Classical information theory, a cornerstone of artificial intelligence, is fundamentally limited by its local perspective, often analyzing pairwise interactions while ignoring the larger, hierarchical architecture of complex systems. Structural entropy (SE) presents a paradigm shift, extending Shannon entropy to quantify information on a global scale and measure the uncertainty embedded in a system's organizational hierarchy. Although its applications have broadened significantly from its origins in community detection across diverse AI domains, a systematic synthesis of its theory, computational methods, and applications is currently lacking. This survey provides a comprehensive overview of SE to fill this critical void in the literature. We offer a detailed examination of its theoretical foundations, computational frameworks, and key learning paradigms, with a focus on its integration with graph learning and reinforcement learning. Through an exploration of its diverse applications, we highlight the power of SE to advance graph-based analysis and modeling. Finally, we discuss key challenges and future research opportunities for incorporating SE principles into the development of more interpretable and theoretically grounded AI systems.

Multi-agent cooperation is essential for tasks that require collaboration to achieve optimal performance or cannot be completed by individual agents alone. These tasks often necessitate a divide-and-conquer strategy, where subgoals are allocated to individual agents or groups. By integrating coalition formation concepts from cooperative game theory, we demonstrate the implicit learning of coalition formation and task assignments, resulting in emergent cooperative behavior. We propose a novel COaLition LABeling technique for Multi-Agent Reinforcement Learning (COLLAB-MARL) to encourage coalition formation and introduce a structural entropy measure to detect the emergence of coalitions and cooperative behavior. Compared to classical MARL methods, COLLAB-MARL is more effective, explainable, and easier to implement. Experiments on state-of-the-art cooperative MARL benchmarks show that our method’s mean return outperforms the strongest baselines by 8.4% on average. Additionally, visualization and structural entropy analysis reveal that COLLAB-MARL effectively learns meaningful cooperative behavior. The source code is available at https://github.com/SELGroup/collab.

Hierarchical Reinforcement Learning (HRL) is a promising approach for managing task complexity across multiple levels of abstraction and accelerating long-horizon agent exploration. However, the effectiveness of hierarchical policies heavily depends on prior knowledge and manual assumptions about skill definitions and task decomposition. In this paper, we propose a novel Structural Information principles-based framework, namely SIDM, for hierarchical Decision Making in both single-agent and multi-agent scenarios. Central to our work is the utilization of structural information embedded in the decision-making process to adaptively and dynamically discover and learn hierarchical policies through environmental abstractions. Specifically, we present an abstraction mechanism that processes historical state-action trajectories to construct abstract representations of states and actions. We define and optimize directed structural entropy—a metric quantifying the uncertainty in transition dynamics between abstract states—to discover skills that capture key transition patterns in RL environments. Building on these findings, we develop a skill-based learning method for single-agent scenarios and a role-based collaboration method for multi-agent scenarios, both of which can flexibly integrate various underlying algorithms for enhanced performance. Extensive evaluations on challenging benchmarks demonstrate that our framework significantly and consistently outperforms state-of-the-art baselines, improving the effectiveness, efficiency, and stability of policy learning by up to 32.70%, 64.86%, and 88.26%, respectively, as measured by average rewards, convergence timesteps, and standard deviations.

As the spectral library continues to expand, sparse hyperspectral unmixing methods have been developed to solve the mixing problem without the need for end-member extraction or generation. These methods leverage the intrinsic spectral and spatial information to enhance the accuracy of fractional abundance estimation. However, their effectiveness is limited by rigid spatial regularization and insufficient utilization of spectral spatial information, which hampers the improvement of unmixing performance. To overcome this limitation, we present a novel algorithm named Local Spectral Similarity Guided Sparse Hyperspectral Unmixing with Spatial Graph Regularization (SGSU). In SGSU, we introduce a spatial graph regularization to enforce the inter-pixel correlation within spatial clusters and assign them to corresponding abundance vectors. To reduce the computational cost, we employ an adaptive superpixel-based spatial grouping strategy to segment the hyperspectral image, which translates the intrinsic geometry into constraints on abundance. Furthermore, we introduce a weighting factor with two components into the sparse unmixing framework. One component is based on the row sparsity of the estimated abundances, indicating the presence of active end-members; the other component is based on the similarity between neighboring pixels, which promotes piecewise smoothness of the estimated abundances. To obtain a more robust solution, we adopt a double-loop scheme based on the alternating direction method of multipliers (ADMM) algorithm to solve the SGSU model. Experimental results on both simulated and real hyperspectral datasets demonstrate that the proposed SGSU algorithm outperforms state-of-the-art sparse unmixing methods in terms of both accuracy of abundance estimation and end-member identification from spectral libraries. Our algorithm achieves superior unmixing results, which indicates its potential for practical applications in hyperspectral imaging.