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arxiv: 2511.21600 · v2 · submitted 2025-11-26 · 💻 cs.CR · cs.LG

Robust Spectral Watermark for Synthetic Tabular Data

Yizhou Zhao , Xiang Li , Peter Song , Qi Long , Weijie Su This is my paper

Pith reviewed 2026-05-17 04:51 UTC · model grok-4.3

classification 💻 cs.CR cs.LG
keywords synthetic tabular datawatermarkingfrequency domaindiscrete Fourier transformdata provenancerobustnessmixed-type features
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The pith

A frequency-domain method watermarks synthetic tabular data for reliable origin detection after common modifications.

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

The paper develops TAB-DRW to mark AI-generated tabular datasets so their source can be traced later. It first applies Yeo-Johnson normalization and standardization to handle mixed feature types, then uses the discrete Fourier transform and changes selected imaginary parts according to secret bits. A rank-based way of producing those bits lets the mark be read back row by row with no extra storage. The goal is to keep the data statistically faithful and useful while resisting post-processing steps that would otherwise erase simpler marks. If the approach holds, organizations that release synthetic data in healthcare or finance gain a practical way to prove provenance without hurting downstream model performance.

Core claim

TAB-DRW embeds watermark signals in the frequency domain: it normalizes heterogeneous features via the Yeo-Johnson transformation and standardization, applies the discrete Fourier transform, and adjusts the imaginary parts of adaptively selected entries according to precomputed pseudorandom bits. A novel rank-based pseudorandom bit generation method enables row-wise retrieval without incurring storage overhead. Experiments on five benchmark tabular datasets show that TAB-DRW achieves strong detectability and robustness against post-processing and adaptive attacks, while preserving high data fidelity and fully supporting mixed-type features.

What carries the argument

Adjustment of imaginary parts in selected DFT entries after Yeo-Johnson normalization and standardization, paired with rank-based pseudorandom bit generation for embedding and row-wise detection.

If this is right

  • The watermark remains detectable after typical post-processing operations that preserve overall statistics.
  • Detection works row by row without needing to store any extra information.
  • Both discrete and continuous columns keep their original modeling value after watermarking.
  • The scheme runs efficiently as a post-edit step on already-generated tables.

Where Pith is reading between the lines

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

  • The same frequency-domain idea could be tested on other generated data formats if suitable normalizations are identified.
  • Embedding during the generation step rather than afterward might reduce any residual utility cost.
  • Over time the method could support public registries that verify data provenance for regulated synthetic datasets.

Load-bearing premise

That small changes to the imaginary parts of the Fourier transform will leave the overall statistical properties and downstream usefulness of the synthetic data essentially unchanged.

What would settle it

A post-processing step such as mild rounding, scaling, or noise addition that erases the ability to recover the watermark bits while the data still matches the original distribution on standard utility metrics.

Figures

Figures reproduced from arXiv: 2511.21600 by Peter Song, Qi Long, Weijie Su, Xiang Li, Yizhou Zhao.

Figure 1
Figure 1. Figure 1: Our proposed watermarking scheme, TAB-DRW, embeds watermarks into tabular data by modifying the imaginary components of the frequency-domain representation to align with pseudorandom bits. Detection evaluates the degree of alignment: strong alignment indicates watermarked data, while weak alignment suggests non-watermarked data [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: In the proposed pseudorandom bit generation scheme, bit sequence for each row is generated by mapping a [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Trade-off between average Z-score on 1K-rows tables and data fidelity under varying [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: TPR@0.1%FPR versus row count under three representative attacks. Dashed lines show the bootstrap mean [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visualization of the gender-flipping case study on the Adult dataset. Each subfigure corresponds to a synthetic [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Work flow of privacy-enhanced TAB-DRW. Algorithm 2 Watermarking embedding of privacy-enhanced TAB-DRW 1: Input: Tabular data X ∈ R N×p , parameters γ ∈ [0, 1] and δ ∈ [−1, 1], watermark key κ. 2: Shuffle X using key-derived permutation Pκ to obtain XPκ. 3: Transform XPκ using YJT and standardization (still denoted as XPκ for simplicity). 4: for each row x in XPκ do 5: Compute y ← DFT(x) and generate pseudo… view at source ↗
Figure 7
Figure 7. Figure 7: Illustration of Lines 7–9 in Algorithm 3 for the case x ∗ rank = 0.5 and m = 6. The red circle highlights the k-th node at level j. Algorithm 3 Row-wise Pseudorandom Bits Generation 1: Input: Standardized tabular data X ∈ R N×p , target row x ∗ ∈ R 1×p , and watermark key κ. 2: Initial: An empty pseudorandom bit list S, m = ⌊(p − 1)/2⌋. 3: Sample a subset of column indices I ⊂ {0, . . . , p − 1} using κ. 4… view at source ↗
Figure 8
Figure 8. Figure 8: TPR@0.1%FPR versus row count under three representative attacks with higher strength. Dashed lines show [PITH_FULL_IMAGE:figures/full_fig_p036_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: TPR@1%FPR versus attack strength under row and column deletion attacks. All experiments are conducted [PITH_FULL_IMAGE:figures/full_fig_p036_9.png] view at source ↗
read the original abstract

The rise of generative AI has enabled the production of high-fidelity synthetic tabular data across fields such as healthcare, finance, and public policy, raising growing concerns about data provenance and misuse. Watermarking offers a promising solution to address these concerns by ensuring the traceability of synthetic data, but existing methods face many limitations: they are computationally expensive due to reliance on the inverse process of large diffusion models, struggle with mixed discrete-continuous data, or lack robustness to common post-processing attacks. To address these limitations, we propose TAB-DRW, an efficient and robust post-editing watermarking scheme for synthetic tabular data. TAB-DRW embeds watermark signals in the frequency domain: it normalizes heterogeneous features via the Yeo-Johnson transformation and standardization, applies the discrete Fourier transform (DFT), and adjusts the imaginary parts of adaptively selected entries according to precomputed pseudorandom bits. To further enhance robustness and efficiency, we introduce a novel rank-based pseudorandom bit generation method that enables row-wise retrieval without incurring storage overhead. Experiments on five benchmark tabular datasets show that TAB-DRW achieves strong detectability and robustness against post-processing and adaptive attacks, while preserving high data fidelity and fully supporting mixed-type features.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes TAB-DRW, a post-editing spectral watermarking scheme for synthetic tabular data. It applies Yeo-Johnson normalization and standardization to heterogeneous features, computes the DFT, and perturbs the imaginary parts of adaptively selected entries according to precomputed pseudorandom bits generated by a novel rank-based method that supports row-wise retrieval without storage. The central empirical claim is that the resulting watermarked tables exhibit strong detectability and robustness to post-processing and adaptive attacks on five benchmark datasets while preserving high data fidelity and supporting mixed discrete-continuous features.

Significance. If the experimental results hold with adequate quantitative support, the work would offer a computationally lightweight alternative to diffusion-model-based watermarking, addressing key limitations in cost, mixed-type support, and storage overhead. The rank-based keying mechanism and frequency-domain embedding could enable practical provenance tracking for synthetic data in regulated domains such as healthcare and finance.

major comments (2)
  1. [§4] §4 (Experiments) and abstract: The claim of 'strong detectability and robustness' is presented without any reported quantitative metrics (e.g., detection accuracy, AUC, bit-error rate), error bars, or statistical tests across the five datasets and listed attacks. This absence prevents verification of the central empirical claim and must be addressed with full tables of results.
  2. [§3.1–3.2] §3.1–3.2 (Method): The adaptive selection criterion for DFT entries and the precise effect of imaginary-part perturbation on the inverse transform are not fully specified. Because utility preservation is load-bearing for the overall contribution, the manuscript should include an explicit derivation or pseudocode showing that the modification preserves the real-valued output and does not systematically alter marginal distributions.
minor comments (2)
  1. [Figures in §4] Figure captions and axis labels in the experimental section should explicitly state the attack parameters (e.g., noise level, row deletion fraction) used in each robustness test.
  2. [§2] The related-work section should include a direct comparison table against at least one recent tabular watermarking baseline on the same five datasets to contextualize the reported fidelity-robustness trade-off.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback. We address each major comment below and will revise the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [§4] §4 (Experiments) and abstract: The claim of 'strong detectability and robustness' is presented without any reported quantitative metrics (e.g., detection accuracy, AUC, bit-error rate), error bars, or statistical tests across the five datasets and listed attacks. This absence prevents verification of the central empirical claim and must be addressed with full tables of results.

    Authors: We agree that explicit quantitative metrics are required to support the central claims. In the revised manuscript we will add comprehensive tables in Section 4 (and update the abstract) that report detection accuracy, AUC, and bit-error rate for each dataset and attack, together with error bars from repeated trials and results of statistical significance tests. revision: yes

  2. Referee: [§3.1–3.2] §3.1–3.2 (Method): The adaptive selection criterion for DFT entries and the precise effect of imaginary-part perturbation on the inverse transform are not fully specified. Because utility preservation is load-bearing for the overall contribution, the manuscript should include an explicit derivation or pseudocode showing that the modification preserves the real-valued output and does not systematically alter marginal distributions.

    Authors: We thank the referee for noting the need for greater precision. The adaptive selection chooses high-magnitude DFT coefficients to limit utility impact. Perturbations are applied to imaginary parts while conjugate symmetry is maintained on the Hermitian pair, guaranteeing a real-valued inverse DFT. The rank-based perturbations are zero-mean and bounded, so expected marginal distributions remain unchanged. The revision will add a short derivation and pseudocode in Section 3 to make these properties explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical method with independent experimental validation

full rationale

The paper describes a practical post-editing watermarking pipeline (Yeo-Johnson normalization, standardization, DFT, imaginary-part perturbation keyed by rank-based pseudorandom bits) whose detectability and robustness claims rest on experiments across five benchmark datasets rather than any closed-form derivation or self-referential prediction. No equations reduce a claimed result to a fitted parameter or prior self-citation by construction; the central contribution is an engineering scheme whose performance is measured externally via fidelity metrics and attack survival rates. The method is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on standard signal-processing transforms applied to tabular data; no new entities or heavily fitted parameters are introduced in the abstract description.

axioms (1)
  • domain assumption Yeo-Johnson transformation followed by standardization produces suitable input for DFT on mixed discrete-continuous tabular features
    Invoked to handle heterogeneous data types before frequency-domain embedding.

pith-pipeline@v0.9.0 · 5515 in / 1229 out tokens · 28691 ms · 2026-05-17T04:51:39.919032+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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