Large language models (LLMs) have achieved remarkable success in various natural language processing tasks, yet they remain prone to generating factually incorrect outputs—known as "hallucinations". While recent approaches have shown promise for hallucination detection by repeatedly sampling from LLMs and quantifying the semantic inconsistency among the generated responses, they rely on fixed sampling budgets that fail to adapt to query complexity, resulting in computational inefficiency. We propose an Adaptive Bayesian Estimation framework for Semantic Entropy with Guided Semantic Exploration, which dynamically adjusts sampling requirements based on observed uncertainty. Our approach employs a hierarchical Bayesian framework to model the semantic distribution, enabling dynamic control of sampling iterations through variance-based thresholds that terminate generation once sufficient certainty is achieved. We also develop a perturbation-based importance sampling strategy to systematically explore the semantic space. Extensive experiments on four QA datasets demonstrate that our method achieves superior hallucination detection performance with significant efficiency gains. In low-budget scenarios, our approach requires about 50% fewer samples to achieve comparable detection performance to existing methods, while delivers an average AUROC improvement of 12.6% under the same sampling budget.

Instruction Fine-Timing (IFT) is crucial for aligning large language models (LLMs) with human preferences, and selecting a small yet representative subset from massive data significantly facilitates IFT in terms of both efficiency and effectiveness. Nevertheless, existing approaches suffer from two limitations: the use of simple heuristics restricts data diversity, while the singleton data quality evaluation accounts for inconsistent criteria between independent samples. To address the issues, we present TACOS, an innovative method that integrates Open Tagging and Comparative Scoring for IFT data selection. To capture data diversity, we leverage LLMs to assign open-domain tags to human queries, followed by a normalization stage to denoise the open tags and enable efficient clustering. Additionally, we suggest a comparative scoring method that allows the relative quality evaluation of samples within a cluster, avoiding inconsistent criteria seen in singleton-based evaluations. Extensive experiments across diverse datasets and LLM architectures demonstrate that TACOS outperforms existing approaches by a large margin. Notably, it achieves superior instruction-following performance on MT-Bench and ranks 1st among LLaMA2-7B-Based models on AlpacaEval 2.0, illustrating its efficacy for IFT data selection.