AI 中文总结
针对异构分布式系统异步特征子空间计算理论不足的问题，提出格拉斯曼流形上的增量聚合方法，通过外在极更新实现两阶段线性收敛，在PCA实验中较基线提升样本效率与收敛速度。
AI 中文摘要
我们研究异构分布式系统中有限和特征子空间计算的异步优化方法。目前异步特征子空间计算的理论基础仍较为匮乏，现有方法对过时信息下直接在格拉斯曼流形上的动力学覆盖有限。本文提出一种格拉斯曼增量聚合方法，仅对到达的分量进行刷新并复用缓存的梯度，在无需全局同步的前提下保持较低的每次更新成本。该方法采用外在极更新，可保留内在子空间几何，无需对过时切向量进行平行运输。我们的分析建立了目标函数的紧密角度依赖梯度主导特性，以及过时聚合更新的 basin-invariance（ basin不变性）性质，这些性质产生了两阶段线性收敛，包含明确的宽盆地区域和更尖锐的局部区域，其常数由分量的谱展宽控制。在串行和分布式PCA上的实验表明，与代表性基线相比，该方法提高了样本效率并缩短了挂钟时间收敛时间。
英文摘要
We study asynchronous optimization for finite-sum eigenspace computation in heterogeneous distributed systems. The theoretical foundations for asynchronous eigenspace computation remain scarce, with existing approaches offering limited coverage of dynamics directly on the Grassmannian under stale information. In this paper, we propose a Grassmannian incremental aggregation method that refreshes only arriving components and reuses cached gradients, retaining low per-update cost without global synchronization. The method employs an extrinsic polar update that preserves the intrinsic subspace geometry without requiring parallel transport of stale tangent vectors. Our analysis establishes a tight angle-dependent gradient-dominance characterization of the objective and a basin-invariance property for stale aggregated updates. These yield two-phase linear convergence, comprising an explicit broad-basin regime and a sharper local regime, with constants controlled by component spectral spreads. Experiments on serial and distributed PCA demonstrate improved sample efficiency and wall-clock convergence over representative baselines.
