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arxiv: 2604.11344 · v1 · submitted 2026-04-13 · 💻 cs.CR · cs.CL

Recognition: unknown

Geometry-Aware Localized Watermarking for Copyright Protection in Embedding-as-a-Service

Zhimin Chen , Xiaojie Liang , Wenbo Xu , Yuxuan Liu , Wei Lu
Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:52 UTC · model grok-4.3

classification 💻 cs.CR cs.CL
keywords embedding as a servicewatermarkingcopyright protectionlocalized injectiongeometric fidelitymodel stealingrobust verificationmanifold anchors
0
0 comments X

The pith

GeoMark separates watermark triggers from ownership attribution using geometry-aware anchors in embedding manifolds to protect EaaS models.

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

The paper presents GeoMark as a way to break the robustness-utility-verifiability tradeoff in watermarking embedding-as-a-service systems. Existing trigger methods break under paraphrasing, transformation methods shift with dimension changes, and region methods risk false matches from accidental geometry. GeoMark selects a natural point inside the embedding manifold as the shared target, places explicit-margin anchors around it to separate regions, and injects the watermark signal only inside adaptive local neighborhoods. This keeps the trigger local while the attribution signal stays centralized and verifiable. Experiments across four datasets confirm that downstream tasks, geometric structure, and verification accuracy hold up under paraphrasing, dimensional shifts, and clustering-selection-elimination attacks.

Core claim

GeoMark achieves localized triggering and centralized attribution by using a natural in-manifold embedding as the shared watermark target, building geometry-separated anchors with explicit target-anchor margins, and restricting watermark injection to adaptive local neighborhoods around those anchors.

What carries the argument

Geometry-separated anchors with explicit target-anchor margins around a shared natural in-manifold embedding, which confines injection to local neighborhoods while keeping the ownership signal centralized and verifiable.

If this is right

  • Downstream task accuracy stays intact because watermark changes are restricted to small local neighborhoods.
  • Verification remains reliable after paraphrasing or dimension changes because the target point is chosen from the natural manifold.
  • False-positive risk drops because explicit margins prevent coincidental geometric matches outside the intended regions.
  • Ownership attribution works centrally even though the injection trigger is kept strictly local.

Where Pith is reading between the lines

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

  • The same local-neighborhood injection idea could be tested on embedding models for images or time-series data where manifold structure is also present.
  • If the anchor margins prove stable, the method might extend to multi-task or federated embedding services without extra coordination cost.
  • Scaling the adaptive neighborhood size with model dimension could be measured directly to see whether verification stability holds at larger embedding sizes.

Load-bearing premise

Natural in-manifold embeddings exist that can act as stable shared targets whose explicit margins survive paraphrasing, dimensional perturbation, and clustering attacks without raising false positives or hurting utility.

What would settle it

A measurable rise in false-positive rate or loss of verification accuracy when the same model is watermarked with GeoMark and then subjected to clustering-selection-elimination attack on a dataset whose embeddings lack clear natural manifolds.

Figures

Figures reproduced from arXiv: 2604.11344 by Wei Lu, Wenbo Xu, Xiaojie Liang, Yuxuan Liu, Zhimin Chen.

Figure 1
Figure 1. Figure 1: Motivation of GeoMark. Existing EaaS watermark [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overall framework of GeoMark. Given a shared in-manifold watermark target, GeoMark performs geometry-aware [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Effect of local coverage ratio on CSE reconstruction [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Hyper-parameter analysis on the number of anchors [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Hyper-parameter analysis on local coverage ratio [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

Embedding-as-a-Service (EaaS) has become an important semantic infrastructure for natural language and multimedia applications, but it is highly vulnerable to model stealing and copyright infringement. Existing EaaS watermarking methods face a fundamental robustness--utility--verifiability tension: trigger-based methods are fragile to paraphrasing, transformation-based methods are sensitive to dimensional perturbation, and region-based methods may incur false positives due to coincidental geometric affinity. To address this problem, we propose GeoMark, a geometry-aware localized watermarking framework for EaaS copyright protection. GeoMark uses a natural in-manifold embedding as a shared watermark target, constructs geometry-separated anchors with explicit target--anchor margins, and activates watermark injection only within adaptive local neighborhoods. This design decouples where watermarking is triggered from what ownership is attributed to, achieving localized triggering and centralized attribution. Experiments on four benchmark datasets show that GeoMark preserves downstream utility and geometric fidelity while maintaining robust copyright verification under paraphrasing, dimensional perturbation, and CSE (Clustering, Selection, Elimination) attacks, with improved verification stability and low false-positive risk.

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 paper proposes GeoMark, a geometry-aware localized watermarking framework for copyright protection in Embedding-as-a-Service (EaaS). It selects a natural in-manifold embedding as a shared watermark target, constructs geometry-separated anchors with explicit target-anchor margins, and restricts watermark injection to adaptive local neighborhoods. This design aims to decouple localized triggering from centralized attribution. Experiments on four benchmark datasets are claimed to show that GeoMark preserves downstream utility and geometric fidelity while remaining robust to paraphrasing, dimensional perturbation, and CSE attacks, with improved verification stability and low false-positive risk.

Significance. If the empirical claims hold, GeoMark could meaningfully advance EaaS watermarking by addressing the robustness-utility-verifiability tension through explicit geometric margins and adaptive neighborhoods. The decoupling of trigger location from attribution target offers a potentially useful separation not present in prior trigger-based, transformation-based, or region-based approaches, provided the margins remain stable without utility degradation.

major comments (2)
  1. Abstract: The abstract states experimental outcomes on four datasets but supplies no metrics, baselines, attack implementations, or statistical details; the central robustness and utility-preservation claims therefore cannot be evaluated from the provided text.
  2. Framework construction (likely §3): The design relies on the existence and stability of natural in-manifold embeddings serving as reliable shared targets with explicit target-anchor margins that survive paraphrasing, dimensional perturbation, and CSE attacks; no formal invariance proof, bound on margin stability, or analysis of adaptive-neighborhood behavior under perturbation is supplied, which is load-bearing for the claimed decoupling of localized triggering from centralized attribution.
minor comments (2)
  1. The acronym CSE is introduced in the abstract without prior expansion; consider spelling it out on first use.
  2. Consider adding a dedicated table or section summarizing quantitative results (e.g., verification accuracy, utility metrics, false-positive rates) with direct comparisons to baselines.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive feedback. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: Abstract: The abstract states experimental outcomes on four datasets but supplies no metrics, baselines, attack implementations, or statistical details; the central robustness and utility-preservation claims therefore cannot be evaluated from the provided text.

    Authors: We agree that the current abstract is high-level and omits quantitative details. In the revised version we will expand the abstract to include key metrics (e.g., downstream task accuracy retention, attack success rates under paraphrasing/dimensional perturbation/CSE), the four benchmark datasets, and brief references to the baselines and statistical evaluation protocol used in the experiments. revision: yes

  2. Referee: Framework construction (likely §3): The design relies on the existence and stability of natural in-manifold embeddings serving as reliable shared targets with explicit target-anchor margins that survive paraphrasing, dimensional perturbation, and CSE attacks; no formal invariance proof, bound on margin stability, or analysis of adaptive-neighborhood behavior under perturbation is supplied, which is load-bearing for the claimed decoupling of localized triggering from centralized attribution.

    Authors: The referee correctly notes that the paper provides no formal invariance proof or analytic bounds. Our contribution is empirical: the geometry-separated anchors and adaptive neighborhoods are shown, across four datasets, to maintain sufficient target-anchor margins under the listed attacks while preserving utility. We will add a dedicated subsection (likely in §3 or a new §4.5) that reports quantitative margin-stability statistics, sensitivity plots for neighborhood size, and observed bounds derived from the experimental perturbations. This will strengthen the empirical grounding for the decoupling claim without claiming a general proof. revision: partial

standing simulated objections not resolved
  • A general formal proof of margin invariance under arbitrary paraphrasing, dimensional, and clustering perturbations in embedding space.

Circularity Check

0 steps flagged

No circularity: GeoMark is a novel construction with no derivation chain reducing to inputs or self-citations

full rationale

The paper presents GeoMark as a new framework that selects a natural in-manifold embedding, constructs geometry-separated anchors with explicit margins, and restricts injection to adaptive neighborhoods. No equations, fitted parameters, or predictions are described that reduce by construction to prior inputs. The abstract and provided text frame the work as an original design addressing robustness-utility tension, with experimental validation on benchmarks rather than any self-referential derivation or load-bearing self-citation. The central claims rest on the proposed construction and empirical results, not on renaming or fitting that collapses to the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit parameters, axioms, or invented entities; all technical details are deferred to the full manuscript.

pith-pipeline@v0.9.0 · 5501 in / 1018 out tokens · 29490 ms · 2026-05-10T15:52:09.560175+00:00 · methodology

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