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

Hongbin Ye; Haixu Liu; Shenwei Kang; Wenxiu Wei; Tinglan Wang; Hongdong Zhu; Fan Tang; Qi Gao

cs.CVOct 9, 2026

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

Authors: Hongbin Ye, Haixu Liu, Shenwei Kang, Wenxiu Wei, Tinglan Wang, Hongdong Zhu, Fan Tang, Qi Gao,

Abstract

Existing 3D Gaussian Splatting (3DGS) pruning methods primarily rely on global Top-K selection based on independent importance scores, lacking regional budget control and ignoring joint deletion effects. Consequently, they cannot ensure balanced reconstruction quality across a scene. We propose SplatQ, a combinatorial pruning algorithm that coordinates regional budget allocation and joint Gaussian selection under a fixed budget. SplatQ partitions Gaussians by spatial proximity and appearance similarity into size-limited blocks, decomposing global selection into subproblems of a specific size. It then smooths importance-based block retention quotas to prevent excessive budget concentration. Finally, it constructs a quadratic approximation of joint deletion effects using the responses of representative pixel colors to changes in Gaussian opacity. Individual responses, pairwise interactions, and quota penalties are incorporated into a quadratic unconstrained binary optimization (QUBO) objective, solved using simulated annealing (SA) or a coherent Ising machine (CIM) to jointly select Gaussians. Experiments on 5 benchmarks demonstrate that SplatQ outperforms state-of-the-art pruning methods in aggregate reconstruction quality, spatial quality balance, and rendering speed. Ablations confirm that budget smoothing improves local detail reconstruction, while interaction modeling improves Gaussian selection quality under a fixed budget.

Figures & tables

Figure 1: Addressing spatial quality imbalance in 3DGS pruning. (a) Comparisons with baselines illustrate uneven detail preservation across image regions, while SplatQ preserves the highlighted structures more consistently. (b) Component ablations show how block quotas, budget assignment, and quadratic selection progressively improve spatial quality balance over global Top- $K$ pruning.

Figure 2: Overview of SplatQ. We partition Gaussians, compute a response matrix $R_{b}$ for each block using sampled pixels from multiple views. Diagonal scores determine block retention quotas, while the full matrix is used to formulate a blockwise QUBO that determines which Gaussians to delete. The retained Gaussians are then fine-tuned without changing their count. For iterative pruning, the process repeats on the updated model.

Figure 3: Normalized Gaussian-volume distributions across five benchmarks. Curves farther left indicate smaller volumes at the same cumulative fraction.

Figure 4: Overall reconstruction quality and spatial quality variation across five benchmarks. The horizontal axis shows the variance of PSNR over 256 image patches, and the vertical axis shows full-image PSNR. Bubble area represents the patch-PSNR range and is comparable only within each dataset. Higher positions, smaller horizontal values, and smaller bubbles indicate better results.

Method	Mip-NeRF 360				Deep Blending				Tanks and Temples
	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FPS $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FPS $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FPS $\uparrow$
3DGS	27.47	0.8123	0.2216	214.73	29.43	0.8984	0.2460	216.03	23.36	0.8378	0.1860	285.66
LightGaussian [-.15ex]	26.47 [-.15ex]26.17	0.7711 [-.15ex]0.7671	0.2950 [-.15ex]0.2994	600.25 [-.15ex]	28.92 [-.15ex]28.99	0.8918 [-.15ex]0.8926	0.2840 [-.15ex]0.2828	792.80 [-.15ex]	23.08 [-.15ex]22.80	0.7992 [-.15ex]0.7973	0.2640 [-.15ex]0.2624	1063.42 [-.15ex]
MesonGS [-.15ex]	26.90 [-.15ex] 26.54	0.7903 [-.15ex] 0.7841	0.2665 [-.15ex]0.2755	716.36 [-.15ex]	29.32 [-.15ex]29.30	0.8979 [-.15ex]0.8977	0.2644 [-.15ex]0.2662	973.20 [-.15ex]	23.30 [-.15ex] 22.92	0.8154 [-.15ex] 0.8113	0.2371 [-.15ex]0.2404	1286.88 [-.15ex]
EAGLES [-.15ex]	26.81 [-.15ex]26.43	0.7903 [-.15ex] 0.7841	0.2663 [-.15ex] 0.2753	707.75 [-.15ex]	29.28 [-.15ex]29.29	0.8979 [-.15ex]0.8977	0.2642 [-.15ex]0.2664	1006.56 [-.15ex]	23.08 [-.15ex]22.77	0.8107 [-.15ex]0.8068	0.2405 [-.15ex]0.2441	1254.02 [-.15ex]
C3DGS [-.15ex]	26.87 [-.15ex]26.47	0.7889 [-.15ex]0.7817	0.2698 [-.15ex]0.2797	747.66 [-.15ex]	29.34 [-.15ex]29.34	0.8984 [-.15ex]0.8982	0.2640 [-.15ex]0.2658	1005.52 [-.15ex]	23.27 [-.15ex]22.90	0.8143 [-.15ex]0.8104	0.2369 [-.15ex] 0.2401	1299.13 [-.15ex]

Table 1: Main and picture-free comparisons at 90% pruning. Best among pruned methods is bold and second best is underlined .

Panel of Figure 5 — Figure 5: Top: 2D pruning-percentage figure at 10k fine-tuning iterations. Bottom: Pruning-round 3D figure at 90% final removal. SplatQ denotes the SA variant.

Variant	Mip-NeRF 360			Deep Blending			Tanks and Temples
	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Top- $k$	26.68	0.7787	0.2640	29.09	0.8944	0.2649	22.72	0.8034	0.2469
+ Uniform block quotas	26.52	0.7755	0.2685	28.98	0.8930	0.2668	22.64	0.8004	0.2505
+ Budget assignment	26.74	0.7889	0.2626	29.15	0.8958	0.2638	22.81	0.8050	0.2455
+ Quadratic, greedy	27.03	0.7928	0.2552	29.42	0.9020	0.2568	23.15	0.8135	0.2357
Quadratic, uniform quotas	26.79	0.7811	0.2602	29.36	0.8985	0.2585	23.07	0.8093	0.2424

Table 2: Component and solver ablations at 90% pruning. Boldface marks SplatQ’s default config.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
$\mathcal{G},N,K$	Current Gaussian model, its Gaussian count, and target retained count for the current pruning round.
$\mathbf{x}_{b},\mathbf{z}_{b}$	Block retention and deletion vectors in $\{0,1\}^{n_{b}}$ , with $\mathbf{z}_{b}=\mathbf{1}-\mathbf{x}_{b}$ . Subscripts are omitted in local derivations.
$\mathcal{C}_{b},n_{b},M$	Set of Gaussian indices in block $b$ , its size $n_{b}=\|\mathcal{C}_{b}\|$ , and maximum allowed block size.
$B,K_{b}$	Number of blocks and block retention budget, updated from the initial Top- $K$ count to the final integer budget.
$\bm{\eta}$	Continuous opacity multipliers in $[0,1]^{N}$ .
$v,p,q$	Camera index, pixel index, and RGB channel index.

Appendix

Table 3: Principal method notation. Other scalar parameters are defined at their first use.

	Mip-NeRF 360			Deep Blending			Tanks & Temples
Method	Scoring	Solving	Memory	Scoring	Solving	Memory	Scoring	Solving	Memory
LightGS	4.63	–	9.91	5.26	–	7.74	6.12	–	5.52
MesonGS	6.17	–	7.64	20.34	–	6.50	8.59	–	4.02
EAGLES	1.10	–	8.36	1.12	–	7.80	1.01	–	5.00
C3DGS	4.37	–	10.05	4.31	–	8.48	3.24	–	5.47
PUP	17.5	–	10.1	16.3	–	8.7	20.1	–	5.5

Appendix

Table 4: Scoring time, solver time, and peak GPU memory across three datasets. Times are reported in seconds and memory in GB. For SplatQ, scoring denotes

R_{b}

calculation. A dash indicates that no separate QUBO solver is used.

Parameter	Setting
Maximum block size $M$	512
Neighbors per Gaussian per pass $k$	4
Comparison group size limit	512
Spatial passes	2
maximum growth iterations	16
Response views	All training views

Appendix

Table 5: Partitioning, response, and budget settings. Parameters without dedicated symbols in Section 3 are described by name.

Variant	Mip-NeRF 360			Deep Blending			Tanks and Temples
	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Top- $k$	26.68 [-.4ex] $\pm$ 4.1e-3	0.7787 [-.4ex] $\pm$ 2.50e-5	0.2640 [-.4ex] $\pm$ 7.40e-5	29.09 [-.4ex] $\pm$ 1.31e-2	0.8944 [-.4ex] $\pm$ 5.85e-5	0.2649 [-.4ex] $\pm$ 7.42e-5	22.72 [-.4ex] $\pm$ 7.6e-3	0.8034 [-.4ex] $\pm$ 8.67e-5	0.2469 [-.4ex] $\pm$ 1.158e-4
+ Uniform block quotas	26.52 [-.4ex] $\pm$ 5.5e-3	0.7755 [-.4ex] $\pm$ 2.75e-5	0.2685 [-.4ex] $\pm$ 8.31e-5	28.98 [-.4ex] $\pm$ 1.42e-2	0.8930 [-.4ex] $\pm$ 5.37e-5	0.2668 [-.4ex] $\pm$ 8.32e-5	22.64 [-.4ex] $\pm$ 8.1e-3	0.8004 [-.4ex] $\pm$ 9.12e-5	0.2505 [-.4ex] $\pm$ 1.269e-4
+ Budget assignment	26.74 [-.4ex] $\pm$ 4.8e-3	0.7889 [-.4ex] $\pm$ 2.79e-5	0.2626 [-.4ex] $\pm$ 8.07e-5	29.15 [-.4ex] $\pm$ 1.35e-2	0.8958 [-.4ex] $\pm$ 5.87e-5	0.2638 [-.4ex] $\pm$ 7.92e-5	22.81 [-.4ex] $\pm$ 8.3e-3	0.8050 [-.4ex] $\pm$ 9.03e-5	0.2455 [-.4ex] $\pm$ 1.240e-4
+ Quadratic, greedy	27.03 [-.4ex] $\pm$ 5.2e-3	0.7928 [-.4ex] $\pm$ 2.82e-5	0.2552 [-.4ex] $\pm$ 8.27e-5	29.42 [-.4ex] $\pm$ 1.38e-2	0.9020 [-.4ex] $\pm$ 5.26e-5	0.2568 [-.4ex] $\pm$ 7.05e-5	23.15 [-.4ex] $\pm$ 7.5e-3	0.8135 [-.4ex] $\pm$ 8.77e-5	0.2357 [-.4ex] $\pm$ 1.141e-4
Quadratic, uniform quotas	26.79 [-.4ex] $\pm$ 4.7e-3	0.7811 [-.4ex] $\pm$ 2.65e-5	0.2602 [-.4ex] $\pm$ 8.01e-5	29.36 [-.4ex] $\pm$ 1.53e-2	0.8985 [-.4ex] $\pm$ 5.65e-5	0.2585 [-.4ex] $\pm$ 7.81e-5	23.07 [-.4ex] $\pm$ 8.6e-3	0.8093 [-.4ex] $\pm$ 8.45e-5	0.2424 [-.4ex] $\pm$ 1.374e-4

Appendix

Table 6: Component and solver ablations at 90% pruning. Each dataset cell reports the mean above its

\pm

standard deviation across five runs of the complete pruning and fine-tuning pipeline.

	Mip-NeRF 360			Deep Blending			Tanks & Temples
Objective	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Diagonal	21.57	0.6848	0.3330	26.51	0.8543	0.3018	18.71	0.7195	0.2871
Quadratic	21.91	0.6890	0.3272	26.81	0.8572	0.2984	18.99	0.7215	0.2844

Appendix

Table 7: Effect of pairwise interactions after a single round of 80% pruning without fine-tuning. Both variants use identical pretrained models, partitions, and block quotas. Values are dataset averages; PSNR is measured in dB and LPIPS uses the VGG backbone. Better results are shown in bold.

Figure 6: Visual comparison after a single round of 80% pruning without fine-tuning.

	Block size $M$				Smoothing strength $\beta$
Metric	256	512	1024	2048	1	2	3	4	5
PSNR $\uparrow$	27.02	27.07	27.05	27.09	27.02	27.04	27.07	27.06	27.05
SSIM $\uparrow$	0.7927	0.7932	0.7934	0.7937	0.7926	0.7929	0.7932	0.7929	0.7925
LPIPS $\downarrow$	0.2556	0.2547	0.2539	0.2528	0.2549	0.2547	0.2547	0.2550	0.2553
Scoring time	1636.8	1005.0	541.6	310.2	–	–	–	–	–
Solver time	940.4	845.9	784.0	536.3	–	–	–	–	–

Appendix

Table 8: Sensitivity to block size

M

and smoothing strength

\beta

on Mip-NeRF 360 using SA. We fix

\beta=3

when varying

M

and

M=512

when varying

\beta

. PSNR is measured in dB, and scoring and solver times are reported in seconds. Bold indicates the best quality result within each sweep, including ties at the reported precision. For the

beta

part, we report quality only and omit timing results.

Figure 7: Reconstruction quality across pruning percentages and fine-tuning budgets. Columns correspond to Mip-NeRF 360, Deep Blending, Tanks and Temples, NeRF Synthetic, and Ref-NeRF; rows show PSNR, SSIM, and LPIPS-VGG. Axes indicate removal percentage, fine-tuning iterations in thousands, and the corresponding metric. SplatQ uses SA.

Figure 8: Effect of fine-tuning duration with two pruning rounds and 90% final removal. Columns correspond to the five datasets, and rows show PSNR, SSIM, and LPIPS-VGG. Fine-tuning steps on the horizontal axis are per round. The SplatQ curves use SA.

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