LLMs Meet Isolation Kernel: Lightweight, Learning-free Binary Embeddings for Fast Retrieval

Cam-Tu Nguyen; Kai Ming Ting; Yang Xu; Zhibo Zhang

REVIEW 3 major objections 4 minor 6 references

LLMs Meet Isolation Kernel: Lightweight, Learning-free Binary Embeddings for Fast Retrieval

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Binary codes built from isolation trees compress LLM embeddings for fast search without retraining.

desk verdict Solid empirical paper on learning-free binary hashing of LLM embeddings; the theoretical packaging is softer than it looks, but the results justify a serious review. read the letter →

arxiv 2601.09159 v4 pith:LZNQEFNK submitted 2026-01-14 cs.IR

Zhibo Zhang , Yang Xu , Kai Ming Ting , Cam-Tu Nguyen This is my paper · ORCID

classification cs.IR

keywords IsolationKernelbinaryembeddinglearning-freehashingLLMembeddingstextretrievalForestapproximatenearestneighborsearchbitwisesimilarity

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that the high-dimensional embeddings produced by large language models can be converted into short binary codes using a learning-free method called Isolation Kernel Embedding (IKE), without giving up retrieval accuracy. IKE replaces each 4096-dimensional embedding with a compact code of tree-leaf indices, so documents and queries are compared by counting how often they fall into the same random isolation-tree leaf. The authors claim this yields up to 16.7x faster search and up to 16x lower memory than the original embeddings, while keeping ranking quality at 98-101% of the original space. If true, this would make billion-scale neural retrieval practical on commodity CPUs, with no costly training or model adaptation. The paper also argues that IKE works because it satisfies four criteria for effective binary hashing: full space coverage, entropy maximization, bit independence, and a newly emphasized fourth property, high diversity among the random partitions.

What carries the argument

Isolation Kernel (IK), the data-dependent similarity defined as the probability that two points fall in the same cell of a random partition of the space. IKE estimates IK with an ensemble of t isolation trees (or, in a variant, Voronoi diagrams), where each tree recursively splits the data along a random dimension at a random threshold; each point gets an index for the leaf it lands in per tree. Similarity between two points is the fraction of trees in which they share a leaf, computed with bitwise XOR, OR, shifts, masks, and popcount for speed. The machinery works by adapting partition granularity to data density — large cells in sparse regions, small cells in dense regions — and by making

What would settle it

Run IKE on a corpus whose embeddings are deliberately arranged into well-separated, skewed clusters, keep ψ fixed, increase t to thousands, and measure MRR@10 relative to the original LLM embeddings; if accuracy falls below the claimed 98% floor at large t, the ensemble-averaging premise collapses.

Watch

Extended reading notes

Core claim

The central claim is that Isolation Kernel Embedding (IKE) — a learning-free transform built from an ensemble of random isolation trees — maps LLM embeddings into binary codes whose Hamming-like similarity closely approximates the ideal retrieval kernel in the original space. The key discovery is that high diversity among the random partitions, not just the previously known three hashing criteria, is what makes this work for the non-uniform, high-dimensional distributions typical of LLM embeddings. The paper shows that when the Voronoi-based VDeH method uses all dimensions, it produces correlated, low-diversity partitions and performs poorly; by restricting each partition to a random low-dim

Load-bearing premise

The proof that IKE's bits are independent and the entropy is maximized assumes the embedding space is uniform, but LLM embeddings are not uniform; the method relies on the unproven premise that averaging over thousands of independent isolation trees erases the bias and bit-correlation caused by that non-uniformity.

Editorial extensions

If this is right

If IKE is correct, large-scale text retrieval can run with 8-16x less memory and several-fold lower latency than raw LLM embeddings, making 4096-dimensional models feasible for CPU-only deployments.
Because the binary codes are built from independent trees, they can be truncated to any length at query time, giving an MRL-like accuracy-speed tradeoff without retraining the language model.
IKE's compatibility with graph-based and inverted-file approximate-nearest-neighbor indexes means it can accelerate not just exhaustive search but also ANN pipelines, with reported throughput gains of up to 10x over other learning-free compression methods.
The identification of high partition diversity as a fourth essential criterion suggests a design principle for future hashing methods: random, decorrelated partitions matter as much as coverage, entropy, and bit independence.
A learning-free transform that preserves retrieval accuracy could lower the cost of updating embeddings when the underlying LLM changes, since no adapter or hash function needs retraining.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The diversity argument likely generalizes beyond LLM embeddings: any high-dimensional, non-uniform, structured dataset where VDeH underperforms might benefit from restricting each partition to a low-dimensional random subspace or using axis-aligned random splits; this is a testable extension of the paper's fourth criterion.
IKE's bitwise similarity could be further accelerated on hardware with advanced popcount or SIMD instructions, and the code length t could in principle be tuned adaptively per query to trade latency for accuracy in overloaded serving systems.
A natural next experiment would be applying IKE to cross-modal retrieval (e.g., image-text) despite the modality gap noted as a limitation; the diversity criterion suggests that per-modality random partitions might bridge part of the gap without alignment training.
The theoretical justification depends on uniform-data assumptions that real embeddings violate; this suggests exploring whether enforcing approximate equal-occupancy leaves in each tree (e.g., via split-point selection from data quantiles) would make the entropy claim hold for non-uniform distributions and further stabilize accuracy.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

I gave arXiv:2601.09159 a full read. Punchline: it's a solid empirical paper that deserves a real referee; the theory in Section 3.3/Appendix C is the weakest link, but the results stand on their own.

What is actually new: IKE adapts Isolation Kernel hashing (a generalization of the same group's VDeH) to LLM embeddings, adding a random-subspace Voronoi version, an iForest implementation, and a fourth 'diversity' criterion. The experiments are the main event: six text retrieval datasets, two 4096-dim LLM encoders, exhaustive and ANN search, ten seeds for the main table, and fair comparisons against CSR, rpLSH, PQfs, and ScaNN. The headline numbers—8–16x memory reduction, 2.5–16.7x faster search, MRR@10 at 98–101% of the original—are plausible and practically useful. The tuning study on t is a nice addition, and the anonymous code is a plus.

The soft spots are real but not fatal. Theorem 1 proves entropy maximization and bit independence only under a uniform data distribution; the paper immediately admits LLM embeddings are non-uniform and argues that the large ensemble averages out bias. That is an assertion, not a proof, and as a theoretical claim it needs much more support. Then there's a mismatch: the text and the storage complexity assume exactly ψ leaves per iTree, but the construction in Appendix D.1 stops at height ⌈log2 ψ⌉ and can terminate early, so fewer leaves are possible. That is a minor technical inconsistency, presumably easy to fix. The diversity proof (Theorem 2) also assumes independent input dimensions, which LLM embeddings likely violate. So the theoretical framework is best read as intuition, not a formal guarantee for the actual data.

None of this undermines the empirical core. The retrieval labels are held out, the baselines are external, and the results are reproducible in principle. The central claim—that a learning-free binary hash can compress LLM embeddings with minimal accuracy loss—holds up.

This paper is for people building large-scale embedding retrieval systems who want a cheap alternative to retraining. It should definitely be sent to peer review; a good referee can push the authors to clean up the theory and the leaf-count discrepancy. I would cite it in my own work on embedding compression.

Referee Report

3 major / 4 minor

Summary. The paper proposes IKE (Isolation Kernel Embedding), a learning-free method that converts high-dimensional LLM embeddings into binary codes using ensembles of random partitions (iForest or Voronoi diagrams). The authors claim that IKE cuts memory by 8–16× and speeds up exhaustive retrieval by 2.5–16.7× while retaining 98–101% of original MRR@10, and that it also improves ANN throughput under IVF/HNSW. The theoretical section argues that IKE satisfies four criteria for effective binary hashing: full space coverage, entropy maximization, bit independence, and a new 'diversity' criterion. Experiments cover six datasets, two 4096-dim LLM encoders (LLM2Vec and Qwen3), exhaustive and ANN settings, and comparisons against CSR and learning-free compression methods.

Significance. If the claims hold, IKE is a practical, training-free compression scheme for LLM embeddings with strong empirical support: six datasets, two LLM encoders, 10-seed stability for the main table, and publicly available code. The introduction of 'diversity' as a fourth hashing criterion is conceptually interesting. However, the theoretical guarantees for the iForest variant are proved only under a uniform-data assumption that the paper concedes is false for LLM embeddings, and the diversity theorem assumes independent input dimensions. These gaps undermine the paper's stated explanation of why IKE works, although the empirical method may still be valuable as a heuristic. The central claim of the paper—that IKE works because it satisfies four criteria—is therefore not presently supported by the theory.

major comments (3)

[Appendix C.3, Theorem 1] Theorem 1 proves entropy maximization and bit independence under the explicit assumption of a uniform data distribution. The paper immediately concedes that 'LLM embedding is non-uniform.' The following paragraph asserts that ensemble averaging over t iTrees erases bias and correlation, but this is not proved; averaging reduces variance, not systematic bias in the kernel estimate. Since the abstract and Section 1 claim IKE satisfies four essential criteria and this is the paper's main theoretical contribution, this is a load-bearing gap. Please either prove the properties for non-uniform distributions (or under a weaker, realistic assumption) or reframe the theoretical claims as conditional and support the non-uniform case empirically.
[Section 3.1 vs. Appendix D.1] Section 3.1 states that each iTree has exactly ψ leaf nodes, because each point is eventually isolated. However, Appendix D.1 defines termination conditions that include a height limit l = ⌈log2 ψ⌉ and failed splits, so a tree can stop with fewer than ψ leaves and leaves can contain multiple points. The proof of Theorem 1 and the storage complexity t⌈log2 ψ⌉ bits both assume exactly ψ leaves of equal occupancy. This inconsistency affects the entropy and bit-independence proof for the implemented method, and also the claim of uniform leaf indices used by the binary code. Please reconcile the implementation description with the theoretical model.
[Appendix C.4, Theorem 2] The diversity theorem asserts ρIKEVD(m=1) = ρdata/d and the inequality ρVDeH > ρIKEVD(m=1) > ρIKE ≥ 0. The proof of the first equality relies on the assumption that input dimensions are independent, so that covariance across different dimensions is zero. LLM embeddings are highly correlated in practice, so this assumption is violated. Since the diversity criterion is the paper's novel theoretical contribution and is the stated reason IKE outperforms VDeH, the theorem does not apply to the target data. Please provide a proof for correlated dimensions or present the diversity advantage as an empirical observation rather than a proven theorem.

minor comments (4)

[Table 1] The table header appears garbled: 'SpaceTypeSpace Time' and the column labels 'Other' and 'Search' are not fully explained. Please reformat for clarity.
[Section 4.1 / Appendix E.2] Touche2020.V3 uses a random 30% of the official test set as a validation set for tuning ψ. Since the validation split overlaps with the test distribution, this is a mild form of test-set leakage; please state this explicitly or use a separate validation set.
[Appendix C.2] The proof of entropy maximization for IKE_VD relies on Lemma 1 of Xu and Ting (2025) without reproducing it. This is acceptable if the source is accessible, but please make the dependence explicit in the main text, especially because the cited work shares authors with this paper.
[Appendix C.3] The proof of Theorem 1 computes the expected probability of going left averaged over both the random split point and the data point, but the property requires the probability for an arbitrary (fixed) point to be uniform across leaves. The current argument only establishes a mean over data points, not the claimed per-point uniformity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: IKE's retrieval claims are evaluated on held-out labels against external baselines; theoretical gaps are assumption failures, not input-output equivalence.

full rationale

The derivation chain is not circular. IKE's binary code is literally the Isolation Kernel's finite-partition estimate (Eq. 3: Kψ(x,y|D)≃1/t Σ_i I(Φidx_i(x)=Φidx_i(y))), so the similarity measure is defined, not fitted, from the same random partitions; the empirical claims are tested on held-out query relevance labels against the original LLM space and external baselines, not against quantities used to build the iTrees. Hyperparameter ψ is chosen on a validation set, which is standard tuning, not a fit relabeled as a prediction. The main theoretical support for the default iForest variant is stated in-paper (Theorem 1, Appendix C.3), and although it assumes a uniform data distribution and the paper concedes 'LLM embedding is non-uniform,' that is an unproven transfer/robustness gap, not a reduction: the theorem's conclusion is not used as an input to the method or to the evaluation. The IKEV D properties are inherited from Xu and Ting (2025), a prior published framework by two of the present authors, but those lemmas have their own stated assumptions (i.i.d. anchors and cell-index encoding) and do not assume the present paper's retrieval result; this is legitimate citation rather than a self-citation chain that forces the conclusion. The diversity analysis (Appendix C.4) is a Monte-Carlo variance decomposition; its inequality for iForest contains an asserted rather than fully proved step, but that is again a correctness risk, not circularity. No equation in the paper reduces a predicted quantity to a fitted parameter by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claims rest on per-dataset choices of ψ and t and on theoretical assumptions that are acknowledged not to hold for LLM embeddings (uniformity, dimension independence, exact ψ leaves). No new physical or mathematical entity is postulated.

free parameters (3)

ψ (number of isolating partitions / leaf cells per tree) = Per dataset: e.g., LLM2Vec: HotpotQA 12, FiQA2018 6, FEVER-HN 15, Istella22 16, TREC DL23 3, Touche2020 7; Qwen3: 10, 15
Grid-searched on a validation set over [2,16] (Appendix E.2); controls code length, memory, and retrieval accuracy. The reported speed/memory/accuracy ratios depend on this per-dataset choice.
t (number of iTrees) = Default d=4096; in Section 4.4 t=8192/4096/2048/1024 for code lengths 1024/512/256/128 bytes at ψ=2; varied in Figure 7
Ensemble size controls variance, memory, and mapping cost. Not learned, but chosen per experimental setting and used to build the QPS-accuracy trade-off curves.
m (random subspace dimension for IKEVD) = Optimally tuned m=7 (FiQA, LLM2Vec) and m=5 (FiQA, Qwen3); also m=1 evaluated
Only for the Voronoi variant, Table 2. An extra hyperparameter not needed by default IKE, but its tuning is part of the IKEVD comparison.

assumptions (5)

ad hoc to paper Uniform data distribution for entropy maximization and bit independence of iForest IKE
Theorem 1 (Appendix C.3) proves Pr(x ∈ Vi) = 1/ψ only under a uniform distribution; the same section concedes LLM embeddings are non-uniform. This assumption makes the 'four criteria' theoretical justification not apply to the target data.
ad hoc to paper Independent input dimensions for the diversity theorem
Theorem 2 (Appendix C.4) assumes dimensions are independent to conclude ρVDeH > ρIKEVD > ρIKE. LLM embedding dimensions are not independent, so the ordering is unproven for actual embeddings.
domain assumption Validity of VDeH's Lemma 1 and Theorem 1 from Xu and Ting (2025)
Propositions 2 and 3 for IKEVD are inherited from Xu and Ting (2025), a paper by two of the current authors. The proofs are not reproduced in this manuscript.
ad hoc to paper Each iTree yields exactly ψ leaf cells with uniform occupancy
Section 3.1 says an iTree has exactly ψ leaves and ψ−1 internal nodes; Section 3.2 sets the height limit to ⌈log2 ψ⌉, which can stop splitting before all points are isolated, producing fewer leaf cells. The entropy/bit-independence proofs assume exactly ψ equally likely cells.
domain assumption LLM embedding space similarity is a valid retrieval relevance signal
The method compresses LLM embeddings and evaluates quality relative to nearest-neighbor ranking in that space; if the embeddings were not semantically meaningful, preserving their similarity would not help retrieval.

how reviews work

0 comments

Cite this review

Pith. "Pith review of LLMs Meet Isolation Kernel: Lightweight, Learning-free Binary Embeddings for Fast Retrieval." pith.science (2026). https://pith.science/paper/LZNQEFNK

@misc{pith2026260109159,
  author       = {Pith},
  title        = {Pith review of: LLMs Meet Isolation Kernel: Lightweight, Learning-free Binary Embeddings for Fast Retrieval},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LZNQEFNK}},
  note         = {Machine review of arXiv:2601.09159}
}

read the original abstract

Large language models (LLMs) have recently enabled remarkable progress in text representation. However, their embeddings are typically high-dimensional, leading to substantial storage and retrieval overhead. Although recent approaches such as Matryoshka Representation Learning (MRL) and Contrastive Sparse Representation (CSR) alleviate these issues to some extent, they still suffer from retrieval accuracy degradation. This paper proposes Isolation Kernel Embedding or IKE, a learning-free method that transforms an LLM embedding into a binary embedding using Isolation Kernel (IK). Lightweight and based on binary encoding, IKE offers a low memory footprint and fast bitwise computation, lowering retrieval latency. Experiments on multiple text retrieval datasets demonstrate that IKE offers up to 16.7x faster retrieval and 16x lower memory usage than the original LLM embeddings, while maintaining comparable accuracy. Theoretically, we show that IKE works because it satisfies four essential criteria for effective binary hashing that other methods do not possess. Compared to CSR, IKE consistently achieves better retrieval efficiency and effectiveness. IKE also works effectively with graph-based indexing, demonstrating its superiority in balancing accuracy and latency compared to alternative compression techniques in the approximate nearest neighbor (ANN) search setting.

Figures

Figures reproduced from arXiv: 2601.09159 by the authors.

**Figure 2.** Effect of parameter m in IKEV D (t=4096) on nDCG@10 across two LLM embedding datasets. The pentagram marker indicates the performance of IKEV D when m = d, which is equivalent to the VDeH method. Voronoi Diagram Encoded Hashing In the preliminary study, Voronoi Diagrams (VD) are explored as an implementation of the Isolation Kernel for transforming LLM embeddings into binary codes. This approach, known as VDeH (X… view at source ↗

**Figure 4.** QPS vs. MRR@10 for Four ANN Methods on the HotpotQA dataset. The curves are obtained by adjusting the ANN search parameters. The detailed configuration is described in Appendix F.2. Hyperparameter Settings. Following the original Isolation Forest framework (Liu et al., 2008), we set the maximum iTree height to l = ⌈log2 (ψ)⌉. Unless otherwise specified, the number of iTrees t equals the embedding dimension d. The p… view at source ↗

Figures from the paper (6 more)

**Figure 5.** Figure 5: Comparison of Retrieval Accuracy and Search [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: Performance Comparison of Compression Methods on ANN Retrieval: QPS vs. nDCG@10 on the HotpotQA (LLM2Vec) dataset. The curves are obtained by adjusting the search parameter of the index structures. (a) Exhaustive Search (HotpotQA, LLM2Vec) (b) HNSW (HotpotQA, LLM2Vec) …

**Figure 7.** Figure 7: Effect of parameter t (the number of iTrees) on Search Time and Retrieval Accuracy. The gray dashed lines denote the corresponding retrieval performance in the LLM embedding space [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: QPS vs. MRR@10 for Four ANN Methods on Istella22 and TREC DL 23. [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]

**Figure 9.** Figure 9: Comparison of Retrieval Accuracy and Search Time between CSR and IKE in the exhaustive search setting on the Istella22 (LLM2Vec) and TREC DL 23 (LLM2Vec) datasets. The search time includes both the mapping time for all queries and the similarity computation time, rathe…

**Figure 10.** Figure 10: Performance Comparison of Compression Methods on ANN Retrieval: QPS vs. nDCG@10 on HotpotQA (Qwen3), Istella22 and TREC DL 23. The curves are obtained by adjusting the search parameter of the index structures [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

6 extracted references · 2 linked inside Pith

[2]

The faiss library.IEEE TBD, pages 1–17. Kenneth Enevoldsen, Isaac Chung, Imene Kerboua, Márton Kardos, Ashwin Mathur, David Stap, Jay Gala, Wissam Siblini, Dominik Krzemi ´nski, Genta Indra Winata, Saba Sturua, Saiteja Utpala, Mathieu Ciancone, Marion Schaeffer, Gabriel Se- queira, Diganta Misra, Shreeya Dhakal, Jonathan Rystrøm, Roman Solomatin, and 67 o...

arXiv 2025
[5]

Our study falls within the hashing paradigm, yet demonstrates strong po- tential to preserve—and in some cases even im- prove—retrieval accuracy

are commonly applied, though often at the expense of accuracy. Our study falls within the hashing paradigm, yet demonstrates strong po- tential to preserve—and in some cases even im- prove—retrieval accuracy. Hashing techniques can be broadly categorized into training-based approaches (Learning to Hash, L2H) (Liu et al., 2024a; Weiss et al., 2008; Yu et a...

2008
[6]

HN” in the dataset name indicates “Hard Negatives

for an effective hashing: full space coverage, entropy maximization, and bit independence. Recently, Xu and Ting (2025) showed that V oronoi Diagrams (VD) offer a natural alterna- tive to L2H, as they inherently satisfy these three properties. Building on this insight, they pro- posed VDeH, a learning-free method that lever- ages a VD–based implementation...

2025
[2011]

Pattern Anal

Product quantization for nearest neighbor search.IEEE Trans. Pattern Anal. Mach. Intell., 33(1):117–128. Aditya Kusupati, Gantavya Bhatt, Aniket Rege, Matthew Wallingford, Aditya Sinha, Vivek Ra- manujan, William Howard-Snyder, Kaifeng Chen, Sham Kakade, Prateek Jain, and 1 others. 2022. Matryoshka representation learning.NeurIPS, 35:30233–30249. Yinhe La...

arXiv 2022
[2015]

InCVPR, pages 3332–3339

Sparse projections for high-dimensional binary codes. InCVPR, pages 3332–3339. Yang Xu and Kai Ming Ting. 2025. V oronoi diagram encoded hashing. InECML PKDD, page 87–103, Berlin, Heidelberg. Zhilin Yang, Peng Qi, Saizheng Zhang, Yoshua Bengio, William Cohen, Ruslan Salakhutdinov, and Christo- pher D. Manning. 2018. HotpotQA: A dataset for diverse, explai...

arXiv 2025
[2025]

ACM Manag

Graph-based vector search: An experimental evaluation of the state-of-the-art.Proc. ACM Manag. Data, 3(1). Parishad BehnamGhader, Vaibhav Adlakha, Marius Mosbach, Dzmitry Bahdanau, Nicolas Chapados, and Siva Reddy. 2024. LLM2Vec: Large language mod- els are secretly powerful text encoders. InCOLM. Leo Breiman. 2001. Random forests.Machine learning, 45(1):...

2024

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [2]

The faiss library.IEEE TBD, pages 1–17. Kenneth Enevoldsen, Isaac Chung, Imene Kerboua, Márton Kardos, Ashwin Mathur, David Stap, Jay Gala, Wissam Siblini, Dominik Krzemi ´nski, Genta Indra Winata, Saba Sturua, Saiteja Utpala, Mathieu Ciancone, Marion Schaeffer, Gabriel Se- queira, Diganta Misra, Shreeya Dhakal, Jonathan Rystrøm, Roman Solomatin, and 67 o...

arXiv 2025

[2] [5]

Our study falls within the hashing paradigm, yet demonstrates strong po- tential to preserve—and in some cases even im- prove—retrieval accuracy

are commonly applied, though often at the expense of accuracy. Our study falls within the hashing paradigm, yet demonstrates strong po- tential to preserve—and in some cases even im- prove—retrieval accuracy. Hashing techniques can be broadly categorized into training-based approaches (Learning to Hash, L2H) (Liu et al., 2024a; Weiss et al., 2008; Yu et a...

2008

[3] [6]

HN” in the dataset name indicates “Hard Negatives

for an effective hashing: full space coverage, entropy maximization, and bit independence. Recently, Xu and Ting (2025) showed that V oronoi Diagrams (VD) offer a natural alterna- tive to L2H, as they inherently satisfy these three properties. Building on this insight, they pro- posed VDeH, a learning-free method that lever- ages a VD–based implementation...

2025

[4] [2011]

Pattern Anal

Product quantization for nearest neighbor search.IEEE Trans. Pattern Anal. Mach. Intell., 33(1):117–128. Aditya Kusupati, Gantavya Bhatt, Aniket Rege, Matthew Wallingford, Aditya Sinha, Vivek Ra- manujan, William Howard-Snyder, Kaifeng Chen, Sham Kakade, Prateek Jain, and 1 others. 2022. Matryoshka representation learning.NeurIPS, 35:30233–30249. Yinhe La...

arXiv 2022

[5] [2015]

InCVPR, pages 3332–3339

Sparse projections for high-dimensional binary codes. InCVPR, pages 3332–3339. Yang Xu and Kai Ming Ting. 2025. V oronoi diagram encoded hashing. InECML PKDD, page 87–103, Berlin, Heidelberg. Zhilin Yang, Peng Qi, Saizheng Zhang, Yoshua Bengio, William Cohen, Ruslan Salakhutdinov, and Christo- pher D. Manning. 2018. HotpotQA: A dataset for diverse, explai...

arXiv 2025

[6] [2025]

ACM Manag

Graph-based vector search: An experimental evaluation of the state-of-the-art.Proc. ACM Manag. Data, 3(1). Parishad BehnamGhader, Vaibhav Adlakha, Marius Mosbach, Dzmitry Bahdanau, Nicolas Chapados, and Siva Reddy. 2024. LLM2Vec: Large language mod- els are secretly powerful text encoders. InCOLM. Leo Breiman. 2001. Random forests.Machine learning, 45(1):...

2024