This supplementary content is mainly organized in the order of being referenced in the main manuscript. The architectures of the R networks are shown in Table 3. The training curve is shown in Figure 1. B.1 Where is the secret image encoded? Is every channel equally important?

Advances in generative models have made it possible for AI-generated text, code, and images to mirror human-generated content in many applications. Watermarking, a technique that aims to embed information in the output of a model to verify its source, is useful for mitigating the misuse of such AI-generated content. However, we show that common design choices in LLM watermarking schemes make the resulting systems surprisingly susceptible to attack---leading to fundamental trade-offs in robustness, utility, and usability. To navigate these trade-offs, we rigorously study a set of simple yet effective attacks on common watermarking systems, and propose guidelines and defenses for LLM watermarking in practice.

In this paper, we introduce a novel technique called Tree-Ring Watermarking that robustly fingerprints diffusion model outputs. Unlike existing methods that perform post-hoc modifications to images after sampling, Tree-Ring Watermarking subtly influences the entire sampling process, resulting in a model fingerprint that is invisible to humans. The watermark embeds a pattern into the initial noise vector used for sampling. These patterns are structured in Fourier space so that they are invariant to convolutions, crops, dilations, flips, and rotations. After image generation, the watermark signal is detected by inverting the diffusion process to retrieve the noise vector, which is then checked for the embedded signal. We demonstrate that this technique can be easily applied to arbitrary diffusion models, including text-conditioned Stable Diffusion, as a plug-in with negligible loss in FID. Our watermark is semantically hidden in the image space and is far more robust than watermarking alternatives that are currently deployed.

Out-of-distribution (OOD) detection aims to identify OOD data based on representations extracted from well-trained deep models. However, existing methods largely ignore the reprogramming property of deep models and thus may not fully unleash their intrinsic strength: without modifying parameters of a well-trained deep model, we can reprogram this model for a new purpose via data-level manipulation (e.g., adding a specific feature perturbation). This property motivates us to reprogram a classification model to excel at OOD detection (a new task), and thus we propose a general methodology named watermarking in this paper. Specifically, we learn a unified pattern that is superimposed onto features of original data, and the model's detection capability is largely boosted after watermarking. Extensive experiments verify the effectiveness of watermarking, demonstrating the significance of the reprogramming property of deep models in OOD detection.

Neural networks have been shown effective in deep steganography for hiding a full image in another. However, the reason for its success remains not fully clear. Under the existing cover ($C$) dependent deep hiding (DDH) pipeline, it is challenging to analyze how the secret ($S$) image is encoded since the encoded message cannot be analyzed independently. We propose a novel universal deep hiding (UDH) meta-architecture to disentangle the encoding of $S$ from $C$. We perform extensive analysis and demonstrate that the success of deep steganography can be attributed to a frequency discrepancy between $C$ and the encoded secret image.

Split Federated Learning (SFL) is renowned for its privacy-preserving nature and low computational overhead among decentralized machine learning paradigms. In this framework, clients employ lightweight models to process private data locally and transmit intermediate outputs to a powerful server for further computation. However, SFL is a double-edged sword: while it enables edge computing and enhances privacy, it also introduces intellectual property ambiguity as both clients and the server jointly contribute to training. Existing watermarking techniques fail to protect both sides since no single participant possesses the complete model. To address this, we propose RISE, a Robust model Intellectual property protection scheme using client-Server watermark Embedding for SFL. Specifically, RISE adopts an asymmetric client-server watermarking design: the server embeds feature-based watermarks through a loss regularization term, while clients embed backdoor-based watermarks by injecting predefined trigger samples into private datasets. This co-embedding strategy enables both clients and the server to verify model ownership. Experimental results on standard datasets and multiple network architectures show that RISE achieves over $95\%$ watermark detection rate ($p-value \lt 0.03$) across most settings. It exhibits no mutual interference between client- and server-side watermarks and remains robust against common removal attacks.

Large language models now draft news, legal analyses, and software code with human-level fluency. At the same time, regulations such as the EU AI Act mandate that each synthetic passage carry an imperceptible, machine-verifiable mark for provenance. Conventional logit-based watermarks satisfy this requirement by selecting a pseudorandom green vocabulary at every decoding step and boosting its logits, yet the random split can exclude the highest-probability token and thus erode fluency. WaterMod mitigates this limitation through a probability-aware modular rule. The vocabulary is first sorted in descending model probability; the resulting ranks are then partitioned by the residue rank mod k, which distributes adjacent-and therefore semantically similar-tokens across different classes. A fixed bias of small magnitude is applied to one selected class. In the zero-bit setting (k=2), an entropy-adaptive gate selects either the even or the odd parity as the green list. Because the top two ranks fall into different parities, this choice embeds a detectable signal while guaranteeing that at least one high-probability token remains available for sampling. In the multi-bit regime (k>2), the current payload digit d selects the color class whose ranks satisfy rank mod k = d. Biasing the logits of that class embeds exactly one base-k digit per decoding step, thereby enabling fine-grained provenance tracing. The same modular arithmetic therefore supports both binary attribution and rich payloads. Experimental results demonstrate that WaterMod consistently attains strong watermark detection performance while maintaining generation quality in both zero-bit and multi-bit settings. This robustness holds across a range of tasks, including natural language generation, mathematical reasoning, and code synthesis. Our code and data are available at https://github.com/Shinwoo-Park/WaterMod.

Despite progress in watermarking algorithms for large language models (LLMs), real-world deployment remains limited. We argue that this gap stems from misaligned incentives among LLM providers, platforms, and end users, which manifest as four key barriers: competitive risk, detection-tool governance, robustness concerns and attribution issues. We revisit three classes of watermarking through this lens. \emph{Model watermarking} naturally aligns with LLM provider interests, yet faces new challenges in open-source ecosystems. \emph{LLM text watermarking} offers modest provider benefit when framed solely as an anti-misuse tool, but can gain traction in narrowly scoped settings such as dataset de-contamination or user-controlled provenance. \emph{In-context watermarking} (ICW) is tailored for trusted parties, such as conference organizers or educators, who embed hidden watermarking instructions into documents. If a dishonest reviewer or student submits this text to an LLM, the output carries a detectable watermark indicating misuse. This setup aligns incentives: users experience no quality loss, trusted parties gain a detection tool, and LLM providers remain neutral by simply following watermark instructions. We advocate for a broader exploration of incentive-aligned methods, with ICW as an example, in domains where trusted parties need reliable tools to detect misuse. More broadly, we distill design principles for incentive-aligned, domain-specific watermarking and outline future research directions. Our position is that the practical adoption of LLM watermarking requires aligning stakeholder incentives in targeted application domains and fostering active community engagement.

This supplementary content is mainly organized in the order of being referenced in the main manuscript. The architectures of the R networks are shown in Table 3. The training curve is shown in Figure 1. B.1 Where is the secret image encoded? Is every channel equally important?

The growing deployment of Large Language Models (LLMs) in real-world applications has raised concerns about their potential misuse in generating harmful or deceptive content. To address this issue, watermarking techniques have emerged as a promising solution by embedding identifiable binary messages into generated text for origin verification and misuse tracing. While recent efforts have explored multi-bit watermarking schemes capable of embedding rich information such as user identifiers, they typically suffer from the fundamental trade-off between text quality and decoding accuracy: to ensure reliable message decoding, they have to restrict the size of preferred token sets during encoding, yet such restrictions reduce the quality of the generated content. In this work, we propose MajorMark, a novel watermarking method that improves this trade-off through majority bit-aware encoding. MajorMark selects preferred token sets based on the majority bit of the message, enabling a larger and more flexible sampling of tokens. In contrast to prior methods that rely on token frequency analysis for decoding, MajorMark employs a clustering-based decoding strategy, which maintains high decoding accuracy even when the preferred token set is large, thus preserving both content quality and decoding accuracy. We further introduce MajorMark$^+$, which partitions the message into multiple blocks to independently encode and deterministically decode each block, thereby further enhancing the quality of watermarked text and improving decoding accuracy. Extensive experiments on state-of-the-art LLMs demonstrate that our methods significantly enhance both decoding accuracy and text generation quality, outperforming prior multi-bit watermarking baselines.