SplatQ: Interaction-Aware Pruning of 3D Gaussian Splatting via Quadratic Selection

Recent significant advances in 3D scene representation have been driven by 3D Gaussian Splatting (3DGS), which has enabled real-time rendering with photorealistic quality. 3DGS often requires a large number of primitives to achieve high fidelity, leading to redundant representations and high resource consumption, thereby limiting its scalability for complex or large-scale scenes. Consequently, effective pruning strategies and more expressive primitives that can reduce redundancy while preserving visual quality are crucial for practical deployment. We propose an efficient, integrated reconstruction-aware pruning strategy that adaptively determines pruning timing and refining intervals based on reconstruction quality, thus reducing model size while enhancing rendering quality. Moreover, we introduce a 3D Difference-of-Gaussians primitive that jointly models both positive and negative densities in a single primitive, improving the expressiveness of Gaussians under compact configurations. Our method significantly improves model compactness, achieving up to 90% reduction in Gaussian-count while delivering visual quality that is similar to, or in some cases better than, that produced by state-of-the-art methods. Code will be made publicly available.

Scalable 3D Gaussian Splatting allows one scene representation to serve different Gaussian-count budgets, yet its quality-budget curve may lag behind models optimized separately for each budget. Reducing the number of Gaussians changes both the selected members and the reconstruction tasks carried by the survivors; parameters inherited from a high-budget model may fit a low-budget representation poorly. We propose ParetoGS, which describes member changes and parameter evolution with a small set of adapted budget anchors and decodes intermediate budgets without separate optimization at every requested count. ParetoGS alternates pruning and fixed-member adaptation to build nested anchors with persistent identities, and encodes their parameter changes relative to the full model in a compact residual atlas. At decoding, it interpolates the states of shared members and gradually introduces the rendering contributions of new members, connecting sparse anchors into a continuous-budget representation. Across 13 scenes, ParetoGS attains better average PSNR, SSIM, and LPIPS with fewer Gaussians than the compared prefix methods at 10% of each method's own full model. From a shared full model, it also outperforms FlexGS-imp at its trained 1%, 5%, and 10% budgets and NanoGS-imp at the 1% and 0.1% budgets. On Garden, its non-anchor quality approaches an empirical reference from independently optimized GNS models at higher retention ratios and exceeds it at some lower-budget points. Across 13 scenes, encoding reduces mean additional state from 390.0 to 85.7 MB with an average PSNR change of 0.01 dB. Project page: https://xiaobin2001.github.io/ParetoGS-Web/

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.