Vulnerability of Frontier language models to misuse has prompted the development of safety measures like filters and alignment training seeking to ensure safety through robustness to adversarially crafted prompts. We assert that robustness is fundamentally insufficient for ensuring safety goals due to inferential threats from dual-intent queries, with current defenses and evaluations failing to account for these risks. To quantify these risks, we introduce a new safety evaluation framework based on $\textit{impermissible information leakage}$ of model outputs and demonstrate how our proposed question-decomposition attack can extract dangerous knowledge from a censored LLM more effectively than traditional jailbreaking. Underlying our proposed evaluation method is a novel information-theoretic threat model of $\textit{inferential adversaries}$, distinguished from $\textit{security adversaries}$, such as jailbreaks, in that success involves inferring impermissible knowledge from victim outputs as opposed to forcing explicitly impermissible victim outputs. Through our information-theoretic framework, we show that ensuring safety against inferential adversaries requires defenses which bound impermissible information leakage, and, such defenses inevitably incur safety-utility trade-offs.

Large language models (LLMs) have exhibited impressive capabilities in comprehending complex instructions. However, their blind adherence to provided instructions has led to concerns regarding risks of malicious use. Existing defence mechanisms, such as model fine-tuning or output censorship methods have proven to be fallible at ensuring that LLMs do not return semantically impermissible responses. We present fundamental limitations of verifying the semantic properties of LLM outputs and identifying compositional threats, illustrating inherent challenges of current approaches to censoring LLM outputs. Specifically, we demonstrate that semantic censorship can be perceived as an undecidable problem, and semantic properties of LLM outputs can become impossible to verify when the LLM is capable of providing "encrypted" outputs. We further show challenges of censorship can extend beyond just semantic censorship, as attackers can reconstruct impermissible outputs from a collection of permissible ones. Consequently, we call for a re-evaluation of the problem of censorship and its goals, stressing the need for new definitions and approaches to censorship. In addition, we provide an initial attempt toward achieving this goal through syntactic censorship, drawing from a security perspective to design censorship methods that can provide guarantees.