Non-Halting Queries: Exploiting Fixed Points in LLMs

We introduce a new vulnerability that exploits fixed points in autoregressive models and use it to craft queries that never halt, i.e. an LLM output that does not terminate. More precisely, for what we call non-halting queries, the LLM never samples the end-of-string token (<eos>). We rigorously analyze the conditions under which the non-halting anomaly presents itself. In particular, at temperature zero, we prove that if a repeating (cyclic) sequence of tokens is observed at the output beyond the context size, then the LLM does not halt. We demonstrate the non-halting anomaly in a number of experiments performed in base (unaligned) models where repeating tokens immediately lead to a non-halting cyclic behavior as predicted by the analysis. Further, we develop a simple recipe that takes the same fixed points observed in the base model and creates a prompt structure to target aligned models. We study the recipe behavior in bypassing alignment in a number of LLMs including GPT-4o, llama-3-8b-instruct, and gemma-2-9b-it where all models are forced into a non-halting state. Further, we demonstrate the recipe's success in sending most major models released over the past year into a non-halting state with the same simple prompt even at higher temperatures. Further, we study direct inversion based techniques to craft new short prompts to induce the non-halting state. Our experiments with the gradient search based inversion technique ARCA show that non-halting is prevalent across models and may be easily induced with a few input tokens. While its impact on the reliability of hosted systems can be mitigated by configuring a hard maximum token limit in the sampler, the non-halting anomaly still manages to break alignment. This underlines the need for further studies and stronger forms of alignment against non-halting anomalies.