这篇论文用强化学习让拓扑图动态演化，既能压缩复杂度又能保留关键结构，比静态分析多了一条时间维度。
该框架利用强化学习在持久图空间上构建随机动力学，通过拓扑感知的局部编辑操作驱动图演化。研究者证明其马尔可夫链满足不可约、非周期和几何遍历条件，从而保证唯一平稳分布存在。目标函数结合分布匹配、任务特定拓扑统计和结构保持压缩，兼顾保真度与复杂度降低。在合成及神经影像持久图数据上，该方法在降低图复杂度的同时保留了主要拓扑结构。
Stochastic Dynamics on Persistence Diagram Space via Reinforcement Learning
Persistence diagrams (PDs) provide stable and interpretable summaries of multiscale topological structure. While substantial progress has been made in the statistical analysis of PDs, existing literature often treats diagrams as static objects and provide limited frameworks for probabilistic modeling and stochastic evolution on PD space. We introduce a reinforcement learning framework for stochastic dynamics on PD space, where diagrams evolve through topology aware local edit operations. The dynamics define controlled Markov processes on spaces of finite PDs with variable cardinality. We establish conditions under which the induced Markov chains are irreducible, aperiodic, and geometrically ergodic, implying the existence of unique stationary probability laws on PD space. To guide the dynamics toward scientifically relevant topological targets, we formulate objectives that encompass distribution matching, task specific topological statistics, and structure-preserving compression. The resulting rewards balance task specific distributional targets, diagram fidelity, and complexity reduction, and yield a framework for adaptive topological simplification and probabilistic modeling. Experiments on synthetic and neuroimaging PDs demonstrate that the proposed framework can preserve dominant topological structure while reducing diagram complexity.