Title: Automatically Auditing Large Language Models via Discrete Optimization. Abstract: Auditing large language models for unexpected behaviors is critical to preempt catastrophic deployments, yet remains challenging. In this work, we cast auditing as a discrete optimization problem, where we automatically search for input-output pairs that match a desired target behavior. For example, we might aim to find non-toxic input that starts with ``Barack Obama'' and maps to a toxic output. Our optimization problem is difficult to solve as the set of feasible points is sparse, the space is discrete, and the language models we audit are non-linear and high-dimensional. To combat these challenges, we introduce a discrete optimization algorithm, ARCA, that is tailored to autoregressive language models. We demonstrate how our approach can: uncover derogatory completions about celebrities (e.g. ``Barack Obama is a legalized unborn'' $\rightarrow$ ``child murderer'), produce French inputs that complete to English outputs, and find inputs that generate a specific name. Our work offers a promising new tool to uncover models' failure-modes before deployment. $\textbf{Trigger Warning: This paper contains model behavior that can be offensive in nature.}$