain, with expected in-filter neighbor count $M' = M\alpha$ . When $M\alpha \lesssim \log N$ , the induced subgraph becomes fragmented, impeding or collapsing best-first traversal (Jin et al., 3 Jan 2026).
Inefficiency of partition-based indexes: Partition schemes such as IVF or hierarchical k-means must scan potentially many clusters, most of which contain no qualified vectors when $\alpha$ is small, resulting in increased I/O and computation (Jin et al., 3 Jan 2026).
Trade-off in post-filter and hybrid strategies: Post-filtering (searching the full index and then dropping out-of-filter hits) and hybrid (constructing one-off filtered indexes) incur high search cost and/or index build overhead as selectivity decreases (Liang et al., 2024).

These effects result in sharp recall/throughput degradation when using unmodified classical ANNS methods in the low-selectivity regime.

2. Attribute-Vector Fusion Methods: FusedANN

FusedANN proposes a geometric framework that relaxes hard attribute filters into continuous penalty terms, enabling approximate search in a convexified fused vector-attribute space (Heidari et al., 24 Sep 2025). The classical constrained nearest neighbor problem is relaxed from

$\min_{x \in X} \rho(v_q, v_x) \quad \text{subject to } g(a_x, a_q) = 0$

to the penalized unconstrained form

$\min_{x \in X} \rho(v_q, v_x) + \lambda \cdot g(a_x, a_q)$

where $g$ is typically a norm (e.g., $||a_x-a_q||_2$ ), and $\lambda > 0$ weights attribute-match strictness.

FusedANN embeds vector-attribute pairs via

$\Psi(v, a; \alpha, \beta) = \left[ (v^{(1)} - \alpha a)/\beta, (v^{(2)} - \alpha a)/\beta, \ldots \right]$

partitioning $v$ into blocks of attribute dimension size and jointly encoding content and attribute differences. $\alpha$ amplifies attribute mismatches, pushing unmatched records further in the fused space, while $\beta$ normalizes overall scale. As $\alpha \to \infty$ , only exact attribute matches appear near the query; for finite $\alpha$ , nearest-attribute records are included when exact matches are absent.

Approximate nearest neighbor guarantees in the fused space transfer to the original metric, with error bounds that depend on $\alpha$ , $\beta$ , intra-cluster distortion $\varepsilon_f$ , and normalized attribute deviation (Heidari et al., 24 Sep 2025). Empirically, FusedANN achieves 3×–6× higher throughput at fixed recall (e.g., Recall@10=0.90–0.98) than classical graph-filter pipelines on standard benchmarks, maintaining strong performance even for selectivity as low as 1%, where classical “filter-first” methods collapse (Heidari et al., 24 Sep 2025).

3. Dual-Index and Partition-Based Architectures: Curator

Curator addresses the connectivity breakdown of graph-based filtered search by pairing a graph index for high-selectivity filters ( $\alpha \gg 0.1$ ) with a partition-based index specialized for the low-selectivity regime ( $\alpha \ll 0.1$ ) (Jin et al., 3 Jan 2026). The partition index reuses a global hierarchical k-means tree and, for each label, maintains a per-label subtree, using Bloom filters for efficient routing and sorted buffers at the leaves for rapid access.

Key features include:

Dynamic selection: A runtime policy chooses graph traversal for high $\alpha$ , switching to partition-based search when $M\alpha \lesssim \log N$ to avoid graph fragmentation.
Shared structure: Partition indices share centroid and tree structure, keeping memory overhead low, with only per-label buffers and Bloom filters added.
Efficient complex predicate handling: For arbitrary predicates (conjunctions, ranges, etc.), the system builds a predicate-specific index by mapping the predicate-matching IDs as a “virtual label” and constructing a corresponding subtree.
Completeness and latency guarantees: Curator guarantees complete recall down to very low selectivity, with worst-case search time scaling with $\alpha N$ (the number of qualified vectors) rather than the full dataset size.
Empirical results: On the YFCC-10M and arXiv datasets, Curator reduces low-selectivity query latency by up to 20.9× at 90% recall, with only 5.5% and 4.3% respective increases in build time and memory (Jin et al., 3 Jan 2026).

4. Optimization Planning and Multi-Attribute Query Processing: PathFinder

PathFinder introduces a cost-based, two-phase optimizer to select the most efficient search plan for arbitrary complex filters over multiple attributes (Wu et al., 2 Nov 2025). The selectivity $\sigma(F)$ of filter $F$ determines whether to use a single small dense graph (for extremely low selectivity), a union of multiple graphs, or higher-level parent graphs from attribute-specific indexes.

Key components:

Search Utility Metric: $U(G, F) = \frac{|R_F|}{\sum_{g \in G} |g| \cdot |G|^{\alpha}}$ balances answer set size and access cost, with best plans minimizing the denominator.
Two-Phase Optimization: Conjunction-phase finds efficient plans for conjunctive subclauses, typically leading to small, dense graphs; disjunction-phase merges and collapses plans to minimize redundant graph accesses.
Index Borrowing: When the requested filter lacks a direct index, the optimizer borrows an index from a correlated attribute, tightening filter ranges where possible (Wu et al., 2 Nov 2025).
Empirical validation: PathFinder achieves up to 9.8× speedup at recall 0.95 over baselines for selectivity between 0.1% and 1% (e.g., RedCaps: 290 qps vs. best prior’s 30 qps), and maintains $\geq$ 0.95 recall while classical graph-based methods experience severe QPS collapse (Wu et al., 2 Nov 2025).

5. Unified Range Filtering: UNIFY and Hierarchical Segmented Inclusive Graphs

UNIFY proposes SIG (Segmented Inclusive Graph) and its hierarchical variant HSIG as universal index structures for Range-Filtered ANNS (RF-ANNS), supporting the full spectrum of attribute range selectivity (Liang et al., 2024). UNIFY segments the dataset by attribute values and constructs inclusive proximity graphs whose subgraphs correspond to any attribute range union.

SIG: Partitions the dataset into $S$ attribute bins and constructs an adjacency list per segment, such that for any filter range, the union’s proximity graph is a subgraph of SIG.
HSIG: Stacks multiple SIG layers in an HNSW-style hierarchy. For low-selectivity (large range) queries, HSIG supports efficient “post-filtering” (full-graph search followed by filter application), yielding $O(\log n)$ complexity.
Practical hybridization: HSIG additionally supports skip-list pointers for fast pre-filtering, and compressed edge sets for hybrid and post-filtering, enabling optimal strategy choice per-query using estimated selectivity thresholds $\tau_A,\tau_B$ ( $\sim$ 1%, 50% from experiments).
Empirical findings: For [l, h] ranges covering >50% of SIFT1M or GloVe, QPS increases by 37.5%+ over best post-filter baseline. For mid-range selectivity (5–50%), hybrid search outperforms reconstruct-at-query-time strategies (Liang et al., 2024).

6. GPU-Accelerated and High-Selectivity Indexing: VecFlow

While most research focuses on low-selectivity (i.e., “narrow” filters), VecFlow addresses the setting where attribute filters are weak (large selectivity) using label-centric inverted file (IVF) partitioning and GPU-optimized traversal (Xi et al., 1 Jun 2025). When selectivity is high ( $\geq 0.8$ ), VecFlow’s IVF-Graph design, with redundancy-bypassing and batched traversal, sustains multi-million query-per-second rates and outperforms all known CPU-based and prior GPU-ANNS filtered search by up to two orders of magnitude for modest recall targets ( $>0.9$ ).

Label-centric index: Maintains inverted lists per label, partitioned by size, with specialized small-graph or BFS search per list.
GPU implementation: Highly coalesced memory layout, persistent kernel launch, warp-level parallelism, and batch adaptivity.
Throughput scaling: For large selectivity filters, throughput remains stable; with smaller batches, persistent kernels give >6× improvement on A100 (Xi et al., 1 Jun 2025).

A plausible implication is that as selectivity increases, optimal strategies shift from partition/attribute-specific structures (Curator, FusedANN, HSIG) to high-throughput global traversals as leveraged by VecFlow.

7. Parameter Tuning, Practical Integration, and Trade-Offs

Systematic parameter selection and system integration are essential for low-selectivity filtered ANNS performance:

Penalty/Trade-off parameters: In penalty-based methods (e.g., FusedANN), attributes such as $\lambda$ , $\alpha$ , and $\beta$ must be tuned so that unmatched records are excluded from top-k while maintaining recall, with practical rules derived from distance and intra-cluster statistics (Heidari et al., 24 Sep 2025).
Tree and buffer tuning: Partition tree branching factor, buffer size, and Bloom filter parameters control memory/latency trade-offs in Curator (Jin et al., 3 Jan 2026).
Beam/ef selection: Search expansion parameters balance completeness and throughput, with careful tuning required near the crossover region between graph and partition index selection (Jin et al., 3 Jan 2026).
Index sharing/overhead: Architectures such as Curator and UNIFY demonstrate that per-label or per-filter partitioning can be achieved with <5% memory and build-time increase, conferring 10–20× speedup in low-selectivity regimes (Jin et al., 3 Jan 2026, Liang et al., 2024).
Filter-aware routing: Many systems derive per-query routing rules (e.g., by online selectivity estimation), directing queries to the optimal index and algorithm given anticipated recall, throughput, and latency (Liang et al., 2024, Jin et al., 3 Jan 2026).

References Table

System	Low-Selectivity Approach	Key Performance at Low Selectivity
FusedANN	Geometric penalty, fused embedding	3–6× QPS gain at 0.9–0.98 recall vs. graph+filter (Heidari et al., 24 Sep 2025)
Curator	Dual (graph+partition), shared tree	up to 20.9× latency reduction at 90% recall, +5% res. overhead (Jin et al., 3 Jan 2026)
PathFinder	Cost-based, adaptive graph plan	up to 9.8× QPS speedup at 95% recall (Wu et al., 2 Nov 2025)
UNIFY/HSIG	Segment-inclusive, hierarchical PG	37.5%+ QPS gain for range $\geq$ 50% (Liang et al., 2024)
VecFlow	GPU, high-sel. label-centric IVF-Graph	2.6M QPS at 90% recall, 1–2 orders of mag. over CPU (Xi et al., 1 Jun 2025)

In summary, low-selectivity filtered ANNS has driven the development of penalty-based convexification, robust partitioning, dynamic dual-index systems, inclusive graph structures, and adaptive cost-based planning. These advances collectively enable efficient vector search with tight, complex filters over large, heterogeneous datasets, making high-recall, low-latency filtered search feasible at scale.