Reliable uncertainty quantification (UQ) is essential for deploying large language models (LLMs) in safety-critical scenarios, as it enables them to abstain from responding when uncertain, thereby avoiding ``hallucinating'' falsehoods. However, state-of-the-art UQ methods primarily rely on semantic probability distributions or pairwise distances, overlooking latent semantic structural information that could enable more precise uncertainty estimates. This paper presents Semantic Structural Entropy (SeSE), a principled UQ framework that quantifies the inherent semantic uncertainty of LLMs from a structural information perspective for hallucination detection. SeSE operates in a zero-resource manner and is applicable to both open- and closed-source LLMs, making it an ``off-the-shelf" solution for new models and tasks. Specifically, to effectively model semantic spaces, we first develop an adaptively sparsified directed semantic graph construction algorithm that captures directional semantic dependencies while automatically pruning unnecessary connections that introduce negative interference. We then exploit latent semantic structural information through hierarchical abstraction: SeSE is defined as the structural entropy of the optimal semantic encoding tree, formalizing intrinsic uncertainty within semantic spaces after optimal compression. A higher SeSE value corresponds to greater uncertainty, indicating that LLMs are highly likely to generate hallucinations. In addition, to enhance fine-grained UQ in long-form generation, we extend SeSE to quantify the uncertainty of individual claims by modeling their random semantic interactions, providing theoretically explicable hallucination detection. Extensive experiments across 29 model-dataset combinations show that SeSE significantly outperforms advanced UQ baselines.

This paper introduces MANGO (Multilayer Abstraction for Nested Generation of Options), a novel hierarchical reinforcement learning framework designed to address the challenges of long-term sparse reward environments. MANGO decomposes complex tasks into multiple layers of abstraction, where each layer defines an abstract state space and employs options to modularize trajectories into macro-actions. These options are nested across layers, allowing for efficient reuse of learned movements and improved sample efficiency. The framework introduces intra-layer policies that guide the agent's transitions within the abstract state space, and task actions that integrate task-specific components such as reward functions. Experiments conducted in procedurally-generated grid environments demonstrate substantial improvements in both sample efficiency and generalization capabilities compared to standard RL methods. MANGO also enhances interpretability by making the agent's decision-making process transparent across layers, which is particularly valuable in safety-critical and industrial applications. Future work will explore automated discovery of abstractions and abstract actions, adaptation to continuous or fuzzy environments, and more robust multi-layer training strategies.

State abstraction optimizes decision-making by ignoring irrelevant environmental information in reinforcement learning with rich observations. Nevertheless, recent approaches focus on adequate representational capacities resulting in essential information loss, affecting their performances on challenging tasks. In this article, we propose a novel mathematical Structural Information principles-based State Abstraction framework, namely SISA, from the information-theoretic perspective. Specifically, an unsupervised, adaptive hierarchical state clustering method without requiring manual assistance is presented, and meanwhile, an optimal encoding tree is generated. On each non-root tree node, a new aggregation function and condition structural entropy are designed to achieve hierarchical state abstraction and compensate for sampling-induced essential information loss in state abstraction. Empirical evaluations on a visual gridworld domain and six continuous control benchmarks demonstrate that, compared with five SOTA state abstraction approaches, SISA significantly improves mean episode reward and sample efficiency up to 18.98 and 44.44%, respectively. Besides, we experimentally show that SISA is a general framework that can be flexibly integrated with different representation-learning objectives to improve their performances further.

In this paper, we develop a framework to obtain graph abstractions for decision-making by an agent where the abstractions emerge as a function of the agent's limited computational resources. We discuss the connection of the proposed approach with information-theoretic signal compression, and formulate a novel optimization problem to obtain tree-based abstractions as a function of the agent's computational resources. The structural properties of the new problem are discussed in detail, and two algorithmic approaches are proposed to obtain solutions to this optimization problem. We discuss the quality of, and prove relationships between, solutions obtained by the two proposed algorithms. The framework is demonstrated to generate a hierarchy of abstractions for a non-trivial environment.