Flip, Don't Shuffle: Watermarking LLMs at the Speed of Inference

We introduce Stateless Bernoulli Watermarking (SBW), a new statistical watermark for Large Language Models that determines green list membership through independent per-token Bernoulli trials. Unlike KGW's vocabulary permutation or SynthID's multi-layer tournament, SBW requires only a single comparison per token against a counter-based random number generator, reducing membership complexity to $O(1)$ and enabling single-kernel execution with zero intermediate allocations. We prove that this formulation preserves the same detection guarantees as fixed-size green lists: the z-score test remains $\mathcal{N}(0,1)$ under the null. The stateless architecture enables capabilities unavailable to existing methods: full-vocabulary self-salt watermarking (over 6000$\times$ faster than KGW's self-salt and 2$\times$ faster than SynthID despite biasing the entire vocabulary with candidate-dependent seeding) and architectural compatibility with distributed inference. In end-to-end generation benchmarks, SBW adds less than 1\% overhead at all batch sizes. We additionally identify hash function design as a previously unexplored axis for watermark quality, showing that a GPU-native Jenkins hash improves null calibration by 1.8$\times$ while producing more diverse text. Experiments across two seeding schemes and eight $(γ, δ)$ configurations confirm statistical equivalence with ROC-AUC differences below 0.01.

Rent-a-RAG: Embedding-Space Watermarks for Auditing Third-Party RAG

Third-party retrieval-augmented generation (RAG) marketplaces create a new auditing problem: data providers may license corpora to a RAG operator, yet later have no visibility into whether their documents are being reused without compensation. Auditing this misuse is difficult because the operator is non-cooperative, answers are paraphrased by the generator, and one response may combine evidence from many providers. We propose DirBucket, a provider-side semantic watermarking and black-box auditing framework for document-level reuse in multi-provider RAG. DirBucket watermarks documents by meaning-preserving paraphrases whose embeddings are biased toward provider-bucket secret directions, enabling detection from black-box answers while preserving retrieval utility. On a challenging benchmark that reflects mixed-provider reuse under black-box access, DirBucket is the only method that consistently achieves strong target detection with no non-target activation, detecting non-compliance in every audit within 23 audited answers on our primary benchmark. The watermark survives adversarial post-answer laundering, and none of the evaluated evasion strategies simultaneously defeats detection while preserving user-perceived answer quality. Detection transfers unchanged to a second benchmark built from real clinical, cyber-threat-intelligence, and legal provider corpora. These results suggest that embedding-space watermarking can make document reuse in third-party RAG statistically auditable.

Minimax bounds for watermarked and masked recursive discrete distribution estimation

Watermarking has been proposed as a way to identify synthetic samples in estimation settings where no metadata is available to distinguish them from real samples, but its precise effects remain unexplored. In the absence of a distinguishing mechanism, it has been shown that adding synthetic samples significantly reduces the marginal efficacy of new real samples. In this work, we study the minimax loss of such recursive discrete distribution estimation in the presence of watermarks in contrast to the unassisted and oracle-assisted losses. When the fraction of real samples vanishes asymptotically, we provide a lower bound that shows that it is impossible to improve performance by adding watermarks unless the false negative rate of detection also vanishes. Additionally, we show that in most regimes, the worst-case losses of a sequence of simple deterministic estimators match the corresponding lower bounds up to constants. Finally, we propose masking, a randomization procedure that narrows the gap in the remaining regimes to a Jensen gap. We conjecture that a tighter lower bound argument can close this gap.

SemTrace: Source-Grounded Semantic Signatures for Tracing LLM Exposure to Protected Documents

Large language models are increasingly used to read documents and produce downstream text, creating a provenance problem when the document owner cannot control or inspect the model that performs the generation. We introduce SemTrace, a source-grounded semantic watermark for detecting whether a generated review was influenced by a known protected manuscript copy. Rather than biasing token probabilities or imposing surface-form patterns, SemTrace constructs a document-specific binary signature from factual propositions that are directly supported by the manuscript itself. A protected PDF invisibly carries a content contract that selects one fact from each binary pair and asks an instruction-following reviewer to express those facts in fixed review slots without changing its independent evaluation. A frozen natural language inference model then decodes the resulting semantic evidence with explicit erasures and scores the recovered bits against the codeword assigned to that copy. This design targets model-agnostic, assigned-copy exposure detection while keeping the watermark semantically tied to the source document.

Asymmetric Phase Coding Video Watermarking

Existing video watermarking systems are symmetric: the party that can verify a mark holds the extractor weights or generator secret and can therefore also embed one. Benchmarks confirm the consequence, reporting that white-box forgery defeats all evaluated methods. We present a training-free video watermark that removes the shared secret. The signer embeds a complete Ed25519 signature into the phase spectrum of the chroma plane; any party holding the 32-byte public key and public per-video metadata verifies offline, with no model, no registry, and no network. The payload, 1024 bits of signed message with error correction, is an order of magnitude above common learned payloads and is carried by three design elements: a run-length temporal layout whose decoder identifies payload groups by correlation and never reads a frame index, a payload-free search that recovers scale, rotation, and translation from the carrier itself, and a closed-loop signing procedure that selects each video's embedding strength by self-verification through the unchanged public verifier. On 1000 uncurated real-world clips the system ships a verifying signature for 99.3% of the corpus and accepts a wrong public key zero times in 1000 attempts. An attack-aware acceptance gate yields embeddings that survive H.264 re-encoding at 100% and 50% rescaling at 97.4% on gated clips. The signature also verifies through a real display and capture loop, an axis absent from published evaluations.

Learning to Follow In-Context Watermark Instructions via Self-Distillation

In-context watermarking (ICW) prepends an instruction to a query asking the model to embed a statistically detectable signal in its response. It thus equips LLMs with a watermarking interface that third parties can invoke without access to model internals. Its reliability hinges on the LLM following the instruction without degrading answer quality, yet how well current LLMs do so has not been measured. We introduce $\mathsf{ICWBench}$, a benchmark of three verifiable ICW instruction families, each scored on both detectability and answer quality. Evaluating 14 frontier proprietary and open-source LLMs, we find that none of the evaluated LLMs achieves both objectives across all three families. To address this, we propose a self-contained two-stage training method, requiring no distillation from a stronger model, no manual annotation, and no pre-existing ICW IF ability. The first stage, self-distillation with logits perturbation (SDLP), uses the same base LLM as both teacher and student: an instruction-equivalent decoding-time logits perturbation makes the teacher follow the ICW instruction, and the student is trained to match the teacher's output distribution. The second stage applies reinforcement learning with the automatic verifier as the reward. Applied to Qwen3-14B and GPT-OSS-20B, our method raises average TPR@$1\%$FPR across three ICW instructions from $0.100$ to $0.974$ and from $0.337$ to $0.968$, respectively, while maintaining high response quality under both perplexity evaluation and LLM-as-a-Judge.

Semantic Watermarking with Order-Robust Detection over Sub-sentence Units

Semantic watermarks tie the mark to sentence meaning rather than token choices, promising robustness to content-preserving edits. However, the detector only observes attacker-supplied text, which can be reworded, reordered, or resegmented to evade detection without content loss. Rewording, reordering, and resegmentation all cause embedding displacement: detection tests embeddings different from those selected during watermarking and can therefore lose the mark. Our adaptive embedding displacement attack (EDA) admits all three edits under a single objective that maximizes this displacement. It uses a public paraphraser and surrogate encoder without access to the provider's generator or secret key. At a 5% false-positive rate (FPR) and content-preservation threshold $\bar{q}=90\%$, EDA successfully removes the mark on between 32.6% and 47.9% of documents across four schemes, the highest among the tested attacks. Therefore, EDA evaluates the schemes' robustness more thoroughly than passive paraphrasing. To address these vulnerabilities, we design (k)-SwordStamp: semantic watermarks with order-robust detection over sub-sentence units, reducing sensitivity to attacker-chosen structure at a small quality cost. Against k-SwordStamp, the strongest no-box attack we test is an EDA variant adapted to its design, with a 10.8% attack-success rate. A stronger EDA with access to the provider's detector and secret key reaches a 39.7% attack-success rate, compared with 65.5% on k-SemStamp. Our code is available at https://github.com/D-Diaa/SwordStamp.

MeMark: Membrane-Space Watermarking for Spiking Neural Networks

Spiking Neural Networks (SNNs) are increasingly distributed as pretrained checkpoints and reused as backbones for new tasks. However, current SNN watermarks are mainly verified against the model output. Thus, a user who replaces the output head can keep most of the original network while removing the evidence used for verification. We present MeMark, a watermark designed for the checkpoint-reuse setting. Instead of storing the watermark in the output head, MeMark embeds a multi-bit identifier in the internal membrane state of selected Leaky Integrate-and-Fire (LIF) neurons. A secret input drives each selected neuron to the chosen side of its own firing threshold, and the same threshold is later used to recover the secret bit, so the verifier does not need a learned decoder. We evaluate MeMark across recurrent, convolutional, residual, and transformer SNNs. On a 215.4M-parameter SpikeGPT checkpoint, all 20 independent 64-bit keys pass the fixed 51/64 verification rule, while none of the $30\,000$ fresh random keys pass when tested against all 20 protected checkpoints and the clean model. All 20 genuine keys also remain above the threshold after fine-tuning, 90\% pruning, int8 quantization, and output-head replacement. Under our stated threat model, adaptive attacks can weaken the watermark but do not remove the ownership evidence in the settings we test. Additionally, we study false ownership claims, key-aware and key-agnostic removal, partial key disclosure, rollback, and extraction into a student. The results show that MeMark can provide evidence of checkpoint derivatives, while being resistant to the adversary's attacks and complete head replacement.

SAC-Copula: Quality-Preserving Watermarking for Diffusion Language Models via Smooth Correlated Gumbel Fields

Watermarking diffusion language models (DLMs) requires mechanisms compatible with iterative parallel unmasking rather than autoregressive decoding. Existing sampling-based watermarking methods typically inject position-wise i.i.d. perturbations, which can be poorly aligned with DLM decoding dynamics and degrade generation quality. We propose SAC-Copula, a quality-preserving watermarking method for DLMs based on smooth, locally correlated Gumbel perturbation fields constructed via a Gaussian copula. We further develop a SAC-aware detector using covariance-aware filtering and native-sample calibration. Mechanism-level analysis shows that local correlation reduces latent perturbation roughness and better matches iterative refinement dynamics. Experiments on LLaDA show that SAC-Copula achieves a favorable quality-detectability trade-off compared with existing baselines. In particular, further evaluations on Dream-7B and additional datasets show that SAC-Copula substantially improves PPL tail stability over the i.i.d. Gumbel baseline, while maintaining strong low-FPR detectability and competitive overall generation quality. Additional token-edit stress tests further assess watermark robustness under controlled synchronization drift.

Keyed Provenance Watermarking with Complementary Lattice-Based Secure Aggregation for Federated Learning

Federated learning (FL) is vulnerable to multi-level attacks. However, existing methods address them separately, leaving FL exposed to data leakage, unauthorized reuse, and malicious gradient manipulation. In this work, we propose an FL framework that couples keyed context-provenance watermarking with verifiable lattice-based secure aggregation of Real-World Anchored Watermarking and Lattice-Based Zero-Knowledge Secure Aggregation. At the data layer, we propose a Kerckhoffs-compliant scheme that utilizes Physical Anchor Metadata (PAM) to ensure data provenance. PAM is defined as a context-provenance token derived from trusted infrastructure data (time, location, and server ID) and then subjected to a keyed HMAC-SHA-256 transformation to produce a watermark payload that cannot be generated without the client's secret key. We further design FMGAN, a GAN-based robust image watermarking framework that embeds this transformed payload using a feature fusion module and a Mamba-guided linear attention mechanism. At the computation layer, we adopt a lattice-based zero-knowledge secure aggregation (LZKSA) protocol that verifies key correctness, L2 norm bounds, and cosine similarity constraints over committed gradients without revealing private updates. The RLWE-based design guarantees post-quantum security. Extensive experiments validate the complementary protection of the two layers under composite attack scenarios. To our knowledge, no prior verification workflow has jointly evaluated both layers in a hybrid, end-to-end trustworthy FL framework.

Auditing Cross-Lingual Fairness in Language Model Watermarking

Watermarking schemes for large language model output are evaluated almost exclusively on English text using each scheme's detection threshold and a narrow set of quality measurements. Multilingual deployment exposes evaluation-design choices that are inconsequential on English but determine conclusions cross-lingually. We propose an evaluation framework with four components: detection thresholds calibrated empirically per deployment context, a threshold-independent companion measurement that distinguishes calibration failures from detection failures, three disjoint quality measurement paradigms (distributional, paired-semantic, and reference-perplexity), and a generalized-entropy decomposition of cross-language disparity over a typological family partition. Applied to six watermarking schemes, three open-weight generators, eleven languages spanning four scripts and eight typological families, and both base and instruction-tuned regimes, the framework reveals failure modes that single-language single-paradigm evaluation cannot surface. Across detection and quality, observed disparity is predominantly between-family on the typological partition, indicating that cross-lingual fairness gaps in watermarking are structural to language properties rather than idiosyncratic to particular languages.

A Locally Tokenized Generative Model for Robust Time-Series Watermarking

Watermarking is a central tool for provenance in generative models, yet its application to multivariate time series remains hindered by reliability failures under post-editing attacks. We show that existing detectors, which rely on globally coupled re-encoding, suffer from bidirectional drift of the null distribution: post-editing attacks can shift the z-score of non-watermarked samples in either direction, invalidating clean-calibrated thresholds. We argue that this instability is a property of the re-encoding, and that reliable detection requires each recovered unit to depend only on a bounded temporal neighborhood. Guided by this principle, we propose L-VQVAE, a generative model in which each discrete token is produced from a short contiguous window, and LVQMark, a watermarking method over this token space that combines logit-bias injection with robust re-encoding for attack-time detection. Experiments on four benchmarks spanning finance, energy, and neuroimaging show that our approach preserves generation quality while stabilizing both detection power and false-positive behavior under post-editing attacks.

Linguistic Holonomy and Statistical Watermarks: Inner Geometry of Meaning-Preserving Transformations

Statistical watermarks for language models live in the freedom of the signifier: they choose among tokens that are nearly equivalent in meaning, and they are therefore eroded by exactly those transformations which move the form of a text while leaving its content in place. The literature measures such transformations by their endpoint, through the semantic similarity between the original and the rewritten text. We show that the endpoint is the wrong statistic. Adapting the formalism of linguistic loops, we prove that the invariant of a chain of meaning-preserving transformations factorises canonically into an endpoint part and a holonomy in the stabiliser of the initial state, the second of which the semantic deficit cannot see; the loop rotation is parallel transport on the unit sphere of the embedding space, so that the analogy with the Wilson loop becomes a theorem rather than a figure of speech. On the side of the detector we prove an exact identity: the residual statistic is proportional to the number of positions whose seeding window survived intact, from which the decay law $ρ^{h+1}$ follows as the independent-edit corollary. The identity has a disconcerting consequence, which we confirm to three decimal places: at one and the same retention rate the surviving signal may be one half of the original, one quarter of it, or exactly nothing, according only to where the edits fall.

NGS-Marker: Robust Native Watermarking for 3D Gaussian Splatting

With the rapid development and adoption of 3D Gaussian Splatting (3DGS), the need for effective copyright protection has become increasingly critical. Existing watermarking techniques for 3DGS mainly focus on protecting rendered images via pre-trained decoders, leaving the underlying 3D Gaussian primitives vulnerable to misuse. In particular, they are ineffective against Partial Infringement, where an adversary extracts and reuses only a subset of Gaussians. In this paper, we propose NGS-Marker, a novel native watermarking framework for 3DGS. It integrates a jointly trained watermark injector and message decoder, and employs a gradientbased progressive injection strategy to ensure full-scene coverage. This enables robust ownership decoding from any local region. We further extend NGS-Marker with hybrid protection (combining native and indirect watermarks) and support for multimodal watermarking. Extensive experiments demonstrate that NGS-Marker effectively defends against partial infringement while offering practical flexibility for real-world deployment.

A Content-Aware Pure Permutation with Intrinsic Avalanche Effect: Breaking the Diffusion-Permutation Dichotomy

Pixel permutation is a fundamental tool in image processing, image encryption, and data hiding (including watermarking and steganography) that rearranges pixels without changing their values. A common assumption in the literature is that permutation alone cannot create differential sensitivity; changing one pixel merely relocates that pixel in the output, producing no avalanche effect. This paper challenges this by introducing the Triangular Content-Aware Permutation (TCA) algorithm. The method extracts edge points using Canny and applies Delaunay Triangulation to edges and corners, creating a unique partition. Since triangulation is highly sensitive to image geometry, changing a single pixel alters the edge map, resulting in a completely different triangulation and global permutation pattern. Unlike classical dimension-based permutations and advanced content-aware methods (2025-2026), which lack differential sensitivity, TCA increases NPCR from near-zero to 97.10% solely through pixel relocation. Experiments on 50 images show that TCA, with an average of 14.81 iterations, achieves NPCR = 97.10% and UACI = 20.06%, proving pure permutation can create significant differential sensitivity. Conventional methods maintain near-zero NPCR. The iteration threshold varies from 6.4 to 30.7 based on content complexity. Low PSNR (11.93 dB) and near-zero correlation (~10^-3) confirm superior statistical performance. Although slower than classical methods due to triangulation, this is a deliberate trade-off for stronger security. Given the non-analytic, content-dependent nature of the pattern, TCA is ideal for reference-based encryption, fragile watermarking, and non-blind steganography.

DeepFreqMark: End-To-End Learnable Frequency-Domain Watermarking with Spherical Attack Simulation for Latent Diffusion Models

The proliferation of AI-generated images produced by Latent Diffusion Models (LDMs) has raised critical concerns regarding copyright infringement and misinformation. Although existing frequency-domain watermarking methods embed handcrafted geometric patterns into the initial latent noise prior to generation, they suffer from limited capacity and rigid pattern designs. We propose DeepFreqMark, an end-to-end learnable frequency-domain watermarking framework that replaces manual pattern engineering with a neural message encoder and decoder. To circumvent the computational bottleneck caused by Denoising Diffusion Implicit Model (DDIM) inversion during training, we introduce a Spherical Linear Interpolation (Slerp)-based attack simulation. This approach operates directly on the noise latent while strictly preserving the Gaussian variance. Extensive experiments demonstrate that DeepFreqMark achieves significantly lower Bit Error Rates (BER) than baseline methods under real-world attacks and scales to 256 bits message capacity. Our source code is available at https://github.com/chenhsiu48/DeepFreqMark.

Reversible Unlearnable Examples: Towards the Copyright Protection in Deep Learning Era

Significant advancements in deep learning have been made possible by the utilization of large datasets, underscoring the critical importance of copyright protection. Adding meticulously designed perturbations to examples, making them unlearnable has become a crucial approach for safeguarding data copyright. Existing methods for creating unlearnable examples overlook the risk of data leakage, which can threaten data ownership. Thus, copyright protection in deep learning faces two main threats: illegal model training and malicious data leakage. We investigate that these two threats cannot be solved by straightforwardly combining existing availability attacks and watermarking techniques as their negative interaction effects. Therefore, in this paper, we propose a novel copyright protection mechanism for the aforementioned security concerns. Considering that the prevention of unauthorized model training requires powerful generalizability of unlearnable perturbations, we generate perturbations to induce the model to learn uncorrelated features of input images. It works by minimizing the mutual information of the input and output of the model. On the other hand, to eliminate the side impact of unlearnable perturbations on the watermark extraction, we design a dual extraction strategy by using two distinct watermark extractors. Extensive experiments on the image datasets {ImageNet, CIFAR10, and Pets} show that our proposed method could provide comprehensive copyright protection to images. The code is available at {https://github.com/Yeah21/ReversibleUnlearnableExamples}.

WorldMark: A Plug-and-Play World Knowledge Interface for Cross-Host Language Model Watermarking

Watermarking traces the provenance of text produced by large language models by embedding statistically detectable signals during decoding. Existing schemes fall into logits-based, sampling-based, entropy-aware, and adaptive-strength families, yet all of them place watermark signals according to local token statistics. In the open-ended text-generation settings evaluated in this work, local statistics may provide insufficient guidance for placing robust watermark signals. We introduce WorldMark, a plug-and-play interface that uses World Knowledge Memory (WKM) to organize semantic and episodic knowledge in a memory graph, converts the retrieved knowledge into a token-level knowledge saliency score, and adjusts the strength of a host watermark through Asymmetric Knowledge Modulation (AKM). WorldMark requires no backbone retraining and introduces no additional detector-side model or parameter. On the primary C4 evaluation, the complete WorldMark interface improves clean and attacked detection across three adaptive-strength host variants while slightly reducing perplexity. Additional pilot experiments on C4 and OpenGen show that direct memory conditioning transfers across multiple watermark families but can be unstable without saliency-aware modulation. WorldMark requires no additional detector-side model or parameter and introduces negligible overhead under the primary protocol.

Attribute-based Undetectable Watermarking for Generative AI Models

Generative AI systems increasingly produce content whose provenance is difficult to verify, motivating watermarking techniques for identifying model-generated outputs. Existing cryptographic watermarking methods provide strong undetectability guarantees: without a detection key, watermarked outputs are computationally indistinguishable from unwatermarked ones. However, these approaches do not address the crucial deployment challenge of how to safely delegate detection capabilities. With an unrestricted detection key, a malicious detector may use the detection key beyond its intended scope, enabling watermark sanitization, scope abuse, and user profiling. To mitigate this safety concern, we introduce, to the best of our knowledge, the first \emph{attribute-based watermarking} for generative AI models, providing fine-grained, policy-controlled watermark detection. In our approach, each generated output is associated with attributes, and each detection key is \emph{constrained by a policy} on potential attributes. A detection key can only be used to detect watermarked outputs whose attributes satisfy the corresponding policy, while watermarked outputs that fall outside the policy remain computationally indistinguishable from unwatermarked ones. We construct such an attribute-based watermarking scheme and formalize its security properties, including consistency, adaptive robustness to bounded corruptions, undetectability, and soundness, along with a security proof under standard cryptographic assumptions. Our construction integrates constrained pseudorandom functions, pseudorandom error-correcting codes, and randomness recovery procedures with generative AI models. Finally, we implement a prototype and an empirical evaluation, demonstrating that attribute-based watermarking is both effective and practical.

FARI: Robust One-Step Inversion for Watermarking in Diffusion Models

Inversion-based watermarking is a promising approach to authenticate diffusion-generated images, yet practical use is bottlenecked by inversion that is both slow and error-prone. While the primary challenge in the watermarking setting is robustness against external distortions, existing approaches over-optimize internal truncation error, and because that error scales with the sampler step size, they are inherently confined to high-NFE (number of function evaluations) regimes that cannot meet the dual demands of speed and robustness. In this work, we have two key observations: (i) the inversion trajectory has markedly lower curvature than the forward generation path does, making it highly compressible and amenable to low-NFE approximation; and (ii) in inversion for watermark verification, the trade-off between speed and truncation error is less critical, since external distortions dominate the error. A faster inverter provides a dual benefit: it is not only more efficient, but it also enables end-to-end adversarial training to directly target robustness, a task that is computationally prohibitive for the original, lengthy inversion trajectories. Building on this, we propose \textbf{FARI} (\textbf{F}ast \textbf{A}symmetric \textbf{R}obust \textbf{I}nversion), a one-step inversion framework paired with lightweight adversarial LoRA fine-tuning of the denoiser for watermark extraction. While consolidation slightly increases internal error, FARI delivers large gains in both speed and robustness: with approximately 20 minutes of fine-tuning on a single NVIDIA RTX A6000 GPU, it surpasses 50-step DDIM inversion on watermark-verification robustness while dramatically reducing inference time. Code and pretrained models are available at https://github.com/0xD009/FARI.

Correlation-Aware and Gaussianity-Preserving Robust Latent Angular Watermarking for Diffusion Models

Latent domain watermarking for diffusion models embeds watermarks directly into the latent prior, enjoying non-intrusiveness to model parameters and seamless integration with the generation process. However, due to the violation of latent Gaussianity or sensitivity to normal and malicious perturbations during latent inversion, existing methods are prone to watermark detection or removal attacks. A further overlooked problem is the violation of the i.i.d. latent condition after watermarking, which leads to latent correlation degradation and generation fidelity loss. Although this has been externally measured by FID, the internal correlation structure has yet to be rigorously characterized. To address the above issues, and motivated by the rotation-invariant property of isotropic Gaussian, we propose \textit{Latent Angular Watermarking (LAW)}, which encodes watermark bits as antipodal angles ($\pmπ/2$ relative to a reference pair) between disjoint pairs of latent elements while preserving the Gaussianity. The antipodal ($π$-separation) encoding maximizes geometric separation between bit values, and we prove that the decoding angular-error variance is proportional to the norm of the latent pair, i.e., $\operatorname{var}(Δφ) \propto 1/ρ^2$. We further propose a magnitude-driven variant, LAW-M, which anchors watermark bits in the most geometrically stable latent dimensions, yielding additional robustness gains. Theoretically, we provide a rigorous characterization of the induced correlation degradation, deriving in closed form the autocorrelation structure of the watermarked latent and proving that correlations are confined to a sparse, structured set of off-diagonal elements with fixed $\pmπ/4$ values.

Efficient Online LLM Watermark Detection via Rao-Blackwellized E-Processes

As large language models (LLMs) are increasingly deployed, reliable and efficient mechanisms for distinguishing AI-generated text from human-written content have become essential. Statistical watermarking has emerged as a promising solution, yet most existing methods are typically fixed-horizon procedures, precluding valid early stopping in streaming generation. In this paper, we develop an efficient online watermark detection framework with anytime-valid inference based on Rao-Blackwellized e-processes, enabling recursive token-level evidence updates without storing the full history. In particular, we instantiate the framework for the Gumbel-max watermark and reduce the original token-level dependence testing problem to a pivot-induced sequential testing problem with an explicit null distribution. Theoretically, we prove anytime-valid Type I error control under arbitrary optional stopping and establish positive asymptotic log-growth under watermarking, implying consistency of the proposed stopping rules. Simulations and experiments on real LLM-generated text demonstrate efficient online detection with rigorous anytime-valid guarantees.

WaterMoE: Expert-Routing-based Watermarking for High Fidelity and Efficiency

Large language models (LLMs) have achieved remarkable success but raise growing concerns about content provenance and misuse, motivating the need for reliable watermarking techniques. However, these techniques have rarely been adopted in practice mainly for two reasons: i) severely degraded model performance, and ii) additional inference overhead. To confirm the problem, we construct a comprehensive benchmark spanning different generation tasks to systematically evaluate 9 representative watermarking methods. We found almost all existing methods are designed for text fluency, but not for restricted and complicated tasks, and their overhead prevents them from deployment in latency-critical systems. To address i) and ii), we propose an LLM watermarking scheme \textit{WaterMoE} for the growingly popular Mixture-of-Experts (MoE) LLMs. WaterMoE embeds watermarking signals through controlled perturbation into the expert selection at each router, which accumulates to token selection shift at the final output. In contrast to watermarking as a post-processing token-sampling approach, WaterMoE embeds watermark within the inference loop incurring negligible quality degradation and computational overhead. Extensive experiments demonstrate that our method achieves a fidelity performance close to the unwatermarked and consistently outperforms state-of-the-art watermarking methods on the benchmark, with up to $4\times$ speedup, incurring merely 1\% additional inference latency compared to native generation. The results demonstrate the capability of WaterMoE to be deployed in real-world tasks.

MusicMark: A Robust Generative Watermarking Framework for Music Generation

AI music generation has rapidly advanced alongside commercial platforms, raising the need for reliable watermarking for provenance and attribution. However, existing audio watermarking research has largely focused on speech, and applying speech-oriented methods to music is challenging due to music's complex structure and rich acoustic texture. Most existing methods are post-hoc, adding imperceptible perturbations after generation rather than embedding watermarks as part of the content. This makes them fragile under transformations and especially vulnerable to neural codec re-synthesis, which can discard imperceptible residual signals. Moreover, since generation and watermarking are decoupled, the watermarking step can be bypassed or omitted, weakening provenance guarantees. To address these issues, we propose MusicMark, which, to the best of our knowledge, is the first generative watermarking framework for music. Specifically, MusicMark embeds watermark messages into the semantic latent space during generation, incorporating the watermark as part of the musical content and ensuring robustness against diverse attacks, particularly neural codec re-synthesis. To this end, we introduce a watermark adapter into a diffusion-based generation model to embed watermark messages across denoising steps. The adapter and detector are trained with a joint objective that preserves fidelity by constraining watermarked latents close to their unwatermarked reference latents, while improving robustness through attack augmentations. Experiments demonstrate that MusicMark substantially outperforms post-hoc baselines across diverse attacks including neural codec re-synthesis, while maintaining comparable generation quality. We further introduce a cover-song attack, converting the singing voice while preserving musical content, and show that MusicMark remains more robust than post-hoc methods.

Observation-Level Watermarking and Detection for Tabular Data

With the development of generative AI, watermarking techniques have been widely used to detect the authenticity of AI-generated data and protect the rights of users and creators. While it is already well applied in data types including imaging and text data, watermarking tabular data is still under-explored. Existing methods primarily focus on numerical data, leaving discrete, categorical, and mixed data less studied. In this work, we propose STAMP (Single-observation Tabular Attribution and Marking Procedure), a novel framework for watermarking tabular data that can accommodate and preserve a wide range of distributions. We also develop a corresponding detection mechanism, which can reliably identify watermarks even when the sample size is as small as one. We establish theoretical guarantees for asymptotic consistency and detection accuracy. Finally, through extensive simulation studies and two real-data applications, we demonstrate that the proposed method is effective and robust to subsetting, while maintaining data fidelity and a high detection rate.

RaMark: Radioactive Watermarking for Generated Tabular Data

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.

TRACE: A Two-Channel Robust Attribution Watermark via Complementary Embeddings for LLM-Agent Trajectories

LLM agents reach users through resellers, who may rebrand a developer's agent or substitute a cheaper model. When provenance is disputed, attribution rests on the trajectory log (the record of tool calls, observations, and executed actions, not the model's reasoning), which the reseller stores and processes to meter usage. A watermark must therefore survive an adversary with full read/write access to the very evidence it is detected from; existing agent watermarks do not, as their attribution is read straight off that log. We present TRACE, to our knowledge the first agent watermark that is distortion-free in its action choices, self-synchronizing under deletion, and unconditionally invariant under rewriting. Deletion desynchronizes a position-derived key and rewriting alters content, so a deletion-robust key must come from content and a rewrite-robust key from position, and no single key serves both. A trajectory, however, has room for two watermarks. TRACE superposes a selection channel that sets which action is chosen, keyed on local content with a distortion-free sampler, so the agent's distribution is provably unchanged and detection resynchronizes after deletions, and a tally channel that sets how many records each decision group holds, keyed on the log's skeleton alone, which no rewriting can touch. We prove this behavioral watermark's signal is bought with decision entropy, each decision paying at least half its entropy and deterministic decisions nothing, and that erasing both channels forces the reseller to corrupt the trajectories it resells. On ToolBench and ALFWorld, TRACE matches the unwatermarked agent's success rate while its selection channel reaches detection scores near z = 100 on long-horizon trajectories, stays detectable under 70% step deletion, and keeps a tally channel exactly unchanged under LLM rewriting of any strength.

Beyond Heuristic Tuning: Power-Calibrated LLM Watermarking

Logit-based watermarking is a widely used mechanism for identifying LLM generated content, yet its effectiveness is governed by a fundamental trade-off between detectability and semantic distortion. Existing analyses provide limited guidance for principled hyperparameter selection, leaving practical deployments reliant on heuristic tuning. In this work, we develop a power-calibrated statistical framework that establishes explicit quantitative relationships between watermark hyperparameters, detection power, and distortion. This characterization transforms watermark design into a guided optimization problem. Building on these results, we derive practical parameter selection procedures that achieve optimal tradeoffs under constraints. Extensive experiments across multiple language models and datasets validate the theory and demonstrate that the proposed framework consistently identifies Pareto-optimal points.

Selective Disclosure Watermarking for Large Language Models

Watermarking methods embed imperceptible and verifiable signals into text generated by large language models (LLMs). Existing approaches include zero-bit schemes for distinguishing synthetic text from human writing and multi-bit schemes for embedding metadata. However, current multi-bit watermarking methods do not allow selective disclosure: verifying any part of the watermark requires revealing the entire embedded message. This lack of control leads to unnecessary information exposure and raises privacy concerns. We propose Hierarchical Vocabulary Routing (HeRo), a watermarking framework that enables selective disclosure of embedded metadata. The method recursively partitions the vocabulary and distributes watermark information across hierarchical layers, so that different verifiers can decode only the portions of the payload corresponding to their access level. We show that the proposed scheme preserves the unbiasedness of the underlying sampling process and thus maintains text quality. Experiments demonstrate that our framework supports fine-grained access control while achieving high detection accuracy and low latency. Code is available at https://github.com/xuyangc03/hero-watermark.

BiSLW: Bi-Spectral Latent Watermarking for Generative Diffusion Models

Diffusion-based generative models have transformed visual content synthesis, yet they remain vulnerable to unauthorized usage and lack reliable attribution methods. Existing watermarking techniques often treat latent tensors as static spatial feature maps or depend on pixel-domain modification, and most do not explicitly leverage the internal frequency structure of the latent space for dual-band redundant embedding, leaving them susceptible to the stochastic nature of diffusion and regeneration attacks. We introduce BiSLW, a trainable bi-spectral latent watermarking framework that jointly embeds aligned identity signals across complementary spectral bands of the decoded diffusion latent using learned encoders and decoders, going beyond fixed-pattern frequency approaches. We leverage the inherent frequency structure of diffusion latents to design a dual-band watermarking framework. Low-frequency components encode global semantics, while high-frequency components capture fine texture. We exploit this structure to embed watermarks across complementary spectral bands. The watermark is independently injected into both bands via learned encoders and recombined before decoding, ensuring it becomes intrinsic to the generative trajectory. Dual spectral decoders recover the watermark from each band, while a cross-band consistency constraint enforces alignment between semantic and textural embeddings. Experiments show that BiSLW achieves a strong balance between perceptual fidelity and robustness, improving PSNR by over 3 dB compared to prior latent diffusion watermarking methods while preserving near-perfect bit accuracy under aggressive regeneration and common distortions, all with negligible computational overhead.