The quality of text generated by large language models depends critically on the decoding sampling strategy. While mainstream methods such as Top-k, Top-p, and Min-p achieve a balance between diversity and accuracy through probability-space truncation, they share an inherent limitation: extreme sensitivity to the temperature parameter. Recent logit-space approaches like Top-n𝜎 achieve temperature invariance but rely on global statistics that are susceptible to long-tail noise, failing to capture fine-grained confidence structures among top candidates. We propose Min-k Sampling, a novel dynamic truncation strategy that analyzes the local shape of the sorted logit distribution to identify "semantic cliffs": sharp transitions from high-confidence core tokens to uncertain long-tail tokens. By computing a position-weighted relative decay rate, Min-k dynamically determines truncation boundaries at each generation step. We formally prove that Min-k achieves strict temperature invariance and empirically demonstrate its low sensitivity to hyperparameter choices. Experiments on multiple reasoning benchmarks, creative writing tasks, and human evaluation show that Min-k consistently improves text quality, maintaining robust performance even under extreme temperature settings where probability-based methods collapse. We make our code, models, and analysis tools publicly available.

Open-ended text generation faces a critical challenge: balancing coherence with diversity in LLM outputs. While contrastive search-based decoding strategies have emerged to address this trade-off, their practical utility is often limited by hyperparameter dependence and high computational costs. We introduce GUARD, a self-adaptive decoding method that effectively balances these competing objectives through a novel “Glocal” uncertainty-driven framework. GUARD combines global entropy estimates with local entropy deviations to integrate both long-term and short-term uncertainty signals. We demonstrate that our proposed global entropy formulation effectively mitigates abrupt variations in uncertainty, such as sudden overconfidence or high entropy spikes, and provides theoretical guarantees of unbiasedness and consistency. To reduce computational overhead, we incorporate a simple yet effective token-count-based penalty into GUARD. Experimental results demonstrate that GUARD achieves a good balance between text diversity and coherence, while exhibiting substantial improvements in generation speed. In a more nuanced comparison study across different dimensions of text quality, both human and LLM evaluators validated its remarkable performance. Our code is available at https://github.com/YecanLee/GUARD.