High-resolution 3D Gaussian Splatting training increases pixel and Gaussian-tile intersection counts, expanding rasterization caches that coexist with projection and gradient state at peak memory. A complete-view update aggregates gradients across the view; each region's forward and backward caches can be released after its contribution is collected. BoundedGS separates rasterization and projection backward passes and bounds the active local rasterization working set according to its measured load. Candidate-indexed projection and compact gradient storage address the view-level peaks exposed by this change, while CPU-assisted structure rebuilding and bounded image supply manage resources outside rendering. In a resolution sweep at a fixed count of about 6M Gaussians, the measured rendering working set stays within 1.073-1.077 GiB from 1K to 16K; at 11K, a warm pass takes 19.79 seconds versus 21.76 for full-frame execution. Across five native 5K outdoor scenes, full training reduces the mean rendering working set from 9.97 to 1.76 GiB (82.3%), retains similar reconstruction quality, and shortens training time from 36.7 to 33.9 minutes. Project page: https://xiaobin2001.github.io/BoundedGS-Web/

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