# The Geometry of Harmfulness in Multi-Turn Attacks

arXiv: https://arxiv.org/abs/2609.38389 · HTML: https://mlsanity.com/paper/2609.38389/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Safety alignment and jailbreak attacks, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 23 of its 62 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Safety alignment and jailbreak attacks](https://mlsanity.com/alignment/safety-alignment-and-jailbreak-attacks/)
- LLM safety and security / [Safety alignment, refusal and guardrails](https://mlsanity.com/safety/safety-alignment-refusal-and-guardrails/)

## Builds on (most cited first, 23 of 23)

- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Tree of Attacks: Jailbreaking Black-Box LLMs Automatically](https://mlsanity.com/paper/2312.02119/) (2023)
- [JailbreakBench: An Open Robustness Benchmark for Jailbreaking Large Language Models](https://mlsanity.com/paper/2404.01318/) (2024)
- [Great, Now Write an Article About That: The Crescendo Multi-Turn LLM Jailbreak Attack](https://mlsanity.com/paper/2404.01833/) (2024)
- [A StrongREJECT for Empty Jailbreaks](https://mlsanity.com/paper/2402.10260/) (2024)
- [WildTeaming at Scale: From In-the-Wild Jailbreaks to (Adversarially) Safer Language Models](https://mlsanity.com/paper/2406.18510/) (2024)
- [LLM Defenses Are Not Robust to Multi-Turn Human Jailbreaks Yet](https://mlsanity.com/paper/2408.15221/) (2024)
- [X-Teaming: Multi-Turn Jailbreaks and Defenses with Adaptive Multi-Agents](https://mlsanity.com/paper/2504.13203/) (2025)
- [LLMs Encode Harmfulness and Refusal Separately](https://mlsanity.com/paper/2507.11878/) (2025)
- [LLMs know their vulnerabilities: Uncover Safety Gaps through Natural Distribution Shifts](https://mlsanity.com/paper/2410.10700/) (2024)
- [Speak Out of Turn: Safety Vulnerability of Large Language Models in Multi-turn Dialogue](https://mlsanity.com/paper/2402.17262/) (2024)
- [Towards Understanding Jailbreak Attacks in LLMs: A Representation Space Analysis](https://mlsanity.com/paper/2406.10794/) (2024)
- [Foot-In-The-Door: A Multi-turn Jailbreak for LLMs](https://mlsanity.com/paper/2502.19820/) (2025)
- [AgentLAB: Benchmarking LLM Agents against Long-Horizon Attacks](https://mlsanity.com/paper/2602.16901/) (2026)
- [Steering Dialogue Dynamics for Robustness against Multi-turn Jailbreaking Attacks](https://mlsanity.com/paper/2503.00187/) (2025)
- [Emerging Vulnerabilities in Frontier Models: Multi-Turn Jailbreak Attacks](https://mlsanity.com/paper/2409.00137/) (2024)
- [A Representation Engineering Perspective on the Effectiveness of Multi-Turn Jailbreaks](https://mlsanity.com/paper/2507.02956/) (2025)
- [What Really Matters in Many-Shot Attacks? An Empirical Study of Long-Context Vulnerabilities in LLMs](https://mlsanity.com/paper/2505.19773/) (2025)

## Abstract (arXiv)

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 with refusal-related representations. The results indicate that multi-turn attacks do not succeed by suppressing the model's internal representation of harmfulness. Instead, harmfulness representations become increasingly separable across conversation turns, while remaining only weakly aligned with refusal-related representations. The findings are one possible explanation for why static single-turn safety probes may degrade in multi-turn settings, and suggest that robust defenses must consider temporal representation dynamics rather than identifying harmfulness with isolated or single-turn prompts.