Prune by Proxy: A Unified Framework for 3D Gaussian Splatting Pruning

Post-hoc pruning makes 3D Gaussian Splatting (3DGS) compact by removing primitives ranked by an importance score. Existing scores rank Gaussians by their attributes, rendering contributions, or parameter sensitivity, yet what pruning actually trades off is the photometric cost of deleting a Gaussian. Evaluating this deletion cost by leave-one-out rendering requires one re-rendering per Gaussian, and no common target or protocol exists to tell which of the tractable scores actually estimate it. We present Prune by Proxy, a framework that fixes the deletion cost as the common target, specifies every score by its scoring information, scored attributes, and aggregation rule, and thereby transfers the zero-cost proxies of NAS-Bench-Suite-Zero from network pruning and architecture search to 3DGS. Within this framework we show that a multiplicative gate on activated opacity is the coordinate of deletion: alpha blending is affine in a single gate, so the deletion-induced image change equals minus the gate derivative, and the gap between a first-order estimate and the exact deletion cost lies entirely in the photometric loss, where it has a closed form. The resulting Corrected $L_1$ and $L_2$ scores equal the exact single-Gaussian deletion cost in the ideal blending model and cost one forward and one backward pass per view. At 90% pruning on Mip-NeRF 360, Tanks & Temples, and Deep Blending, Corrected $L_1$ ranks first in eight of nine dataset–metric comparisons and exceeds PUP on all thirteen scenes by 0.58 dB on average at one-third of its scoring time. The closed-form correction alone adds up to 1.6 dB over its first-order control, and seven transferred proxies also surpass all published 3DGS scores, with deletion alignment explaining which proxies transfer.