VOYAGER: A Training Free Approach for Generating Diverse Datasets using LLMs

Avinash Amballa; Chi-Heng Lin; Srinivas Chappidi; Vivek Kulkarni; Yashas Malur Saidutta

arxiv: 2512.12072 · v2 · submitted 2025-12-12 · 💻 cs.CL · cs.LG

VOYAGER: A Training Free Approach for Generating Diverse Datasets using LLMs

Avinash Amballa , Yashas Malur Saidutta , Chi-Heng Lin , Vivek Kulkarni , Srinivas Chappidi This is my paper

Pith reviewed 2026-05-16 22:25 UTC · model grok-4.3

classification 💻 cs.CL cs.LG

keywords LLM synthetic datadataset diversitydeterminantal point processestraining-free generationiterative selectionsynthetic dataset creation

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The pith

Voyager generates datasets from LLMs that are 1.5 to 3 times more diverse by optimizing determinantal point processes without any training.

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

The paper presents Voyager as an iterative method to produce more varied synthetic datasets from large language models. It directly maximizes a mathematical diversity score using determinantal point processes at each generation step. This tackles the known issue that LLM outputs often repeat similar patterns and thus limit the value of synthetic data for training or testing other models. A sympathetic reader would care because more diverse data could improve how well downstream models generalize without requiring changes to the underlying language model.

Core claim

Voyager is a training-free iterative procedure that selects LLM generations by optimizing the determinant-based diversity quantity from determinantal point processes, supplying both theoretical grounding for why the selections increase spread and experimental evidence of 1.5-3 times higher diversity than standard baselines.

What carries the argument

Determinantal point processes, which quantify diversity by the volume of the parallelepiped spanned by selected points in a kernel matrix and guide iterative selection to maximize that volume.

If this is right

Downstream models trained on the resulting datasets should generalize better because repetitive patterns are reduced.
The same procedure can be applied directly to closed-source LLMs since no parameter updates are needed.
Benchmark construction for model evaluation becomes more trustworthy when the test data exhibits higher measured diversity.
The approach scales to larger dataset sizes because each iteration only requires sampling and kernel evaluation.

Where Pith is reading between the lines

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

Voyager could be combined with prompt engineering or retrieval to target diversity along specific axes such as topic or style.
Higher diversity in synthetic data may reduce certain failure modes like mode collapse in fine-tuned models.
The method invites direct tests on whether the DPP kernel choice affects performance in narrow domains such as code or mathematics.

Load-bearing premise

That the mathematical diversity score from determinantal point processes matches the kind of variety that actually improves downstream model training or evaluation.

What would settle it

A controlled experiment in which models trained or evaluated on Voyager datasets show no measurable gain in accuracy, robustness, or generalization compared with models using baseline-generated datasets of equal size.

Figures

Figures reproduced from arXiv: 2512.12072 by Avinash Amballa, Chi-Heng Lin, Srinivas Chappidi, Vivek Kulkarni, Yashas Malur Saidutta.

**Figure 1.** Figure 1: Overview of VOYAGER We iteratively seek to explore new diverse regions of the data manifold via set of successive voyages carried out by explorers. Each explorer explores a certain region of the manifold. Regions that are very similar to prior explorations are rejected by the central command which keeps track of a key set of salient regions explored (the anchor set). New explorers are encouraged to explore… view at source ↗

**Figure 2.** Figure 2: Rejection rate of samples within a batch over time with “textual gradients” enabled vs disabled to generate the same dataset size for the sports task (all other settings identical). Note that “textual gradients” helps significantly in enabling the algorithm to have a lower rejection rate and also run faster (smaller number of timesteps) highlighting the importance of feedback and prompt refinement. This re… view at source ↗

read the original abstract

Large language models (LLMs) are increasingly being used to generate synthetic datasets for the evaluation and training of downstream models. However, prior work has noted that such generated data lacks diversity. In this paper, we propose Voyager, a novel principled approach to generate diverse datasets. Our approach is iterative and directly optimizes a mathematical quantity that optimizes the diversity of the dataset using the machinery of determinantal point processes. Furthermore, our approach is training-free, applicable to closed-source models, and scalable. In addition to providing theoretical justification for the working of our method, we also demonstrate through comprehensive experiments that Voyager significantly outperforms popular baseline approaches by providing a 1.5-3 times improvement in diversity.

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

Voyager applies iterative DPP optimization to boost diversity in LLM synthetic data without training, but the gains stay tied to the internal metric and lack downstream validation.

read the letter

Voyager's core move is an iterative, training-free procedure that uses determinantal point processes to pick or generate more diverse outputs from an LLM. It directly optimizes a diversity quantity instead of relying on prompting tricks or fine-tuning, and the authors say this delivers 1.5-3x better diversity scores than common baselines while staying usable with closed models. That part is straightforward and addresses a real pain point in synthetic data work. The DPP framing gives it a cleaner mathematical story than most ad-hoc diversity hacks, and the lack of training makes it immediately practical. Experiments are described as comprehensive and show clear numerical lifts on the diversity measures they track. The approach is new enough in this exact combination that it could interest people already using embedding-based selection. The main weakness is that the reported improvements live inside the same DPP or embedding scores being optimized, with no clear results on whether the data actually improves downstream model accuracy, robustness, or generation quality. Without that link, the headline numbers risk being an artifact of the chosen kernel rather than a general advance. Reproducibility would also benefit from more detail on kernel construction and parameter choices for text. This paper is aimed at researchers building synthetic datasets for LLM training or evaluation. Readers who already work with diversity metrics or subset selection will get the most from the method section. It is solid enough on the idea and relevance to deserve peer review, though the referees will probably push for downstream task results and clearer implementation details.

Referee Report

3 major / 1 minor

Summary. The manuscript introduces Voyager, a training-free iterative method that generates diverse synthetic datasets from LLMs by directly optimizing a determinantal point process (DPP) kernel quantity. It supplies theoretical justification for the approach and reports experimental results claiming 1.5-3x diversity gains over popular baselines.

Significance. If the reported diversity gains on the DPP metric are shown to correlate with improved downstream utility, the method would offer a scalable, training-free technique applicable to closed-source LLMs for creating higher-quality synthetic data.

major comments (3)

[Experiments] Experimental section: results are reported only on the internal DPP log-det quantity and embedding-based diversity scores; no downstream task evaluations (e.g., classification accuracy, perplexity, or robustness when training models on Voyager-generated data versus baselines) are provided, leaving the practical utility of the 1.5-3x claim unverified.
[Method] Method section: the specific form of the DPP kernel, the iterative optimization procedure, baseline implementations, and exact metrics used for the 1.5-3x comparison are insufficiently detailed, preventing reproduction or assessment of whether the gains are metric artifacts.
[Theoretical Analysis] Theoretical justification: the assumption that maximizing the DPP volume directly yields practically useful diversity is not supported by any correlation analysis or ablation linking the optimized quantity to task performance; this is load-bearing for the central claim.

minor comments (1)

[Figures/Tables] Figure captions and table legends should explicitly state the exact diversity metric (e.g., log-det of which kernel) being plotted to avoid ambiguity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and will revise the manuscript accordingly to improve reproducibility, add empirical validation, and strengthen the theoretical-empirical linkage.

read point-by-point responses

Referee: [Experiments] Experimental section: results are reported only on the internal DPP log-det quantity and embedding-based diversity scores; no downstream task evaluations (e.g., classification accuracy, perplexity, or robustness when training models on Voyager-generated data versus baselines) are provided, leaving the practical utility of the 1.5-3x claim unverified.

Authors: We agree that downstream evaluations are needed to substantiate practical utility. In the revised manuscript we will add experiments that train downstream models (classifiers on classification tasks and small LMs for perplexity) on Voyager-generated data versus baselines and report accuracy, generalization, and robustness metrics. This directly addresses whether the reported diversity gains translate to improved task performance. revision: yes
Referee: [Method] Method section: the specific form of the DPP kernel, the iterative optimization procedure, baseline implementations, and exact metrics used for the 1.5-3x comparison are insufficiently detailed, preventing reproduction or assessment of whether the gains are metric artifacts.

Authors: We will expand the Method section with the precise DPP kernel definition (embedding-based similarity matrix), full pseudocode for the iterative log-det optimization, hyperparameter settings and implementation details for all baselines, and exact formulas for every diversity metric together with the 1.5-3x calculation procedure. Code will be released to enable verification. revision: yes
Referee: [Theoretical Analysis] Theoretical justification: the assumption that maximizing the DPP volume directly yields practically useful diversity is not supported by any correlation analysis or ablation linking the optimized quantity to task performance; this is load-bearing for the central claim.

Authors: While DPP log-det maximization has established theoretical guarantees for diversity in feature space, we acknowledge the need for explicit linkage to downstream utility. The revision will add a dedicated analysis subsection containing correlation plots and ablations between optimized DPP volume and downstream task metrics, plus comparisons against alternative diversity measures. revision: yes

Circularity Check

0 steps flagged

No significant circularity; DPP optimization is externally defined

full rationale

The paper's core derivation applies standard determinantal point process (DPP) machinery to iteratively select diverse LLM outputs by maximizing log-det of a kernel matrix. This quantity is taken from external DPP literature rather than fitted to the paper's own diversity results or derived tautologically from the target metric. No self-definitional loops, fitted-input predictions, or load-bearing self-citations appear in the chain; the method is presented as training-free and directly optimizes the chosen mathematical objective. Experiments compare against baselines on the same DPP-derived scores, which is consistent with the stated goal rather than a circular reduction. The untested link to downstream task utility is a separate assumption about metric validity, not a circularity in the derivation itself.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that DPP provides a suitable and optimizable measure of diversity for text data; no free parameters or invented entities are mentioned.

axioms (1)

domain assumption Determinantal point processes provide a mathematically justified way to quantify and optimize diversity in sets of LLM-generated text examples.
Invoked to justify the iterative optimization step and theoretical claims.

pith-pipeline@v0.9.0 · 5429 in / 1080 out tokens · 36391 ms · 2026-05-16T22:25:48.258267+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/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

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

Our approach is iterative and directly optimizes a mathematical quantity that optimizes the diversity of the dataset using the machinery of determinantal point processes... det(K_S) measures the volume spanned by the vectors
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

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

the determinant of such a kernel similarity matrix represents the square of the volume spanned by the feature representations

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

Works this paper leans on

4 extracted references · 4 canonical work pages

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Alice Cortinovis, Daniel Kressner, and Stefano Massei

Training verifiers to solve math word prob- lems. Alice Cortinovis, Daniel Kressner, and Stefano Massei

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Jointly reinforcing diversity and quality in language model generations.arXiv preprint arXiv:2509.02534, 2025

PMLR. Tianjian Li, Yiming Zhang, Ping Yu, Swarnadeep Saha, Daniel Khashabi, Jason Weston, Jack Lanchantin, and Tianlu Wang. 2025. Jointly reinforcing diversity and quality in language model generations.arXiv preprint arXiv:2509.02534. Nguyen Nhat Minh, Andrew Baker, Clement Neo, Allen G Roush, Andreas Kirsch, and Ravid Shwartz- Ziv. Turning up the heat: M...

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Alice Cortinovis, Daniel Kressner, and Stefano Massei

Training verifiers to solve math word prob- lems. Alice Cortinovis, Daniel Kressner, and Stefano Massei

work page

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The vendi score: A diversity evaluation metric for machine learning

On maximum volume submatrices and cross approximation for symmetric semidefinite and diag- onally dominant matrices.Linear Algebra and its Applications, 593:251–268. Dan Friedman and Adji Bousso Dieng. 2022. The vendi score: A diversity evaluation metric for machine learning.arXiv preprint arXiv:2210.02410. Sergei A Goreinov and Eugene E Tyrtyshnikov. 200...

work page arXiv 2022

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InFindings of the Association for Com- putational Linguistics: EMNLP 2022, pages 3414– 3427

Truncation sampling as language model desmoothing. InFindings of the Association for Com- putational Linguistics: EMNLP 2022, pages 3414– 3427. Ari Holtzman, Jan Buys, Li Du, Maxwell Forbes, and Yejin Choi. 2020. The curious case of neural text degeneration. Mete Ismayilzada, Antonio Laverghetta Jr, Simone A Luchini, Reet Patel, Antoine Bosselut, Lonneke ...

work page arXiv 2022

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Jointly reinforcing diversity and quality in language model generations.arXiv preprint arXiv:2509.02534, 2025

PMLR. Tianjian Li, Yiming Zhang, Ping Yu, Swarnadeep Saha, Daniel Khashabi, Jason Weston, Jack Lanchantin, and Tianlu Wang. 2025. Jointly reinforcing diversity and quality in language model generations.arXiv preprint arXiv:2509.02534. Nguyen Nhat Minh, Andrew Baker, Clement Neo, Allen G Roush, Andreas Kirsch, and Ravid Shwartz- Ziv. Turning up the heat: M...

work page arXiv 2025