arxiv: 2605.06865 · v1 · submitted 2026-05-07 · 💻 cs.LG

Recognition: no theorem link

Dataset Watermarking for Closed LLMs with Provable Detection

Kamalika Chaudhuri, Pengrun Huang, Yu-Xiang Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-11 00:48 UTC · model grok-4.3

classification 💻 cs.LG

keywords dataset watermarkingclosed LLMsprovable detectionword-pair co-occurrencefine-tuningstatistical testdata mixturebenchmark integrity

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The pith

By rephrasing text to boost specific word-pair co-occurrences, a dataset can be watermarked for closed LLMs with statistical detection provable even after mixed fine-tuning.

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

The paper introduces the first dataset watermarking method designed for closed large language models where internal weights and training details remain inaccessible. It works by selecting random word pairs and rephrasing dataset examples so that those pairs appear together more often, creating a statistical signal at the dataset level. A simple statistical test then checks model-generated text for elevated co-occurrence rates of the chosen pairs to decide whether the watermarked data was used in training. Experiments show reliable detection at p less than 0.01 even when the watermarked portion is only about 1 percent of the fine-tuning tokens, while benchmark accuracy and semantic meaning stay essentially unchanged across several models and datasets.

Core claim

The authors establish that increasing the co-occurrence frequency of randomly selected word pairs through rephrasing embeds a dataset-level watermark signal that can be recovered from model outputs via a statistical test on those same co-occurrence patterns. This signal remains detectable after fine-tuning, including in realistic mixtures where the watermarked data accounts for roughly 1 percent of total tokens, and the rephrasing step does not degrade the original utility or semantic properties of the benchmark data.

What carries the argument

Rephrasing to raise co-occurrence rates of chosen word pairs, which creates the detectable statistical signal tested on model-generated outputs.

If this is right

Detection remains reliable throughout the fine-tuning stage with p-value below 0.01.
The signal persists when the watermarked dataset forms only approximately 1 percent of the total fine-tuning tokens.
Original benchmark performance and semantic content are preserved after the rephrasing step.
The method applies across multiple base models and standard benchmark datasets.

Where Pith is reading between the lines

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

Dataset owners could apply this technique to later verify whether their proprietary data appeared in training runs of closed models.
The same co-occurrence boosting idea might be tested for robustness against deliberate removal attempts such as adversarial fine-tuning or data filtering.
Related signals could be explored for non-text training data where statistical patterns in outputs are still observable.

Load-bearing premise

That the boosted word-pair co-occurrences will reliably appear in the model's generated text after fine-tuning and can be distinguished from natural variation or other training influences.

What would settle it

A controlled experiment in which a model fine-tuned on the watermarked data produces outputs whose word-pair statistics show no significant elevation relative to an identical model trained on the non-watermarked version of the same data.

Figures

Figures reproduced from arXiv: 2605.06865 by Kamalika Chaudhuri, Pengrun Huang, Yu-Xiang Wang.

**Figure 1.** Figure 1: Overview of the proposed dataset watermarking framework. In Stage 1, we randomly sample a set of word pairs as a secret key and rephrase the original dataset using a language model to increase the co-occurrence frequency of these selected word pairs. In Stage 2, we query the target model with some prompts, and analyze the cooccurrence statistics of selected word pairs in the generated text to test for the… view at source ↗

**Figure 2.** Figure 2: Empirical false positive behavior of our detector. We apply our detector to text generated by two base models. Each figure shows the empirical PDF of detection scores under the null hypothesis. The dashed line marks the detection threshold corresponding to p = 0.01; no false positives are observed in either setting. Dataset Method Van. Del. Syn. Emo. MMLU (r = 0.2) STAMP 4.40e-2 0.138 9.27e-2 7.50e-2 Radio… view at source ↗

**Figure 3.** Figure 3: Effect of hyperparameter on detectability. In (a) and (b), Each small marker [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: Trade-off between detectability and semantic similarity under different numbers [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗

**Figure 5.** Figure 5: Trade-off between detectability and semantic similarity under different numbers [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗

**Figure 6.** Figure 6: Effect of τ weak correlations, while larger values are overly restrictive and exclude informative word pairs. The optimal range of τ is approximately 0.02–0.04, where many secret key pairs exceed the threshold while relatively few non-selected pairs do, yielding the strongest detectability. D Proof of Theorem 4.1 Theorem D.1 (False Positive Rate). For any fixed LLM M, ∀t, τ ∈ R, Psk(Detect(M, sk, τ, t) = 1… view at source ↗

read the original abstract

Large language models (LLMs) are pre-trained and post-trained on vast amounts of loosely curated data, raising the possibility that these models may have been trained on proprietary datasets or the same benchmarks used for evaluation. This motivates the need for dataset watermarking: designing datasets such that training on them leaves detectable signatures in the resulting model. Prior work has explored this problem for open models. We introduce the first dataset watermarking method for closed LLMs with provable detection. In particular, we embed a dataset-level watermark signal by increasing the co-occurrence frequency of randomly selected word pairs through rephrasing, and detect it using a statistical test on co-occurrence patterns in model-generated outputs. We evaluate our method with multiple base models and benchmark datasets and show that it reliably detects the watermark ($p <0.01$) in the fine-tuning stage. Notably, our method remains effective in a data mixture setting where the watermarked dataset constitutes only approximately $1\%$ of the total fine-tuning tokens. Furthermore, we show that our method preserves the utility and semantic integrity of the benchmark.

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

This paper introduces a dataset watermark for closed LLMs by boosting random word-pair co-occurrences through rephrasing, with experiments claiming reliable detection at 1% mixture ratios.

read the letter

The main point is a practical scheme for marking fine-tuning data so that closed models trained on it show a detectable statistical signature in their outputs, without needing model access. They pick random word pairs, rephrase text to raise those pairs' joint frequency, then test for elevated co-occurrence in generated text. This is new for closed models, where prior watermarking needed white-box access or direct parameter inspection. The experiments cover several base models and benchmarks, report p<0.01 detection even when the marked data is roughly 1% of the fine-tuning tokens, and check that downstream utility and semantics stay intact. That combination of low mixture ratio and output-only detection is the useful part for real-world provenance questions. The soft spot is exactly the propagation step the stress-test flags. Raising pair frequency in the dataset does not automatically guarantee the fine-tuned model will shift its conditional probabilities enough for a clean statistical signal, especially at 1% and with common words that already have natural variation. The abstract gives no derivation or bound on how large the induced delta needs to be to survive gradient steps, and it does not spell out the exact null distribution, multiple-testing correction, or baseline controls used in the test. If the full paper only shows empirical success on the chosen pairs without those details or ablation on word frequency, the provable-detection claim rests more on the experiments than on a general guarantee. The work is aimed at researchers and practitioners who need data-origin tools for closed models and IP tracking. It is worth a serious referee because the core idea is straightforward, the 1% result is practically relevant if it holds, and the gaps are fixable with more statistical reporting rather than fatal. I would send it to review with a request for tighter bounds or additional controls on the detection test.

Referee Report

2 major / 1 minor

Summary. The paper introduces the first dataset watermarking method for closed LLMs. It embeds a signal by rephrasing text to increase co-occurrence frequencies of randomly selected word pairs, then detects the watermark via a statistical test on co-occurrence patterns in model outputs. Experiments claim reliable detection (p<0.01) after fine-tuning, including when watermarked data is only ~1% of tokens, while preserving benchmark utility and semantics.

Significance. If the central claims hold with full experimental and statistical details, the work would provide a practical tool for detecting unauthorized use of proprietary datasets in closed-model training, filling a gap left by prior open-model watermarking. The low-mixture effectiveness and utility preservation are potentially impactful for real-world deployment, though the absence of explicit bounds or test specifications limits immediate adoption.

major comments (2)

[Abstract] Abstract: the claim of 'provable detection' with p<0.01 success lacks any description of the exact statistical test, null distribution, multiple-testing correction, or power analysis. This is load-bearing for the core contribution, as the detection method must be shown to distinguish the induced signal from natural variation without excessive false positives.
[Abstract] Abstract and evaluation: no derivation, bound, or controlled ablation demonstrates that the rephrasing-induced co-occurrence delta survives gradient updates when the watermarked data is only ~1% of fine-tuning tokens. The central claim that the signal imprints reliably enough for detection therefore rests on unverified propagation from dataset statistics to model behavior.

minor comments (1)

[Abstract] The abstract mentions 'multiple base models and benchmark datasets' but provides no table or section reference listing them or reporting per-model variance in detection rates.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below, agreeing to expand the description of the statistical test and to strengthen the empirical evidence for signal persistence with additional ablations. These changes will be incorporated in the revised manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the claim of 'provable detection' with p<0.01 success lacks any description of the exact statistical test, null distribution, multiple-testing correction, or power analysis. This is load-bearing for the core contribution, as the detection method must be shown to distinguish the induced signal from natural variation without excessive false positives.

Authors: We agree that the abstract and main text require a more explicit description of the detection procedure. In the revision we will add a dedicated subsection detailing the exact hypothesis test (a one-sided test on elevated co-occurrence counts for the chosen word pairs), the null distribution (binomial with parameters fitted from non-watermarked reference outputs), the multiple-testing correction (Bonferroni across the fixed set of pairs), and a power analysis confirming that the number of generations used in our experiments yields p < 0.01 with high probability under the observed signal strength. This will make the 'provable detection' claim fully transparent. revision: yes
Referee: [Abstract] Abstract and evaluation: no derivation, bound, or controlled ablation demonstrates that the rephrasing-induced co-occurrence delta survives gradient updates when the watermarked data is only ~1% of fine-tuning tokens. The central claim that the signal imprints reliably enough for detection therefore rests on unverified propagation from dataset statistics to model behavior.

Authors: The manuscript already reports consistent detection (p < 0.01) across multiple models and benchmarks at the 1 % mixture level, providing direct empirical evidence that the co-occurrence signal reaches the fine-tuned model. We acknowledge, however, the absence of a theoretical bound or controlled ablation that isolates the effect of gradient updates on the delta. We will therefore add a new set of controlled experiments that vary the watermarked-token fraction while measuring the co-occurrence statistics both in the training data and in the model's generated outputs before and after fine-tuning. While a closed-form propagation bound is difficult given the non-convex training dynamics, the expanded ablation will substantially strengthen the empirical support for the low-mixture claim. revision: partial

Circularity Check

0 steps flagged

No circularity: embedding via rephrasing and detection via output statistics are independent empirical steps

full rationale

The paper proposes a concrete procedure—select random word pairs, rephrase data to raise their co-occurrence frequency, fine-tune, then apply a statistical test to generated outputs—without any equation, parameter, or uniqueness claim that reduces to its own inputs by definition or self-citation. The detection result is an observed empirical outcome on held-out generations, not a fitted quantity renamed as a prediction or a bound derived from the same rephrasing statistics. No load-bearing self-citation, ansatz smuggling, or renaming of known results appears in the described chain; the method remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that fine-tuning on rephrased data imprints a detectable co-occurrence signal in outputs without model access, relying on empirical results rather than formal derivation.

free parameters (2)

word pair selection
Random selection of word pairs whose co-occurrence frequency is increased; number and specific pairs chosen affect signal strength.
rephrasing parameters
Details of how sentences are rewritten to boost pair frequency while preserving semantics.

axioms (2)

domain assumption Training on data with elevated word-pair co-occurrence causes the model to generate outputs with similarly elevated co-occurrence rates.
Core premise enabling the watermark to be observable in model outputs.
domain assumption The statistical test on output co-occurrence patterns can achieve low false-positive rates under the null hypothesis of no watermark.
Underpins the p<0.01 detection claim and mixture robustness.

pith-pipeline@v0.9.0 · 5489 in / 1557 out tokens · 87926 ms · 2026-05-11T00:48:25.132811+00:00 · methodology

discussion (0)

Reference graph

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