cs.AIAug 21, 2026

Certified Multi-Turn Robustness for LLM Safety via Compositional Bounds and Safety Persistence

Authors: Yang Liu, Bin Chong, Wenkai Yang, Shuai Zhang, Yancheng Chen, Feiyu Han, GuoZhen, Cheng Zhang, 

Organizations: Peking University · Renmin University of China · Tsinghua University · University of Chinese Academy of Sciences · 

Abstract

Large language models (LLMs) are vulnerable to multi-turn jailbreak attacks that progressively manipulate conversation context. Existing certified robustness methods are limited to single-turn inputs; naive multi-turn composition yields bounds that degrade exponentially in the number of turns. We introduce Multi-Turn Certified Robustness (MTCR), a framework that models conversational safety via State-Adversarial MDPs and defines kk-turn certified robustness as the worst-case safety probability across kk adversarial turns. MTCR comprises: (i) compositional certification via embedding-space mode decomposition, yielding tighter certified lower bounds than naive multiplication; (ii) (α,β)(α,β)-safety persistence, improving the degradation rate from p‾k\underline{p}^{k} to βkβ^k (with β>p‾β> \underline{p}) and yielding interpretable horizon estimates; (iii) matching information-theoretic upper bounds establishing tightness; and (iv) a unified algorithm combining these results. Experiments on six LLMs under εε-bounded and Crescendo-style attacks confirm that empirical safety consistently exceeds the certified bounds.

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