LP-3DGS: Learning to Prune 3D Gaussian Splatting
Authors: Zhaoliang Zhang
Tianchen Song
Yongjae Lee
Li Yang
Cheng Peng
Rama Chellappa
Deliang Fan
Venue: NeurIPS 2024 poster (2024)
Keywords: Novel view synthesis
Gaussian splatting
Learn to prune
Primary area: machine_vision
TL;DR: We propose a learning method to prune the points in 3D Gaussian Splatting by applying trainable mask to the importance score of points and minimize the model size with only one-time training while maintaining the rendering quality.

Abstract: Recently, 3D Gaussian Splatting (3DGS) has become one of the mainstream methodologies for novel view synthesis (NVS) due to its high quality and fast rendering speed. However, as a point-based scene representation, 3DGS potentially generates a large number of Gaussians to fit the scene, leading to high memory usage. Improvements that have been proposed require either an empirical pre-set pruning ratio or importance score threshold to prune the point cloud. Such hyperparameters require multiple rounds of training to optimize and achieve the maximum pruning ratio while maintaining the rendering quality for each scene. In this work, we propose learning-to-prune 3DGS (LP-3DGS), where a trainable binary mask is applied to the importance score to automatically find a favorable pruning ratio. Instead of using the traditional straight-through estimator (STE) method to approximate the binary mask gradient, we redesign the masking function to leverage the Gumbel-Sigmoid method, making it differentiable and compatible with the existing training process of 3DGS. Extensive experiments have shown that LP-3DGS consistently achieves a good balance between efficiency and high quality.

LP-3DGS: Learning to Prune 3D Gaussian Splatting
Zhaoliang Zhang Johns Hopkins University Baltimore, MD 21218 zzhan288@jh.co edu
Tianchen Song Johns Hopkins University Baltimore, MD 21218 tsong150jh.. edu
Yongjae Lee Arizona State University Tempe, AZ 85281 ylee298@asu. edu
Li Yang University of North Carolina at Charlotte Charlotte, NC 28223
Cheng Peng
Johns Hopkins University Baltimore, MD 21218 cpeng260jhu hu edu
1yang50@uncc.edu
Rama Chellappa
Deliang Fan
Johns Hopkins University Baltimore, MD 21218 rchella40jhu. edu
Arizona State University Tempe, AZ 85281 dfan@asu. edu
Abstract
Recently, 3D Gaussian Splatting (3DGS) has become one of the mainstream methodologies for novel view synthesis (NVS) due its high quality and fast rendering speed. However, as a point-based scene representation, 3DGS potentially generates a large number of Gaussians fit the scene, leading to high memory usage. Improvements that have been proposed require either an empirical pre- set pruning ratio or importance score threshold to prune the point cloud. Such hyperparameters require multiple rounds of training to optimize and achieve the maximum pruning ratio while maintaining the rendering quality for each scene. In this work, we propose learning-to to prune 3DGS (LP-3DGS), where a trainable binary mask is applied to the importance score automatically find a favorable pruning ratio. Instead of using the traditional straight-through estimator (STE) method to approximate the binary mask gradient, we redesign the masking function to leverage the Gumbel-Sigmoid method, making it differentiable and compatible with the existing training process 3DGS. Extensive experiments have shown that LP-3DGS consistently achieves good balance between efficiency and high quality.
Introduction
Novel view synthesis (NVS) takes images and their corresponding camera poses input and seeks to render new images from different camera poses after 3D scene reconstruction. Neural Radiance Fields (NeRF) (Mildenhall et al.] (20TT) uses multi-layer perceptron (MLP) to implicitly represent the scene, fetching the transparency and color a point from the MLPs. NeRF has gained considerable attention in the NVS community due to its simple implementation and excellent performance. However, in order to obtain a point in the space, NeRF needs to perform an MLP inference. Each pixel rendered requires processing ray and there are many sample points along each ray. Consequently. rendering an image requires a large amount of MLP inference operations. Thus, rendering speed becomes a major drawback of the NeRF method.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Besides NeRF, explicit 3D representations are also widely used. Compared to NeRF, the advantage of point- based scene representation is that it is well-supported by modern GPU rendering, enabling fast render speed. 3D Gaussian Splatting (3DGS) (Kerbi et al. [2023] achieves both good quality and high rendering speed, making it hot topie in the community. 3DGS uses 3D Gaussian models with color parameters to fit the scene and develops training framework to optimize the model parameters. However, the number of points required to reconstruct the scene is enormous, usually in the millions. In practice, each point has dozens of floating-pone pointt parameters, which makes 3DGS memory-intensive method.
Some recent works have attempted to mitigate this problem by pruming the points, such as Light- Gaussian (Fan et al.J (2023]) RadSplat (Niemeyer et al. (2024)) and Mini-Splatting (Fang and Wang (2024). These methods follow similar pruning approach through defining an importance score for each Gaussian point and prune the points with such importance score below a preset empirical thresh- old. However, a major drawback of these methods is that the preset threshold must be manually tuned through multiple rounds of training process to identify the favorable pruning ratio to minimize the number of Gaussian points while keeping the rendering quality. To make matters worse, such number of points may vary depending on different scenes, which requires manual pruning ratio searching for each scene. For example, the blue and red lines in Figure IT show the rendering quality of Kitchen and Room scenes, respectively, in MipNeRF360 scenes (Barron et al. [2022], ). with sweeping 12 different pruning ratios (i.e., 12 rounds of training) following the prior RadSplat (Niemeyer al. (2024)) and Mini-Splatting (Fang and Wang (2024) method. It is clearly seen that a smaller pruning ratio will not hamper the rendering quality, and the rendering quality will start to decrease with much more aggressive pruning ratios. Both scenes exhibit an optimal pruning ratio region that could maximize the pruning ratio and maintain the rendering quality. It could also be seen that the ideal pruning ratio differs for these two scenes.
PSNR
SSIM f
LPIPS +
0.525
0.902
Σ 5.0573
Ractipal stoom
RacSplut kitchen
0.850
RadSp Ki-Khhh
0.23
3DC5 Kithenn
0.525
LP30-G Kitchon
0.15
Praning Rallo
Protiin Raild
Proninn Racls
The performance changes with the pruning ratio of RadSplat on the MipNeRF360 dataset Kitchen and Room scenes are shown in blue and purple lines, respectively. Red triangles and squares represent the results of LP-3DGS on the importance score of RadSplat. LP-3DGS is able to find the favorable pruning ratio in one training session instead of requiring dozens of attempts to find the best hyperparameter.
Figure I:
In this paper, we propose a learning-to-prune 3DGS (LP-3DGS) methodology where trainable mask is applied to the importance score. Notably, is compatible with different types of importance scores defined in prior works. Instead of preset threshold to determine the 3DGS model pruning ratio, as illustrated by the red triangle symbol in Figure [ our method aims to integrate with existing 3DGS model training process to learn the favorable pruning ratio for minimizing the model size while maintaining the rendering quality. Since the traditional serrd-treesoll--aare based binary masking function is not differentiable, recent prior work, Compact3D (Lee et al. (2233), ), leverages the popular straight through estimator (STE) (Bengio et al. (203)) to bypass the mask gradient for adaption to the backpropagation process. However, this approach often results in suboptimal pruning ratios. In contrast, in our work, we propose to redesign the masking function leveraging the Gumbel-Sigmont activation function to make the whole masking function differentiable and integrate with the existing training process of 3DGS. Consequently, LP-3DGS automatically minimizes the number of Gaussian points for each scene with just a single round of training.
In summary, the technical contributions of our work are:
To address the effortful tuning of 3DGS pruning ratios, we propose a bearning-to-prune 3DGS (LP-3DGSS methodology that leverages the differentiable Gumbel-SSgmoid activation function to embed trainable mask with different types of existing importance scores
2

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designed for pruning redundant Gaussian points. As a result, instead of fixed model size, LP- 3DGS could learn an favorable Gaussian point size for individual scene with only one-time training.
We conducted comprehensive experiments on state-of-the-art (SoTA) ) 3D scene datasets, including MipNeRF330 (Barron et al. (022]), NeRF-Synthetic (Mildenhall al. (202T) D, and Tanks & Temples (Knapitsch et al. [2017]) We compared our method with SoTA pruning methods such as RadSplat (Niemeyer al. (2024)). Mini-Splattingg (Fang and Wang (2024)), and Compact3D (Lee et al. [2023]). ). The experimental results demonstrate that our method can enable the model to learn the favorable pruning ratio and that our trainable mask method performs better than the STE mask.
2 Related Work
Neural radiance fields (NeRFs) NeRFs (Mildenhall et al. [202T] targets to represent the scene in
multilayer perceptrons (MLPs) based on multi-view image inputs, enabling high-quality novel view synthesis. Due to its advancement, numerous follow-up works improved it in either rendering quality
(Barron et al. [202T 2022) or efficienc(MMülle et al. 2022]. Chen et al. [0022] Tridovich-Keil et al.
2022
Although NeRF models demonstrate impressive rendering capabilities across numerous benchmarks, and considerable efforts have been made enhance training and inference efficiency, they typically still face challenges in achieving fast training and real-time rendering.
Radiance Field Based On Points. In addition implicit representations, several works have focused on volumetric point-based methods for 3D presentation (Gross and Pfister (201T). Inspired by neural network concepts, (Aliev et al. (2020)) introduced neural point-based approach to streamline the construction process. Point-NeRF (Ding et al.] (2024)) further applied points for volumetric representation, enhancing the effectiveness point-based methods in radiance field modeling.
Gaussian Splatting 3D Gaussian Splatting (3DGS) (Kerbl et al. [023 represents a significant advancement in novel view synthesis, utilizing 3D Gaussians as primitives to explicitly represent scenes. This approach achieves state-of-the-an rendering quality and speed while maintaining relatively short training time. A series of methods have been introduced to improve the rendering quality through using regularization for better optimization, including depth map (Chung et al. 2023
Li et al. [024a]), surface alignment (Guédon and Lepetit (2023). Li et al. [2024b] and rendered image frequency (Zhang et al. (2024). However, the extensive number of Gaussians required for scene representation often results in a model that is too large for efficient storage. Recent research has focused on compression methods to enhance the efficiency of this representation. Notably, several studies (Fan et al. (2023), Fang and Wang [2024), Niemeyyr et al. (2024)) have proposed using predefined scores as pruning criteria to keep Gaussians that significantly contribute to rendering quality. Compact3D (Lee al. (2023) introduces method that applies trainable mask scale and opacity to each Gaussian and utilizes a straight-through estimator (Bengio et al. (2013) for gradient updates. LightGaussian (Fan al. 2023) employs knowledge distillation reduce the dimension of spherical harmonics. Additionally, Fan et al. (2023), Lee et al. (203)) also explored quantization techniques further compress model storage. The previously proposed pruning methods primarily rely on predefined scores to determine the importance of each Gaussian. These approaches present two main challenges: first, whether the criteria accurately reflect the importance of the Gaussians, and second, the need for a manually selected pruning threshold to decide the level of pruning. In this work, we address these issues by introducing a trainable mask activated by a ftubbel-sigmol function, applied to the scores derived from prior methods or directly to the scale and opacity of each Gaussian for more flexibility. Our approach automatically identifies the balance between the pruning ratio and rendering quality, eliminating the need to test on various pruning ratios.
3 Methodology
The conventional pruning methods leveraging predefined importance score require pruning ratio as a manually tuned parameter to reduce the size of Gaussian points in 3DGS. To seek for favorable
3

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pruning ratio, these methods may need to perform multiple rounds of training for each individual scene, which is inefficient. Motivated by this, we propose learning-to-prums 3DGS (LP-3DGS) algorithm which learns binary mask to determine the favorable pruning ratio for each scene automatically. Importantly, the proposed LP-3DGS is compatible with various types of pruning importance scores. In this section, we will: 1) introduce the preliminary of the original 3DGS and recap different importance metrics for pruning that are proposed by prior works, and 2) present the proposed carning-to-prune 3DGS algorithm.
3.1 3DGS Background
3DGS Parameters 3DGS is an explicit point-based 3D representation that uses Gaussian points model the scene. Each point has the following attributes: position p E R23 opacity a E [0, 1], scale in 3D s E R2 rotation represented by 4D quaternions q E R and fourth-degree spherical harmonics (SH) coefficients k E R248, In summary, one gaussian point has 59 parameters. The center point X of a Gaussian model represented by p and covariance matrix Σ is denoted by s and q. The SH coefficients model the color as viewed from different directions. The parameters of the Gaussians are optimized through gradient backpropagation of the loss between the rendered images and the ground truth.
Rendering 3DGS In order to render image, the first step is projecting the Gaussians to 2D camera plane by world to camera transform matrix W and Jacobian of affine approximation of the projective transform. The covariance matrix of projected 2D Gaussian is
E JWEWT
The projected Gaussians would be rendered as splat (Botsch et al. (2055), the color of one pixel could be rendered
oj Tj GG
Where is the pixel index, j is the Gaussian index and N is the number of the Gaussians in the ray. Cy is the color of the Gaussian calculated by SH coefficients, aj (1- exp pepp))))), o.y is the opacity of the point and 6y is the interval between points. 7, - (1 ax) is the transmittance from the start of rendering this point. G2D is the 2D Gaussian distribution.
Adaptive Density Control of 3DGS At the start of training, the Gaussians are initialized using Mannture-from-Motiee (SfM) sparse points. To make the Gaussians fit the scene better, 3DGS applies an adaptive density control strategy to adjust the number of Gaussians. Periodically, 3DGS will grow Gaussians areas that are not well reconstructed, process called "densification." Simultaneously, Gaussians with low opacity will be pruned.
3.2 Importance Metrics for Pruning
straightforward way to prune the Gaussians is by sorting them based on a defined importance score and then removing the less important ones. Consequently, one of the main objective of prior 3DGS pruning works is to define an effective importance metric.
RadSplat (Niemeyer et al. 2024)) defines the importance score as the maximum contribution along all rays of the training images, written
S =
max of T
Where of T is the contribution of Gaussian G, along ray r. RadSplat performs pruning by applying a binary mask according to the importance score, where the mask value for Gaussian G, is
m, = m( (S,) = 1(; < tprune)
Where tprune E [0, 1] is the threshold of score magnitude for pruning. 1[:] is the indicator function.

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Image
Ganssian Point Adjustment
Operation Flow
Rasterizer
Element-wise Multiplication
Gradient Flow
Initialization
Importencce Score
Dessifsation
Calculation
SfM Points
Prune
Adaptive Densify Control
Mask
Densification Stage
Learning Prune
Figure 2: Overall learning process of the proposed LP-3DGS.
Another recent work, Mini-Splatting (Fang and Wang 20244), uses the cumulative weight of the Gaussian the importance score, which can be formulated
K
Wij
(5)
Where K is the total number of rays intersected with Gaussian Gi wig is the color weight of Gaussian G on the j-th ray.
3.3 Learning-to-Pree 3DGS
The overall LP-3DGS learning process is shown in the Figure 2 In general, mainly can generally be divided into two stages: I) densification stage, and 2) learning- to-pggttteeeeeeeee stage. Following the original 3DGS, densification stage applics an adaptive density control strategy to gradually increase the number of Gaussians. As revealed by prior pruning works (Lee al. 2023 Niemeyer et al. (2024]) ) 3DGS contains significant number of redundant Gaussians. Subsequently, in the learning-to- to-puue stage, the proposed LP-3DGS learns trainable mask upon previously defined importance metric to compress the number Gaussians with an favorable pruning ratio automatically. Specifically, to learn binary mask, first initialize real-value mask m, for each point and then adopt the Gumbel-sigmoid technique to binarize the mask value differentially.
Gumbel-Sigmoid based Trainable Mask The binarization operation for real-value mask in pruning typically involves hard threshold function, determining the binary mask should be 0 or 1. However, such hard threshold function not differentiable during backpropagation. To address this issue, popular straight through estimator (STE) method (Bengio et al. [2013] is widely used, as it skips the gradient the threshold function during backpropagation. Such process may create to a gap between trainable real-value mask and binary mask. As shown in Figure 3(a), the trainable mask values exhibit certain ratios across the entire range from inaccurate when further converting to binary mask via hard threshold function. To better optimize the trainable mask towards binary values, we propose to apply Gumbel-Sigmoid function to learn the binary mask.
after Sigmoid function, which can be
The Gumbel distribution is used to model the extreme value distribution and generate samples from the categorical distribution (Gumbel 1954)). This property is then utilized to create the Gumbel- Softmax (Jang et al. (2066). ) differentiable categorical distribution sampling function. The sample of one category is given by:

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exp((log( (T,) + 9:)/T)
(6)
Σj= == (T)(())((TT) + 9,)/T)
Where T is the input adjustment parameter, is sample from Gumbel distribution. Inspired by the GumbellSoftmax, we treat learning the binary mask of each point as two-class category problem. Thus, we replace the Softmax function to Sigmoid function, referring to Gumbel-Sigmoid:
exp((log(m)) + g0)/7) gs(m) exp((log(m) + 90) + exp(gn/T) 1 + exp((=(lo(()) + 90 - 9)//T)
(7)
2538
150
125-
15300
0.1-
030
050
(a) Mask values after Sigmoid activation
(b) Mask values after Gumbel-Sigmoid activation
Figure 3: Comparison between Sigmoid and Humbel--Sggoidd The Gumbel-Sigmoid function pushes the values closer to 0 and is good approximation of a binarized mask.
By using such Gumbel-Sigmoid function, the output value either close to or 1, as shown in Figure 3 allowing it to be integrated an approximation of binary masking function. More importantly, this function remains differentiable, thus can be integrated during backpropagation.
Moreover, to prune the selected Guassians practically according to the learned binary mask, we further apply the mask value opacity, which can be mathematically formulated
gs(m: * S.)
(8)
where S; is the defined importance score of each Gaussian point. The closer the mask value is to 0, the less corresponding Gaussian point contributes to the rendering. In practice, after learning the trainable mask, one-time pruning is applied the corresponding Gaussian points with mask value of O.
Sparsity regularization In order to compress the model much possible, we apply a L1 regularization term (Lee et al. (0233) to encourage the trainable mask to be sparse, which can be formulated as:
Rmaak
mi
Upon that, the final loss function defined
L = (1 - Agsim) LLa + Assim Lysim + Am * Rmnask
(10)
LLi is the LI loss between rendered image and ground truth. Lusim is the ssim loss. Agsim and An are two coefficients.
Moreover, we find that the trainable mask can be effectively learned in just few hundred iterations, compared the thousands required for the overall training process. In practice, the mask learning function is activated for only 500 iterations. Once the mask values are learned, we follow the 3DGS training setup to further fine-tune the pruned model while maintaining the same total number of training iterations. The detailed hyper parameters are described in the later experiment section.

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4 Experiments
4.1 Experimental Settings
Dataset and Baseline We test method on two of the most popular real-world datasets: Mip- NeRF360 dataset (Barron et al. (0222), which contains scenes, and the Train and Truck scenes from the Tanks & Temples dataset (Knapitsch et al. (2017)) ). We also evaluate
method on the NeRF-Synthetic dataset (Mildenhall et al. j), which includes 8 synthetic scenes. In this section, only present the results on MipNeRF300 360 dataset, rest of them are listed in appendix [ In this paper, we use the SOTA RadSplat (Niemeyer et al. (2024) and Mini-Splatting (Fang and Wang (2024)) as the baselines, both of which propose different pruning importance scores. First, evaluate the performance of these two methods under various pruning ratios. Since neither method is open-sourced at the time of writing, we reproduced them based on the provided equations. For each pruning ratio, we calculate the corresponding threshold based on the magnitude of the importance scores and prune the Gaussians with scores below this threshold. Note that each pruning ratio requires one round of training. We use peak signal-tor signal-tonooiee ratio (PSNR), structural similarity index measure (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) (Zhang et al. (2018) as rendering evaluation metrics.
Implement Details The machine running the experiments is equipped with an AMD 5955WX processor and two Nvidia A6000 GPUs. It should be noted that method does not support multi- GPU training. We ran different experiments simultaneously on two GPUs. We train each scene under every setting for 30,000 iterations and with the mask training occurring from iteration 19,500 to 20,000, updating the importance score every 20 iterations. The value of 7 in Equation 7 is 0.5 and the coefficient Am of mask loss is 5e-4.
4.2 Experimental Results
The blue lines in Figure show the results of sweeping pruning ratios using RadSplat and Mini-Splatting for the Kitchen and Room scenes. Results for other scenes in the MipNeRF 360 dataset are presented in Appendix [A] The result of the learned LP-3DGS model size and rendering quality is indicated by red triangles.
Quantitative Results
The quantitative results fluctuate lower pruning ratios but generally stabilize around certain value. After surpassing that point, the rendering quality decreases significantly. It's worth noting that this critical point varies for different scenes. Rather than manually searching for the favorable pruning ratio, it clearly shows our LP-3DGS method could learn the favorable model size in conjunction with the scene learning process, with only one-time training. The Table lists the quantitative results of all scenes in MipNeRF360 dataset. It clearly shows that each scene converge into different model size leveraging our LP-3DGS method while maintaining almost the same rendering quality. The pruning ratio varies based on what importance score is used, but LP-3DGS effectively identifies the ideal pruning ratio for the corresponding score.
Scene
Bicycle
Bonsai
Counter
Kitchen
Room
Stump
Garden
Flowers
Treehill
AVG
Baseline PSNR 1
25.087
29.079
31.581
31,500
26.655
27.254
21.348
22.561
27.48
LP-3DGS (RadSplat Score)
25,099
32.094
28.936
31.515
31,490
26.687
27.290
21.383
22.706
27.47
1.P. PP3DGS (Mini-Splatting Score)
24.906
31,370
28.4098
30.785
31.132
26.679
27.095
21.150
22.522
27.12
Baseline SSIM
0,7464
0.9460
0.9138
0.9320
0.9299
0,7700
0.8557
0.5876
0.6355
0.8125
T.P-DDSS (RadSplat Score)
0.7458
0.9441
0.9120
0
0.9243
0.7714
0.8548
0.5865
0.8120
PD3DS (Mini Splatiing Score)
0.7373
0.9358
0.9017
0.9249
0.9167
0.7677
0.8493
0.5756
0.6336
0.8047
Haseline T.PISS 4
0.2441
0.1839
0.1
0.1978
0,2423
0.1224
0,3601
0.3469
0.2215
LP-3DGS (RadSplai Score)
0.2516
0.1865
0.1896
0.1194
0.2032
0,2466
0.1270
0.3656
0.3527
0.2269
I.P3DGS MpinitSplatting Score)
0.2642
0.2036
0.2068
0,1292
0.2208
0,2553
0.13
0,3753
0.3618
0.2391
RadSplai Score praming ratio
0.64
0.65
0.66
0.58
0.74
0.65
0.59
0.39
0.59
0.63
Mini-Splatting Score pruning ratio
0.57
0.64
0.56
0.71
0.61
0.60
0.54
0.60
Table 1:
The results comparison on the MipNeRF360 dataset shows that LP-3DGS has similar performance after pruning and achieves different pruning ratios for different scenes. This demonstrates LP-3DGS's s ability to adaptively find the favorable pruning ratio, maintaining performance while effectively compressing the model.
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PSNR
SSIM 1
LPIPS +
Rosbeki
RadSplat
10
0502
0.75
36
2.52
Kitchen
RacSplet
LP-30GS
0.25
RasSonr LP-3355
Puriing 3atlo
manin Rato
Pruting Tado
Mini- SplattSp
MriSnnating LP-10G
5:54
LF-30G5
01
631
Ractpper Ut-ppos
RadSplat
5.00
Room
26
6.0
LP-10GG
0.00
LF-1366
2.23
02
338
Pruning
Pruniin
Mini-Splatting
0.22
2.500
LT-3055
02
0.03
0.20
3.200
0.1
0.2
0.3
07
631
02
Figure 4: The performance changes with the pruning ratio in different scenes
Training Cost Table the training cost of LP-3DGS on Mi6NeRF360 dataset. In setup, after 20000th iteration, the model is pruned based on the learned mask values. The number of Gaussian points will be significantly reduced, resulting in the later stages of training taking much less time than the non-pruned version. Even with the embedding of the mask learning function, the overall training cost is comparable to that of the vanilla 3DGS. In most cases, the peak training memory usage slightly higher because training the mask requires more GPU memory. However, after pruning, the 3DGS model size becomes much smaller, leading significant improvement in rendering speed, measured in terms of FPS.
Scene
Bicycle
Bonsai
Counter
Kitchen
Room
Stump
Garden
Flowers
Trechill
3DGS Training time (Minute)
49
34
26
33
27
37
47
33
32
LP-3DGS (RadSplat Scorc)
43
27
28
34
30
35
46
34
33
LP-3DGS (Mini-Splane SilatSplatiing Score)
28
35
29
34
46
34
33
3DGS Peak Memory (GB)
9.4
9.3
10.6
12.2
13.7
10.3
9.4
LP-3DGS (RadSplat Score)
16.1
8.5
11.3
12.3
11.8
12.1
15.8
10.1
10.3
LP-3DGS Minii-Splutinng Score)
15.5
8.4
12.7
13.0
13.0
12.1
15.2
9.7
9.7
3DGS FFS
421
315
380
164
129
200
205
L.P-DDGS (RadSplat Score)
324
662
670
542
692
371
296
412
411
LP-3DGS (Mini- (Mini-Splattinn Splatting Score)
290
634
650
507
662
341
252
368
384
Table 2:
Training cost and on MipNeRF360 Dataset. Training time of LP-3DGS is similar with baseline but since the model is compressed, the FPS larger.
4.3 Ablation Study
A recent prior work, Compact3D (Lee et al. 2023 proposes to leveraging the straight-through estimator (STE) to train a binary mask based on the opacity and scale of Gaussian parameters. To conduct fair comparison between STE based mask and our LP-3DGS, we perform two ablation
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studies, one involves replacing the STE mask in Compact3D with our method, and the other applies the STE mask the importance score of RadSplat. The formula of STE mask is
((m) = (m)) > > f(m)) + f(m)
(11)
Wmaans stop gradients, 1|| is the indicator function and f(-) is sigmoid function, is masking threshold.
Comparison with Compact3D We first apply the Gumbel-sidmoid activated mask, instead of STE mask, on the opacity and scale of gaussians in the same manner as proposed in Compact3D. The threshold in Equation D and mask loss coefficient follows the default settings in Compact3D. Table 3 shows the comparison between two methods.
Scene
Bizycle
Bonsai
Counter
Kitchen
Room
Stump
Garden
Flowers
Treehill
AVG
Compacta
24.846
32.19
29.066
30.867
31,489
26.408
27.026
21.187
22.479
27.284
LP-INGS
25.087
32.2
29,033
31.213
31,678
26.658
27.223
21.32
22.569
27.442
SSIM
CompactL1
0.7292
0,9462
0.9137
0.225
092211
0.7563
0.8446
0.5773
0.6.015
0.8053
LP-3DGS
0.7438
0,9661
0.9141
0,9305
0.2633
0.7687
0,8547
0.5843
0.6358
0.8116
I.IPS
Compacci:
0.266
0,1815
0.1866
0.124
0.2012
0.2615
0,1401
0.3722
0.3555
0.2320
LP-3DGS
0.2526
0.1833
0.1867
0.1201
0.2013
0,2472
0.1275
0.3668
0.3513
0.2263
#Gaussians
DDmpacci)
2620663
666358
570126
1050079
566332
1902711
2412796
1685224
2089513
1507109
LP-3DGS
2510992
542235
506391
887161
479681
2014270
2836989
1747766
1804155
1481071
Table 3: Results with/without trainable mask on Gaussian opacity and scale
In most cases, our LP-3DGS learns higher pruning ratio, except for Stump, Garden and Flowers scene. In terms of rendering quality, our LP-3DGS outperforms Compact3D using the STE based mask achieving even smaller model sizes in most scenes.
STE Mask on Importance Score We also apply STE mask on the pruning importance score to compare with our method. The Equation would be rewriten as
Orm
Og
M (m,+ * is)
(12)
where M shown Equation default values in Compact3D.
The same as mentioned before, the parameters for STE mask are
Scene
Bicycle
Bonsai
Counter
Kitchen
Room
Stump
Garden
Flowers
Treehill
AVG
PSNR
LP-3DGS
25.099
32.094
28.936
31,515
31.490
26.687
27.290
21,383
22.706
27.470
STE mask
24.833
30,947
28.371
30.705
30.950
26.396
26.793
21.056
22.552
26.955
SSIM
LP-3DGS 0.7458
0.9441
0.9120
0.9311
0.9243
0.7714
0.8548
0.3865
0.6381
0.8120
STE
0.7251
0.9268
0.8925
0.9120
0.7514
0.8289
0.5624
0.6196
0.7922
LPIPS
LP-3DGS
0.2441
0.1799
0.1839
0.1164
0.1978
0.2423
0.1224
0.3601
0.3469
0.2215
STE musk
0.2937
0.2194
0.2274
0.1480
0.2334
0.2899
0,1771
0.3988
0.3983
0.2651
Pruning Ratio
LP33DGS
0.64
0.65
0.66
0.59
0.59
0.63
STE mask
0.84
0.88
0.88
0.87
0.89
0.86
0.85
0.83
0.83
0.86
Table 4: Results using LP-3DGS and STE mask on importance score of RadSplat
Table 4 shows that under the same settings, after applying the mask to the importance score, the STE mask compresses the mode too much and the performance drops lot. Trainable mask keeps the gradient of the mask and the comressed model has a more reasonable size.
Scene
Bicycle
Bonsui
Counter
Kitchen
Room
Stump
Garden
Flowers
Treehill
AVG
LP-3DGS
24.906
31.370
28.4098
30.785
31.132
26.679
27.095
21.150
22.522
27.12
PSNR
STE mask
24.894
30,925
28.334
30.731
31.032
26.470
26.863
20.997
22,559
26.98
LP-3DGS
0.7373
0.9358
0.9017
0.9249
0.9167
0.7677
0.8493
0.5756
0,6336
0.8047
SSIM
STE mask
0.7287
0.9292
0.8978
0,9232
0.9152
0.7562
0.8381
0.5629
0.6247
0.7973
LP-3DGS
0.2642
0.2036
0.2068
0.1292
0.2208
0.2553
0.1353
0.3753
0.3618
012391
LPIPS
STE mask
0.2821
0.2154
0.2145
0.1330
0.2241
0.2797
0.1564
0.3939
0.3852
0.2538
Pruning Ratio
LP-DGGS
0.37
0.67
0.64
0.56
0.71
0.61
0.60
0.54
0.54
0.60
STE mask
0.75
0.77
0.75
0.66
0.79
0.80
0.75
0.75
0.75
0.75
Table 5: Results using LP-3DGS and STE mask on importance score of Mini-Splatting

---

Discussion and Conclusion
Broader Impact and Limitation LP-3DGS compresses the 3DGS model an ideal size in single run, saving storage and computational resources by eliminating the need for parameter sweeping to find the favorable pruning ratio. However, the limitation of this work is that the rendering quality after pruning varies depending on the the definition of importance scores.
Conclusion In this paper, we present a novel framework, LP-3DGS, which guides the 3DGS model
learn the best model size. The framework applies trainable mask on the importance score of the gaussian points. The mask trained for a specific period and used prune the model once. Our method compressed the model as much possible without significantly sacrificing performance and capable to achieve the favorable compression rate for different test scenes. Compared with the STE mask method, ours achieves better performance.
10

---

Acknowledgments and Disclosure of Funding
Supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0076. The U.S. Govern- ment is authorized reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government.
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A
Appendix/siig supplementl material
Code: https://ggchub.cc///ee/ffffffffp 3DGS. git
A.1
Experiment Results on MipNeRF360 Dataset
Ground Truth
3DGS
RadSplat
Mini-Splatting
Bicycle
Bonsai
Counter
Kitchen
Room
Stump
Garden
13

---

Flowers
Trechill
Figure 5: Rendered images MipNeRF360 Dataset
PSNR
SSIM 1
LPIPS 4
RadSplat
RosSabr
24.5
23.5
RadSpar
RadSola
Bicycle
23.
LT-3065
LF-30G5
Pnn fans
Pnrving 1a00
Mini- SpaattSp
25.0
LP-10G5
24.
1.700
675
1.500
Mri-qgaainn
Un-022
0:523
U1-1055
63
Rtato
1,00
0.020
RadScla:
RadSplat
0.2
LP-3005
0.25
Bonsai
LP-3DGG
827
1P-00:G
0.3
6.1
Rato
Mini-Splatting
30
Hi-i-Sfatiing
3525
Lh-10C5
27.
26
1P
1005
0.90
0.20
6.5
84
35
03
61
0.3
02
83
02
03
14

---

RadSplat
26-
3 440
Bustski
Uh-puus
30000
2.23
Counter
LP-3DGG
LF-33GG
1.00
0.2
02
04
05
0.2
0.5
0.2
5.4
0.5
0.2
1.2
5.0
0.2
0.4
Nallo
0.0
Mini-Splattin SpaittSpat
2.33
0.90
Mit--pp etting
(P (P-ibis
23
0.00
0.33
2.23
20
Lo
0.2
07
33
0.3
02
0.2
RadSplat
26.5
0.775
RadSiirr UP-PUS
26.0
35.5
2.000
RatSpai
RazSoki
Stump
0.5
0.5
0.0
0.2
6.0
0.1
0.5
Mini-Splatting
30.5
0.732
LF-3DG
0.72
25.0
200
25.0
LF-3003
0.75
LP-3305
0.25
2/1
0.2
6.1
Non Tatic
huning Tullo
Traning 1600
0.03
RadSplat 530
0.00
RacSglai (P-1665
Garden
1F-1005
Prining Sarb
Radoo
Prusing Sadoo
Mini-Splatting
0.53
95
Solating
Mn sting
L7-5003
0.70
M611 ng
Mun Polls
Pounin kM0
RadSplat
135
2.3
Rottytor
21.0
27.35
20.0
Flowers
RadSplot
LT-3003
2-473
RecSple
L1-10G5
0.43
2.5
0.2
02
Mun fasis
Prining RaTo
Prontig Aario
Wini-Splatting
230
Nosby allang
LP-35i27
3.55
20.0
Mini-Sp
Mri-quating
Lh-3033
2.45
U-1005
02
02
Ra1o
Puring A20
15

---

RadSchr
RadSplat
21.0
Raztppul
Rutboke
Treehill
21.0
Lh-3003
254
L1-5055
mun holis
Patlo
Pluning ta00
WinitSplatiing
2.50
Mid up atting
22.5
0.67
UN30Gs
2.50
2.40
21.0
19-3365
LF 10-3005
0.33
Pan tann
Printig Rato
Figure 6: The performance changes with the pruning ratio in different scenes
16

---

A.2 Experiment Results on NeRF Synthetic Dataset
Scene
Drums
Ficus
Hotdog
Lego
Materials
Ship
AVG
Baseline PSNR
35.546
26.276
35,480
38.081
36.012
30.502
36.795
31.688
33.798
LP-3DGS (RadSplat Score)
35.496
26.221
35.442
37.976
35 35.990
30.374
36.589
31.584
33.709
LP-3DGS MMlii-Splatting
35,419
26.102
35.354
35,769
29.883
36,337
31.375
33.496
Baseline SSIM
0.9877
0.9548
0.9870
0.9854
0,9825
0.9604
0.9926
0.9062
0.9696
L.PADGS (RadSplat Score)
0,9577
0.9867
0.9694
LP-3DGS (Mini-Splatting Score)
0.9874
0.9358
0,9867
0.9846
0.9817
0.9566
0.9919
0.9034
0.966
Baseline LPPISS
0.01046
0.03657
0.01775
0.01977
0.0161
0.03671
0.00635
0.1058
0.03119
LP-3DGS (RadSplat Score)
0.01091
0.03723
0.01213
0.02079
0.01675
0.03817
0,00680
0.1083
0.03139
I. 3DGS (Mini Splatting Score)
0.0111
0.03876
0.01217
0.02211
0.018
0.04323
0.00749
0.1151
0.0335
RadSplal Score pruning
0.76
0.84
0.78
0.71
Mini Splatting Score pruning ratio
0.63
0.65
0.65
0.58
0.58
0.80
0.60
0,50
0.62
Table 6: The quantitative results on NeRF Synthetic Dataset
A.3 Experiment Results on Truck & Train Scenes
Scene
Truck
Train
AVG
Baseline PSNR f
25.263
22.025
23.644
LP-3DGS (RadSplat Score)
25.376
21.822
23.599
LP-3DGS (Mini-Splatting Score)
25.152
21.675
23.414
Baseline SSIM
0.8778
0.8118
0.8448
LP-3DGS (RadSplat Score)
0.8768
0.8072
0.8420
LP-3DGS (Mini-Splatting Score)
0.8724
0.7963
0.8344
Baseline LPIPS $
0.1482
0,2083
0.1783
LP-3DGS (RadSplat Score)
0.1541
0.2217
0.1879
LP-3DGS (Mini-Splatting Score)
0.162
0.2343
0.1982
RadSplat Score pruning ratio
0.72
0.63
0.68
Mini-Splatting Score pruning ratio
0.65
0.57
0.61
Table 7: The quantitative results on Tanks & Temples Dataset
17

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: LP-3DGS is able enable the model learn the favorable size, achieving a good balance between efficiency and quality, as demonstrated in Figure Figure 4 and Figure 6
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made paper.
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The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
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Question: Does the paper discuss the limitations of the work performed by the authors?
Answer:
[Yes]
Justification:
We discuss the limitations in Section
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The authors are encouraged to create a separate "Limitations" section in their paper.
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Answer:
[NA]
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19

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Question: Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes]
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6. Experimental Setting/Details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification:
The detailed experiment settings are listed in Section 4.1
Guidelines:
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The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment Statistical Significance
Does the report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [NA]
Justification; This paper follows the existing work about 3DGS and lists the essential detailed
quantitative results in Section 4.2] Section 4.3 and Appendix A bars.
But it does not list error
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Reviews:
[{"review_id": "HGe7HVErqi", "reviewer": "Reviewer_o7SR", "summary": "Whereas other works set a fixed pruning ratio or threshold, this paper introduces a method to learn how to prune Gaussians from a scene while retaining high image fidelity. Different scenes have a drop in fidelity at different pruning percentages and the goal of this work is to remove the need to train the model multiple times while searching for a pruning percentage near, but before, that drop. Specifically this work uses a Gumbel-Sigmoid — which is a 2-class Gumbel softmax followed by a Sigmoid function —  to enable a differentiable mask that can learn to prune Gaussians during training. This mask is then applied to set the opacity of each Gaussian. Gaussians where the mask goes to 0 are pruned. Evaluations are performed on 2 real world datasets — MipNerf 360 and Tanks & Temples — and one synthetic dataset — NeRF-Sythetic.", "questions": "My biggest concern for this manuscript is that the use of terms “optimal” and “best” is misleading. This method can find a good pruning ratio in one-shot, but it’s not clear that this ratio is optimal. I’m rating this manuscript a borderline reject for now because I strongly think this wording needs to change. I will raise my score if the authors can provide a detailed description of how they will update this wording in their rebuttal.\n\nI would also like to see W2 and W3 addressed, but these are likely computationally expensive and aren’t as important to me as W1.", "limitations": "Once the wording in this manuscript is changed, I think the main limitations will be addressed.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "S1: The writing in this work is quite clear. The methodology is straightforward to understand and the explanations appear to be detailed enough to be able to replicate experiments\n\nS2: This method seems useful to practitioners who are low on resources and want to quickly fit and compress a 3D-GS model.", "weaknesses": "**Main Weaknesses:**\n\nW1: This paper uses the terms “optimal” and “best” to describe the pruning ratio found by learning. Specifically a soft definition of the optimal pruning ratio is given in line 41: “minimize the number of Gaussian points while keeping the rendering quality.” But this method does not “keep” the rendering quality — image quality metrics decrease after pruning. Generally the terms “optimal” and “best” are used to describe maximal or minimal points in some meaningful measure. In the domain of pruning 3D-GS models, a more appropriate definition of optimal pruning would be the highest possible compression that can be applied to the model while retaining rendering quality to some percent of the original rendering quality.\n\nW2: It would be helpful to also provide analysis on pruning threshold vs. image quality metrics. It’s possible that there exists a pruning threshold for RadSplat and/or Mini-Splatting that prunes a large percent of Gaussians while retaining image quality. \n\nW3: Table 2: Minutes isn’t a great metric here. FLOPs or MACs over training would be a lot better. Other works that want to compare to this method will need to use exactly this manuscript’s architecture to replicate its results.\n\n\n\n**Other minor considerations:**\n\nMC1: There are still several hyper parameters that haven’t been ablated. This is mostly fine, but it would be good to know how big of an impact these parameters have:\n- Gumbel $\\tau$\n- $\\lambda_m$\n- Applying the pruning earlier/later than 20000 epochs\n\nMC2: It would be interesting to ablate equation 8 by removing $S_i$. Can you simply just learn $m_i$ parameter without computing an importance score?\n\n\n**Cosmetic issues:**\n\nC1: line 46, line 50, line 62: could -> can\n\nC2: $T$ in eq. 7 should be a $\\tau$\n\nC3: Tables 1 and 2, move the metric to the first column for clarity (like tables 4 and 5)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### Response to W1: \n\nThank you for the comment. Please refer to the Common Question about the term ``optimal\" pruning.\n\n### Response to W2:\n\nFor Radsplat/Mini-Splatting, they calculate their defined importance score for each Gaussian. If the target is to prune 60% of the entire model, the Gaussians are ranked based on this predefined importance score to prune 60% off. Correspondingly, the actual pruning threshold of the importance score value can be calculated.\n\nTo clarify, Figures 1, 4, and 6 show the pruning ratio of the entire model versus the rendering quality, rather than the actual threshold of the importance score. These figures already report what the reviewer asked for. Each point in these figures represents the result of one round of training with a preset pruning ratio, sweeping from 10% to 90%. The results indicate there always exists a balanced pruning ratio region for both Radsplat/Mini-Splatting that can achieve a large pruning ratio with almost no or negligible rendering quality drop. We have never denied this. However, our method can learn such a pruning ratio with only one round of training.\n\n### Response to W3:\n\nFollowing the same training time metric used in most prior 3DGS model pruning works, such as RadSplat, Mini-Splatting, and EAGLES, we also use training time as an important metric for a direct comparison. All experiments we reported are conducted with the same GPU hardware setup, ensuring consistency. Our method learns a smaller 3DGS model, where the saved MACs and FLOPS depend on the learned pruning ratio.\n\nThe training time we report is for only one round of training. This is to show that our proposed method incurs almost no training time overhead or even results in shorter training time due to the smaller pruned model in the later stages of the training pipeline. It is important to note that prior manual pruning works require multiple rounds of training to find the balanced pruning ratio setting, making it challenging to simply report the MACs and FLOPS.\n\n### Response to MC1:\n\nThank you for the comments. We conducted further ablation studies on those hyperparameters.\n\nWe discovered that the parameter $\\tau$ has a very minor effect on the learned pruning ratio.\n\nWe also conducted an ablation study on the parameter $\\lambda_{m}$ using the Room scene. The experimental results are as follows:\n\nAblation Study on Parameter $\\lambda_{m}$ (Room Scene)\n| $\\lambda_{m}$ | PSNR  | SSIM  | LPIPS | Pruning Ratio |\n|---------------|-------|-------|-------|---------------|\n| 3e-4          | 31.488| 0.9241| 0.2035| 73.15%        |\n| 5e-4          | 31.490| 0.9243| 0.2032| 73.78%        |\n| 7e-4          | 31.474| 0.9238| 0.2040| 75.91%        |\n\nThese results indicate that varying $\\lambda_{m}$ has a negligible impact on the PSNR, SSIM, and LPIPS metrics in the Room scene.\n\nRegarding the timing of pruning the model, we found that the best time to perform pruning is at the 20,000th epoch. This timing allows the model extra training epochs to fine-tune based on the pruned model. Pruning the model too early is not advisable, as the 3DGS densification stage stops at the 15,000th epoch, and the model requires additional time to learn the scene. We have already reported the complete set of hyperparameter settings and open-sourced our code on GitHub for researchers to reproduce our results. We will include this ablation study in the final manuscript if space permits.\n\n### Response to MC2:\n\nGiven the rapid development of the 3DGS community, new pruning methods are emerging quickly. We hope our method is compatible with most pruning methods, especially those defining new importance scores for pruning (please refer to the Common Question about Contribution above).\n\n### Cosmetic issues:\n\nWe appreciate your comments and will address all cosmetic issues in the updated manuscript accordingly.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Mq6IKwrWhj", "reviewer": "Reviewer_fvLt", "summary": "This paper proposes a method to optimally prune Gaussians that do not participate in the rendering or optimizing process of the 3D Gaussian Splatting 3D reconstruction algorithm. The key idea in this paper is to use a Gumbel-sigmoid function instead of the standard Sigmoid function to optimize a binary mask based on transmittance of each splatted Gaussian. Experimental results show that by doing so the number of Gaussians can be reduced without losing reconstruction quality, keeping a near optimal balance between quality and computational speed. As a result, higher frame rate can be obtained for rendering.", "questions": "-\tClarify Figure 4 and explain what the meaning of the pruning ratio for the proposed method is.\n-\tAdd more comparative experiments with other compact 3DGS methods.", "limitations": "-\tLimitations are properly discussed in the conclusion section.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "-\tThe idea to use the Gumbel-function is interesting because it allows to naturally binarize the input values while keeping differentiability. \n-\tResults show that higher frame rate can be achieved without losing accuracy or training time. The ablation study is also good because it shows the advantage of optimizing the mask values compared to hard thresholding.", "weaknesses": "-\tExcept for replacing the sigmoid function with the Gumbel-Sigmoid function it seems that there is no other novel technical point in the paper. From the results it seems that a threshold value of 0.6 would be better than the naïve 0.5. I am wondering how the ablation study changes if using different threshold.\n-\tIn the experiments, no comparisons to other methods that focus on optimizing number compressing the model. For example, comparison with LightGaussian would be interesting. It seems from the Figure 4 that the proposed method performs slightly worse than mini splatting.\n-\tWhat is the meaning of the “pruning ratio” for the proposed method in Figure 4? It seems to be different for the different datasets. However, as far as I understood, the proposed method does not use a pruning ratio: l. 194 => pruning […] points with mask values of 0. This is confusing.\n-\tThere is no significant gain in accuracy, training time or memory consumption. The only significant gain is in rendering speed. This is interesting but because original 3DGS is already quite fast, in practice I am not sure the impact is high. For example if using a simple threshold of 0.5 in Compact3D how does frame rate compares?\n-\tWriting can be brushed up.\no\tL.176-178 is not correct.\no\tIn figure 4, it seems legends are wrong in the lines for Mini-splatting => blue is described as RadSplat.\no\tTables are not easy to read. Add some special fonts like bold or underline to emphasize best and second-best results.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### Response to weakness 1\\&3:\n\nPlease refer to the Common Question about the clarification and summary of our technical contributions.\n\nWe would like to highlight that the main contribution of our work is not merely adopting the Gumbel-Sigmoid to prune 3DGS models but rather developing a learning framework that can automatically learn a pruning ratio embedding during the training process of a 3DGS model. This is achieved through our proposed Gumbel-Sigmoid mask pruning technique (Equation 8) and ensemble loss function (Equation 10), with only one round of training.\n\nRegarding the analysis shown in Figure 4, RadSplat/Mini-Splatting calculates their defined importance score for each Gaussian. If the target is to prune 60% of the entire model, the Gaussians are ranked based on this predefined importance score to achieve the 60% pruning. The actual pruning threshold of the importance score value can then be calculated.\n\nTo clarify, Figures 1, 4, and 6 display the pruning ratio of the entire model versus the rendering quality, rather than the actual threshold of the importance score. This is why the x-axis ranges from 0 to 1, where each point corresponds to the rendering quality with a pruning ratio ranging from 0.1 to 0.9 in our experiments. Each point represents the result of one round of training with a preset pruning ratio, sweeping from 10% to 90%.\n\nFor different pruning methods, such as RadSplat and Mini-Splatting, the results indicate that there always exists a balanced pruning ratio region that achieves a large pruning ratio with almost no or negligible rendering quality drop. In contrast, our method can learn such a pruning ratio with only one round of training.\n\nAs observed by the reviewer, our method can automatically learn balanced pruning ratios with respect to different scenes. In other words, our proposed method does not require a pre-defined pruning ratio or threshold like prior pruning works, but instead learns one. We believe this is the greatest contribution of our work, and our method will benefit the community.\n\n### Response to weakness 2:\n\nWe kindly disagree with the reviewer and believe that we have already provided a comprehensive comparison with two of the most recent and best-performing state-of-the-art (SoTA) works, namely RadSplat and Mini-Splatting. The experimental results are reported in Figure 4, Tables 1 and 2, and additional results in the appendix.\n\nIn the paper \"RadSplat: Radiance Field-Informed Gaussian Splatting for Robust Real-Time Rendering with 900+ FPS\", arXiv:2403.13806, the authors compared their method with LightGaussian, demonstrating better rendering image quality and a smaller model size. Consequently, we adopted RadSplat as our baseline.\n\nWe appreciate the reviewer’s comments and, as suggested, we have also included a comparison with LightGaussian as follows:\n\n|                            | **Synthetic NeRF**   |            |            | **MipNeRF360 and Tank & Temple** |            |            |\n|----------------------------|-----------------------|------------|------------|----------------------------------|------------|------------|\n|                            | PSNR                  | SSIM       | LPIPS      | PSNR                             | SSIM       | LPIPS      |\n| LightGaussian              | 32.725                | 0.965      | 0.0370     | 27.206                           | 0.761      | 0.217      |\n| Ours (RadSplat Score)      | 33.709                | 0.9694     | 0.03139    | 27.812                           | 0.863      | 0.189      |\n| Ours (Mini-Splatting Score) | 33.496                | 0.966      | 0.0335     | 27.467                           | 0.856      | 0.201      |\n\nRegarding the comparison with Mini-Splatting, since our method is a learn-to-prune approach, it exhibits slight variations across different scenes. The average performance is reported in Table 1. It appears that the method performs better with the importance score defined in RadSplat compared to the one defined in Mini-Splatting, given our hyperparameter settings. We will investigate this further in our future work.\n\n### Response to weakness 4:\n\nWe kindly disagree with the reviewer on this comment. Please refer to our response to the Common Question about technical contributions for a detailed explanation. Our primary goal is not to simply learn a smaller model with improved performance as in previous works, but to develop a learning-to-prune framework that automatically determines a balanced pruning ratio. This approach achieves an excellent compression ratio without compromising rendering quality, addressing a challenge that has not been previously tackled in the 3DGS community.\n\nThe overall training cost for our learning-to-prune methodology is significantly lower compared to prior manual pruning works, such as RadSplat, Mini-Splatting, and LightGaussian. Even when compared to Compact3D, our method, which uses a differentiable mask rather than a straight-through estimator (STE) binary mask, demonstrates better performance. Tables 4 and 5 present the ablation study that highlights this improvement.\n\n### Response to weakness 5:\n\nWe appreciate the comment. We will correct the image.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "mGp9NLE1d7", "reviewer": "Reviewer_CWFJ", "summary": "This work introduces LP-3DGS, aiming to compress 3DGS by replacing the previously manually set threshold with a learning-to-prune scheme.  In particular, LP-3DGS learns a binary mask to automatically prune 3DGS, where such a mask is regularized with the Gumbel-Sigmoid technique. Experiments on three benchmarks showcase the soundness of the introduced methods.", "questions": "Please kindly refer to the [Weaknesses].", "limitations": "Please kindly refer to the [Weaknesses].", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 1, "strengths": "* Applying Gumbel-Sigmoid to regularize the binary mask is reasonable.\n* Extensive experiments are conducted on several existing benchmarks.\n* The paper is well-structured and easy to follow.", "weaknesses": "* Limited technical contributions. This work seems to be a direct application of Gumbel-Sigmoid, which is a general engineering trick (https://github.com/AngelosNal/PyTorch-Gumbel-Sigmoid) to approximate discrete sampling in a differentiable manner. It needs to be clarified what the main technical insights this work aims to bring to the 3DGS compression community. To me, replacing the threshold setting with the Gumbel-Sigmoid is too intuitive to hit the standard of a top-tier conference.\n\n* It is difficult to know whether the learned binary mask achieves the “optimal Gaussian point size”. This work demonstrates that it learns the “optimal” solutions by plotting several line charts without any theoretical analysis. In some cases, LP-3DGS did not find the best balance, e.g., Fig. 4 Mini-Splatting on Kitchen. Besides, LP-3DGS seems to lose the flexibility of finding better solutions compared to its baseline, e.g., RadSplat can set a smaller ratio to compress further while maintaining reasonable visual quality.\n\n\n* Lack of discussions with some recent related works. Several more recent approaches in the 3DGS compression community need discussion, and it would be better to add some comparisons with them to understand the advantages of LP-3DGS better.\n  * Girish, Sharath, Kamal Gupta, and Abhinav Shrivastava. \"Eagles: Efficient accelerated 3d gaussians with lightweight encodings.\" arXiv:2312.04564.\n  * Lu, Tao, et al. \"Scaffold-gs: Structured 3d gaussians for view-adaptive rendering.\" CVPR2024.\n  * Chen, Yihang, et al. \"HAC: Hash-grid Assisted Context for 3D Gaussian Splatting Compression.\" arXiv:2403.14530.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### Response to weakness 1:\n\nPlease refer to the Common Question about the term \"contribution\" for more details.\n\n### Response to weakness 2:\n\nPlease refer to the Common Question about the term \"optimal\" pruning for more details.\n\n### Response to weakness 3:\n\nWe have comprehensively compared our method with two of the most recent and state-of-the-art (SoTA) 3DGS pruning works, namely RadSplat and Mini-Splatting. The experimental results are reported in Figure 4, Tables 1 and 2, and additional results in the appendix. We appreciate the reviewer’s comment and will include comparisons with the suggested works.\n\nEAGLES primarily modifies the hyperparameters of the densification stage of 3DGS to control the number of Gaussians, which differs from score-based pruning methods such as RadSplat, Mini-Splatting, and LightGaussian. Our method uses a learnable mask on the scores of Gaussian points, making it incompatible with EAGLES.\n\nScaffold-GS and HAC focus on encoding the attributes of 3DGS to compress the model, which is different from score-based pruning methods. These works use encoding methods rather than pruning, making them incompatible with our approach.\n\nWe will cite these works as references and discuss them in the manuscript.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "N1UhCCMRPx", "reviewer": "Reviewer_1UP2", "summary": "The paper proposed a pruning method for Gaussian Splatting training, which employ a learnable mask to find optimal pruning rate.", "questions": "Please see the \"weaknesses\".", "limitations": "No potential negative social impact.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The paper is well-written and the proposed method is easy to understand.", "weaknesses": "* The proposed method use a regularization loss to encourage the model to prune, so that the weight parameter is an important balancing factor. The discussion on how to set such parameter is missing.\n\n* Figure 2 is not clear enough for me to well understand the proposed idea. In Figure 3, why pattern like (b) is better than (a)?\n\n* Experiments section use existing works for comparison, but they are all self-implemented. The performance in their original paper should be included for reference.\n\n* The author claim the proposed method can find optimal pruning ratio. Based on my observation, the conclusion is not solid. First, what is definition of optimal? Second, not all the subfigures in Fig. 4 & 6 support this conclusion.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### Response to weakness 1:\n\nWe would like to emphasize that the main contribution of our work is not merely the use of a regularization loss to encourage the model to prune, but rather the development of a learning framework that can automatically learn a pruning ratio embedding during the training process of a 3DGS model. This is achieved through our proposed Gumbel-Sigmoid mask pruning technique (Equation 8) and our ensemble loss function (Equation 10), all with only one round of training. We kindly request that the reviewer refer to our summary of technical contributions in the Common Question.\n\nFor the setting of $\\lambda_{m}$, we used a value of 5e-4 in all the reported experimental results. We have further conducted an ablation study on this hyperparameter based on the Room scene, as detailed below.\n\n| $\\lambda_{m}$ | PSNR  | SSIM  | LPIPS | Pruning Ratio |\n|---------------|-------|-------|-------|---------------|\n| 3e-4          | 31.488| 0.9241| 0.2035| 73.15%        |\n| 5e-4          | 31.490| 0.9243| 0.2032| 73.78%        |\n| 7e-4          | 31.474| 0.9238| 0.2040| 75.91%        |\n\n$\\lambda_{m}$ have little impact on the final rendering quality.\n\n### Response to weakness 2:\n\nFigure 2 is based on the vanilla 3DGS, with our proposed pruning method highlighted within the green box. This box indicates that a mask is learned for each Gaussian to determine whether it should be pruned during the training process. The detailed technique described mathematically relates to Equations 7, 8, and 10.\n\nFor Figure 3, since the pruning process involves a binary decision (i.e., whether to prune or not prune), it is preferable for the learned mask distribution to naturally reflect a binary distribution—where values close to 0 indicate the Gaussian should be pruned, and values close to 1 indicate it should not be pruned.\n\n### Response to weakness 3:\n\nSince we need to report the training time for an apples-to-apples comparison, it is essential to use the same GPU hardware setup. We have open-sourced all our code and experimental results on GitHub for peer researchers to verify and benchmark.\n\nFor 3DGS and Mini-Splatting, we reported results using their open-source codes on our GPU hardware. Additionally, because RadSplat is not open-sourced, we re-implemented and benchmarked their method ourselves. It is important to note that all our self-implemented results are consistent with the rendering quality reported in the original papers. To further clarify, we have provided a comparison of the original paper results for 3DGS and our self-implemented results as follows:\n\n| Scene           | Bicycle | Bonsai | Counter | Kitchen | Room | Stump | Garden | Flowers | Treehill | **AVG** |\n|-----------------|---------|--------|---------|---------|------|-------|--------|---------|----------|---------|\n| **Original paper PSNR** | 25.246  | 31.980 | 28.700  | 30.317  | 30.632 | 26.550 | 27.410 | 21.520  | 22.490  | 27.205  |\n| **Self-Implemented PSNR**   | 25.087  | 32.262 | 29.079  | 31.581  | 31.500 | 26.655 | 27.254 | 21.348  | 22.561  | 27.480  |\n||\n| **Original paper SSIM** | 0.771   | 0.938  | 0.905   | 0.922   | 0.914 | 0.775 | 0.868  | 0.605   | 0.638   | 0.8151  |\n| **Self-Implemented SSIM**   | 0.7464  | 0.9460 | 0.9138  | 0.9320  | 0.9249 | 0.770 | 0.8557 | 0.5876  | 0.6358  | 0.8125  |\n||\n| **Original paper LPIPS** | 0.205   | 0.205  | 0.204   | 0.129   | 0.220 | 0.210 | 0.103  | 0.336   | 0.317   | 0.2143  |\n| **Self-Implemented LPIPS**   | 0.2441  | 0.1799 | 0.1839  | 0.1164  | 0.1978 | 0.2423 | 0.1224 | 0.3601  | 0.3469  | 0.2215  |\n\n\n### Response to weakness 4:\n\nPlease refer to the Common Question about the term \"optimal\" pruning for additional details.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
## Common question about the term "optimal" pruning (Reviewer o7SR and Reviewer 1UP2 )

We agree with Reviewer o7SR that the term "optimal" may be misleading. We will change it to "learned pruning ratio" and provide a more detailed definition in the updated manuscript. In the domain of 3DGS model pruning, the primary objective is to compress the model size as much as possible using a predefined importance factor, without significantly affecting rendering image quality, which involves a trade-off process.

As demonstrated in Figure 4, which shows the rendering quality versus pruning ratio, a small pruning ratio typically does not hamper rendering quality due to model redundancy. However, a very large pruning ratio will significantly degrade the rendering quality. There exists a small region that can achieve a relatively large pruning ratio with almost no or slightly degraded rendering quality, which is the optimal or more balanced pruning ratio range we aim to target.

In all existing works on 3DGS model pruning, the optimal or final reported balanced pruning ratio is usually determined empirically by manually sweeping the pruning ratio from low to high (e.g., 0.1 to 0.9). Each predefined pruning ratio sweep point requires one round of model training, necessitating multiple rounds of pruning-aware training to optimize or balance the compression (i.e., pruning) ratio and rendering quality.

In contrast, our proposed methodology can automatically learn a pruning ratio embedding during the training process of the 3DGS model through our proposed Gumbel-sigmoid mask pruning technique and ensemble loss function (Equation 10), with only one round of training. The experiments in Figure 4 and other reported tables clearly show that our method consistently learns an equivalent or even better pruning ratio compared to manual tuning in existing works.

## Common question about technical contributions (Reviewer fvLt and Reviewer CWFJ)

As discussed in the previous common question, identifying the optimal or balanced pruning ratio in prior works is both compute- and time-consuming. We would like to highlight that the main contribution of our work is not merely the adoption of the Gumbel-sigmoid to prune 3DGS models, but rather the development of a learning framework that can automatically learn a pruning ratio embedding during the training process of a 3DGS model. This is achieved through our proposed Gumbel-sigmoid mask pruning technique (Equation 8) and ensemble loss function (Equation 10), all with only one round of training.

Specifically, to distinguish our approach from prior pruning works in 3DGS, the advantages of the proposed method are:

* Highly Efficient: Identifying balanced pruning ratio candidates from 0.1 to 0.9 with a 0.1 sweeping resolution typically requires 9 rounds of training. In contrast, our proposed method requires only one training round, reducing the overall training cost by up to 9x.

* General: Our proposed Gumbel-sigmoid mask pruning technique can be applied to a general importance score (e.g., opacity, or any other importance score indicating the importance of Gaussian) as defined in Equation 8. This means it is orthogonal and compatible with the pruning criteria defined in prior and potentially future 3DGS model pruning works.

* Effective: Our experimental results strongly demonstrate that our proposed learning-to-prune method successfully learns a pruning ratio that is always within the balanced pruning range, maintaining a good trade-off between compression ratio and rendering quality compared to existing works.

Meta-review: This paper received mixed scores (two Weak Accepts, Borderline Reject, and Borderline Accept) from 4 reviewers. Three reviewers (o7SR, fvLt, 1UP2) are mainly satisfied with the responses from the authors during the rebuttal phrase. Reviewer CWFJ initially suggests Borderline Reject and has concerns in technical contribution, optimal Gaussian point size, and discussion with existing works. During the rebuttal phase, the reviewer did not response. These concerns are shared by other reviewers and are believed that they are clarified. The AC agrees with the majority of reviewers that the work can be accepted. The authors are encouraged to include these important clarifications into the final paper when preparing the camera ready version.
Decision: Accept (poster)