The Geometry of Harmfulness in Multi-Turn Attacks

Yelyzaveta, Husieva, Lauren Alvarez

Large language models (LLMs) remain vulnerable to adversarial attacks that circumvent safety alignment to elicit harmful outputs. It remains unclear how harmfulness and refusal representations evolve over the course of multi-turn attacks, and why single-turn defenses are less effective in multi-turn settings. This work investigates how the geometry and temporal dynamics of harmfulness and refusal representations evolve across multi-turn attacks. We analyzed hidden-state representations from three instruction-tuned LLMs (Llama-3.1-8B-Instruct, Qwen2.5-7B-Instruct, and Gemma-2-9B-it) using three multi-turn attack frameworks (Crescendo, ActorAttack, and X-Teaming), and examined representation behavior across conversation turns, model layers, and token positions under various context configurations. Across models and frameworks, we found that (1) each attack framework traverses different geometric directions, yet each achieves comparable success in eliciting harmful outputs; (2) multi-turn harmfulness directions became increasingly linearly separable at the end-of-turn token position across turns in middle to late model layers; and (3) harmfulness representations are weakly aligned…