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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.

  • 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.

  • 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.

  • Takeaways & Limitations

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

  • Takeaways & Limitations

    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.

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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.

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.
  • 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.
  • 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.
  • Mask Activation: 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.
  • 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.
  • 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.

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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.

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.
  • The method tunes slope τ and ratio ρ on held-out data, then fixes them across scenes.
  • The brief mask window can under-discriminate specular or transparent regions, while global ρ sets an overall rather than per-region budget.
  • LinearMask-GS inherits its backbones’ static-scene assumption, leaving scene-adaptive scheduling and dynamic-scene extensions for future work.

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.
  • The supplementary material covers training convergence, hyperparameter sensitivity, mask-entropy evolution, ranking reliability, window effects, and benchmark and qualitative comparisons.

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.
  • 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.
  • 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.

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.
  • 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.
  • Ranking reliability: 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].
  • 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.

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.

  • LinearMask-GS consistently matches or outperforms LP-3DGS in LPIPS, PSNR, and SSIM while using fewer Gaussians and less storage.The comparison covers all nine Mip-NeRF 360 scenes.
  • LinearMask-GS reaches comparable or lower LPIPS than LP-3DGS with substantially fewer Gaussians across scenes.The lower-left region represents the preferred quality–compression trade-off.
  • Tables 2–6 provide scene-wise comparisons of LPIPS, PSNR, SSIM, Gaussian count, and storage size against LP-3DGS and other baselines.

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

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.
  • 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.
  • 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.
  • 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.

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.
  • 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.
  • 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.
  • 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.
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