LinearMask-GS: Stable-Mask Importance Pruning for Compact 3D Gaussian Splatting

Existing pruning methods for 3D Gaussian splatting (3DGS) suffer from either severe quality degradation or prohibitive computational overhead. In this paper, we propose REFINE, a highly accelerated 3DGS pruning framework centered on a novel rendering-free primitive importance metric. Our approach leverages an analytically approximated, rendering-aware Hessian field to quantify the expected perceptual error induced by the removal of individual primitives. By modeling the joint modulation of visibility, projection geometry and the content adaptive hyperparameter, we entirely bypass costly forward rendering passes and derive an anisotropic perceptual weight field that serves as a high-fidelity proxy for primitive importance. Extensive experiments across multiple benchmark datasets demonstrate that REFINE maintains highly competitive rendering quality while achieving a $3,000\times$ reduction in pruning-related computational complexity, translating to a practical $\sim 20\times$ speedup in device latency compared to state-of-the-art pruning methods.

3D Gaussian Splatting (3DGS) enables high-quality real-time novel-view synthesis, but practical scenes often contain millions of Gaussians, making compression essential for deployment on limited hardware. Existing reduction methods are effective but mostly heuristic: they provide no multiplicative approximation guarantee for the rendered objective, and thus rely heavily on costly post-pruning finetuning to recover quality. We ask a basic question: can a 3DGS scene be provably replaced by a much smaller weighted subset (coreset) while preserving the objective of interest? We first show that, in the unrestricted setting, no non-trivial multiplicative 3DGS coreset exists. We then show that multiplicative guarantees are not impossible, but resolution-dependent. For a prescribed rendering resolution, such as representative views or grids of views/rays, we provide the first weighted coreset construction theorem for 3DGS. The construction samples Gaussians by sensitivity: provable importance scores measuring each Gaussian's role in the full-scene objective. Finally, under explicit validity and log-transmittance stability assumptions, we turn this objective guarantee into a rendering guarantee. Empirically, our method is strongest where deployment needs it most: aggressive compression with no or minimal recovery compute. In prune-only and very short finetuning regimes, it achieves state-of-the-art performance, showing that principled importance estimation can be both theoretically meaningful and practically useful. Open-source code is available at https://github.com/waseem-m/3dgs_provable_coresets.

3D Gaussian Splatting (3DGS) achieves remarkable novel view synthesis quality with real-time rendering, yet suffers from excessive memory consumption due to millions of Gaussian primitives. Existing pruning methods rely on heuristic importance scores or synchronous batch updates, leading to suboptimal compression and training instability. We propose VEDAL, a principled framework that formulates Gaussian pruning as variational free energy minimization. Our approach introduces (1) a prediction-error gating mechanism that asynchronously activates pruning based on per-Gaussian reconstruction uncertainty, and (2) a variational uncertainty head that models pruning decisions as latent variables with learnable priors. The free energy objective naturally balances reconstruction fidelity against model complexity through an information-theoretic lens. Extensive experiments on Mip-NeRF 360, Tanks&Temples, and Deep Blending demonstrate that VEDAL achieves 5.2x compression with only 0.31 dB PSNR drop, outperforming PUP 3D-GS by +0.05 dB at a higher compression ratio and LightGaussian by +0.35 dB at comparable quality, while maintaining real-time rendering at 185 FPS.