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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, Yin Ma, Kai Wen, Hai Wei, Nuo Qian, Wei-Shi Zheng, Shaobo Chen, Fa-Ting Hong, Jingke Meng

arXiv:2610.13503v1cs.CVcs.GR

TL;DR

With a fixed Gaussian budget, global independent-score pruning lacks direct regional budget control and does not account for joint deletion effects, leaving balanced scene reconstruction unresolved. SplatQ combines spatial- and appearance-based partitioning, regional budget allocation, and interaction-aware quadratic selection. Across five benchmarks, it achieves the best overall reconstruction metrics and rendering speed among eight baselines at 90% pruning, while providing more uniform regional quality.

  • Problem

    Global importance ranking neither directly controls how retention budgets are distributed across regions nor accounts for joint deletion effects, leaving balanced reconstruction quality under a fixed budget unresolved.

    Source: §1 · p. 1

  • Method

    SplatQ partitions Gaussians by spatial proximity and appearance similarity, allocates regional retention quotas, and jointly selects Gaussians using interaction-aware quadratic optimization.

    Source: §1 · p. 2, §3 · p. 4

  • Results

    At 90% pruning across five benchmarks, SplatQ achieves the best overall reconstruction metrics and rendering speed among eight baselines, with more uniform reconstruction quality across image regions.

    Source: §1 · p. 2, §5 · p. 10

  • Takeaways & Limitations

    Ablations support interaction modeling as useful for improving Gaussian selection quality under a fixed budget.

    Source: §4.3 · p. 8

Abstract

from arXiv · show

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.

1 INTRODUCTION

SplatQ addresses uneven regional quality and non-additive deletion effects under a fixed pruning budget by combining blockwise budget assignment with interaction-aware Gaussian selection.

1 INTRODUCTION

  • Global Top-K ranking does not control regional retention, so score distributions can concentrate the fixed budget in some regions and leave others underrepresented.Similar overall image-quality metrics can therefore conceal uneven local degradation under aggressive pruning.Source: §1 · p. 1
  • Independent deletion scores miss overlapping Gaussian contributions: multiple individually important Gaussians may redundantly support the same pixels, making joint deletion effects non-additive.Thus, accurate individual scores alone may not identify the best retained set under a fixed budget.Source: §1 · pp. 1–2
  • SplatQ partitions Gaussians by spatial proximity and appearance similarity, assigns smoothed block quotas from importance estimates, then uses opacity-response interactions in a quota-constrained QUBO for selection.The retained set is fine-tuned without changing its count; iterative pruning repeats the process on the updated model.Source: §1 · p. 2, Figure 2 · p. 3
  • At 90% pruning, SplatQ achieves the best overall image quality and rendering speed among compared methods while providing more uniform regional reconstruction quality.Across 27 scenes from 5 benchmarks and eight open-source methods, it also surpasses MesonGS in dataset-macro PSNR in the picture-free setting.Source: §1 · p. 2, Figure 1 · p. 2
  • Ablations validate partition-based budget assignment and interaction-aware combinatorial optimization, while CIM experiments show competitive selection results with an alternative solver backend.SplatQ examines CIM as a hardware backend because classical QUBO solving requires more computation than direct Top-K ranking.Source: §1 · pp. 2–3

2 RELATED WORK

The related work identifies limits in independent or region-insensitive Gaussian pruning and motivates SplatQ’s combination of balanced regional budgets with joint, interaction-aware selection.

Gaussian compression and pruning

Balancing Rendering Quality Across Image Regions

3 METHOD

SplatQ retains exactly K of N Gaussians while modeling joint rendering effects and reducing regional retention disparities. It partitions Gaussians into size-limited blocks, models opacity responses, allocates smoothed quotas, selects members with a quadratic objective, and fine-tunes the retained model.

3.1 SIMILARITY GUIDED PARTITION

  • Spatial- and appearance-aware partitioning groups potentially redundant Gaussians into size-limited blocks so their joint effects can be evaluated together.A 3D grid and Morton ordering generate candidate pairs; an affinity graph guides block growth, with Morton order filling any unreached members.Source: §3.1 · p. 4

3.2 OPACITY RESPONSE MODELING

  • Opacity-response derivatives at representative rendered pixels form a Gram matrix whose diagonal scores measure individual image influence and off-diagonal entries capture signed pairwise interactions.The sampled pixels include projected Gaussian centers and neighboring offsets across training views.Source: §3.2 · p. 5

3.3 BUDGET ASSIGNMENT

  • Smoothed block quotas use diagonal importance scores to allocate exactly K retentions while reducing disparities that could leave blocks, including distant regions, with none.The continuous quotas are rounded and remaining units assigned by fractional remainders, subject to block capacities.Source: §3.3 · p. 5

3.4 QUADRATIC SELECTION

  • Within each block, a QUBO combines an approximation of joint deletion-induced rendering change with a penalty for deviating from its allocated quota.Blocks are solved independently by greedy selection, simulated annealing, or an Ising solver; infeasible outputs are repaired before combining masks to retain exactly K Gaussians.Source: §3 · p. 4, §3.4 · p. 6

3.5 FINE-TUNING AND ITERATIVE PRUNING

  • After combining block masks, SplatQ fine-tunes retained Gaussians with densification disabled; iterative pruning repeats the selection stages on the refined model until the target retention ratio is reached.The refinement loss weights L1 image loss by 0.8 and ground-truth image loss by 0.2.Source: §3.5 · p. 6

4 EXPERIMENTS

Across five benchmarks, SplatQ achieves strong reconstruction quality and rendering speed while reducing regional quality variation. Ablations show gains from smoothed budget allocation and quadratic interaction modeling, and evaluations span different pruning and fine-tuning configurations.

4.1 EXPERIMENTAL SETTINGS

  • Experiments cover 27 scenes from five benchmarks and compare pruning methods at 10% final retention after shared two-round pruning and fine-tuning.Each round removes 80% of the original Gaussians, then 50% of survivors, with 10,000 fine-tuning iterations per round; spatial balance is measured using variance and range across 256 patch PSNR values.Source: §4.1 · p. 6

4.2 COMPARISON WITH STRONG BASELINE

  • SplatQ (SA) has the lowest patch-PSNR variance and range on all five benchmarks, and the highest full-image PSNR on four while remaining close to the best on Tanks and Temples.Patch-PSNR statistics are computed over 256 image patches per view; lower variance and range indicate smaller regional quality differences.Source: §4.1 · p. 6, Figure 4 · p. 7, §4.2 · p. 7
  • Across most evaluated configurations, SplatQ outperforms compared open-source pruning methods, with occasional slightly lower quality metrics than the best baseline on Tanks and Temples.The sweep covers pruning ratios from 10% to 90%, one to four rounds, and fine-tuning budgets from 0 to 30,000 steps; the authors note room for improvement on datasets with distant regions.Source: §4.2 · p. 7
  • In qualitative examples, SplatQ preserves highlighted details more consistently than PUP, MesonGS, and EAGLES, whose results show uneven degradation.The comparisons use representative test views selected based on Table 1 results.Source: §4.2 · pp. 7–8
  • At 90% pruning, SplatQ reaches 28.426 dB macro-average PSNR, 0.224 dB above MesonGS and 0.300 dB above PUP, with best SSIM and lowest LPIPS-VGG on all five datasets and highest pruning-method FPS on each.In the picture-free setting, SplatQ records macro-average PSNR, SSIM, and LPIPS-VGG of 28.250 dB, 0.88216, and 0.17936, respectively; its macro-average PSNR exceeds MesonGS by 0.238 dB.Source: §4.2 · pp. 6–7, Table 1 · p. 8

4.3 ABLATION EXPERIMENTS

  • Macro PSNR is 27.858 dB with uniform quotas, 28.060 dB with budget allocation, 28.374 dB with greedy quadratic selection, 28.426 dB with SA, and 28.488 dB with CIM.Global first-order top-k reaches 27.978 dB; greedy quadratic selection reaches 28.374 dB versus 28.224 dB without budget allocation. Uniform-quota and budget-allocation variants select top-scoring Gaussians within each block, while quadratic variants use the full objective.Source: §4.1 · p. 6, §4.3 · p. 8
  • Uniform block quotas alone do not consistently recover highlighted details, while progressively adding budget allocation and quadratic selection with SA improves local reconstruction in the examples.The component ablations repeat the full pruning and fine-tuning pipeline with five random seeds.Source: §4.1 · p. 6, §4.3 · p. 8

5 CONCLUSION

SplatQ combines regional budget allocation with interaction-aware joint Gaussian selection, and the paper reports the best overall reconstruction metrics and rendering speed among eight baselines across five benchmarks at 90% pruning.

5 CONCLUSION

  • SplatQ combines spatial- and appearance-based partitioning, regional budget allocation, and joint Gaussian selection, and models joint deletion error with a QUBO solved experimentally on CIM hardware.The work also introduces metrics for regional quality imbalance.Source: §5 · pp. 8, 10
  • At 90% pruning, SplatQ achieves the best overall reconstruction metrics and rendering speed in comparisons against 8 baselines across 5 benchmarks.The paper also evaluates different pruning ratios, pruning-round counts, and fine-tuning budgets.Source: §5 · p. 10

AI USE STATEMENT

  • Generative AI assisted with manuscript drafting, editing, translation, figure and table preparation, and LaTeX formatting; the authors state numerical results came from experimental records.The authors take responsibility for the paper’s final content and accuracy.Source: AI USE STATEMENT · p. 10

ETHICS STATEMENT

  • Experiments use existing public benchmark datasets; the authors flag risks of private-space sharing and visual-detail loss under aggressive pruning, and note that compression provides no privacy guarantee.Scene-asset use and redistribution should respect applicable licenses and privacy requirements.Source: ETHICS STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

  • The reproducibility materials specify datasets, baseline adaptations, hyperparameters, seeds, protocols, and hardware; Table 2 reports means and standard deviations across five complete-pipeline runs.The method and derivations are described in Section 3 and Appendix A; computational costs and additional ablations are in Appendix B.2, and source-code release is planned.Source: REPRODUCIBILITY STATEMENT · p. 10

A METHOD DERIVATIONS AND IMPLEMENTATION DETAILS · A.1 NOTATION · A.2 SAMPLING AND GRAM ACCUMULATION

The appendix defines the block-budget and response notation used in SplatQ, then details how representative pixels are sampled and accumulated to estimate blockwise Gram matrices.

A.1 NOTATION

  • The model has N Gaussians partitioned into disjoint blocks of size at most M; final integer block budgets K_b sum to target K.Each block budget is updated from its initial Top-K count during allocation.Source: §A.1 · p. 13
  • For block b, J_b is the sampled opacity Jacobian, R_b = J_b^T J_b is its Gram matrix, and (R_b)_ii scores each Gaussian by summed squared sampled-channel responses.The sampled channel count is m_b = 3|P_b|.Source: §A.1 · p. 13
  • The depth rank ℓ is distinct from Gaussian identity i, and response evaluation uses the current model at each pruning round rather than one fixed model across rounds.For pixel p in view v, g_ℓ is the global Gaussian ID at depth rank ℓ, and α_ℓ(η) = η_gℓα_ℓ.Source: §A.1 · p. 13

A.2 SAMPLING AND GRAM ACCUMULATION

  • Sampling uses each block Gaussian with positive projected radius to generate its center and eight neighboring candidate pixels, then rounds coordinates and removes duplicates and out-of-image locations.Offsets are δ ∈ {(0, 0), (±0.5, 0), (0, ±0.5), (±0.35, ±0.35)}, scaled by max(h_vi, 1).Source: §A.2 · pp. 13–14
  • Responses are rendered through the full scene while Jacobian columns are restricted to block members, so other Gaussians and the background remain in each response.Batch accumulation yields the full Gram product up to floating-point rounding without storing the full Jacobian.Source: §A.2 · pp. 13–14
  • Similarity-guided partitioning builds Gaussian affinity edges in two spatial passes, grows blocks in parallel from strongest assigned neighbors, and fills remaining capacity in first-pass Morton order.The procedure caps blocks at M and allows at most 16 growth iterations.Source: §A.2 · p. 14
  • If no valid pixels are sampled across selected views, the initialized matrix and its diagonal allocation scores remain zero.Source: §A.2 · p. 14

A.3 DERIVATION OF THE OPACITY RESPONSE … A.7 GREEDY SELECTION, SIMULATED ANNEALING AND CIM SOLVERS

The appendices derive opacity responses and joint-deletion costs, enforce integer block capacities, and describe how block selection is implemented with greedy, simulated-annealing, and coherent-Ising-machine solvers.

A.3 DERIVATION OF THE OPACITY RESPONSE

  • With other opacity multipliers fixed, a Gaussian’s rendered-channel response combines its direct color contribution with the visibility change to content behind it.With fixed projected footprints and unclamped alpha values, a single deletion is represented exactly by its derivative; multiple deletions are generally approximate, and clamping, thresholds, or early termination can break the single-deletion correspondence.Source: §A.3 · pp. 14–15

A.4 CAPACITY HANDLING

  • Integer block budgets are clipped to capacities, then residual budget is repeatedly assigned to eligible blocks by descending fractional remainder until the total equals K.The procedure terminates with 0 ≤ Kb ≤ nb and sum_b Kb = K; without clipping, it reduces to largest-remainder rounding.Source: §A.4 · p. 15

A.5 JOINT DELETION

  • For binary deletions, the approximate block cost is quadratic: diagonal terms encode individual squared responses, while off-diagonal terms encode reinforcement or cancellation between responses.The objective approximates rendering changes from the current model, not error against ground truth; responses are recomputed after refinement each pruning round because many simultaneous deletions can reduce accuracy.Source: §A.5 · p. 15

A.6 QUBO COEFFICIENTS AND THE ISING MAPPING

  • The QUBO is stored as linear coefficients and sparse quadratic pairs, then mapped to spins with a reference spin, requiring n + 1 spins for an n-variable block.The encoding uses xi = (1 + σiσ0)/2, with pair entries Wij = −Jij/2 and reference-spin field entries Wi0 = W0i = −hi/2.Source: §A.6 · p. 16

A.7 GREEDY SELECTION, SIMULATED ANNEALING AND CIM SOLVERS

  • Greedy selection deletes exactly n − K members by repeatedly choosing the retained member with the smallest incremental quadratic cost.Its incremental cost is Δadd(j) = 2(Rz)j + Rjj, so the exact-count constraint is satisfied by construction without a count penalty.Source: §A.7 · p. 16
  • SA uses λ = 1 and geometrically cooled Metropolis updates, while CIM uses λ = 0.0625 and signed 14-bit matrix coefficients; neither guarantees an exact retained count.SA defaults to temperatures 100 and 10^-3, cooling factor 0.99, 10 iterations per temperature, and a solution limit of 100 per block; each method selects its lowest-energy returned state.Source: §A.7 · p. 16

A.8 POSTPROCESSING

SplatQ postprocessing repairs solver outputs to meet the exact retention budget, then optionally refines feasible selections through count-preserving swaps.

A.8 POSTPROCESSING

  • Capacity repair changes one bit at a time until exactly K Gaussians are retained, prioritizing feasibility even if the unpenalized cost increases.When too many are retained, it deletes the retained member with the smallest energy increase; when too few are retained, it restores the deleted member with the smallest increase.Source: §A.8 · p. 16
  • One-swap refinement accepts the best exchange only when its energy change is below −τ, preserving the count and decreasing the objective.It stops when no qualifying exchange remains or the swap limit is reached; without an active limit, it terminates at a one-swap local optimum within tolerance.Source: §A.8 · p. 16
  • The same refinement rule and stopping criteria are applied after greedy selection, SA, and CIM, keeping postprocessing fixed in solver comparisons.The comparisons evaluate each solver together with this shared postprocessing step.Source: §A.8 · pp. 16–17

B EXPERIMENT

This section supplements the experimental results presented in Section 4.

B EXPERIMENT

B.1 EXPERIMENT SETTINGS

The experiments compare pruning methods across five benchmarks under a shared pruning and fine-tuning pipeline. They also define separate settings for ablations, solvers, rendering-speed measurements, and spatial-quality analyses.

Datasets and Metrics

  • Evaluation covers 27 scenes across five benchmarks, comparing unpruned 3DGS and eight pruning baselines using dataset-average PSNR, SSIM, LPIPS-VGG, and measured FPS.Macro scores equally average the five dataset means.Source: §B.1 · p. 17

Implementation Details

  • All methods start from the same 30k-iteration pretrained model, retain 10% of its Gaussians through two pruning rounds, and receive 20k total fine-tuning iterations.The rounds remove 80% of the original Gaussians and then 50% of the survivors; fine-tuning uses the same loss with densification and attribute compression disabled.Source: §B.1 · p. 17

QUBO solver settings

  • SplatQ uses simulated annealing in the main comparison, with greedy and CIM as solver ablations; the SA and CIM backends repair decoded counts and refine selections.SA uses a temperature of 100, cutoff 10^-3, cooling factor 0.99, and 10 iterations per temperature; CIM truncates Ising coefficients to signed 14-bit precision.Source: §B.1 · pp. 17–18

Ablation settings

  • Ablations compare global Top-k, uniform and smoothed block quotas, and quadratic-objective variants; each variant repeats the full pipeline five times with seeds 0–4.The quadratic variants use greedy selection, simulated annealing, or CIM; the no-allocation variant uses uniform quotas and greedy selection.Source: §B.1 · p. 17

Fine-tuning settings

  • In picture-free experiments, pruning and fine-tuning avoid original training images, using the pretrained model’s rendered images for supervision; ground-truth test images are evaluation-only.Evaluation preserves resolution up to 1600 pixels in width and resizes wider images to approximately 1600 pixels while preserving aspect ratio.Source: §B.1 · p. 18

Metrics methods

  • Figure 4 measures patch-PSNR variance and range over 16×16 image grids, while Figure 3 summarizes per-scene Gaussian-volume quantiles normalized by a shared scene reference.Patch statistics are averaged over views and then equally across scenes within each benchmark; full-image PSNR is reported alongside them.Source: §B.1 · p. 18

B.2 ADDITIONAL EXPERIMENTAL RESULTS

Additional experiments quantify the effect of pairwise interactions, pruning cost, parameter sensitivity, and fine-tuning budgets, and report component and solver ablations across repeated runs.

Ablations with standard deviations

  • Table 6 reports component and solver ablations at 90% pruning as means and standard deviations across five complete pruning-and-fine-tuning runs.For each run, scene-level metrics are averaged within each dataset, then dataset averages are summarized across runs.Source: §B.2 · p. 18, Table 6 · p. 19

Pruning Time and Memory

  • Greedy selection reduces solver time by approximately 7.6–8.4× versus SA, although Rb calculation remains SplatQ’s main computational cost.Scoring takes 1005.0, 1237.2, and 3456.3 s across the three datasets; peak GPU memory is similar to LightGS and C3DGS. The cost is offline, and the main setting includes 20k fine-tuning iterations.Source: §B.2 · p. 19

Effect of Pairwise Interactions without Fine-tuning

  • Pairwise interactions improve PSNR by 0.34, 0.30, and 0.28 dB on Mip-NeRF 360, Deep Blending, and Tanks and Temples, respectively, without fine-tuning.The comparison uses identical pretrained models, partitions, and block quotas, with one 80% pruning round and no fine-tuning.Source: §B.2 · p. 19, Table 7 · p. 20, Figure 6 · p. 20

Sensitivity to Block Size and Smoothing

  • Across M ∈{256, 512, 1024, 2048}, PSNR varies by only 0.07 dB, while M = 2048 achieves the best quality across all three metrics.Increasing M from 256 to 2048 reduces scoring time from 1636.8 to 310.2 s and solver time from 940.4 to 536.3 s. The default M = 512 supports the CIM backend’s limit of fewer than 1,000 variables; across β ∈{1, 2, 3, 4, 5}, PSNR varies by 0.05 dB, and β = 3 has the highest PSNR and SSIM while tying β = 2 for lowest LPIPS at reported precision.Source: §B.2 · p. 20, Table 8 · p. 21

Sensitivity to Pruning and Fine-Tuning

  • Figures 7–8 examine reconstruction quality across pruning percentages and fine-tuning budgets, including two rounds with 90% final removal.In Figure 8, the reported fine-tuning budget is per round, so R rounds with T updates each require RT total updates; both figures show SplatQ using SA.Source: §B.2 · p. 21, Figure 7 · p. 21, Figure 8 · p. 22
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