Structure vs. Chaos: Asymmetric Entropic Optimization for Enforcing Instruction Hierarchy

Large language models (LLMs) deployed as agents remain vulnerable to prompt-based instruction injection, where user inputs induce the model to violate higher-priority system directives. Existing methods often treat violations as a coherent class or rely on surface text patterns, which can limit robustness as attack strategies evolve. In this paper, we investigate LLM hidden-state dynamics under attack and uncover a phenomenon we term Asymmetric Logic: the model's response generations concentrate in a relatively low-variability region of latent representation space when it's compliant to the system prompt, while compromised behaviors exhibit diverse deviations. Based on this observation, we propose Asymmetric Entropic Optimization (AEO), a novel framework that monitors the internal shifts in latent representations to detect and proactively rectify anomalous behaviors. Our method effectively identifies logic deviations by quantifying the entropic divergence between the compliant manifold and the chaotic violation space. Across a range of state-of-the-art LLM backbones, AEO demonstrates strong robustness to diverse instruction injection attacks. For instance, on Qwen2.5-14B-Instruct, AEO attains a detection AUC of 97.28% with FPR95 of only 10.38%. The same chaos score also gates a lightweight post-hoc correction module that lifts overall instruction-following accuracy from 63.94% to 76.00% on IHEval, without any model fine-tuning. The code is available at https://anonymous.4open.science/r/AEO-code-56D2/.