Cardinality Estimation for High Dimensional Similarity Queries with Adaptive Bucket Probing

Qintian Guo; Ruiyuan Zhang; Xiaofang Zhou; Zhonghan Chen

arxiv: 2604.04603 · v1 · submitted 2026-04-06 · 💻 cs.DB · cs.AI

Cardinality Estimation for High Dimensional Similarity Queries with Adaptive Bucket Probing

Zhonghan Chen , Qintian Guo , Ruiyuan Zhang , Xiaofang Zhou This is my paper

Pith reviewed 2026-05-10 19:56 UTC · model grok-4.3

classification 💻 cs.DB cs.AI

keywords cardinality estimationsimilarity searchlocality-sensitive hashinghigh-dimensional datamulti-probeproduct quantizationquery optimization

0 comments

The pith

A locality-sensitive hashing framework with adaptive probing and progressive sampling estimates the number of similar items in high-dimensional data accurately and efficiently.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a lightweight method to estimate how many points in a high-dimensional dataset lie within a given distance of a query point, without examining every vector. It starts by using locality-sensitive hashing to divide the space into buckets that keep nearby points together, then adaptively checks neighboring buckets according to the query threshold. Progressive sampling limits the number of full distance calculations while asymmetric product quantization speeds up those that remain, and separate update procedures handle insertions and deletions in changing collections. A sympathetic reader would care because such estimates let query planners decide whether a similarity search will return few or many results and allocate resources accordingly.

Core claim

The proposed framework partitions high-dimensional space with locality-sensitive hashing, then applies adaptive multi-probe exploration of neighboring buckets scaled to the query distance threshold; progressive sampling combined with asymmetric distance computation in product quantization reduces the cost of each estimate, while dedicated update algorithms maintain the structure under data changes.

What carries the argument

Adaptive multi-probe locality-sensitive hashing that selects buckets according to distance thresholds, paired with progressive sampling to limit distance computations.

If this is right

Query optimizers in database systems can use the estimates to select execution strategies for similarity searches.
The same structure supports both static collections and large-scale dynamic datasets through its update procedures.
Fewer distance calculations are needed during estimation, improving online response times in high-dimensional settings.
Cardinality estimates remain usable even when the similarity threshold changes between queries.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach might be combined with other index structures to estimate result sizes for approximate nearest-neighbor queries.
Similar sampling ideas could be tested for estimating the number of points inside range queries in metric spaces beyond vectors.
Performance on datasets whose dimensionality greatly exceeds those used in the experiments would indicate whether the sampling bias grows with dimension.

Load-bearing premise

Locality-sensitive hashing and the chosen sampling strategy preserve enough distance information that estimates remain accurate across different thresholds and data distributions.

What would settle it

Compute both the estimated and the exact cardinality for the same set of high-dimensional queries on a public vector dataset; a large, consistent gap between the two values at any threshold would show the method fails to deliver accurate estimates.

Figures

Figures reproduced from arXiv: 2604.04603 by Qintian Guo, Ruiyuan Zhang, Xiaofang Zhou, Zhonghan Chen.

**Figure 1.** Figure 1: Motivation of our work: 𝑥-axis is the distance between the central bucket B𝑐𝑒𝑛𝑡𝑟𝑎𝑙 with its 𝑘-step neighbor N𝑘 , where 𝑘 ∈ [0, 14] and 𝑘 is the hamming distance, and 𝑦-axis is the selectivity in N𝑘 . We use 5 datasets, each containing 10 queries, for demonstration. As N𝑘 becomes more distant from B𝑐𝑒𝑛𝑡𝑟𝑎𝑙 , the selectivity of the neighbor decreases, which means that closer neighbor are more likely to conta… view at source ↗

**Figure 4.** Figure 4: Dynamic Prober V.S. Dynamic Prober-PQ: Speedup [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

**Figure 5.** Figure 5: Parameter Study - 𝜖: Accuracy and Efficiency SIFT GIST GloVe FastText YouTube Datasets 0 100 200 300 400 500 Segmented Latency (s) Initial Consutrction Update Consutrction [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: Dynamic Prober: Dynamic Update Efficiency ( [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

**Figure 7.** Figure 7: Dynamic Prober: Dynamic Update Accuracy (The [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

read the original abstract

In this work, we address the problem of cardinality estimation for similarity search in high-dimensional spaces. Our goal is to design a framework that is lightweight, easy to construct, and capable of providing accurate estimates with satisfying online efficiency. We leverage locality-sensitive hashing (LSH) to partition the vector space while preserving distance proximity. Building on this, we adopt the principles of classical multi-probe LSH to adaptively explore neighboring buckets, accounting for distance thresholds of varying magnitudes. To improve online efficiency, we employ progressive sampling to reduce the number of distance computations and utilize asymmetric distance computation in product quantization to accelerate distance calculations in high-dimensional spaces. In addition to handling static datasets, our framework includes updating algorithm designed to efficiently support large-scale dynamic scenarios of data updates.Experiments demonstrate that our methods can accurately estimate the cardinality of similarity queries, yielding satisfying efficiency.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A solid engineering paper on LSH-based cardinality estimation that integrates known techniques with an adaptive and dynamic twist, but without clear theoretical novelty.

read the letter

This paper builds a cardinality estimator for high-dimensional similarity queries by partitioning space with LSH, then using adaptive multi-probe to check neighboring buckets according to the query's distance threshold. It layers on progressive sampling to cut distance computations and product quantization with asymmetric distances for speed, plus a separate update procedure for dynamic data inserts and deletes. The goal is a lightweight structure that stays efficient at query time while supporting both static and changing collections. That combination is the main contribution. The adaptive probing and the dynamic update routine are the parts that feel most useful in practice, since real vector databases rarely stay frozen. The framework stays coherent on its own terms and avoids obvious circularity or hidden fitting loops. The soft spots are the limited novelty and the evaluation. The method is mostly a re-assembly of standard LSH multi-probe, quantization, and sampling ideas rather than a new primitive or bound. The abstract asserts accurate estimates and satisfying efficiency, yet supplies no concrete error numbers, baselines, or dataset descriptions, so it is hard to judge whether the accuracy holds up once sampling bias and quantization distortion are measured properly. If the full experiments only show results against weak baselines or on easy data, the practical value shrinks. This is the kind of work that belongs in a database systems venue rather than a theory track. Practitioners tuning query optimizers for high-dimensional indexes might pick up implementation details from the progressive sampling and update logic. I would bring it to a reading group focused on vector search or query optimization, but not to a general theory group. I would not cite it unless the experiments prove stronger than the abstract suggests. It deserves peer review because the problem is relevant, the components are assembled sensibly, and the dynamic case is handled explicitly; referees can push for tighter evaluation and clearer comparison to prior estimators.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a framework for cardinality estimation of similarity queries in high-dimensional spaces. It partitions the space with locality-sensitive hashing (LSH), applies adaptive multi-probe exploration of neighboring buckets to handle varying distance thresholds, uses progressive sampling and asymmetric product quantization to reduce distance computations, and includes an update algorithm for dynamic data. The central claim is that experiments demonstrate accurate cardinality estimates with satisfying efficiency.

Significance. If the experimental claims hold with strong quantitative support, the work could offer a practical, lightweight approach to cardinality estimation for high-dimensional similarity search in databases, extending established LSH and quantization techniques to both static and dynamic settings. The adaptive probing and sampling components address a relevant efficiency challenge, but the absence of concrete metrics, baselines, or dataset details in the provided description limits assessment of improvement over prior methods.

major comments (2)

[Abstract] Abstract: The assertion that 'Experiments demonstrate that our methods can accurately estimate the cardinality of similarity queries, yielding satisfying efficiency' supplies no quantitative results (e.g., relative error, recall, or runtime), no baselines, no error metrics, and no dataset details. This is load-bearing for the paper's empirical contribution and prevents evaluation of the central claim.
[Evaluation] Evaluation section: The description of experiments must include specific accuracy numbers, comparisons to standard LSH cardinality estimators or sampling baselines, details on datasets and query thresholds, and analysis of bias from sampling or quantization to substantiate the accuracy claim.

minor comments (2)

[Introduction] Clarify the precise definition of 'cardinality' in the context of similarity queries (e.g., number of points within a radius) and how it differs from standard selectivity estimation.
[Dynamic Updates] The description of the dynamic update algorithm should specify the time complexity and how it maintains the LSH structure without full rebuilds.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We agree that the abstract and evaluation section would benefit from greater specificity to strengthen the empirical claims, and we will revise the manuscript accordingly while preserving the core technical contributions.

read point-by-point responses

Referee: [Abstract] Abstract: The assertion that 'Experiments demonstrate that our methods can accurately estimate the cardinality of similarity queries, yielding satisfying efficiency' supplies no quantitative results (e.g., relative error, recall, or runtime), no baselines, no error metrics, and no dataset details. This is load-bearing for the paper's empirical contribution and prevents evaluation of the central claim.

Authors: We agree that the abstract would be strengthened by including concrete quantitative results. In the revised version we will add specific metrics such as average relative error (typically under 15% across tested thresholds), runtime reductions relative to naive sampling, and references to the datasets and query distance thresholds used. This will make the central empirical claim more self-contained without altering the technical narrative. revision: yes
Referee: [Evaluation] Evaluation section: The description of experiments must include specific accuracy numbers, comparisons to standard LSH cardinality estimators or sampling baselines, details on datasets and query thresholds, and analysis of bias from sampling or quantization to substantiate the accuracy claim.

Authors: We acknowledge the need for more explicit experimental detail. The current evaluation already reports results on standard high-dimensional datasets (e.g., SIFT and GloVe) with varying query thresholds and includes comparisons against uniform sampling and basic LSH estimators. In revision we will expand the section with (i) tabulated mean relative error and recall figures, (ii) a new subsection quantifying bias introduced by progressive sampling and asymmetric product quantization (including both theoretical bounds and empirical measurements), and (iii) additional runtime and accuracy plots against the suggested baselines. These additions will directly address the request for substantiation. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents an empirical framework for cardinality estimation in high-dimensional spaces using LSH partitioning, adaptive multi-probe exploration, progressive sampling, and product quantization, with experimental validation for accuracy and efficiency on static and dynamic data. No derivation chain, first-principles predictions, or mathematical reductions are claimed or visible in the abstract or method description. All components are standard techniques combined practically, with performance claims resting on experiments rather than any self-referential definitions, fitted inputs renamed as predictions, or load-bearing self-citations. The approach is self-contained without circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The framework implicitly relies on standard LSH collision properties and sampling assumptions that are not detailed here.

pith-pipeline@v0.9.0 · 5447 in / 1021 out tokens · 54948 ms · 2026-05-10T19:56:59.559537+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We leverage locality-sensitive hashing (LSH) to partition the vector space while preserving distance proximity. Building on this, we adopt the principles of classical multi-probe LSH to adaptively explore neighboring buckets... progressive sampling... asymmetric distance computation in product quantization
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Experiments demonstrate that our methods can accurately estimate the cardinality of similarity queries, yielding satisfying efficiency.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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√𝑝− √︂𝑎 2𝑤 2 > ˆ𝑝+ 2𝑎 2𝑤 # (5) =Pr 𝑝−2 √𝑝 √︂𝑎 2𝑤 + 𝑎 2𝑤 > ˆ𝑝+ 2𝑎 2𝑤 (6) ≤Pr

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