AI 中文总结
提出选择器锚定扩散与局部创新（D+LI）的分布式向量组装方法，通过正交选择器与局部创新结合拉普拉斯扩散，实现全局收缩与有限时间稳定性，并证明KL收敛，实验验证了其有效性。
AI 中文摘要
我们提出了一种带有局部创新的选择器锚定扩散（D+LI）方法，这是一种分布式向量组装原语，能够从独立拥有的权威数据块中构建完整的局部副本。正交选择器保持数据块的身份，局部创新锚定每个所有者的贡献，而拉普拉斯扩散则将这些贡献在网络中传播。我们证明了，使用原始加性选择器源的纯平均方法无法隔离出该副本。D+LI的误差算子按坐标分解为单位矩阵减去一个基于所有者的拉普拉斯算子，从而实现了与总维度和数据块维度无关的全局收缩因子。对于时变的外部目标，我们建立了有限时间T的输入到状态稳定性（ISS）界，以及针对Lipschitz协调映射（包括非势映射）的自洽估计器-控制器增益条件。对于半代数势问题，我们证明了在显式时间尺度分离条件下，耦合决策-组装迭代具有Kurdyka-Lojasiewicz（KL）有限长度收敛性，且每次外部迭代具有固定的有限通信预算。三个数值实验展示了收缩紧性和有限时间跟踪，验证了可接受的KL时间尺度，并说明了离散和非势外部映射。
英文摘要
We introduce Selector-Anchored Diffusion with Local Innovation (D+LI), a distributed vector-assembly primitive that constructs complete local replicas from independently owned authoritative blocks. Orthogonal selectors preserve block identity, local innovation anchors each owner's contribution, and Laplacian diffusion propagates these contributions across the network. We show that pure averaging with raw additive selector sources cannot isolate this replica. The D+LI error operator decomposes coordinatewise as the identity minus an owner-grounded Laplacian, yielding global contraction with a factor independent of the total and block dimensions. For time-varying outer targets, we establish a finite-T input-to-state stability (ISS) bound and a self-consistent estimator-controller gain condition for Lipschitz coordination maps, including non-potential ones. For semi-algebraic potential problems, we prove Kurdyka-Lojasiewicz (KL) finite-length convergence of the coupled decision-assembly iteration with a fixed finite communication budget per outer iteration under explicit timescale-separation conditions. Three numerical experiments demonstrate contraction tightness and finite-horizon tracking, verify an admissible KL timescale, and illustrate discrete and non-potential outer maps.
Commentsrevised version
