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LinearMask-GS: Stable-Mask Importance Pruning for Compact 3D Gaussian Splatting

Donghun Ryu, Minhyeok Lee

arXiv:2609.10095v1cs.CV

TL;DR

3DGS produces many primitives through adaptive densification, motivating compact pruning methods, but Gumbel-Sigmoid masks can saturate before importance rankings stabilize. LinearMask-GS uses a linear increment activation to preserve a stable mask ranking, achieving better quality–compression trade-offs across several benchmarks and backbones.

  • Problem

    Adaptive densification creates substantial 3DGS storage overhead, while learned-mask pruning can suffer premature Gumbel-Sigmoid saturation that makes importance rankings unreliable.

    Source: §1 · p. 1

  • Method

    LinearMask-GS replaces Gumbel-Sigmoid with a linear increment activation that keeps mask values away from 0 and 1, preserving their ranking for hard pruning.

    Source: §1 · p. 2, Method · p. 4

  • Results

    LinearMask-GS achieves better quality–compression trade-offs than learned-mask and pruning baselines across Mip-NeRF 360, Tanks & Temples, and Deep Blending, while transferring unchanged across several Gaussian backbones.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Stable mask rankings enable reliable top-ρN hard pruning without architectural modifications to diverse Gaussian-based backbones.

    Source: §1 · p. 2

    The slope and survival ratio are tuned on a held-out set and fixed across scenes; brief mask training can under-discriminate specular or transparent regions, and the method assumes static scenes.

    Source: §5 · p. 14

Abstract

from arXiv · show

3D Gaussian Splatting (3DGS) enables real-time novel view synthesis but produces millions of primitives through adaptive densification, leading to significant storage overhead. Learned-mask pruning methods such as LP-3DGS address this by assigning each Gaussian a learnable mask to identify and prune redundant primitives. However, we identify a limitation of this paradigm: the steep slope of the Gumbel-Sigmoid activation drives mask values to the extremes within the short mask-training window, before the importance ranking has stabilized, producing a sharply bimodal distribution from which that ranking can no longer be reliably recovered. We propose LinearMask-GS, which replaces Gumbel-Sigmoid with a linear increment activation that keeps mask values in a mid-confidence regime throughout mask training, producing a stable, unimodal mask distribution whose ranking tracks importance. On Mip-NeRF 360, our method achieves 3.6x and 1.6x Gaussian reductions over 3DGS and LP-3DGS, respectively, while maintaining or improving rendering quality. For outdoor scenes, it yields a 1.6x reduction (from 2.18M to 1.36M) with notable gains in PSNR (+0.38 dB), SSIM (+0.025), and LPIPS (-0.029).

1 Introduction

3DGS delivers real-time novel view synthesis but adaptive densification creates millions of Gaussians, increasing storage and rasterization costs. LinearMask-GS addresses learned-mask pruning instability by preserving importance rankings during training and improves quality–compression trade-offs across datasets and Gaussian backbones.

  • 3DGS produces millions of explicit Gaussian primitives through adaptive densification, creating substantial storage overhead despite efficient rendering.A standard outdoor Mip-NeRF 360 scene can exceed 1GB in storage.Source: §1 · p. 1
  • LP-3DGS jointly learns per-Gaussian masks with scene parameters, but its Gumbel-Sigmoid activation does not reliably preserve importance information before hard pruning.The learned-mask paradigm couples pruning with scene optimization while retaining the saturation problem.Source: §1 · p. 2, §2.3 · p. 3
  • Gumbel-Sigmoid masks saturate near 0 or 1 before importance rankings stabilize, producing a bimodal distribution whose pruning ranking is unreliable.Extending the mask-training window worsens saturation, so the problem is attributed to activation steepness rather than merely limited training time.Source: §1 · p. 2
  • LinearMask-GS replaces Gumbel-Sigmoid with a gentle linear increment activation that keeps masks in a mid-confidence regime and preserves their relative ranking for top-ρN pruning.The resulting mask distribution is unimodal rather than sharply two-peaked.Source: §1 · p. 2
  • LinearMask-GS achieves better quality–compression trade-offs than learned-mask and pruning baselines across Mip-NeRF 360, Tanks & Temples, and Deep Blending.The masking module also transfers without modification to 2DGS, DropGaussian, Octree-GS, and FastGS.Source: §1 · p. 2
  • Attribute compression leaves primitive count and rasterization cost unchanged, while post hoc pruning lacks scene-optimization feedback and can remove geometrically essential Gaussians.These limitations motivate jointly learned pruning decisions.Source: §1 · pp. 1–2, §2.2 · p. 3, §2.3 · p. 3

Method

LinearMask-GS jointly learns importance-aware masks with Gaussian scene parameters, then ranks and prunes Gaussians using stable mask values rather than saturated binary outputs.

Pruning Framework

  • The framework computes importance, optimizes learnable masks with linear increment activation, retains the top-ρN Gaussians, and fine-tunes the pruned scene.The default minimum-survival ratio is ρ = 0.30.Source: Method · p. 4, §3.3 · p. 6

Importance Score

  • Max-pooling aggregates each Gaussian’s peak blending contribution across views, reducing view-count inflation in the importance score.Summation-based scores can favor Gaussians in densely observed regions, whereas max-pooling provides a view-count-invariant relevance measure.Source: §3.2 · p. 5

Mask Activation

  • Gumbel-Sigmoid saturates masks at 0 or 1 before importance rankings stabilize, and longer mask windows worsen this saturation.This instability reflects the activation’s steepness rather than insufficient mask-training duration.Source: §3.3 · p. 5
  • Linear increment keeps mask values near the midpoint, preserving their relative order for reliable hard-pruning decisions.Across nine Mip-NeRF 360 scenes, 99.99% of linear-mask values lie in [0.3,0.7], compared with 20.28% for Gumbel-Sigmoid.Source: §3.3 · pp. 5–6

Training Objective

  • The objective combines photometric reconstruction, structural similarity, and mask sparsity while separate optimization updates the mask parameters.The method uses λD = 0.2, λm = 5×10−4, τ = 0.1, and a mask-parameter learning rate of 5×10−2.Source: §3.4 · p. 6

Training Schedule

  • Training warms up the standard pipeline for 19,500 iterations, performs 500 mask-training iterations with periodic score recomputation, then prunes at iteration 20,000.The scores are recomputed every 20 iterations during mask training.Source: §3.4 · p. 7

Experiments

Across three benchmarks and multiple Gaussian-based backbones, LinearMask-GS delivers strong quality–compression trade-offs, reduces primitives, and preserves or improves rendering quality. Its linear activation also improves ranking reliability over Gumbel-Sigmoid and supports efficient pruning across settings.

Mip-NeRF 360

  • 3.6× fewer Gaussians than 3DGS, from 3.36M to 0.94M, while improving PSNR from 27.21 to 27.70 dB on Mip-NeRF 360.Against LP-3DGS, it achieves 1.6× fewer Gaussians while improving PSNR by 0.23 dB and SSIM by 0.0135, with comparable rendering speed.Source: §4.2 · pp. 8–9

Efficiency

  • LinearMask-GS yields the highest efficiency score across 109/(LPIPS × #G), PSNR/#G, and SSIM/#G on Mip-NeRF 360.The comparison covers the 3DGS and LP-3DGS reference rows.Source: §4.2 · p. 9

Tanks & Temples and Deep Blending

  • 24.18 dB PSNR with 0.29M Gaussians on Tanks & Temples and 30.11 dB with 0.29M on Deep Blending, achieving the best reported benchmark-average PSNRs.The FastGS-backbone variant surpasses FastGS and other fast-training methods on these metrics.Source: §4.2 · p. 9

Generality across backbones

  • 2.9× fewer 2DGS Gaussians, from 1.06M to 0.36M, while improving PSNR by 0.22 dB and SSIM by 0.009.LPIPS rises only marginally by 0.008 in this nine-scene Mip-NeRF 360 evaluation.Source: §4.3 · pp. 10–12

Ranking reliability

  • At the pruning decision point, linear masks produce 0.00% saturated values and 0% noise-induced decision flips, versus 52.2% saturation and 47.3% flips for Gumbel-Sigmoid.Spearman correlation with the held-out importance proxy is 0.29 for linear masks versus 0.16 for Gumbel-Sigmoid.Source: §4.4 · p. 13

Sensitivity analysis

  • The default survival ratio ρ=0.30 balances quality and compression, while higher retention adds primitives for minimal PSNR gains.From ρ=0.30 to 0.50, PSNR increases by only 0.04 dB for the linear activation; ρ=0.20 reduces PSNR by 0.28 dB.Source: §4.4 · p. 13

Generality across backbones

  • The linear activation prunes 40% more DropGaussian primitives and 41% more Octree-GS primitives than Gumbel-Sigmoid while maintaining or improving quality.The activation comparison holds the mask window, sparsity loss, importance score, and target keep ratio fixed.Source: §4.4 · p. 14

5 Conclusion

LinearMask-GS addresses learned-mask instability by preserving mask rankings during pruning and transfers unchanged across diverse Gaussian-based backbones. Its scope is bounded by fixed hyperparameters, possible under-discrimination of special regions, global budgeting, and a static-scene assumption.

  • LinearMask-GS replaces steep Gumbel-Sigmoid masking with a linear-increment activation that preserves mask rankings for top-ρN pruning and transfers across diverse Gaussian-based backbones.The linear activation keeps masks in a mid-confidence regime rather than collapsing them to 0 or 1.Source: §5 · p. 14
  • The method tunes slope τ and ratio ρ on held-out data, then fixes them across scenes.Source: §5 · p. 14
  • The brief mask window can under-discriminate specular or transparent regions, while global ρ sets an overall rather than per-region budget.Source: §5 · p. 14
  • LinearMask-GS inherits its backbones’ static-scene assumption, leaving scene-adaptive scheduling and dynamic-scene extensions for future work.Source: §5 · p. 14

3D Gaussian Splatting

The document identifies the authors and supplementary-material scope for the 3D Gaussian Splatting section. The supplied passages provide no substantive technical discussion beyond this metadata.

  • The listed affiliations are Chung-Ang University’s Department of Intelligent Semiconductor Engineering and School of Electrical and Electronics Engineering.Source: 3D Gaussian Splatting · p. 18
  • The supplementary material covers training convergence, hyperparameter sensitivity, mask-entropy evolution, ranking reliability, window effects, and benchmark and qualitative comparisons.Source: 3D Gaussian Splatting · p. 18

1 Additional Experimental Results

Additional experiments show faster convergence than LP-3DGS and favorable sensitivity to the default sparsity weight and slope. The reported defaults balance efficiency and quality across the tested ranges.

Training convergence

  • LinearMask-GS reaches higher PSNR and SSIM than LP-3DGS during the 500-iteration mask-training phase and maintains the advantage through fine-tuning.The convergence comparison begins at iteration 19,500 and ends at 20,000.Source: §1.1 · p. 18, Figure 1 · p. 19

Sensitivity to λm

  • The default λm = 5 × 10−4 achieves the best LPIPS-based efficiency score, while larger values increase sparsity at perceptual-quality cost.Values from λm = 10−4 to 5 × 10−4 robustly outperform LP-3DGS.Source: §1.2 · p. 19, Figure 2 · p. 19

Sensitivity to τ

  • The default τ = 0.1 gives the best balance, with efficiency remaining high for 0.01 ≤ τ ≤ 0.5 and PSNR within 0.1 dB of default for τ ∈ [0.05,0.5].Only extreme values such as τ = 1.0 show a noticeable efficiency reduction.Source: §1.3 · p. 19, Figure 3 · p. 20

2 Prevention of Premature Binarization

The experiments test whether LinearMask-GS prevents premature mask binarization and preserves reliable rankings during pruning. Compared with Gumbel-Sigmoid, the linear mask maintains higher entropy, deterministic decisions, and far lower saturation, even as mask windows lengthen.

Mask entropy evolution

  • LinearMask-GS maintains substantially higher mask entropy than LP-3DGS during pruning, indicating masks remain near active evaluation rather than collapsing to early keep/prune decisions.Mean entropy is approximately 0.69 for LinearMask-GS versus approximately 0.33 for LP-3DGS across nine scenes.Source: §2 · pp. 20–21, Figure 4 · p. 20

Ranking reliability

  • Re-sampling Gumbel noise flips 47.3% of keep/prune decisions and yields below-0.1 rank correlation, whereas the linear mask has 0% flips.The protocol compares mask evolution with hard pruning disabled and evaluates ranking against a held-out contribution proxy.Source: §3 · p. 21, Figure 5 · p. 22
  • Gumbel-Sigmoid reaches 52.2% saturation versus 0.00% for the linear mask under the no-pruning protocol.Saturation is the fraction of mask values outside [0.1,0.9].Source: §3 · p. 21

Mask-window effects

  • Lengthening the mask window increases saturation for both activations, but the linear increment remains at least 700× below Gumbel-Sigmoid at every tested setting.The comparison holds the pruning point fixed at 20k and varies window placement and length.Source: §4 · pp. 21–22, Table 1 · p. 22

Per-Scene Quantitative Metrics on Mip-NeRF 360

LinearMask-GS matches or exceeds LP-3DGS across Mip-NeRF 360 quality metrics while using substantially fewer Gaussians and less storage. Per-scene trade-offs favor LinearMask-GS in the lower-left direction of LPIPS-versus-count comparisons.

7 Per-scene qualitative comparison (remaining six scenes)

Across the remaining six Mip-NeRF 360 scenes, LinearMask-GS produces lower rendering error than LP-3DGS and 3DGS while exposing a favorable quality–compression trade-off. The ρ sweep shows that ρ=0.30 is the practical knee, and linear masks outperform Gumbel-Sigmoid at matched budgets.

7 Per-scene qualitative comparison (remaining six scenes)

  • Across six additional scenes, LinearMask-GS produces lower MAE and fewer saturated high-error regions than LP-3DGS and 3DGS.The scenes include three outdoor and three indoor environments.Source: §7 · pp. 24–25, Figure 7 · p. 25

8 Minimum-survival ratio ρ sweep

  • ρ=0.30 is the quality–compression knee: ρ=0.20 visibly worsens LPIPS, whereas ρ=0.40 retains 34% more Gaussians for only +0.03 dB and a 0.006 LPIPS gain.The default operating point is therefore ρ=0.30.Source: §8 · p. 25, Figure 8 · p. 26

9 ρ sweep: linear increment vs. the matched Gumbel-Sigmoid baseline

  • Both activations show diminishing quality returns beyond ρ=0.30, so stable ranking shifts the trade-off curve upward rather than changing its slope.Retained Gaussian count scales nearly linearly with ρ while quality gains collapse past the knee.Source: §8 · pp. 26–27
  • At every ρ, linear increment is 0.40–0.48 dB PSNR above Gumbel-Sigmoid at the same budget.The Gumbel-Sigmoid best point reaches 27.33 dB / 0.2321 LPIPS at 1.57M Gaussians, below linear ρ=0.20 at 27.42 dB / 0.2194 LPIPS with 0.63M.Source: §8 · pp. 26–27

10 Direct pruning by the raw max-pooled score

The learned mask improves over direct raw-score pruning and generalizes across alternative backbones and pruning frameworks. Additional results show better matched-budget quality, reduced primitive counts, and a net training-time saving on the FastGS backbone.

10 Direct pruning by the raw max-pooled score

  • The learned mask beats direct top-30% pruning by raw max-pooled importance on eight of nine Mip-NeRF 360 scenes.Both methods use the same schedule and fine-tuning, isolating the learned mask contribution.Source: §10 · p. 27
  • At a matched 0.30M budget, LinearMask-GS⋆ achieves 27.40 dB / 0.798 / 0.230 versus Speedy-Splat’s 26.91 / 0.781 / 0.295.The comparison averages nine Mip-NeRF 360 scenes over three independent seeds and favors LinearMask-GS⋆ on all three metrics.Source: §11 · p. 27
  • On Octree-GS, anchor counts fall by 40.2% relative to the Gumbel variant with a mean PSNR change of −0.11 dB on two added Mip-NeRF 360 scenes.Across three evaluated scenes, quality changes by at most approximately 0.1 dB in either direction.Source: §12 · p. 28
  • LinearMask-GS⋆ saves 6.3 s per scene overall because rendering fewer primitives offsets its 4.6 s mask-learning cost.The 20k–30k iteration range takes 28.3 s versus 39.2 s for native FastGS, while the masking formulation remains unchanged across backbones.Source: §13 · pp. 28–29

14 Supplementary Video

The supplementary materials provide visual comparisons across all 13 evaluated scenes and document the parameter sweeps, cross-method evaluations, and training-time behavior underlying the paper’s claims. These materials emphasize quality preservation at substantially reduced Gaussian counts.

14 Supplementary Video

  • The supplementary video compares ground truth, 3DGS, LP-3DGS, and LinearMask-GS for all 13 evaluated scenes in a 2×2 layout.Each panel displays the total number of Gaussians used.Source: §14 · p. 29
  • The supplementary tables extend evaluation to Tanks & Temples, Deep Blending, LLFF, Octree-GS, and Speedy-Splat comparisons.They include scene-wise results, matched-budget evaluation, and cross-backbone experiments.Source: Table 7 · p. 30, Table 10 · p. 31, Table 11 · p. 31
  • The ρ sweeps use matched top-ρN budgets to compare linear increment against Gumbel-Sigmoid across overall, outdoor, and indoor averages.The sweeps report PSNR, SSIM, LPIPS, and Gaussian count.Source: Table 8 · p. 31, Table 9 · p. 31
  • The FastGS-backbone variant reduces net training time by 6.3 s per scene after a 4.6 s mask-learning stage is offset by 10.9 s saved during later rendering.The speed decomposition attributes the mask-learning gap to pre-pruning and rasterizer differences.Source: Table 14 · p. 32, Table 15 · p. 33

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