VEDAL: Variational Error-Driven Asynchronous Learning for 3D Gaussian Splatting Pruning

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 Splat (3DGS) enables high-fidelity, real-time novel view synthesis by representing scenes with large sets of anisotropic primitives, but often requires millions of Splats, incurring significant storage and transmission costs. Most existing compression methods rely on GPU-intensive post-training optimization with calibrated images, limiting practical deployment. We introduce \textbf{NanoGS}, a training-free and lightweight framework for Gaussian Splat simplification. Instead of relying on image-based rendering supervision, NanoGS formulates simplification as local pairwise merging over a sparse spatial graph. The method approximates a pair of Gaussians with a single primitive using mass preserved moment matching and evaluates merge quality through a principled merge cost between the original mixture and its approximation. By restricting merge candidates to local neighborhoods and selecting compatible pairs efficiently, NanoGS produces compact Gaussian representations while preserving scene structure and appearance. NanoGS operates directly on existing Gaussian Splat models, runs efficiently on CPU, and preserves the standard 3DGS parameterization, enabling seamless integration with existing rendering pipelines. Experiments demonstrate that NanoGS substantially reduces primitive count while maintaining high rendering fidelity, providing an efficient and practical solution for Gaussian Splat simplification. Our project website is available at \href{https://saliteta.github.io/NanoGS/}{https://saliteta.github.io/NanoGS/}.