Topology_GRPO_v3:Adaptive q-Deformed Message Fusion via Macro Effective DualityCoupling

This manuscript presents a revised version of the Topology-GRPO framework, introducing an adaptive q-deformed message fusion mechanism driven by macro effective duality coupling to address information propagation defects in graph-structured multi-group reinforcement learning systems. Existing graph-based group policy optimization methods adopt fixed commutative aggregation for inter-group message passing, failing to distinguish weak coupling and strong coherent coupling regimes among policy groups, which leads to biased state representation and unstable policy updates under intensive cross-group interactions. To solve this limitation, this work defines the normalized macro effective duality coupling metric C_{eff}^{(g)} to quantify inter-group coherent intensity, and sets a critical threshold to dynamically switch fusion strategies: classical Concat+MLP commutative fusion is applied under weak coupling, while the proposed Q-Fuse non-commutative fusion module is activated for strong coherent states. The Q-Fuse operator incorporates a learnable twist angle \tilde{\theta} to generate asymmetric interaction terms, capturing non-commutative topological correlations between group states and neighbor messages; the twist angle is only updated in the strong coupling regime to balance optimization overhead. We further refine the three-component topological advantage function purely via reward normalization without intra-group critics, and retain the original clipped policy loss, inter-group consistency loss and KL regularization as the overall training objective. A complete training pipeline is summarized, and backward compatibility is verified—when coupling strength approaches zero or twist angle vanishes, the framework degenerates to the original Topology-GRPO. Comprehensive ablation experiments are designed to dissect the independent contribution of C_{eff} threshold control, Q-Fuse non-commutative fusion and decoupled twist angle optimization. All modeling modules are self-contained and validated via downstream task performance metrics, offering a flexible graph RL paradigm for multi-group graph policy optimization. This work is first released, archived and updated on Hongqiao University Tech Academic Site (https://hongqiao.tech). The site provides the official long-term version of this manuscript.