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.

Tool-augmented Large Language Models (LLMs) provide a robust theoretical foundation for AI agents, with the generation of reasoning plans being a crucial stage. Previous methods for generating reasoning plans primarily rely on In-Context Learning (ICL) or Supervised Fine-Tuning (SFT). However, methods based on ICL struggle with accurately utilizing tools, while those based on SFT face challenges in adapting to new toolsets and tasks. To address these issues, we introduce ToolFiVe, a general, plug-and-play, self-correction-based framework for leveraging specialized tools in compositional reasoning tasks. ToolFiVe redesigns the process of reasoning plan generation and integrates the tool-execution stage. Specifically, in the reasoning plan generation stage, ToolFiVe employs a filtering module to exclude task-irrelevant tools, creating a candidate toolset. ToolFiVe then constructs prompts using the candidate toolset and iteratively generates and refines the reasoning plan. Subsequently, a verification module evaluates the completeness of the reasoning plan, providing feedback for the self-correction loop. Ultimately, the reasoning plan developed during this stage guides the execution of the tools. Extensive experiments demonstrate that ToolFiVe outperforms other state-of-the-art (SOTA) methods, highlighting the significance of reasoning plan generation for general tool-augmented LLMs.