SPARE-GS: Structural Parsimony and Resource Efficiency for 3D Gaussian Splatting

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/}.

3D Gaussian splatting (3DGS) is a state-of-the-art representation for real-time photorealistic novel-view synthesis, yet a single high-fidelity scene typically occupies hundreds of megabytes to several gigabytes, exceeding the budgets of mobile, immersive, and volumetric video platforms. Existing 3DGS compression methods (e.g., HAC++, FlexGaussian, LP-3DGS) treat pruning, quantization, and entropy coding as separate stages and rely on hand-tuned heuristics (opacity thresholds, fixed bit-widths, SH truncation), limiting cross-scene generalization and preventing users from specifying a target rate or quality budget. We propose GETA-3DGS, to our knowledge the first end-to-end automatic joint structured pruning and quantization framework for 3DGS. Building on GETA for joint pruning-quantization of deep networks, we contribute: (i) a 3DGS-aware quantization-aware dependency graph (QADG) treating each Gaussian primitive as a group with five attribute sub-nodes and degree-aware SH sub-nodes; (ii) a render-aware saliency fusing transmittance-weighted contribution, screen-space gradient, and pixel coverage into a Gaussian-level importance score; and (iii) a heterogeneous per-attribute mixed-precision scheme co-optimized with structural sparsity under a projected partial saliency-guided (PPSG) descent guarantee. On Mip-NeRF 360, Tanks and Temples, and Deep Blending, GETA-3DGS operates directly on raw Gaussian primitives rather than a post-hoc anchor representation, delivering ~5x storage reduction over Vanilla 3DGS with no per-scene thresholds. Bit-width policy is the dominant rate-distortion lever: a uniform 6-bit cap costs up to -6.74 dB on view-dependent scenes versus our heterogeneous allocation, matching an information-theoretic reverse-water-filling analysis we develop. GETA-3DGS is complementary to existing codecs: entropy coding (HAC++, CompGS) is downstream, so the two can be composed.

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.