Title: Catch-22: Pareto Frontier for Detectability and Robustness in LLM Watermarking
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: Watermarking, LLM, Undetectability, Information Leakage, Privacy, Robustness

Abstract: Large Language Models (LLMs) generate text through probabilistic token sampling, a mechanism increasingly leveraged for inference-time watermarking to verify AI-generated content. As watermarking schemes proliferate, assessing their robustness-detectability trade-off becomes essential to determine whether watermarks can survive output editing while remaining invisible to adversaries. Current evaluation relies on empirical tests lacking provable guarantees. In this work, we present the first information-theoretic framework that rigorously characterizes this fundamental trade-off. We first prove that detectability is determined solely by the sampling strategy, not the model architecture, thereby establishing a hierarchy ranging from undetectable (distribution-preserving) to highly detectable (biased sampling) schemes. Second, we demonstrate an inverse relationship: watermarks robust to text modifications are inherently more detectable by adversaries, creating an irreducible trilemma: no scheme simultaneously achieves high robustness, low detectability, and reliable verification. Motivated by these theoretical constraints, we propose a hybrid watermarking system that adaptively switches sampling strategies based on LLM output edit levels, achieving Pareto-optimal trade-offs. We show that distribution-preserving schemes provide perfect undetectability; however, they are only robust to near-zero adversarial edits. On the other hand, bias-free and biased sampling offer high robustness guarantees at 15-20\% output editing, but with detectable output statistics. At high output editing rates, no watermarking provides robustness guarantees. Lastly, we empirically validate our theoretical trade-off claims with Llama-2 7B and Mistral 7B models under paraphrasing attacks, thereby confirming that Pareto-optimality is only achieved by a hybrid watermarking scheme. Overall, our framework provides watermark evaluation beyond empirical testing via principled design, revealing that sampling-based watermarking faces fundamental constraints rooted in information theory rather than implementation limitations.

TL;DR: This work identifies Pareto-optimal LLM watermarking solutions and establishes theoretical foundations for practical watermark designs, even when the conflicting goals of high robustness and undetectability cannot be simultaneously achieved.