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

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.

With LLM watermarking being deployed commercially and now required by regulations, improving its reliability and effectiveness has become crucial. Yet, recent progress in the field of LLM watermarking has increasingly been driven by improving details of existing methods, an effort fundamentally limited by the pace of human researchers. In this work, we enable for the first time the autonomous discovery of new distortion-free state-of-the-art watermarking schemes. To enable this, we (i) establish strict criteria to ensure that watermarks are reliable (e.g., they do not have an unexpectedly high false positive rate), (ii) propose rigorous statistical tests to automatically evaluate whether a watermarking scheme satisfies our criteria, and (iii) design an evaluation suite to rank watermarks along three key dimensions: detectability, quality, and robustness. By running our framework with 3 frontier models (GPT-6 Astra, Opus 5, Gemini-3.8 Flash), we discover over 50 different watermarking schemes, including several that outperform prior works along all key dimensions. We complement this by a manual study of the discovered schemes, distilling the key ideas into smaller components, and individually studying the impact of each component across dimensions (detectability, quality, robustness) to better understand how the proposed schemes operate. Importantly, we find that the agents, on top of improving existing ideas, also discover fundamentally new ideas (e.g., aligning watermark scores with random per-request direction). Overall, our work establishes the first steps of fully autonomous watermarking research, enabling the discovery of more reliable and effective watermarks. Our code is available at https://github.com/eth-sri/automark, and a blogpost to visualize our results at https://www.sri.inf.ethz.ch/blog/automark.

Detecting unauthorized knowledge distillation from a deployed LLM API is hard because the defender controls neither the attacker's training pipeline nor the next-token logits. Existing defenses operate on the teacher's output tokens -- biasing the next-token distribution (green-list watermarks, cryptographic schemes, antidistillation sampling) or rewriting outputs after generation. Recent work shows a paraphrasing attacker can strip these signals without losing the underlying knowledge. We propose interaction-layer antidistillation watermarks, which move the trace one layer higher, into the teacher's interaction behavior: the defender wraps the teacher with a system prompt that intermittently induces a behavioral marker -- an explicit follow-up question, a low-frequency variant, or a declarative restatement. An oblivious distiller inherits the behavior, and the defender audits via black-box queries with a human-validated LLM-as-judge (Cohen's kappa = 0.84/0.78 on strong/style rubrics). Across 63 LoRA-distilled students under a Llama-3.3-70B-Instruct teacher (35,343 judged samples), behavioral watermarks transfer at 88.9% (Gemma) / 80.9% (OLMo) / 45.2% (Qwen) relative fidelity (H1, H2). Under non-adaptive DIPPER paraphrasing, robustness decomposes into a teacher-self ceiling (about 66.4%) and student-relative retention of 21-112%, with OLMo preserving the watermark above the teacher itself (H3, F-Amp). Low-density (about 20%) explicit and implicit declarative variants transfer above per-family baseline (H4, F-Style). An N=20 in-lab study (pre-registered Latin-square) shows all marker variants within 0.22 Likert step of baseline; TOST, Friedman, and Bonferroni-Wilcoxon support H5. The interaction layer is a viable design locus for antidistillation watermarking, complementary to token-, model-, and reasoning-trace-layer defenses.