Search Results (2)

Deep Reinforcement Learning (DRL) has achieved remarkable success in robotic control, autonomous driving, and game-playing agents. However, its decision-making process often remains a black box, lacking both interpretability and verifiability. In robotic control tasks, developers cannot pinpoint decision errors or precisely adjust control strategies based solely on observed robot behaviors. To address this challenge, this work proposes an interpretable DRL framework based on a Causal Correction and Compensation Network (C²-Net), which systematically captures the causal relationships underlying decision-making and enhances policy robustness. C²-Net integrates a Graph Neural Network-based Neural Causal Model (GNN-NCM) to compute causal influence weights for each action. These weights are then dynamically applied to correct and compensate the raw policy outputs, thereby balancing performance optimization and transparency. This work validates the approach on OpenAI Gym’s Hopper, Walker2d, and Humanoid environments, as well as the multi-agent AzureLoong platform built on Isaac Gym. In terms of convergence speed, final return, and policy robustness, experimental results show that C²-Net achieves higher performance over both non-causal baselines and conventional attention-based models. Moreover, it provides rich causal explanations for its decisions. The framework represents a principled shift from correlation to causation and offers a practical solution for the safe and reliable deployment of multi-robot systems. Full article

This paper explores the common neighborhood energy ($E_{CN}\left(\mathsf{\Gamma }\right)$) of graphs derived from the dihedral group $D_{2n}$ and generalized quaternion group $Q_{4n}$, specifically the non-commuting graph (NCM-graph) and the commuting graph (CM-graph). Studying graphs associated with groups offers a powerful approach to translating algebraic properties into combinatorial structures, enabling the application of graph-theoretic tools to understand group behavior. The common neighborhood energy, defined as the sum of the absolute values of the eigenvalues of the common neighborhood (CN) matrix, i.e., ${\sum }_{i=1}^p\left|{\zeta }_i\right|$, where ${\left\{{\zeta }_i\right\}}_{i=1}^p$ are the CN eigenvalues, provides insights into the structural properties of these graphs. We derive explicit formulas for the CN characteristic polynomials and corresponding CN eigenvalues for both the NCM-graph and CM-graph as functions of n. Consequently, we establish closed-form expressions for the $E_{CN}$ of these graphs, which are parameterized by n. The validity of our theoretical results is confirmed through computational examples. This study contributes to the spectral analysis of algebraic graphs, demonstrating a direct connection between the group-theoretic structure of $D_{2n}$ and $Q_{4n}$, as well as the combinatorial energy of their associated graphs, thus furthering the understanding of group properties through spectral graph theory. Full article