arXiv:2603.03415v1 Announce Type: cross Abstract: In this work, we investigate how Large Language Models (LLMs) adapt their internal representations when encountering inputs of increasing difficulty, quantified as the degree of out-of-distribution (OOD) shift. We reveal a consistent and quantifiable phenomenon: as task difficulty increases, whether through harder reasoning questions, longer contexts, or adding answer choices, the last hidden states of LLMs become substantially sparser. In short, \textbf{\textit{the farther the shift, the sparser the representations}}. This sparsity--difficulty relation is observable across diverse models and domains, suggesting that language models respond to unfamiliar or complex inputs by concentrating computation into specialized subspaces in the last hidden state. Through a series of controlled analyses with a learning dynamic explanation, we demonstrate that this sparsity is not incidental but an adaptive mechanism for stabilizing reasoning under OOD. Leveraging this insight, we design \textit{Sparsity-Guided Curriculum In-Context Learning (SG-ICL)}, a strategy that explicitly uses representation sparsity to schedule few-shot demonstrations, leading to considerable performance enhancements. Our study provides new mechanistic insights into how LLMs internalize OOD challenges. The source code is available at the URL: https://github.com/MingyuJ666/sparsityLLM.

arXiv:2603.04057v1 Announce Type: cross Abstract: Autonomous navigation in congested maritime environments is a critical capability for a wide range of real-world applications. However, it remains an unresolved challenge due to complex vessel interactions and significant environmental uncertainties. Existing methods often fail in practical deployment due to a substantial sim-to-real gap, which stems from imprecise simulation, inadequate situational awareness, and unsafe exploration strategies. To address these, we propose \textbf{Sim2Sea}, a comprehensive framework designed to bridge simulation and real-world execution. Sim2Sea advances in three key aspects. First, we develop a GPU-accelerated parallel simulator for scalable and accurate maritime scenario simulation. Second, we design a dual-stream spatiotemporal policy that handles complex dynamics and multi-modal perception, augmented with a velocity-obstacle-guided action masking mechanism to ensure safe and efficient exploration. Finally, a targeted domain randomization scheme helps bridge the sim-to-real gap. Simulation results demonstrate that our method achieves faster convergence and safer trajectories than established baselines. In addition, our policy trained purely in simulation successfully transfers zero-shot to a 17-ton unmanned vessel operating in real-world congested waters. These results validate the effectiveness of Sim2Sea in achieving reliable sim-to-real transfer for practical autonomous maritime navigation.