While prompt engineering enhances the capabilities of Large Language Models (LLMs), it also exposes critical safety concerns. Due to the inherent brittleness of their static safety boundaries, LLMs are vulnerable to jailbreak prompts, i.e. adversarial inputs designed to bypass safeguards and induce the generation of harmful content. Existing detection mechanisms rely on static model components or fixed decision thresholds, limiting their ability to generalize to evolving attack patterns and continual model updates. To bridge this gap, we propose RLShield, a dynamic jailbreak detection framework that employs reinforcement learning for adaptive threshold selection. RLShield incorporates three key innovations: (i) a dynamic retrieval and LLM-based rewriting module to simulate diverse adversarial contexts; (ii) a cross-layer representation analysis to pinpoint safety-critical parameters; and (iii) a Soft Actor-Critic (SAC) based agent that learns to predict optimal, sample-specific detection thresholds. Experimental results demonstrate that RLShield consistently outperforms state-of-the-art baselines in detection performance while maintaining high computational efficiency. Notably, it improves F1 by up to 7.3%, while achieving an average of 3× gain in inference efficiency across multiple LLM backbones.

Transformer-based models excel in various tasks but their generalization capabilities, especially in arithmetic reasoning, remain incompletely understood. Arithmetic tasks provide a controlled framework to explore these capabilities, yet performance anomalies persist, such as inconsistent effectiveness in multiplication and erratic generalization in modular addition (e.g., modulo 100 vs. 101). This paper develops a unified theoretical framework for understanding the generalization behaviors of transformers in arithmetic tasks, focusing on length generalization. Through detailed analysis of addition, multiplication, and modular operations, we reveal that translation invariance in addition aligns with relative positional encoding for robust generalization, while base mismatch in modular operations disrupts this alignment. Experiments across GPT-family models validate our framework, confirming its ability to predict generalization behaviors. Our work highlights the importance of task structure and training data distribution for achieving data-efficient and structure-aware training, providing a systematic approach to understanding of length generalization in transformers.