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A watermark that lives inside the data distribution stays detectable after an adversary retrains a generative model and regenerates high-utility tabular data.

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2026-07-13 01:05 UTC pith:HR3FBZUB

load-bearing objection First radioactive watermark for continuous tabular data that actually survives retraining, with clean concentration theory and careful large-scale experiments; the MLE-to-W1 proxy is the only real soft spot. the 2 major comments →

arxiv 2607.09000 v1 pith:HR3FBZUB submitted 2026-07-10 cs.CR cs.LG

RaMark: Radioactive Watermarking for Generated Tabular Data

Xin Che , Lingyang Chu , Qiqi Zhang , Xinyu Ma , Xuan Luo , Jian Pei This is my paper
classification cs.CR cs.LG
keywords radioactive watermarkretraining attackgenerated tabular datasinusoidal dependencydiffusion samplingownership verificationspectral detection
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Generated tabular data is now shared as a privacy-preserving substitute for real records, yet ownership watermarks are easily stripped by a retraining attack: the adversary simply trains a new generative model on the watermarked set and samples fresh rows that keep utility but lose the mark. RaMark answers this by making the watermark radioactive—an intrinsic sinusoidal dependency among continuous attributes that becomes part of the data distribution itself. Any model that still matches the distribution closely enough to preserve utility must also reproduce that sine wave, so spectral detection at a secret frequency continues to fire. Theory links small Wasserstein distance between watermarked and attacked distributions to preserved spectral power; experiments against seven baselines under 100 000 owners and four generative retraining models confirm the gap. The practical stake is clear: without radioactivity, ownership claims on shared synthetic tables cannot survive ordinary reuse pipelines.

Core claim

Embedding a secret sinusoidal dependency among continuous attributes as a stable component of the data distribution yields a radioactive watermark: any generative model that preserves data utility (small distributional distance) necessarily preserves elevated spectral power at the secret frequency, so the mark remains detectable after retraining and mild modification attacks.

What carries the argument

Watermark-guided diffusion sampling that multiplies the reverse-step density by an analytic watermark likelihood Pr(W|z_t) = exp(-|v_t - sin(2 pi omega u_t)|), shifting the Gaussian mean so samples are biased onto the target sine curve in a secret two-dimensional projection; detection recovers the same projection and scores spectral power via the Lomb–Scargle periodogram.

Load-bearing premise

The paper treats Machine Learning Efficiency under a 1 percent budget as a faithful proxy for the adversary’s utility goal, and assumes that keeping that score high forces the attacked distribution to stay close enough in Wasserstein distance for the spectral bound to hold.

What would settle it

Produce a regenerated table whose Machine Learning Efficiency drops by less than 1 percent relative to the watermarked set, yet whose spectral power at the owner’s secret frequency falls below the detection threshold used for the 100 000-owner AUC evaluation.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper introduces radioactivity for continuous tabular data watermarking: a watermark that remains detectable after an adversary retrains a generative model on the watermarked table and regenerates high-utility data. RaMark embeds a secret sinusoidal dependency v = sin(2 pi omega u) among continuous attributes via watermark-guided diffusion sampling (Algorithm 2, Theorem 3.1), detects it by Lomb-Scargle spectral power in a secret 2-D projection (Algorithm 1), and proves high-probability bounds linking Wasserstein-1 closeness of tables to closeness of spectral power (Theorems 4.1-4.2, Remarks 1-3). Under a common 1% MLE budget, experiments on Higgs Small and House-16H with 10^5 owners show Det_AUC/Tra_AUC near 1.0 under TabDDPM/TabDiff retraining and superior robustness to noise, row/column edits versus seven baselines.

Significance. If the result holds, RaMark supplies the first practical radioactive watermark for continuous tabular data under realistic retraining attacks, a setting where prior generative and database methods fail. The contribution is concrete: an explicit embedding/detection pipeline, concentration bounds that convert distributional closeness into spectral-power preservation, and a large-scale multi-owner evaluation that aligns watermark strength by a shared MLE budget. Strengths include the appendix proofs (McDiarmid + Kantorovich-Rubinstein), the clear utility-watermark trade-off, and the empirical demonstration that the sine wave survives the four tested generators when MLE is preserved. These elements make the work a useful advance for ownership verification of generated tabular assets in privacy-sensitive domains.

major comments (2)
  1. The radioactivity claim rests on the chain high MLE => small W1(T_wm, T_atk) => spectral power preserved (Theorems 4.1-4.2 and Remarks 1-2). Section 4.1.1 and Equation (10) define utility solely via CatBoost MLE under a 1% budget; the paper never shows that every high-MLE generator must stay close in W1, only that the four tested models that keep MLE also keep the sine. An adversary that deliberately flattens the secret-frequency component while matching the moments CatBoost cares about could break detectability without violating the stated utility budget. A concrete additional experiment (or a stronger theoretical link from MLE to W1) is needed before the claim can be stated as holding for any utility-preserving generator.
  2. Table 2 shows that under CTAB-GAN+ and TVAE, RaMark Det_AUC/Tra_AUC falls to approximately 0.79-0.82 while MLE(Q_atk) drops 10-15% relative to MLE(Q_wm). The abstract and Section 5.3 still describe the method as achieving substantially stronger radioactivity than all baselines; the gap between near-perfect scores under diffusion retraining and the weaker scores under GAN/VAE retraining should be quantified more carefully and the claim scoped to the regime in which the attacked distribution remains sufficiently close.
minor comments (4)
  1. CCS Concepts and ACM Reference Format still contain the placeholder text "Do Not Use This Code" and "Make sure to enter the correct conference title"; these must be replaced before publication.
  2. Figure 5 reports only mean MLE across methods; adding per-method curves (or a short table) would make the claim of comparable attack strength fully transparent.
  3. The scope paragraph (Section 3.2.4) correctly notes the continuous-attribute requirement, but a one-sentence discussion of how many real-world tables satisfy the "at least two continuous columns" precondition would help readers assess applicability.
  4. Notation for the detection score DS(omega) versus DS(omega) is inconsistent in a few places in Section 5.5; a single spelling would improve readability.

Circularity Check

0 steps flagged

No significant circularity: the sinusoidal embedding objective and the Lomb–Scargle detection statistic are related but not definitionally identical, and the utility–watermark trade-off is derived from external concentration inequalities rather than tautological re-labeling.

full rationale

RaMark’s central claim is that embedding a sinusoidal dependency as an intrinsic component of the continuous-attribute distribution yields a radioactive watermark: any generative model that keeps the attacked distribution close in Wasserstein-1 distance must also keep elevated spectral power at the secret frequency (Theorems 4.1–4.2 and Remarks 1–3). The embedding step (Algorithm 2, Theorem 3.1) steers samples toward the curve v = sin(2π ω u) via a mean-shift proportional to the gradient of log Pr(W|z_t) = −|v_t − sin(2π ω u_t)|. Detection (Algorithm 1, Eq. 4) maps the same secret projection, forms a binned discrete-time signal, and evaluates the independent Lomb–Scargle periodogram power L(ω) together with its false-alarm probability. These two quantities are statistically coupled under the paper’s concentration bounds, but they are not algebraically identical by construction; the detection score is not a re-labeling of the embedding loss. Theorems 4.1 and 4.2 invoke McDiarmid’s inequality, Kantorovich–Rubinstein duality, Chernoff and Hoeffding bounds—standard external tools—rather than a uniqueness theorem or ansatz imported from the authors’ prior work. The only mild self-reference is that the same secret key (projection directions, bin width, frequency) is used for both embedding and detection, which is the ordinary private-key design of any watermarking scheme and does not force the radioactivity claim. Parameter α is tuned under an external MLE budget (Eq. 10) and is not fitted to the detection scores that are later reported as “predictions.” Consequently the derivation chain is self-contained against the paper’s own equations and external probabilistic machinery; the score is 1 solely for the trivial shared-key design, not for any load-bearing circular reduction.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 1 invented entities

The central radioactivity claim rests on standard concentration tools, the modeling choice that MLE under a 1 % budget is the right utility proxy, and the design decision to realize the watermark as a sine wave of secret frequency. No new physical entities are postulated; free parameters are the usual watermarking knobs (guidance strength, bin width, scale, frequency) that are tuned under the MLE budget rather than fitted to invent the result.

free parameters (5)
  • guidance strength alpha = range [5,10] recommended
    Controls the mean-shift magnitude in each reverse denoising step (Eq. 9); tuned in [5,10] to keep MLE loss <=1 % while raising DS(omega).
  • bin width beta = 0.01–0.09 stable
    Sets quantization granularity of the u-projection (Eq. 2); sensitivity table shows stable DS only for intermediate values.
  • scaling factor s = 1000–9000 stable
    Rescales discrete-time spacing after binning; likewise tuned so the signal spans enough periods.
  • designated frequency omega = example 30
    Secret frequency of the target sine; part of the owner key, chosen once per owner.
  • MLE budget gamma = 1 %
    Maximum allowed utility drop used to align watermark strength across methods (Eq. 10).
axioms (5)
  • standard math Wasserstein-1 closeness of table distributions is preserved (with high probability) by the projection-and-binning map phi, up to finite-sample terms controlled by bin mass and occupancy (Theorem 4.2).
    Uses Chernoff, Hoeffding and elementary floor inequalities; standard concentration toolkit.
  • standard math Spectral power of the Lomb–Scargle periodogram concentrates around its expectation and is Lipschitz in the signal values, so W1 closeness of signals implies closeness of L(omega) (Theorem 4.1).
    McDiarmid + Kantorovich–Rubinstein; standard for periodogram analysis.
  • domain assumption An adversary who wishes to keep high Machine Learning Efficiency must keep the attacked distribution close in Wasserstein-1 to the watermarked distribution.
    Stated in Section 4.1 and Remark 1; MLE is a common but not universal utility proxy for tabular generative models.
  • domain assumption At least two continuous-valued attributes are available so that a two-dimensional projected space can be formed.
    Explicit scope limitation in Section 3.2.4 and Conclusion.
  • ad hoc to paper The watermark is realized as the specific functional form v = sin(2 pi omega u) rather than another learnable dependency.
    Design choice that makes spectral detection convenient; other periodic or non-periodic dependencies could in principle be substituted.
invented entities (1)
  • radioactive watermark for continuous tabular data (sinusoidal distributional dependency) no independent evidence
    purpose: Provides a watermark signal that is an intrinsic, learnable component of the data distribution and therefore survives generative retraining.
    The entity is the method itself; independent evidence is the empirical survival under four retraining models and the concentration theorems, but the construction is new to this paper.

pith-pipeline@v1.1.0-grok45 · 40168 in / 3287 out tokens · 31422 ms · 2026-07-13T01:05:47.706485+00:00 · methodology

0 comments
read the original abstract

Recent advances in generative modeling have made generated tabular data a practical solution for privacy-sensitive data sharing, where watermarking enables ownership verification. However, existing watermarking methods fundamentally fail under retraining attacks, in which an adversary retrains a generative model on a watermarked dataset and regenerates high-utility data that no longer carries the watermark. We address this challenge by introducing radioactivity, the property that a watermark remains detectable after generative model retraining, and propose RaMark, a radioactive watermarking method that embeds a sinusoidal dependency as an intrinsic component of the data distribution. By coupling the watermark with the underlying distribution, RaMark ensures that any generative model preserving data utility also has to preserve the watermark. We theoretically show that with high probability removing watermark degrades utility and alters data distribution. Extensive experiments on two real-world tabular datasets, under a large-scale ownership verification setting with $10^5$ independent data owners, demonstrate that RaMark achieves substantially stronger radioactivity than seven state-of-the-art methods and consistently outperforms them against both retraining and data modification attacks.

Figures

Figures reproduced from arXiv: 2607.09000 by Jian Pei, Lingyang Chu, Qiqi Zhang, Xin Che, Xinyu Ma, Xuan Luo.

Figure 1
Figure 1. Figure 1: Illustration of retraining attack and radioactive [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Watermarked and unwatermarked signals in the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: An example of points and mean points. The vertical [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: The mean and standard deviation of the MLE(𝑄𝑤𝑚) and MLE(𝑄𝑎𝑡𝑘 ) for all the watermarking methods in the de￾tectability experiments. The 𝑥-axis shows the attack strength 𝜌 ∈ {𝜌𝑛𝑎, 𝜌𝑟𝑑, 𝜌𝑟𝑖, 𝜌𝑐𝑑 } of each data modification attack. The 𝑦-axis shows the MLE for each attack. The leftmost point on each curve shows MLE(𝑄𝑤𝑚) when the attack strength is zero, which means watermarked datasets are not attacked. The ot… view at source ↗
Figure 6
Figure 6. Figure 6: The Det_AUC under different attack strengths. The attack strengths 𝜌𝑛𝑎, 𝜌𝑟𝑑, 𝜌𝑟𝑖, 𝜌𝑐𝑑 are defined in Section 4.2. S2R2W TabularMark WGTD PKF TabWak MUSE B2Mark RaMark 0.0 0.2 0.4 0.6 0.8 1.0 na 0.00 0.50 1.00 T r a _ A U C (a) Noise Addition, HS 0.0 0.2 0.4 0.6 0.8 1.0 na 0.00 0.50 1.00 T r a _ A U C (b) Noise Addition, HO 0.0 0.2 0.4 0.6 0.8 1.0 rd 0.00 0.50 1.00 T r a _ A U C (c) Row Deletion, HS 0.0 0.2… view at source ↗
Figure 7
Figure 7. Figure 7: The Tra_AUC under different attack strengths. The attack strengths 𝜌𝑛𝑎, 𝜌𝑟𝑑, 𝜌𝑟𝑖, 𝜌𝑐𝑑 are defined in Section 4.2. DS( ) MLE 0 15 30 0.00 0.50 1.00 D S( ) 0.70 0.71 0.72 M L E (a) HS 0 15 30 0.00 0.50 1.00 D S( ) 0.53 0.58 0.63 M L E (b) HO [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The effect of the guidance strength 𝛼. At the same time, MLE gradually decreases as 𝛼 increases. This is because increasing 𝛼 strengthens the watermark guidance term and shifts samples further away from the distribution learned from 𝑄𝑜𝑟𝑖. While this improves watermark alignment, it also introduces distributional distortion that reduces sample fidelity and degrades the performance of downstream learning tas… view at source ↗

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