Prune Wisely, Reconstruct Sharply: Compact 3D Gaussian Splatting via Adaptive Pruning and Difference-of-Gaussian Primitives

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 state-of-the-art rendering quality at real-time speeds but suffers from "model bloat" - a large number of redundant, low-opacity Gaussians that inflate memory usage and training costs. This inefficiency stems from the standard "densify-then-prune" paradigm, which expands the model aggressively before relying on pruning to achieve compactness. To mitigate this problem, we present an efficient training framework that builds an intrinsically compact representation, replacing the conventional densify-then-prune cycle. Our method leverages a synergistic design: an L2 reconstruction loss to provide error-proportional gradients that stabilize optimization, and a novel Polarized Opacity Prior (POP) to actively manage the Gaussian population. POP steers informative primitives toward full opacity and uninformative ones toward transparency, enabling natural pruning and accelerating rendering through Early Ray Termination. Experiments on three public datasets demonstrate that our approach consistently achieves accelerated 3DGS training with significantly fewer Gaussians while maintaining comparable visual reconstruction quality. These results show that the proposed framework provides a simple and effective path toward fast and inherently compact 3DGS training.