A Step to Decouple Optimization in 3DGS
Authors: Renjie Ding
Yaonan Wang
Min Liu
Jialin Zhu
Jiazheng Wang
Jiahao Zhao
Wenting Shen
Feixiang He
Xiang Chen
Venue: ICLR 2026 Poster (2026)
Keywords: 3DGS
optimizer
regularization
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: 3D Gaussian Splatting (3DGS) has emerged as a powerful technique for real-time novel view synthesis. As an explicit representation optimized through gradient propagation among primitives, optimization widely accepted in deep neural networks (DNNs) is actually adopted in 3DGS, such  as synchronous weight updating and Adam with the adaptive gradient. However, considering the physical significance and specific design in 3DGS, there are two overlooked details in the optimization of 3DGS: (i) update step coupling, which induces optimizer state rescaling and costly attribute updates outside the viewpoints, and (ii) gradient coupling in the moment, which may lead to under- or over-effective regularization. Nevertheless, such a complex coupling is under-explored. After revisiting the optimization of 3DGS, we take a step to decouple it and recompose the process into: Sparse Adam, Re-State Regularization and Decoupled Attribute Regularization. Taking a large number of experiments under the 3DGS and 3DGS-MCMC frameworks, our work provides a deeper understanding of these components. Finally, based on the empirical analysis, we re-design the optimization and propose AdamW-GS by re-coupling the beneficial components, under which better optimization efficiency and representation effectiveness are achieved simultaneously.

Published as a conference paper at ICLR 2026
A STEP TO DECOUPLE OPTIMIZATION IN 3DGS
Renjie Ding',
Yaonan Wang
Min Liu'
Jialin Zhu Xiang Chen'
Jiazheng Wang'
Jiahao Zhao'
Wenting Shen
Feixiang He
National Engineering Research Center of Robot Visual Perception and Control Technology, School of Artificial Intelligence and Robitics, Hunan University 2 Baidu Inc., 3 Central South University
fregi, yaonan, liu.min wea.minnehnu.c edu. cn, mi salssaleeett wal.ee@@outook.cco com (wjiazheng, zhaojiahao, wenting) edu. en drfxhe@gmail il com, xiangcehnu.edu.co
https://eliottd gi thub. 1 adamwgs/
ABSTRACT
3D Gaussian Splatting (3DGS) has emerged as powerful technique for real-time novel view synthesis. As an explicit representation optimized through gradient propagation among primitives, optimization widely accepted in deep neural net- works (DNNs) is actually adopted in 3DGS, such as synchronous weight updating and Adam with the adaptive gradient. However, considering the physical signif- icance and specific design in 3DGS, there are two overlooked details in the opti- mization of 3DGS: (i) update step coupling, which induces optimizer state rescal- ing and costly attribute updates outside the viewpoints, and (ii) gradient coupling in the moment, which may lead to under- or ofer-effective regularization. Never- theless, such a complex coupling is under-explored. After revisiting the optimiza- tion of 3DGS, we take step to decouple it and recompose the process into: Sparse Adam, Re-State Regularization and Decoupled Attribute Regularization. Taking a large number of experiments under the 3DGS and 3DGS-MCMC frameworks, our work provides a deeper understanding of these components. Finally, based on the empirical analysis, we re-design the optimization and propose Adam W-GS by re-coupling the beneficial components, under which better optimization efficiency and representation effectiveness are achieved simultaneously.
INTRODUCTION
Novel view synthesis is a fundamental task in both computer graphics and computer vision. Ow- ing to its highly parallelized design and efficient of GPU, 3DGS (Kerbl et al., 2023) leverages explicit primitive-based representations to achieve significantly higher efficiency than implicit rep- resentation NeRF (Mildenhall et al., 2020), while still delivering competitive reconstruction quality. 3DGS sparks a wave of research and rapid extensions to various downstream applications (Matsuki al., 2024; Chen et al., 2024; Dai al., 2024).
As representation directly optimized via backpropagation, 3DGS inherits the Adam (Kinga et al., 2015) from DNNs, and in default attributes of all primitives are updated simultaneously within each iteration, which we call synchronous optimization in this work. Given the viewpoint relationship, an idcal scenario is that the optimization of primitives is guided by gradients from visible viewpoints in different directions. However, upon closer examination, invisible under a given viewpoint and their gradients are set to zero, the update-step coupling in- duced by Adam and synchronous optimization implicitly rescales the optimizer state and causes updating in these invisible viewpoints. From the perspective of optimization efficiency, (Mallick al., 2024) introduces Sparse Adam, which restricts updates to primitives visible under viewpoints while filtering out those invisible with zero gradients, thereby enabling asynchronous optimization. Nevertheless, this optimizer has not been widely adopted, since its efficiency gains come the ex-
observe that even when primitives are
"Corresponding authors.

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Published as a conference paper at ICLR 2026
pense of degraded performance. However, we think that such viewpoint- relatee optimizer remains promising, with the current limitation lying in the insufficient recognition of update-step coupling.
Furthermore. previous study (Loshchilov & Hutter, 2017) in DNNs points out the gradient coupling in Adam makes the regularization unstable. In current 3DGS, a variety of regularization losses (Yu et al., 2024) are introduced to improve reconstruction quality or mitigate redundancy'. With limited regularization intensity controlled via adaptive gradients and decoupled from the photometric loss, natural question arises as to whether existing regularization is appropriately effective. In practice, the regularization loss is thought to be controlled through hyperparameters, yet it remains unclear whether they provide sufficient flexibility. Moreover, can further decoupling enable more precise control over regularization itself? In this work, we focus on opacity and scaling regularization, which are closely tied to reconstruction quality in the 3DGS-MCMC framework (Kheradmand et al., 2024) and redundancy removal in the vanilla 3DGS framework (Papantonakis et al., 2024). Prior studies have shown that the densification stage often produces a large number of redundant primitives (Liu et al., 2025b), while the framework lacks native mechanism to automatically remove them. Even with opacity regularization, existing pipelines usually rely on additional pruning operations or direct modifications to the densification process. However, if regularization can be well recomposed, is it possible to achieve redundancy removal without resorting to such extra pruning operations?
Considering the coupling in 3DGS optimization, this work takes step to decouple it and recom- pose it. Building on the analysis, the optimization is then redesigned to improve efficiency and/or reconstruction quality. To summarize, our contributions are:
Reanalyzing the complex coupling during 3DGS optimization, we take a step to decouple it and recompose it into 3 effective components: Sparse Adam, Re-State Regularization and Decoupled Autribute Regularization.
We take a step to explore the contribution of them, including the characteristic of Sparse Adam, activation of regularization, role of the regularization hyperparameter, risk of implicit update and necessity of controllable regularization as well as exploration.
Based on the experiments and analysis, we propose the AdamW-Gr with controllable attribute regularization and adopt it into vanilla 3DGS, 3DGS-MCMC and more variants. Experiments show that our optimization method yields better reconstruction quality and optimization efficiency, and significantly reduces redundancy in 3DGS without introducing additional pruning operations.
2 RELATED WORK
"Coupling" in 3DGS Optimization: 3DGS commonly inherits the Adam optimizer from DNNs. However, its synchronous optimization causes primitives in invisible viewpoints to undergo over- looked update steps. Sparse Adam (Mallick et al., 2024) introduces asynchronous updates that improve efficiency, yet the insufficient recognition of update-step coupling results in degraded per- formance. Regularization in 3DGS is also coupled with the photometric loss, akin to L2 weight regu- larization in adaptive gradient algorithms for DNNs. As analyzed in AdamW (Loshchilov & Hutter, 2017), the coupling of adaptive gradients in Adam makes the effective strength of regularization governed by the second moment, thereby motivating weight decay decoupling. A similar idea is flected in (Rota Buld et al., 2025), which-though not explicitly designed for decoupling-ree repplces opacity reset in vanilla 3DGS with a constant opacity decay during densification, effectively con- structing an Adam w-syle optimizer. Nevertheless, this approach neglects the physical properties of opacity and the varying significance of individual primitives. The central contribution of this work is to further decouple and recompose 3DGS optimization and, through this process, reinterpret redundancy in 3DGS and reconstruction quality
from an optimization perspective.
Redundancy during Optimization: Typically, 3DGS requires careful treatment of the special pro- cess of primitive generation and pruning (or death (Kheradmand et al., 2024; Zhu et al., 2025)). Current studies generally observe that optimization produces abundant redundant primitives, while pruning (in adaptive density control (Kerbl et al., 2023)) alone remains insufficient to eliminate them. Four main strategies have been proposed to address this redundancy: (1) Densification refinement (Fang& & Wang, 2024; Mallick et al., 2024; Wang et al., 2025); (2) Hand-crafted criterion (Fan et al., 2024; Niemeyer et al., 2025; Hanson al., 2025); (3) Learning- based pruning (Lee et al., 2024; Liu
R RRedundancy is strictly defined as minimizing active primitives without sacrificing reconstruction quality.
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et al., 2025b; Zhang et al., 2024a). More details can be found in Sec. H. (4) Optimization- operations: Optimization together with additional opacity LI regularization has become a common technique for redundancy removal, even extending beyond Efficient 3DGS tasks (Papantonakis et al., 2024; Lee et al., 2024; Kheradmand et al., 2024; Liu et al., 2025a; Svitov et al., 2024).
3 PRELIMINARY: 3DGS(-MCMC) AND ADAM
3DGS approximates the radiance field of a target scene using a set of Gaussian primitives param- eterized by location, opacity (o), scale (s), and other attributes, and renders images from given viewpoints via alpha blending. Further details are provided Appendix Sec. D.
Typically, the training pipeline can be divided into densification and pure optimization (P-Op). During densification, new primitives are generated to enhance scene representation while redundant ones are pruned (low-opacity primitives are removed) (Kerbl et al., 2023), or new primitives sam- pled from existing primitives while dead primitives are reallocated to new locations (Kheradmand et al., 2024). After densification, there is P-Op stage, during which only gradient propagation and attribute updates occur. In this training pipeline, photometric loss (left in Eq. 1) is adopted with Adam optimizer. For 3DGS-MCMC, extra regularization loss in Eq. is utilized to promote respawning.
X1 + CDSSSS + Aolo/1 + 1,
photometric loss: é
regularization loss:R
In this work, & and R denote photometric loss and any regularization, while Vł and VR are the corresponding gradient.
Adam is the first-order stochastic optimization method that adaptively estimates moment statistics of the gradients. Specifically, it maintains exponential moving averages of the first moment m m()),
and second moment v()).. which are bias-corrected to m0(),, and 6(0).. The parameter update is then performed as Eq.3, where 1) denotes the learning rate and ensures numerical stability.
m(f): 31 m -1 + (1 B1) x g(0)c v()), B2 v0)). + (1 (2) x g
(2)
m()),
0++1 = 0: - X
(3)
00(0).+ +
We omit the expression of bias correction procedure; in this paper, and g denote the primitive attribute in 0 and gradient information respectively.
Consistent with the DNNs(Goodfellow et al., 2016), Adam by default updates all attributes syn- chronously, including both the primitives visible under the current viewpoint and those that not. In spite the 0 gradient, they are still included the update step, during which their moment are rescaled and attributes are still updated. In this paper, updates of points in invisible viewpoints are referred to as Implicit Update, which are influenced by the previous moment.
4 METHODOL.OGY
4.1 CHARACTERISTICS OF SPARSE ADAM
Table 1: Quantitative results in MipN-
As discussed in 1ec.1, using Sparse Adam directly im- proves the optimization efficiency but causes degraded performance. Denoted V as filter that takes the value 1 only for primitives visible under the current viewpoint and for others, Sparse Adam can be obtained by replac- ing 9 in Eq. 2 via:
erf360 of 3DGS with different optimiz- ers. The definition of the metrics can be found in Sec.5. (m: million)
Cite PSNR SSIM I.PIPS N,.m Nu/m
GSI 27.507 0.815 0.216 3.331
0.232
27.285 0.809
0.228
2.532
0.039
GS3 27.567 0.816 0.216
3.342 0.048
8 = - (1-1)
(4)
However, from the perspective of viewpoit updates, Sparse Adam is effectively viewpoint- stable: the update of primitives influenced only by steps in visible viewpoints at the moment and does not undergo implicit updates in invisible viewpoints.
To conduct a preliminary investigation, three experiments were performed on vanilla 3DGS: (GSI) training with the original Adam optimizer, (GS2) replacing Adam with Sparse Adam, and (GS3)
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Figure The vo(o) in 3DGS- with the different optimizer. More examples can be found in Appendix Figure 5, b: the opacity regularization decisive term in EDGS-MCME with the different optimizer. c-d: The average and max magnitude of m(o)/ (loo//v(o) vv(o) in every iteration.
employing Adam during the densification stage while applying Sparse Adam in the P-Op stage. Based on these comparisons Table 1, we make the following observations: Observation Sparse Adam is more stable: Since densification is governed by gradient magnitudes, the smaller number of primitives observed under Sparse Adam suggests that more primitives fail to meet the gradient threshold. Moreover, Sparse Adam holds on more active primitives, especially the GS3 Table (0.048 million dead primitives in Sparse Adam v.s. 0.232 million in Adam), which implies com- ponents in Adam are potential for pruning redundant primitives. Observation Sparse Adam is less explorative: although it quickly drives primitives toward stability and results in fewer primi- tives overall, its performance degrades noticeably. Experiments on 3DGS-MCME show the similar observation in some scenes that Sparse Adam makes smaller reallocated primitive number, and this phenomenon can be found Figure f.
4.2 UPDATE-STEP DECOUPLING: RE-STATE REGULARIZATION
The key question is what components differentiate Adam from Sparse Adam. To answer this, revisit synchronous optimization with Adam introduced in Sec.3. The ignored update-step coupling arises zero-gradee grro-gradient updates rescale the moment (m(#), 33 (m) (-) v(0), subsequently induce implicit update based on the rescaled moment. This first implies that the op- timizer state of primitives in invisible viewpoints continues change. As visualized in Figure a, the second moment in 3DGS-MCMC with Adam is notably smaller than with Sparse Adam, sug- gesting potential amplification the first moment. To verify this, we compare the effective strength of opacity regularization in Figure b, Vol V o(o), and observe that Adam induces stronger reg- ularization, consistent with our discussion in Sec. 4.1. The moment rescaling helps regularization activation. The comparison Figure 1 also shows that the magnitude remains consistently high for Sparse Adam, underscoring the importance of moment rescaling; when inappropriate gradients accumulate one view, they are difficult to dissipate, thereby hindering optimization. The role of implicit updates is direct: in invisible viewpoints, primitives are continuously updated based on the past moment. However, no prior work has explicitly examined the impact of these components on optimization. Motivated by this, construct decoupled variants for Sparse Adam.
= (0))() and
The implementation moment rescaling is straightforward. define an optimization interval and, proposing milestone style State Sampling Schedule (StSS), uniformly sample the current primi- tives at the fixed interval. The sampled primitives are directly processed as in Eq. 5 to deliberately attenuate the state. This process is referred Re-State Regularization (RSR).
m(0) new = =0 X m())
v(0) =2 x v(0).ld
0 a1 < 1, 0 a2 <
(5)
Here, the subscript follows asynchronous mode different from synchronous mode in Eq.2, meaning that each primitive has its own distinct t. detailed hyperparameters discussion in Sec. J.2.
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Figure 2: a-d: The primitive number change during training in 4 methods (Vanilla 3DGS, Redundant Primitivs Removal/RePR, MaskGaussian and 3DGS with Our proposed AdamW-GS). illustrates the iteration ranges over which different components affect the primitives number.
We also construct an implicit update study its role. While implicit updates can be beneficial in some cases, they may introduce negative effects, potentially linked to redundancy (see Appendix Sec. 1.4). In the experiment section of the mainbody, we retain implicit updates only as a tool to amplify attribute regularization under Sparse Adam to study the influence of regularization: when (VR( /N, Eq. is large, maintaining implicit updates further strengthens regularization. Con- cretely, our Artificial Implicit Update (AIU) is defined as uniform sampler that selects a random subset of invisible primitives for extra updates, while their moments remain unchanged in invisible viewpoints in Sparse Adam.
VE(O) AVR(O), +
m(0), = m()) + 31)(
(6)
Nr
N.
where the N₂ and the No are the scale of image pixel and the primitive number at the present viewpoint respectively, decided by the code project'.
4.3 GRADIENT DECOUPLING: DECOUPLED ATTRIBUTE REGULARIZATION
We view attribute regularization an essential component of optimization. In efficient 3DGS and related tasks, the widely-used opacity LI regularization exemplifies this idea, analogous to weight regularization in DNNs, though with a different role. As discussed in Sec. 3, our understanding of how regularization effectively constrains each primitive remains limited. Implicit updates may further exaggerate the effect of regularization: when XVR(0)) in Eq. 6 approaches or exceeds V((0)/N, the regularization term continues to influence the optimization via the adaptive gradient or implicit updates. The coupling of photometric and regularization losses in Eq. 6 therefore raises a natural question: is the current regularization over- or umder-effective?
First, we return to the factors actually govern the effect of the current attribute regularization loss (L1 loss with the gradient coupling). The role of the hyperparametens serves to maintain stability between losses, ensuring that the regularization remains relatively small critical moments without interfering with the photometric loss. Relevant results are presented in Appendix Sec. I.1. Regarding the modulation by the moment, the regularization is activated when (V)( N₂ takes the majority or the moment is rescaled during synchronous optimization in Adam or reset in 3DGS-MCMC
VE(0) N
VE(O), N
(0)) 81 m00) + 3
v00) = B, x (1-
)² (7)
Using Sparse Adam or Adam in 3DGS-MCMC clearly alters the effect of attribute regularization. As illustrated in Figure 3 e-f, different optimizers yield different numbers of reallocated primitives
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and PSNR, indicating over- under-effective regularization. This suggests that stronger regulariza- tion may be required to improve reconstruction quality in some cases. However, due to the gradient coupling in the moment (Eq. 6), directly amplifying VR easily leads to update steps that become overly atrribute-dependent and less guided by the photometric gradient, while the coupling also sus- tains the effect of regularization across iterations. In extreme cases, such as when hyperparameters are scaled by 10x, optimization fails entirely. When amplification relies on the second moment, the effect of regularization depends on its relative scale Vt. Furthermore, if VR aligns with Ve, the second moment grows rapidly; if they are opposed, it grows slowly, which is contrary to expectations. This coupling prevents effective control of regularization. As shown in Figure 1 c,d, gap between average and maximum mío)/ / (o)) further illustrates that
the wuder-of-magnittee improper amplification under coupling easily results in over-effective regularization. Decoupling Vl and VR and recomposing the regularization enables more reliable control without destabilizing optimization. Further empirical experiments in Sec. 5 will show the side effect of coupling as well.
Therefore, the first step is to decouple the gradients in the moment (Eq, 6). This step is the same as AdamW, and readily yields Eq. 7. which defines the moment update term containing only the gradi- ent of the photometric loss Vl. For (R(@). Adam W constructs updates that are not controlled by the second moment. This AdamW-style decoupling is effectively equivalent to constant penalty on opacity (Rota Buld et al., 2025). The experiments are presented in Sec. 1.2. Clearly, this approach is not optimal. Unlike DNNs, each attribute in 3DGS has physical meaning, and each primitive car- ries distinct importance. Penalizing all primitives with the same strength fails to remove redundant primitives when the penalty is too weak, while overly strong penalties hinder optimization.
Adam Adam W-style decoupling suggests that effective regularization assigns different penalties to differ- ent primitives. Such assignment, however, cannot be arbitrary: (i) it must not interfere with normal optimization, particularly in under-construcct function of suppressing overfitting when Vi small (Srivastava et al., 201 4). This implies that regu- larization should adapt to the geometry of the data (Pascanu & Bengio, 2013), naturally linking back to adaptive gradient (Duchi et al., 201 1; Kinga et al., 2015) where adjustments are made via /e. The empirical success of vanilla regularization over the constant penalty further highlights its potential. Since we have already disentangled the moment in Eq. 7, vō now provides more faithful estimate of the parameter space. Motivated by this, we introduce the regularization form VR/Vē (Vū is from Eq. 7). This design brings 4 benefits: (I) updates are preserved in under-constructed regions with large Ve; (2) when a primitive lies near saddle point (small V regularization facilitates cape, consistent with saddle point analyses in (Wang et al., 2025) and long-ax primitive gradients in (Zhang et al., 2024b); (3) regularization remains small in general but amplifies adaptively when it becomes influential; and (4) it enables explicit control over regularization via moment modulation, e.g., through RSR. Building on this rationale, we extend this approach and propose Eq.
regions (Vl is large); (ii) it must still fulfill its core
m(0) /6(0) +E + min(Ap VR(OY/N,
04+1 02 - 1 x
7000%+ C+)
We maintain the loss balance through Ao and normalize the regularization scale by N,. Regulariza- tion aligned with /o(0y, improves stability while removing dependence on primitive number, which can vary by orders of magnitude across training, views, and scenes. C. keeps on the same order as maximum step size of Adam, matches the maximum observed in Figure 1 c-d, and extensive results confirm its robustness. Then, this recomposed regularization is referred to as Decoupled Attribute Regularization (DAR). We provide detailed hyperparameter selection in Appendix Sec. J.2.
4.4 RECOUPLING: ADAMW-GS
Building on Sec. 4.1, 4.2, and 4.3, we propose Adam for better 3DGS optimization by recou- pling Sparse Adam, RSR, and DAR. In detail, attributes of primitives are optimized asynchronously with Sparse Adam and supervised via photometric loss and DAR. At fixed training intervals, RSR uniformly samples primitives and rescales their moments via Eq. 5 to better activate regularization. The rescaled moment replaces the old one and directly participates in subsequent optimization.
We consider two DAR variants variants-opacity and scaling regularization both of which are already employed in 3DGS-MCMC Considering the bad transportation in vanilla 3DGS (Jung et al., 2024), exploration in this work means better primitive movement. We directly use noise regularization in

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Figure 3: a-d: Reconstruction results visualization. More can be found in Appendix Sec. e-f: The Reallocated Primitive Number in 3DGS-MCME Framework. For outdoor scenes, MC17 and MC8 differ only in the StSS sampling ratio, where RSR. For indoor scenes, MC8 uses StSSMCI, More information can be checked in Table 2.
MGGS-MCMC'RR as an extra position regularization, which is similar DAR, but controlled by opacity and primitive shape not the second moment. However considering the sensitivity to noise (Jung et al., 2024), the noise excluded for MipNerf360 indoors scenes with fewer primitives. To explore the effectiveness of exploration, et al., 2023). Opacity reset encourages exploration via lowering the opacity. Opacity Correction is adopted for cloning in densification as well, which is thought to be necessary (Kheradmand al., 2024). We adopt the similar operations for opacity as (Rota Bulò et al., 2025).
provide contrast experiments with without opacity reset(Kerbl
5 EXPERIMENTS
Dataset and Metric Following existing research (Kerbl et al., 2023), we employ 13 scenes from datasets, including scenes Mip-Nerf360 (Barron et al., 2022), scenes from the Tanks&Temples dataset (Knapitsch et al., 2017) and 2 scenes provided by Hedman et al. (Hedman et al., 2018).
We use a train/test split for datasets, using the methodology suggested by Mip-NeRF360, taking every 8th photo for test, for consistent and meaningful comparisons to generate the error metrics, using the standard PSNR, SSIM, and L-PIPS(vVg) metrics used most frequently in the literature. We also present the total primitive number Np. the active primitives number Na and the dead primitives number Na. Given the significant variation in primitive number across methods (often differing by
Neunille where E {a, (. d)) to better illustrate primitive number variations. The active/dead primitive is defined by opacity larger than 1/255 not. This definition follows the underlying 3DGS implementation, where primitives with opacity below 1/255 are excluded from rendering, differing from (Kheradmand et al., 2024).
millions), we employ normalized changes to the vanilla (AN, N, Vy-Naanull
To evaluate the impact of different components the training pipeline, conduct tensive experiments on both the vanilla 3DGS and 3DGS-MCMC frameworks. These two baselines respectively represent approaches without or with an N₂ maximum. Without explicitly introducing pruning operations, we observe that substantial number of redundant primitives can be automati- cally removed under the vanilla 3DGS with AdamW-GS. For comparison, we include two adaptive pruning methods, baaning-based MaskGaussian (Liu et al., 2025b) and Redundant Primitive Re- moval (RePR) (Papantonakis et al., 2024) with hand-crafted criterion. Unlike approaches with a predefined pruning rate, these methods automatically identify redundant primitives and claim to achieve this with negligible performance degradation. All methods are run on a single A6000 GPU.
Baselines

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Table 2: Quantitative results in MipNerf-360 with different components. Detailed descriptions of Sparse Adam, AIU/RSR, and DAR are provided in Sec. 4.1, Sec. 4.2, and Sec. 4.3, respectively. All RSR and DAR settings remain fixed across experiments, except for the StSS schedule. The SISS sampling ratios used in this table are follows: for outdoor scenes, MC8 (StSSMC3) > MC7 (StSSMC2) > others (StSSMCI), while for indoor scenes, MC8 = MC7 = others (SISSMCI). The complete StSS schedules for each configuration are illustrated in Figure 9. Appendix Sec. K provides per-scene experimental results, including detailed configurations and additional experiments with a broader range of settings.
Ciie
Sparse Adam
AIU
RSR
R.
R2
PSNR
SSIM
LPIPS
AN
N,,/m
MCI
1.1
27.948
0.833
0.199
-3.75%
3,313
MC2
L1
27.998
0.832
0.199
+4.28%
3.313
MC3
L1
28.050
0.833
0.198
+3.62%
3.313
MC4
V
28.017
0,834
0.191
+0.51%
3.313
3DGS MCMC
MC19
V
28.075
0.837
0.190
+2.97%
3.313
DAR
DAR
0.839
0.182
+4.72%
DAR
DAR
0.182
+4.52%
5.1 RESULTS AND ANALYSIS
Over- or Under-Effective Regularization To examine the controllability of regularization, we in- troduce AIU during densification as direct tool to amplify its effect. Its role is straightforward: when the moment of a primitive places it under regularization, AIU preserves its update, yielding more dead primitives and thus making stronger regularization. Figure 3 e-f visualizes the reallocated primitives change in 3DGS-M MCMM with AIU, Enhanced regularization promotes exploration and improves reconstruction quality in some cases (MC3 and MC4 in Table 2), but the effeet is scene- dependent. For instance, in Kitchen (shown in Figure 3 f), rapid growth of reallocated primitives degrades performance. This suggests that regularization can be under-effective in some scenes, requiring amplification (e.g., via AIU or other methods), but also over-effective when its strength is excessive or inapposite.
Activated via the Moment Within the 3DGS-MCMC framework, we evaluate the effect of our proposed RSR on regularization, way of activating regularization via rescaling the moment. Re- gardless of the original L1 form subject to gradient coupling or our proposed DAR, attribute regu- larization remains tied the second moment. Figure c-f shows that applying RSR substamtially increases the number of dead primitives, thereby strengthening attribute regularization. This di- rectly demonstrates the effectiveness of RSR as component to amplify regularization. However, as highlighted by the comparison between MCMC-Sparse-RRS RSSR and CCCMC-AdamWGS--- Figure e, the influence of RSR with same SISS is weaker under LI regularization with gradient coupling than under DAR. By decoupling the gradient in the moment and recomposing the attribute regularization, RSR more effectively amplifies its impact, which also translates into improved re- construction quality under stronger regularization.
in
Side Effect in Coupling To further examine this effect, we increase the sampling ratio of RSR in MidNeRF-360 indoor scenes (which typically involve fewer primitives), with results summarized in Appendix, from Sec. K.6 to Sec. K.9, MC20 and MC21, in which we replace the low-ratio StSSMC1 in original 3DGSMCMC with LI regularization and 3DGSMCMC with our proposed AdamW-GS with higher-ratio StSSMC2. As the sampling ratio increases, original 3DGS-MCMC with LI reg- ularization exhibits significant drops reconstruction quality across all four scenes (e.g., Room: 22.514-31.179 dB; Kitchen: 32.289-33.997 -3.994 dB). The same phenomenon is also observed in the experiments on outdoor scenes. In contrast, EDGS-MCMS in Room, Counter, and Bosai, and only minor drop in Kitchen 122.54-+32.222 tently outperforming I.1 regularization under the same settings. These results confirm that coupling hinders effective control of regularization and can easily introduce negative effects on reconstruc- tion quality. Thus, decoupling the gradient from the moment and recomposing regularization is necessary for stable and effective optimization.
with DAR shows little to no degradation
dB), while consis-
Experiments with RSR also highlight the issue of over- or under-effective regularization. For scenes with more primitives, such as MipNeRF360 outdoor datasets, we adopt higher sampling ratio in RSR. As the sampling ratio increases, the number of reallocated primitives grows further (Fig- ure e), strengthening regularization and enhancing the exploration ability of 3DGS-MCMC. A
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Table 3: Quantitative results in MipNerf360 of different methods. MC8 and GS8/GS7 denote our proposed AdamW-GS variants. More information of MC8 is provided in Table 2. All variants share the same hyperparameters except for the StSS schedule. Following the design used in 3DGS- MCMC, outdoor scenes for vanilla 3DGS use high-ratio StSS, while indoor scenes use low- ratio SISS. As discussed in Sec. 4.4, GS7 is the noise without opacity reset version to study the effectiveness of exploration. A per-scene organization of results, including detailed configurations and additional experiments, is presented in Sec. K.
All
Outdrar
Indoor
Methods
PSNR1
SSIM|
I.PISS)
AN,
time/mins.
PSNRT
SSIM1
I.PISS]
A.N.
PSNR1
SSIM1
I.PISS..
A.N.
Original MCMC
27.948
0.833
0.199
-3.75%
25.105
0.755
0.212
-.38%
31,502
0.930
0.182
-2.97%
28.219
0.840
0.182
+4.52%
39.77
25.247
0.764
0.191
+3.07%
31,934
0.935
0.172
+6.33%
vanilla 3DGS
27.506
0.815
0,216
(3.098m)
30.58
24.648
0.728
0.239
(4)512m)
31,080
0.925
0.189
(1.331m)
(ddaWW-GS(GSB)
27.678
0.822
0,220
.4..3%
18.53
24.854
0.740
0.243
-48.4%
31.209
0.925
0.191
-504%
27.730
0.820
0.222
46.9%
19.18
24.949
0.737
0.248
44.0%
RePR
27.503
0.815
0.218
-1111%
26,73
24.661
0.728
0.241
-41.5%
31.055
0.924
0.190
-40.6%
MaskGaussia
27.485
0.815
0.219
-53.1%
26.80
24,683
0.728
0.240
.46.4%
30.988
0.924
0.192
-61.5%
direct comparison between MC7 and MC8 shows that higher sampling ratios improve reconstruc- tion quality. This further demonstrates the effectiveness of RSR to control regularization.
AdamW-GS in 3DGS-MCMC With properly tuned hyperparameters, we evaluate our proposed AdamW-GS within the EDGS-MCME framework. As shown in Table 3, our approach achieves su- perior PSNR, SSIM, and LPIPS over vanilla 3CGS-MCMC. By decoupling gradient coupling and recomposing regularization, we obtain more stable regularization; and by decoupling update-step coupling, our proposed RSR provides finer control of regularization. Furthermore, eliminating nu- merous ineffective zero- graddgradeent updates via Sparse Adam improves overall optimization efficiency.
Robust Hyperparameter Test and Autonomously Redundancy Removal Given that AdamW- GS, equipped with DAR and RSR, introduces many hyperparameters, we test their robustness by directly applying the method to vanilla 3DGS with same hyperparameters. Following the training division of vanilla 3DGS, we design several StSS configurations, as shown in Figure 9, Similar to our observations in 3DGS-MCMC with AdamW-GS, where moment rescaling and opacity DAR encourage large number of dead primitives for exploration, our experiments show that with our proposed Adam AdS, a large number of redundant primitives can be autonomously removed for 3DGS without extra pruning components, and the improvement in reconstruction quality also indi- cates enhanced exploration (Observation 2 issue in Sparse Adam in Sec.4. 1).
We compare vanilla 3DGS trained with Adam M-SS against two adaptive pruning methods. Im- portantly, our approach contains no extra pruning component; instead, relies solely on opacity DAR. In terms of pruning performance, AdamW-GS achieves results comparable to MaskGaussian and even outperforms it by 2% on outdoor scenes. Beyond pruning efficiency, our method also improves reconstruction quality: in outdoor scenes, it reduces the number of primitives by 48.4% while increasing PSNR by 0.2 dB and SSIM by 0.01. In indoor scenes, it removes 50% of primitives while still improving PSNR by 0.1 dB. By contrast, MaskGaussian removes 61% of primitives but degrades PSNR by 0. dB, which is because MaskGaussian suffers from potential reconstruction quality risk (see Figure 2 c). Visualization in Figure 3 c-d also demonstrates better detail recon- struction in our methods compared to vanilla 3DGS, which is one of the reasons for relatively more primitives than MaskGaussian. Ultimately, our objective not simply minimize the number of active primitives, but to strike preferable balance achieving higher reconstruction quality with as few primitives as necessary.
Table 4: Quantitative results in Deep Blending and Tank & Temples (m: million.)
Additional datasets are also evaluated with our proposed method. As shown in Table 4, experiments on Deep Blend- ing and Tanks&Temples further demon- strate the superiority of our approach. On Deep Blending in particular, 3DGS equipped with AdamW-GS passes the PSNR of the original 3DGS-
Deep blending
Tank Temples
PSNR SSIM LPIPS A PSNR
SSIM
LPIPS
A
3DGSMCMC
30.089
0.914
0.239
.24%
24.563
0.869
0.0
-3.1%
AdamW-GG
30.417
0.916
0.228
2.8%
24.726
0.875
0.150
6.7%
3DGS
29.694
0.904
0.247
2.60m
23.677
0.848
0.178
1.60m
+AdamW-GS 30,260
0.912
0.245
40%
24.303
0.855
0.181
-40%
sur-
MaskGaussian 29.895
0.908
0.248
65%
23.607
0.846
0.181
-50%
MCMC. In Appendix Sec. E.4, we also report results long-sequence datasets for vanilla 3DGS
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and EDGS-MCME both with and without our proposed AdamW-GS, where method continues
to show clear advantages.
Table 5: Quantitative results for MaskGaussian.
To further validate findings and the robustness of our method, we apply AdamW-GS to additional pipelines. As shown in Table and discussed therein, MaskGaussia exhibits potential reconstruction-quaaity risk on indoor datasets- phenomenon consistent with Observation 1 in Sec. 4.1 from the Adam vs. Sparse Adam experiments. We at- tribute this issue the synchronous updating of mask scores in MaskGaussian (a brief introduc- tion to MaskGaussian is given in Sec. E). Results in Table 5 further support this hypothesis: when trained with AdamW-GS, MaskGaussian no longer suffers from the quality risk and additionally prunes about 7% redundant primitives indoor scenes. This also demonstrates that our method compatible with additional pruming operations. Appendix Sec. E, we provide results of more pipeline variants with AdamW-GS, offering further evidence of the robustness.
Indoor
Outdoor
PSNR SSIM LPIPS AN, PSNR SSIM LPIPS A.
MaskGaussian 30,988 0.924 0.192 -61.5% 24,683 0.728 0,240 -6644%
+Adiam GS 31.199 0.925 0.193 -68.6% 24,939 0.739 0.244 48.1%
To better understand how our method penalizes redundant primitives, we further visualize the prim- itive number dynamics during training, as shown in Figure 2. PePR, which relies solely opacity L1 regularization during densification, shows limit in reducing redundancy. In contrast, with our proposed regularization, the number of primitives remains consistently lower. Even in cases where ANa is larger than that of MaskGaussian, our method (vanilla 3DGS with AdamW-GS)-restriiee to the densification still outperforms MaskCaussian in reducing redundancy during densification.
Extra Exploration is Necessary Previous studies have highlighted the role of exploration in 3DGS (Jung et al., 2024; Kheradmand et al., 2024), and here we investigate its interplay with re- dundancy. AdamW-GS benefits from the noise-based position regularization, yielding improved pruning efficiency and higher SSIM. As shown in Table GS7 and GS8, removing opacity reset weakens the noise-based regularization, leading to less improvement in SSIM and redundancy re- moval. We attribute the effectiveness of the noise-based regularization in AdamW-GS appropriate attribute regularization. Overall, our results underscore that additional exploration is necessary. However, the noise-based position regularization from 3DGS-MCME cannot be directly applied to scenes with relatively few primitives (e.g., indoor scenes), where their higher sensitivity to noise results in a drop in reconstruction quality. In Appendix Sec. F, we provide a more detailed analysis of the exploration ability induced by our method. We also introduce two additional explo- ration strategies that can be combined with current AdamW-GS and yield further improvements on certain indoor scenes as well.
its more
Efficiency Analysis Benefiting from Sparse Adam, as shown in Table 3, 3DGS-MCMC further improves optimization efficiency. Vanilla 3DGS enjoys the same benefit, while our method achieves additional gains by substantially reducing redundancy during the densification stage, thereby further enhancing optimization efficiency. More detailed analysis is provided in Appendix Sec. C.
6 DISCUSSION AND CONCLUSION
This work takes a step to decouple the complex 3DGS optimization and analyzes key mechanisms. AdamW-GS is further proposed, which improves efficiency and enables more controllable regu- larization. The method enhances reconstruction quality in the MCMC framework and achieves notable redundancy removal in vanilla 3DGS with slight quality gains and even without pruning. Our results indicate that efficiency and effectiveness can be jointly improved given appropriate reg- ularization. While we focused on opacity and scaling, more common DAR in different attribute or alternative strategies may yield further improvements. Despite the robust current hyperparameters and hand-crafted SStS, changing the parameters during training in an adaptive manner may offer a more promising direction. Finally, although noise-driven exploration shows necessary, it can harm certain scenes. Other provided exploration strategies offer limited improvement. A more systematic investigation of exploration strategies may be promising direction for future research.
Acknowledgments This work was supported by China Mobile Hunan Company Limited, China Mobile Communications Group Co., Ltd., and by the National Natural Science Foundation of China under Grant U22B2050, 62425305, 02221002. and 62503161. This work was conducted as part of the project "Networked Robotic System for Major Equipment Manufacturing (SG+Roboties)".
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A REPRODUCIBILITY
The datasets are directly available from (Kerbl et al., 2023). Methodological steps and formulas are detailed Secs. 4.4 and J.1, while all hyperparameters are reported Secs. J.2 and K.
More rendering visualization can be found in Figure 10.
B THE USE OF LARGE LANGUAGE MODELS (LLMs)
In this work, LLMs used solely to assist in writing and polishing the manuscript; they do not contribute to the discovery or experimental design.
C TIME COST ANALYSIS
Within the 3DGS-MCMC framework, employing Sparse Adam leads to substantial reduction in step time approximately 50% (see Table by- directly eliminating implicit updates. The fluc- tuations in forward and backward costs stem from variations in the number of activated primitives during training. Although DAR encourages a larger proportion of dead primitives, Sparse Adam exhibits greater stability and tends retain more activated primitives.
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Table 6: Time cost different methods, which is divided into time cost of densification, forward, backward and update step. In all experiments, the loss function is implemented consistently. Base- line methods employ the native Adam optimizer in PyTorch, whereas our AdamW-GB follows the implementation described in this work.
Methods
Avg.
Bicycle
Flowers
Gardea
Stump
Trechill
Room
Counter
Kichen
Bosai
Densification
0.37
0.43
0,38
0:49
0.39
0.37
0.32
0.34
0.34
0.32
Forward
6,91
8.35
6,09
8.47
6.44
6.08
6.70
6.67
7.61
5.86
vanilla 3DGS
Backward
13:72
14.26
11.27
15.75
11.54
11.38
14.69
14.62
17.38
12.59
Step
9.55
16.30
10.25
17.08
13.65
10.53
4.63
3,75
5.69
4.12
25.40
Densification
0.95
1.40
0.99
1.29
1.54
1.07
0.58
0.50
0.54
0.62
Forward
6.07
6.55
5.41
6.85
5.73
5,40
6.00
6.23
7.04
5,50
RePR
Backward
12.75
12.23
10.52
13.82
10.73
10.69
13.72
14.24
16.79
12.05
Step
6.92
11.20
7.39
11.51
11.05
7.84
3.10
2.75
4,51
3.01
All
26.73
31.40
24.33
33.48
29.06
25.02
23.41
23.83
28.90
21.20
Densilication
0.37
0.46
0.36
0.49
0.41
0.38
0.31
0.30
0.32
0.33
Forward
5.91
7.42
5.26
7.40
5,46
5.30
5.60
6.41
4.96
MaskGaussian
Backward
15.66
14.15
14.81
17.61
12.69
Step
7.64
9.38
2.39
2.29
3.94
All
26.8
34.59
24.48
36.09
26.46
25.36
22.16
23.01
28.30
20.75
Densification
0.33
0.34
0.33
0.34
0.35
0.33
0.32
0.31
0.34
0.33
Forward
5.19
5.21
4.45
4,81
4.75
4.49
5.54
5.69
6.27
5.56
3DGS
Backward
10.80
9,76
8.59
9,70
9.07
8.61
12.1
12.73
14.25
12.47
Step
2.17
3,90
2,89
3,76
4,19
3.05
0.34
0.40
0,58
0.43
WGS(GS8)
All
18.53
19.23
16.28
18.62
18.37
16.50
18.39
19.15
21.45
18.81
Densification
0.04
0.03
0.04
0.04
0.02
0.02
0.02
Forward
9.79
9.67
9.47
10.45
3DGSMMMC
Backward
19.19
22.20
24.54
19.97
Step
21.09
31.51
19:45
33.76
24.68
20.46
10.23
8.12
12.17
8.75
All
46.81
58.08
43.13
62.79
47.60
42.61
42.49
39.81
47.19
37.63
Densification
0.03
0.05
0.03
0.05
0.04
0.03
0.02
0.02
0.02
0.02
Forward
9.18
9.50
8.10
10.15
8.51
7.91
9.55
9.26
10.84
8.85
3DGSMCMC
Backward
11.46
18.33
15.25
21.32
16.02
14,41
21.18
19.91
25.61
19.66
Step
11.46
18.75
12.04
20.64
14.84
12.35
6.20
5.06
7.89
5.40
+Adam WGS(MC8)
35.44
52.17
34.27
44.39
For vanilla 3DGS, the reduction in time cost benefits from both the decrease in update-step overhead achieved by Sparse Adam and the reduced forward and backward costs resulting from fewer prim- itives. Overall, our method achieves more than 40% reduction in total runtime. In indoor scenes with fewer primitives, the update-step cost becomes negligible, as illustrated in Figure 4. Due to extra loss in MaskGaussian its pruning strategy, it yields almost improvement in the backward time cost.
D PRELIMINARY
3DGS(-MMCC) 3DGS approximates the radiance field of targeted scenes via group of Gaus- sian primitives {G.)* parameterized with 0 = (0; E 0) where 0 (ju: E, oz, ci), l4 R3 denotes the primitive position, ()) E gix3 is the positive semi-definite covariance matrix decou- pled into quaternion and scaling vector, (0)) is considered the opacity value. The color attribute c(t) (3) is typically stored as spherical harmonics coefficients and converted into RGB when rendering.
Given viewpoint is and transformation (Kerbl et al., 2023), the pixel p the screen is rendered via a-blending according to the projected depth of primitives:
c² (p: = Σ &o (p: 0.)
(1-00ppp:0)
(p:0))
Trensmittance (p.0.)
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Carrect
3000000
Peitikg Migharr-W0
3catin
Miyler330
Finidra
Faniic
Figure 4: Training Time Cost Comparison.
Here the superscript & denotes the corresponding parameters under the given viewpoint after the respective transformation, whereas G exp(-1 ( p) TE -p)).
Optimization The 3DGS training pipeline typically initializes from Structure-from-Motion (SfM) (Schonberger & Frahm, 2016) followed by several warm-up iterations (Kerbl al., 2023; Jung al., 2024). The primitives then undergo densification, wherein new primitives are generated to enhance scene representation while redundant ones are pruned. In the vanilla pipeline (Figure 9 a), both operations are governed by adaptive density control: new primitives are created via cloning or split- ting based on gradient magnitude, whereas low-opacity primitives are removed. After densification, optimization proceeds in pure optimization (P-Op) stage, during which only gradient propaga- tion and attribute updates occur. Throughout warm-up, densification, and P-Op, training employs photometric loss (left in Eq. !) with the Adam optimizer. Building on Stochastic Gradient Langevin Dynamics (SGLD), EDGS-MCMA
(Kheradmand et al., 2024) follows a similar stage division, as shown in Figure 9 b: primitive sampling and dead primitive reallocation during densification, followed by shortened P-Op. also adopts Adam, augmented with a regularization loss in Eq. promote respawn and additional positional noise for exploration adherence the SGLD form.
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Spiae Adee
Parrs Vie
Rear
Figure The average of the second moment in valid primitives.
Table 7: Quantitative results in MipNerf360 of vanilla 3DGS and MaskGaussian (Liu et al., 2025b) with or without AdamW-GS.
Pipeline
Adam GS
PSNR1
SSIM1
LPIPS)
AN,
PSNRT
SSIM
LPIPS]
AN.
PSNRT
SSIM
LPIPS
A.N
27.506
0.815
0.216
(3.098m)
24.648
0.728
0.239
(4.512m)
31,080
0.925
0.189
(1.33lm)
vanilla 3DGS
27.678
0,822
0.220
-49.3%
24.854
0,740
0.243
-48.4%
31.209
0.925
0.191
-50.4%
MaskGaussin
27.485
0.815
0.219
53.1%
24.683
0.728
0.240
-46.4%
30,988
0.924
0.192
-61.5%
27.721
0.821
0.221
57.2%
24.939
0.739
0.244
48.15%
31.199
0.925
0.193
-68.6%
E MORE PIPELINE VARIANTS WITH ADAMW-GS OR EXPERIMENTS ON DIFFERENT DATASETS
E. MASKGAUSSIAN WITH ADAMW-GS. MORE STABLE UPDATING OF MASK SCORE
Mask Gaussian introduces a probabilistic formulation of 3D Gaussian primitives, where each primi- tive is assigned learnable probability of existence that governs dynamic sampling process during rendering. This mechanism enables adaptive pruning of redundant primitives throughout the 3DGS optimization. Specifically, each primitive is associated with mask score n. from which binary mask M; is stochastically sampled using the Gumbel-Softmax reparameterization. The standard rendering equation Eq. is thus modified incorporate the mask in both color accumulation and transmittance updates, as shown in Eq. 10. Detailed derivations and implementation are provided in (Liu et al., 2025b).
(p: -- Mi oi
(p: (.000)-Tf.0. (p: where M₁ GumbelSoftmax(rt (10)
T+ -. x m((T))
(11)
When MaskGaussian is equipped with AdamW-GS, the observed PSNR improvement aligns with that of vanilla 3DGS using AdamW-GS. Additionally, for indoor scenes, it enables extra pruning of approximately 7% primitives. This suggests that synchronous updates mask scores may lead potentially "destructive pruning behavior". In contrast, our method cannot only be jointly used with such pruning strategies to stabilize their inherent training dynamics, but also further improve overall efficiency, pruning performance, and representation quality simultaneously.
E.2 TAMING-3DGS WITH ADAMW-GS
Taming-3DGS (Mallick et al., 2024) constrains the total number of primitives by restricting the number of new primitives added at each densification step, as defined by Eq. 12. During every densification step, Taming-3DGS computes score for each primitive to determine its probability of being selected for densification. Based on these scores, a fixed number of primitives are sampled for densification. Additionally, Taming-3DGS incorporates further optimizations, such as enhanced
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Taming-3DGS (final count)
Taming-3DGS with AdamW-GS
Taming-3DGS (multiplier)
Taming 3DGS AdamW-GG (multiplier)
(Ginal count)
Figure 6: Rendering visualization of Taming- Baming-3DGS with or without Adam W-GS.
Table 8: Quantitative results in MipNerf360 of Taming- 3DG (Mallick et al., 2024) with or without A. brief introduction to the Taming-3DGS can be found in Appendix Sec. E.2. All Primitive Number (Np, N₂) is reported in millions; Time cost is reported in mins.
Adam
All SSIMP LPIPS.)
Indoor
Outdoor
Pipeline
-GS
PSNR
N₂ Na Time PSNR
SSIM LPIPS N2 Na
PSNR
SSIM LPIPS
N₂ N,
Taming-3DGS
27.386
0.796
0.258
0,668 0.620 7.44 31.025 0.918 0.208 0.357 0.329
24.479 0.698 0,299 0.916 0.853
(multiplier)
27.537
0.799
0.254
0,646 0,575 5.27
31,268 0.920 0,200 0.357 0.313
24.552 0,703 0.297 0,877 0.785
Taming-3DGS
27.912
0.822
0.207
3,205
2,609 20.30
31.603
0,928 0.181 1,377 1.144
24.959
0.736 0.228
4.667 3.776
(final count)
28.034
0.826
0.207
3,109 1.847 10.46
31.720
0.928
1,408
0.759
25.085
0.744 0.229
4.469 2.717
Taming-3DGSSpp
28.038
0.828
0.205
2.160
2.160 8.44
31.724 0,930
0.177 0.804 0.804
25.089
0,745
0,227 3.246 3,246
(final count)
parallelization. For detailed implementation and algorithmic design, please refer to (Mallick al., 2024).
A(stop..) Qdeusi 24 2stopdensi step2 - 2step, + Qdensi
(12)
stepăensi
Where step,, denotes the current number of densification steps, stepdensi represents the total num- ber of densification iterations, Qdensi refers to the upper bound on the number of primitives after densification, and 2o indicates the initial number of primitives.
Two operating modes are provided in Taming-3DGS* final count and multiplier, which correspond higher and lower upper bound on the final total primitive number N,. respectively. Experi- ments were conducted under both modes for Taming-3DGS as well as Taming-3DGSS with AdamW- GS. DAR in this setting only includes opacity and scaling regularization as well, following the same configuration as in Sec. 4.4. Noise regularization is omittee because the growth rate in Taming- 3DGS is constrained. Considering that AdamW-GS imposes stronger penalties on redundant primi- tives, leading to the generation of large number of dead primitives that are rapidly pruned and thus reduce the total primitive count significantly, we propose replace the conservative pruning strat- egy in Taming-3DGS with the pruning method used in vanilla 3DGS when integrating AdamW-GS We denote this modified pipeline as Taming-3DGS. -p. Related experimental results are summarized in Table 8.
As shown in Table 8, under the same constraint on the final Ny, the variants trained with Adam GS consistently achieve better reconstruction quality compared with their original counterparts, while also providing additional advantages in training speed. Visual comparisons in Figure 6 further demonstrate that method more faithfully preserves fine scene details. When relatively large final primitive budget is given (the final count mode in Table 8), Adam W-GS reduces the total train- ing time by nearly half (20.30 mins in the original Taming-3DGS vs. 10.46 mins for Taming-3DGS with A-G). Since A-GMW-GS effectively penalizes redundant primitives at an early stage, we further incorporate the pruning strategy from vanilla 3DGS to construct Faming-3DGSS, With
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Table Quantitative results MipNerf360 of Deformable Beta Splatting (Liu al., 2025a) with or without AdamW-GS. A brief introduction to the T'mming3DGSS can be found in Appendix Sec. E.3. Treehill from MipNeRF360 is excluded here.
Outdlee
Indoor
AdamW-GS
PSNR
SSIMT
LPIPS,
SSIMT
LPIPS
PSNRT
LPIPS
29.362
0.864
0.165
26.029
0.787
0.187
32,696
0.940
0.143
29.643
0.871
0.158
208108
0.798
0.175
33.178
0.945
0.140
Table 10: Quantitative results in OMMO (Lu et al., 2023) vanilla 3DGS and 3DGSMCMC with without AdamW-GS. All Primitive Number (Np, p. No) is reported in millions.
3DGSMCMC
3DGS
Adam PSNRT
SSIMT
LPIPS
N₂
No
PSNRT
SSIMT
LPIPS,
Nvp
No
30.359
0.925
0.135
1,600
1.673
30,040
0.914
0.154
1.878
1.640
1.765
1.245
1.211
our optimizer, this variant achieves additional GPU memory savings during training (3.205 million in the original Taming-3DGS vs. 2.160 million for Taming-3DGS with AdamW-GS).
E.3 DEFORMABLE BETA SPLATTING WITH ADAMW-GS
Deformable Beta Splatting (DBS) (Liu al., 2025a) shares similar pipeline design and same loss with 3DGSMCMC (Kheradmand et al., 2024), as both are formulated under the Stochastic Gradient Langevin Dynamics framework. Unlike 3DGSMCMC, DBS replaces the Gaussian kernel with the Beta kernel B(p; 0:) and introduces the Spherical Beta function to better represent complex geometries and diverse appearance attributes. Consequently, the rendering process is reformulated shown in Eq. 13.
No Σ & o, (p: 0.) II (1 - or (p; (p: 0.))
C² 0)
(13)
Consistent with our experiments on 3DGSMCMC, we apply AdamW-GS to DBS, and the results are summarized in Table 9. Across eight of the nine scenes (excluding Trechill), we observe clear im- provements in reconstruction quality when using AdamW-GS For the Trechill scene, however, find that DBS suffers from pronounced overfitting and triggers early stopping prematurely. Mean- while, observe that during the densification stage, N₂ has been closed early to zero, indicating that DAR cannot effectively exert its intended effect in this scenario. Our method may be less effec- tive in such heavily overfitting scenario.
E.4 VANILLA 3DGS OR 3DGSMCMC WITH ADAMW-GS ON OMMO DATASETS
provide results on the OMMO dataset (Lu et al., 2023), which contains large-scale outdoor scenes with long-range sequences. Our data processing follows the settings described in (Kherad- mand et al., 2024) and its associated Github repository However, the image preprocessing failed for scene #10; thus, report the average results for the left scenes. All results are summarized in Table 10. Our method demonstrates effectiveness on long sequence datasets as well.
F EXPLORATION STRATEGIES
In Sec. 4.1, we observe that Sparse Adam exhibits less explosive characteristic. Part of this comes from the stability described in Observation 1, and part is attributable to the inherent bad trans- portation property of 3DGS (Jung et al., 2024), which we briefly discussed in Sec. 4.4. This phe- nomenon causes larger portion of primitives to remain in a stable state during optimization with Sparse Adam neiherr triggering further primitive generation nor enabling continued improvements
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Table 11: Quantitative results in MipNerf360 of vanilla 3DGS in our different modifications. More detailed information can be found in Sec. F. "+ Only RSR" demotes only using the Sparse Adam and RSR in 3DGS pipeline.
All
Outdoor
Indoor
Pipeline
PSNRT
SSIM
LPIPS)
AN,
PSNR1
SSIMT
LPIPS)
AN,
PSNR1
SSIM
LPIPS.
AN
vamilla 3DGS
27.506
0.815
0,216
(3.098m)
24.648
0.728
0.239
(4.512m)
31,080
0.925
0.189
(1.331m)
Only RSR (GSD)
27.483
0.818
0,217
-28.6%
24.685
0.733
0.238
-27.9%
30.981
0.924
0.190
29.55
Addam--GS (GS8)
27.678
0,822
0.220
-493%
24.854
0,740
0.243
-48.4%
31.209
0.925
0,191
-50.4%
+AdamW-GS (GS8) ABE
27.751
0.822
0.220
-111%
24.909
0.740
0.243
-38.5%
31,304
0.925
0.191
-443%
+Adam GS (GS8) Longer Densi
27.715
0.824
0.218
48.4%
24.857
0.744
0.240
-4.6%
31 31,288
0.925
0.190
-53.2%
in scene reconstruction. As result, we obtain a primitive group with a smaller N₂ but inferior recon- struction quality. In Sec. (Extra Exploration is Necessary), examine the necessity of additional exploration through experiments that introduce noise regularization. Here, exploration is deliber- ately to encourage primitives undergo larger movements, which is consistent with the notion of bad transportation described in (Jung et al., 2024). We have given the discussion in Sec. 4.4.
Exploration in Current AdamW-GS In Sec. we argue that the current AdamW improves exploration. This enhancement arises from several factors: (1) RSR. We provide additional ablation studies showing that, when using only Sparse Adam together with RSR, training the vanilla 3DGS pipeline on Mip-NeRF 360 yields reconstruction quality comparable to vanilla 3DGS with Adam. The corresponding results are reported in Table under "+ Only RSR (GSO)". (2) The influence of DAR around saddle points. The analysis in (Wang et al., 2025) indicates that many primitives become trapped near saddle points, preventing further effective optimization. The presence DAR encourages these primitives continue participating in optimization rather than stagnating. (3) Improved gradient flow after removing redundant primitives. When large number of redun- dant primitives are eliminated, the gradient flow within primitive groups becomes more coherent and effective. (4) Noise regularization for outdoor scenes. For outdoor datasets, we intentionally introduce noise regularization to further encourage extra exploration.
Existing work provides only limited discussion of exploration strategies for the 3DGS pipeline. Noise regularization, while helpful in certain cases, has inherent limitations and is not applicable to all datasets. Nevertheless, we argue that developing extra exploration strategies is a promising direc- tion, as such mechanisms encourage primitives explore broader region of the space. Building on our current work, we introduce two additional exploration strategies: Adaptive Bound- Expanding Split (Jung et al., 2024) and Densification Extending. (For outdoor scenes, the following exper- iments still employ noise regularization; we further demonstrate that these strategies can be used jointly.)
Adaptive Bound-Expandee Split (ABE-Split) divides each Gaussian into three, where the loca- tion of the third cross-region primitive initialized using a constant factor proportional to the scene extent. The corresponding results reported in Table 11 "+ AdamW-GS (GS8) ABE". ABE- Split consistently improves reconstruction quality across both indoor and outdoor scenes. In some cases, the gains particularly clear-for example, on the Room scene from Mip-NeRF 360, the PSNR/SSIM increases from 31.500 dB / 0.920 (vanilla 3DGS) to 32.121 dB / 0.923.
Densification Extending: We extend the original densification phase from 15,000 iterations to 25,000 iterations, leveraging the densification mechanism. Thanks to the ability of our method to quickly penalize redundant primitives, this extension does introduce the risk of memory explo- sion. The corresponding results are reported in Table 11 under "+ AdamW-GS (GS8) + Longer Densi". Extending the densification phase further benefits indoor scenes and additionally reduces the number of active primitives.
G FAILURE CASES
Although AdamW-GS yields improved reconstruction quality-bool quantitatively and qualita- tively in terms of rendering coualization-compaal with the original method, it only offers an
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5) Anti-Fact Boundary Area:
Blurry Detail Rackgrouad:
A'lleel-Ca Go
JIGANC MC
Mar Mudts
<) Anti-Fact in Geumetric Information:
Rendene Doyah
Readire Dopts
Geometric Information:
Figure 7: More examples to show the failure cases: a) the rendering results from Room to show the
anti-fact boundary area; b) the rendering results from Garden to show the blurriness in background; c) the rendering results and normalized depth maps from Bosai to show anti-fact in geometric infor- mation; d-e) the ellipsoid visualization from Bicycle.
optimization-leve enhancement and does not fundamentally resolve the inherent limitations of the pipeline itself.
Severe artifacts boundary regions with insufficient view coverage. As shown Figure 7 a), boundary areas walls exhibit substantial artifacts, floaters, and even incorrect colors due the lack of sufficient multi-view constraints.
Insufficient refinement of background regions. These areas often remain under-optimized and may suffer from blurriness. We give an example in Figure 7 b).
Geometric inconsistency despite reasonable rendering results. Our current optimization does incorporate any additional geometric priors. Obtaining the normalized depth map (Figure 7 c), Rendered Depth) using Eq. 14, can be observed that many regions clearly violate geometric plausibility-ffo for example, reflective books or shadowed chairs. Without explicit geometric priors, W-GS cannot fully recover the correct underlying geometry. Nonetheless, certain improve- ments in geometry can be observed for instance, the tree trunk region highlighted by the purple box in Figure 7 r)).
Persisting floater issues when the original pipeline suffers from floaters. Even with Adam W-GS, floaters may remain, as illustrated in Figure 7 d).
Failure under severe overfitting. When the reconstruction pipeline significantly overfits the scene, AdamW-e W-GS may break down. We encountered this issue when using DBS to reconstruct Treehill from the Mip-NeRF 360 dataset. Overfitting can prematurely trigger early stopping, and the sharp decreasing of N, leads to the failure of DAR.
D* = Σ d -p)
(14)
where di is the depth of the primitive in the corresponding camera coordinations.
H MORE ABOUT RELATED WORK
Redundancy during Optimization (1) Densification refinement: Several works optimize the den-
sification rule (Fang & Wang, 2024; Mallick et al., 2024; Wang et al., 2025). SteepGS (Wang
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Compartion of Hathoch Jome Scanes
34
Compariion baatoo Tro Methode Acmis Soannn
3DGS MCMC
venilla 3DGS +AdamiN-GS
+AdamWW6G
20
Ioed
10/then
BoW
Pendeene Berne PSNK JPUNICI
to Pardomme Berne
30K25
The PSNR error bar plot across nine scenes is shown for both methods, while the other metries exhibit no notable variation. A more detailed per-scene result provided in Sec. K.
Figure 8:
al., 2025) mitigates redundancy through optimization conditiionn densification or alleviates sub- optimization by densification, but its reconstruction quality and pruning effectiveness remain infe- rior to learning-basee methods. (2) Hand-crafted criterion: importance or redundancy criteria are designed to guide pruning after densification. LightGaussian (Fan et al., 2024) scores each Gaussian product times ray contributions. RadSplat (Niemeyer et al., 2025) uses the maximum alpha-transmittance product across views. (Papantonakis et al., 2024) propose the pipeline to prune primitives based on their degree of overlap. PUP-3DGS(Hanson et al., 2025) proposes principled sensitivity pruning score which is computed of the reconstruction eтrоr on the training views. (3) Learning- based pruning that leverages learning- based strategies adaptively remove redundant primitives, often via mask. Compact3DGS (Lee et al., 2024) introduces Gaussian masks with L.1 regularization on active mask count. MaskGaus- sian (Liu et al., 2025b) models the existence primitives, measures the importance via learning. L.-3DGS(Zhhang et al., 2024a) redesigns the masking function to leverage the Gumbel-Sigmod operations: Optimization together with additional opacity LI regularization has become common technique for redundancy removal, even extending beyond Ef- ficient 3DGS tasks (Papantonakis et al., 2024; Lee al., 2024; Kheradmand et al., 2024; Liu al., 2025a; Svitov et al., 2024).
by seriity-rranmittanee--eee
second- -oddrr approximation
method. (4) Optimization-relatee
Optimizing redundancy and training efficiency constitute subtopic of efficient 3DGS, correspond- ing to acceleration in inference and training (with partial overlap between the two). For inference, approaches include vector quantization (Lee et al., 2024), knowledge distillation (Fan et al., 2024), and entropy coding (Huang et al., 2025). For training, efforts target backward acceleration and loss redesign (Mallick et al., 2024). These topics fall beyond the scope of this work: for fair comparison, maintain the same loss function and refrain from using additional compression techniques.
Optimizer and Regularization The development of adaptive first-order optimizers be traced back to RProp (Riedmiller & Braun, 1993). AdaGrad (Duchi et al., 201 adapted the learning rate of features by estimated geometry and assigns larger learning rate infrequent features. RMSProp (Hinton et al., 2012) further stabilized training by normalizing updates with an exponential moving average of squared gradients. Building on this, Adam (Kinga al., 2015) incorporated momentum into RMSProp through an exponential average of gradients, quickly becoming the default optimizer for modern DNNs (Vaswani et al., 2017). Numerous refinements and extensions Adam have since been proposed et al., 2019; Chen et al., 2023). Regularization has long been recognized as key technique to improve model generalization and has also been employed as tool facilitate more effective optimization (Srivastava et al., 2014; Shalev-Shwartz & Ben-David, 2014; Andriushchenko et al., 2023; Brown et al., 2020; Radford et al., 2021). Importantly, Loshchilov & Hutter (2017) demonstrated that L2 regularization and weight decay are not equivalent, and further showed that weight decay provides a more appropriate formulation for Adam.
Optimization for 3DGS Sparse Adam (Mallick et al., 2024) introduces asynchronous updates that improve efficiency, yet the insufficient recognition of update-step coupling results in degraded performance. 3DGS-LM (Höllein et al., 2025) proposes a tailored Wevenberg-Marqueee optimizer for acceleration. However, it still relies on Adam for the initialization densification. Although Adam has become de facto indispensable optimizer for 3DGS, our understanding of its behavior in this context remains limited. A similar situation arises for regularization: despite the widespread use
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Table 12: Quantitative results in Mip360 of 3DGS-MCMC Sparse Adam with different opacity regularization.
Outdoor
Indoor
Methods
Cite
An
PSNR
SSIM
LPIPS
A.N.
PSNR
SSIM
LPIPS
AN
PSNR
SSIM
LPIPS
ANa
MC2
0.01
25,160
0,754
0.212
3.92%
31,546
0,930
0.183
4.74%
27.998
0.832
0.199
4.28%
10/2
MC101
17.379
0.400
0.604
-77.8%
29.957
0,906
0.220
400.%%
22,969
0.625
0.433
-5..3%
MC102
0.001
24.585
0.731
0.220
5.18%
31,342
0,930
0.179
8.13-
27,588
0.819
0.202
6.28%
MC103
24.298
30.687
0.193
2.08%
0.806
2.83%
AdamW
MC104
24.155
0.698
0.288
3.80%
30.326
0.917
0.203
-7.47%
26.898
0.795
0.250
5.43%
MC105
10
17.031
0.350
0.654
-19.8%
20.134
0.680
0.457
-11.6%
18.410
0.497
0.567
-16.1%
AdamW
MC106
0.1
24.239
0.713
0.242
5.77%
30,992
0.928
0.182
9.66%
27.240
0,808
0.215
7.50%
clip
MC107
24.381
0.713
0.260
5.08%
30.850
0.922
0.194
8.76%
27.256
0.806
0.231
6.71%
(max 10)
MC108
10
19.358
0.440
0.560
2.69%
21.901
0.727
0.436
7.99%
20.488
0.568
0.505
5.04%
of various regularization techniques in 3DGS, there is currently little work examining the interplay between regularization and the optimizer, even though this has already been explored in the deep neural networks (Loshchilov & Hutter, 2017).
I PREPARATION FOR DECOUPLED ATTRIBUTE REGULARIZATION
LI HYPERPARAMETEN ADJUSTMENT
This section discusses the influence of hyperparameters on regularization. For both opacity and scaling regularization in 3DGS-MCMC, default value of 0.01 is adopted. Here, vary only the opacity typerparameter by scaling it up or down by a factor of 10, with the results summa- rized in Table 12. When increased to 0. the stronger regularization leads to severe degradation in reconstruction quality. Conversely, reducing to 0.001 weakens the regularization effect to the extent that the primitive reallocation process significantly disrupted, also resulting in quality loss. These results suggest that hyperparameters alone are insufficient to effectively regulate the strength of regularization
1.2 ADAMW STYLE DECOUPLING
The Adam AdamW-style decoupling implies equal penalty applied to attributes, which can be formally expressed in Eq. 15 and Eq. 16. This formulation is equivalent to imposing a constant penalty on opacity (Rota Buld et al., 2025). Within the 3DGS-MCMC framework, we apply AdamW-style decoupling to opacity and evaluate it under three hyperparameter settings representing different strengths. To disentangle the effect of magnitude, tude of the Adam W-style decoupling, as given in Eq. 17. The results are summarized in Table 12. Consistent with the findings in Appendix Sec. 1.1, excessively large hyperparameters hinder conver- gence, while overly small values render the regularization ineffective. A key limitation of AdamW- style decoupling that it enforces uniform penalties across all primitives, despite their varying importance.
also experiment with constraining the magni-
VE(O) N
x VE(O)
m(0) 8i m(00)11+00 (1
v00, = 3/ x x(0)
)2 (15)
N
m());
0,+1 8, n
+ AVR(O))
(16)
Vo(O), +
m())
0,11 = 01 1 x
+ min((AVR(0).C.)
(17)
Vity,, +
I.3 ADDITIONAL DISCUSSION REGARDING THE FORMULATION IN BQ.8
A thorough decoupling-iss i..., activation via the second moment of VR-is unreasonable: be- sides extra computational and memory cost, it reduces regularization to trivial attribute-eependent penalty (e.g., higher opacity automatically incurs stronger regularization).
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1.4 DISCUSSION RELATED TO IMPLICIT UPDATE
Ineffective when stable: Implicit updates allow primitives in invisible viewpoints to be updated based on their current moment. Our reasoning, grounded in experimental results, is as follows. When primitives are in a stable state- ceste-moreppe precisely, at saddle points, which are abundant in 3DGS when no external perturbation is applied (Wang et al., (125)-implicii updates are largely ineffective while incurring additional computational cost. In vanilla 3DGS, we implemented AIU (see GS4 and GS3 in Sec. K), and observed negligible improvement.
Less controllable when unstable: In contrast, when primitives are unstable, such during the early training phase (e.g,, densification, where newly generated primitives often have zero moment), or when the update step is relatively large, or when moment is rescaled, implicit updates can become problematic. We designed several experiments to highlight their uncontrollability. For instance, adopting AIU during densification in vanilla 3DGS with Sparse Adam can lead to more primitives but worse performance, as shown in GS6 in Appendix Sec. K, as even small update steps for in- visible primitives introduce instability. Based on Obsidian 1, Sparse Adam tends be stable, with which fewer primitives meet the gradient condition. AIU disrupts this stability: when primitives overfit certain views due to implicit updates, they induce larger gradients in other views, triggering unnecessary densification. The additional primitives do not necessarily improve rendering quality. In the Appendix Sec.K, we provide multiple AIU configurations: although in some cases the qual- ity approaches that of vanilla 3DGS, the more common results are in worse quality, confirming the uncontrollable nature of implicit updates.
Another related phenomenon is the dead primitives or more reallocated primitives (see Sec.5. The comparison between GS1 and GS3 in Table 1 (or can be found in Appendix Sec. K) shows that more dead primitives are caused by Adam (0.232m vs. 0.048m). A natural conjecture is that when the update step, in a certain viewpoint, encourages primitives to become dead primitives, the implicit update accelerates this process, thereby producing more dead primitives. We provide some comparative experiments in Appendix Sec. K. (1) MC2 vs. MC3 in Appendix Sec. K, comparing the original 3DGSMCMC with Sparse Adam against the original 3DGSMCMC with Sparse Adam + AIU. (2) Similar comparisons can be found in GS3 and GS4, examining the effect of AIU on dead primitives when Sparse Adam applied after densification ends. We observe that using AIU results in additional dead primitives. (3) Figure 3 likewise shows that adding AIU leads to more reallocated primitives during the densification stage of 3DGSMCMC. For certain scenes, such as Kitchen, the corresponding reconstruction quality decreases, further reflecting the increased number of dead primitives. This also indicates that the phenomenon is not part of a normal optimization process; in Sec. 5.1, we relate this behavior to over-effective regularization. (4) The comparison between MC6 and MC7 in Appendix Sec. K similarly shows that adding AIU after densification
produces additional dead primitives as well; note that in application RSR is only added during densification. (5) When training MaskGaussian with Cd, MaskGaussian will not suffer from the quality risk.
J IMPLEMENTATION DETAILS
J.1 ADAMW-GS
Specifically, each parameter of the optimizer can be expressed in the form:
Since both opacity and scaling are strictly positive, the gradient of the L1 regularization reduces to a constant value of +1.
For opacity:
1
o 0= O(T = Ite- =
(18)
Te+1 = T, - fr x m(7)
+ min(A, Vo(T)/N1 C.)
(19)
Vo(T)++ +E Vo(T) +
For scaling:
8 =xp(p()) exp(())
(20)
23

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Published as a conference paper at ICLR 2026
Stgee:
Warth
Densilication
Pure OptimizationPPOp
Densification
Henation:
510
15000
25000
Optiiiiationn
Debil: Aaperre Density ContoRADD
Now Primitives Sempling Dead Primities Realleration]
Opsio Li Regulatzationn Staling Regularizatinn
Vanilla 3DGS Foencwork
3DGS-MCMC Frenzwark
565 MCI
385 MC
565
Sangliee Prtk
5455 MC3
Sumplie
565 US4
Ude
10:0
3008
11:00
2.00
11.82
SISS Vanilla IDGS
(d) SISS 3DGS MCMC
MDGS
Figure 9: a-b:: This illustrates the training pipeline of 3DGS and 3DGS- Since our method encourages primitive reallocations, postpone the densification stage by 1000 iterations compared to the original 3DGS-MCMC. In contrast, the original 3DGS-MCMC at 25k iterations produces almost no dead primitives. c-d: This shows the SiSS used in this paper.
K++1 K 7h x m(n)
Vo(K)/+ -E + min(A. Vexp(R)/NI C.)
(21)
Vo(N)++
For position:
Ry = f/ a0 (->p(0 -e)) Ey 7~ N(0,
(22)
mi()) + YR. Ry
M++1 = 14 Tp x Vo(u)) +E
(23)
na
For the other:
m(0))
0ut1 01 170
(24)
Vi(0); +e
J.2 HYPERPARAMETER SELECTION
For vanilla 3DGS(Kerbl et al., 2023) and DDGGsMCMCCKKerradnaadd al., 2024), all pipeline parameters follow the original settings, with noise parameters identical to those in 3DGS-MCMC. Operation for the opacity is similar as (Rota Buld et al., 2025).
m(0)
VR(O)/N1 C.) Vo(0y, +
O++1 0. 7 x
+ min(A, Ao
(25)
/0O0), +
StSS in RSR We fix the sampling interval at 100. Currently, StSS is manually StSS is used to sample the current set primitives, followed by RSR rescaling. The configuration StSS must take into account the generation and reallocation behavior in the pipeline, as these processes typically introduce additional primitives with zero state. When such zero-state primitives constitute a large proportion of the population, a smaller sampling ratio generally preferred. In the main text, Figure and Figure 2 respectively show the number of reallocated primitives for 3DGS-MCMC and the evolution of the primitive count under different scenes for 3DGS. Understanding these curves provides useful guidance for designing an effective StSS strategy.
In general, the differences between these schedules arise from two main factors: (1) variations in the underlying pipelines (e.g., 3DGS vs. 3DGS 3DGS-MCMC), which naturally require distinct schedules; and (2) variations across scenes, where different schedules are needed to obtain the best performance on indoor versus outdoor datasets. The discrepancies introduced by the pipelines themselves are un- avoidable. Nevertheless, for each pipeline we design a conservative schedule-denoted SISSGSI and SiSSMCI-under which both 3DGS and 3DGS-MCMC outperform their original configura- tions. For outdoor scenes, which typically involve higher primitive generation or reallocation rates, find that more aggressive schedule further improves performance. All StSS schedules used in this paper are illustrated in Figure 9. Appendix Sec.K summarizes the results obtained by applying different StSS configurations across various pipelines and scenes.
24

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Published as a conference paper at ICLR 2026
The three existing designed operations provide guidance for selecting the pa- rameters 01 and ag in RSR. (1) The states of newly generated primitives 3DGS, or reallocated primitives in 3DGS-MCMC, can be viewed as naturally constrained by RSR with a Q2 0.
Scaling in RSR
is necessary to impose the (2) To properly control the magnitude of the update step Vo(oy++
relation a2 a②. (3) A very small a2 is consistent with the design philosophy of DAR, we rely on such a small value to rescale the second moment and thereby activate regularization. Therefore, when 01 and 02 are chosen to be sufficiently small while satisfying 02 = af. the configuration is safe. We conducted a search over different combinations of ai and a2. For larger configura- tions-for example, 01 = 0.5, 022 = 0.25 0.25-RSR becomes less effective, and some combinations even lead to gradient explosion. For smaller values of and 02 the performance differences are minor, and we find that a1 = 0.2, 02 0.04 generally performs best. In Appendix Sec.K, we report results for both d1 0g 0 and dr 0.2, 0g 0.04, cited as MC19 and MC18. Hence, we adopt 01 = 0.2, 02 = 0.04 as default all experiments.
DAR We use two DAR variants: opacity and scaling regularization. Regularization constrained to the densification stage, as no clear benefit is observed in P-Op. This is consistent with the smaller max magnitude of adaptive gradients in P-Op (Figure 1). Opacity regularization starts after 3000 iterations, since a large percent of generated primitives initially have zero moment, motivating delayed start.
For the two hyperparameters, we select values by considering activation derivatives, original set- tings, and Adam's 's parameters. We set A, 0.001 and, since scaling activations are two orders larger than opacity, X = le-5. Comparative DAR experiments with X 0.001 and X = 1e-5 show that 1e-5 performs better (see experiments MC14 and MC17 in Appendix Sec. K). In our application, only the most significant digit of N, is retained and then scaled down by one order of magnitude.
For opacity, C2 is set 10, guided by the max magnitude of adaptive gradients in Figure 1. Without C, over-effective regularization occurs (see MC9 in Appendix Sec. K). Smaller values (e.g.. 5 or 1) reduce reallocated primitives, leading to slight drops in PSNR and SSIM, though the MCMC framework still explores effectively. For scaling, we adopt C, = 10 by analogy with opacity, which yields good results; scaling less sensitive C. (e.g.. Ct shows little change in reconstruction quality; see MC8-MC17 in Appendix Sec. K).
K
ALL RESULTS
More rendering visualization can be found in Fig. 10.
25

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Published as a conference paper at ICLR 2026
3DGSMCMC A-AdmWWGS
original 3DGSMMMC
Ground Truth
Figure 10: Rendering visualization comparison.
26

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Published as a conference paper at ICLR 2026
K.1 BICYCLE FROM MIPNERF-360
Table 13: Quantitative results in Bicycle from MipBerf-360 with different components for vanilla 3DGS pipeline. For AIU, the brackets denote its active iteration range (e.g., [15,30] means 15k-30k iterations). ProAIU is the sampling probability of primitives, and JJAU constrains the extra update step applied to sampled primitives. [-I[-] denote the scale value and the iteration at which it takes effect. For example, 1.5.0.1[(0.11. means JAIU = 0.5 after 0. iterations, 1/ATI: = 0.1 after 3k, and VJAI 0 before 0.1k. In Ours, AdamW-GS uses the same configuration but different StSS settings. Sparse denotes using Sparse Adam or Adam, and Half means using Adam in densification but Sparse Adam P-Op. RSR here means only adding RSR to the pipeline.
cite
Sparse
AIU
ProATU
NATO
noise reset
Ours
PSNR
SSIM
LPIPS
Na/m
Na/m
AN
GSI
23.238
0.765
0.211
5,438
0.548
GS2
25.142
0.752
0.235
4,052
0.100
-2.55%
GS3
Half
25.260
0.766
0.211
5.879
0.109
8.11%
V
SiSSGS RSR
25.337
0.770
3,929
-28.4%
GS4
Half
[15,30]
[0.1
25.284
0.766
0.210
5,832
0.176
7.24%
GS15
Half
[15,30]
1.0
[0.11115]
25 256
0.766
0.210
5.651
0.285
3.91%
GS16
10.1.15
[0.11]0.11
25.145
0.756
GS17
[0.1.]]
0.2
[0.5][0.1]
15.166
0.755
0,228
5.026
0,103
-7.57%
[0.2.0.5.0.1]
GS18
< [0.1,15]
0.2
25.166
0.757
0.226
5,290
0,102
-2.72%
(0.1.1.71
[0.5,0.1]
GS19
< [0.1,15]
0,2
25.133
0.754
0.229
4,726
0.097
-13.1%
[0.1.3]
10.8.0.5.0.11
GSS 10.1.15
0,2
[0.1.3.7]
25.116
0.756
0.226
5.343
0.103
-1.74%
GS6
<
[0.1,30]
1.0
[0.1][0.1]
25.206
0.760
0.220
6.087
0.203
11.9%
GS9
SISSGS2
25.481
0.776
0.219
3.116
0.013
.42.7%
GS7
SiSSGSS
25.470
0.775
0.223
3.066
0.011
.43.6%
GS10
SISSGS1
25.514
0.780
0.215
2.853
0.021
-47.5%
SiSSGS2
25.454
0.778
2.717
-50.0%
Table 14: Quantitative results in Bicycle from MipBerf-360 with different components for 3DGS-
MCMC pipeline. AIU definitions follow the table description above (Table 13). For RSR, the sampler defaults to uniform (interval 100) except SISS. R denotes the form of regularization, its hyperparameter, and max corresponds to C2 in the paper; other parameters remain default. 0 in SISSMC1 denotes using 01 = 02 = 0 here.
cite
Sparse
ATU PrOAIU/RAIU
RSR
R.
An/max.
R.
A./max,
PSNR
SSIM
LPIPS
Nalm
Na/m
A N,.
MCI
L1
0.01/.
L1
0.01/
25,537
0.794
0.181
5.189
0.790
4.57%
MC2
L.I
0.01/-
T.1
0.01/-
25,630
0.793
0.178
5.835
0.145
7.30%
MC3
V
[0.1.30]
0.1/0.1
LI
0.01/-
L1
0.01/
25.649
0.794
0.177
5.819
0.161
7.0%
MC4
[3,30]
0.1/0.1
SISSMCI
0.01/-
25.746
0.803
0.167
5.645
3.80%
V
[26.30]
SISSMCI
DAR
9/10
0.163
5.99%
MC6
V
[26,30]
0.01/1
SISSMC2
DAR
0.001/10
DAR
P/10
25.298
0.801
0,161
5.789
6.45%
MC18
S
LI
0,011-
LI
0.014
25.779
0.804
0.170
5.734
0,246
5.44%
MC19
SISSMCI
L1
0014
LI
0.014
25.777
0.803
0.166
5.722
0.258
5.22%
MC20
SISSMC2
L.
0,11
0,01/
25.539
0,180
5.189
0.791
-4.57%
MC9
SISSMCT
DAR 0.001/-
LI
0.01A
25.766
0.803
0.167
5.715
0.265
5.09%
MC10
SISSMCI
0.001/10
25.768
0.160
7.4%
MC11
SISSMC2 DAR 0.001/10
0.01A
25.813
0.807
0.158
5.835
0,144
7.31%
MC12
SISSMCI DAR 0.001/5
L1
0.01/
25.753
0.804
0.159
5.843
0.137
7.44%
MC13
SISSIII DAR
0,001/1
T.I
0.011-
25,666
0.800
0,162
5.871
0,109
7.96%
MC14
SISSMCI DAR 0.001/10
DAR
0.001/10
25.727
0.803
0,159
5.873
0.107
7.99%
MCIS
SISSICI 0.001/10
DAR
0.001/1
25.743
0.159
5.863
0.117
7.81%
MC16
SISSMII 0.001/10
DAR
10
25.791
0.158
5.807
6.78%
MC17
/
SISSMCI DAR 0.001/10
DAR
110P/10
25.781
0.806
0.158
3.807
0,173
6.78%
MC?
SiSSMC2 DAR 0.001/10
DAR
10
1/10
25.826
0.807
0.158
5.799
0,181
6.63%
MC8
SISSMC3 DAR
0.001/10
DAR
P01P/10
25.874
0.809
0.158
5.781
0.199
6.30%
27

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Published as a conference paper at ICLR 2026
K.2 FLOWERS FROM MIPNERF-360
Table 15: Quantitative results in Flowers from MipBerf-360 with different components for vanilla 3DGS pipeline. For AIU, the brackets denote its active iteration range (e.g., [15,30] means 15k-30k iterations). ProAIU is the sampling probability of primitives, and IJAU constrains the extra update step applied to sampled primitives. [-I[-] denote the scale value and the iteration at which it takes effect. For example, 1.5.0.1[(0.11. means JAIU = 0.5 after 0.1k iterations, 1/ATI: = 0.1 after 3k, and VJAI 0 before 0.1k. In Ours, AdamW-GS uses the same configuration but different StSS settings. Sparse denotes using Sparse Adam or Adam, and Half means using Adam in densification but Sparse Adam P-Op. RSR here means only adding RSR to the pipeline.
cite
Sparse
AIU
PROATU
DAJU
Doise
reset
Ours
PSNR
SSIM
LPIPS
N,/m
Ny/m
AN,
GS1
21.527
0.605
0.336
3.421
0.239
GS2
21.463
0.598
0.346
2.737
0.030
-1.99%
GS3
Half
21.589
0.605
0.337
3.616
0.033
5.70%
GSD
RER
31.698
0.336
2.506
0.011
-26.7%
GS4
Half
[]5.30]
0.5
[0.1115]
21.598
0.606
0.336
3,581
0.056
4.67%
GS15
Half
[15.30]
1.0
[0.111151
21.585
0.605
0.336
3,518
0.098
2.83%
GS16
[0.1.15]
0.5
[0.1110.11
21.488
3.198
0.032
6.51%
GS17
[0.1.7]
0.2
[0.5][0.1]
21,535
0.600
0.342
3.153
0.032
-7.8%%
[0.200.5.0.11
GS18
[0.1.15]
0.2
21.563
0.601
0.342
3,240
0.032
-5.29%
10.1.1.71
10.5.0.11
GS19
[0.1.15]
0.2
21,524
0.599
0.344
2.940
0.029
-14.0%
[0.1.3]
10.800...0.11
GSS
[0.1.15]
0.2
10.13.7]
21.548
0.601
0.342
3.330
0.003
22.6%
GS6
[0.1.30]
1.0
[0.1][0.1]
21.551
0.601
0.340
3.599
0.077
5.20%
GS9
SISSGS2
21.762
0.609
0.343
2.026
0.004
40.7%.
GS7
SISSGSS
21.718
0.606
0.349
1,951
0.003
-42.9%
GS10
SISSGSI
21.70%
0.612
0.339
1.917
0.007
.43.9%
GS8
SISSGS2
21.711
0.344
1.832
0.005
-46.4%
Table 16: Quantitative results in Flowers from MipBerf-366 with different components for 3DGS- MCMC pipeline. AIU definitions follow the table description above (Table 15). For RSR, the sampler defaults to uniform (interval 100) except SISS. R denotes the form of regularization, its hyperparameter, and max corresponds to C2 in the paper; other parameters remain default. 0 in SISSMC1 denotes using 01 = 02 = 0 here.
cite
Sparse
ATU PrOAIU/RAIU
RSR
R.
An/max.
R.
A./max,
PSNR
SSIM
LPIPS
Nalm
Na/m
A A.
MCI
L1
0.01/.
L1
0.01/
22.028
0.641
0.296
3.352
0.248
-2.11%
MC2
L.I
0.01/-
T.1
0.014-
21,966
0.635
0.304
3.534
0.066
3.30%
MC3
V
[0.1.30]
0.1/0.1
LI
0.01/-
L1
0.01/
22.072
0.638
0,301
3.529
0.071
3.15%
MC4
[3,30]
0.1/0.1
SISSMCI
0.01/-
0.19%
V
[26.30]
DAR
9/10
288%
MC6
V
[26,30]
0.01/1
SISSMC2
DAR
0.001/10
DAR
P/10
21,511
0.646
0.275
3.524
0.076
3.01%
MC18
S
LI
0,014-
LI
0.014
22.195
0.649
0.292
3,510
0.090
2.60%
MC19
SISSMCI
L1
0014
LI
0.014
22.038
0.650
0.277
3.524
0.076
3.01%
MC20
SISSMC2
L.
0,11
0,014
22.017
0.641
0,295
3.352
0,248
-2.01%
MC9
SISSMCT
DAR 0.001/-
LI
0.01A
21,288
0.588
0.349
MC10
SISSMCI
0.001/10
21.887
MC11
SISSMC2 DAR 0.001/10
0.01A
22.017
0.656
0.268
3.548
0,052
3.71%
MC12
SISSMCI DAR 0.001/5
LI
0.01/
21.876
0.650)
0.266
3.554
0.046
3.88%
MC13
SISSIII DAR
0,001/1
T.I
0.011-
21.726
0.646
0,264
3.565
0.035
4.20%
MC14
SISSMCI DAR 0.001/10
DAR
0.001/10
21.923
0.650)
01269
3.563
0.037
4.15%
MCIS
SISSICI 0.001/10
DAR
0.001/1
21,962
0.270
3.561
4.15%
MC16
SISSMII 0.001/10
DAR
10
21,936
0.271
3.39%
MC17
/
SISSMCI DAR 0.001/10
DAR
10-P/10
22.034
0.653
0.270
3,539
0.061
3.44%
MC?
SiSSMC2 DAR 0.001/10
DAR
10
1/19/10
22.003
0.654
0.267
3,535
0.065
3.33%
MC8
SISSMC3 DAR
0.001/10
DAR
10-P/10
22.108
0.658
0.268
3.525
0.075
3.04%
28

---

Published as a conference paper at ICLR 2026
K.3 GARDEN FROM MIPNERF-360
Table 17: Quantitative results Garden from MipBerf-360 with different components for vanilla 3DGS pipeline. For AIU, the brackets denote its active iteration range (e.g., [15,30] means 15k-30k iterations). ProAIU is the sampling probability of primitives, and JJAU constrains the extra update step applied to sampled primitives. [-][-] denote the scale value and the iteration at which it takes effect. For example, 10.5.0.100 ][0.1.3) means 7JAIU = 0.5 after 0.1k iterations, YJATU = 0.1 after 3k, and JJau before 0.1k. In Ours, AdamW-GS uses the same configuration but different StSS settings. Sparse denotes using Sparse Adam or Adam, and Half means using Adam in densification but Sparse Adam P-Op. here means only adding RSR to the pipeline.
cite
Sparse
AIU
PROATU
DAJU
Doise
reset
Ours
PSNR
SSIM
LPIPS
N,/m
Ny/m
AN,
GS1
27.334
0.865
0.108
5.614
0,318
GS2
27.237
0,860
0.117
4.064
0.059
-27.6%
GS3
Half
27.409
0.866
0.107
5,878
0.059
4.70%
GSD
RER
27.318
3.026
0.019
-46.9%
GS4
Half
[]5.30]
0.5
[0.1115
27,430
0.806
0.107
5,827
0.112
3.79%
GS15
Half
[15,30]
1.0
[0.111151
27.455
0.866
0.107
5.672
0.265
1.03%
GS16
[0.1.15]
0.5
[0.1110.11
27.268
5.138
0.068
-8.7%
GS17
[0.1.7]
0.2
[0.5][0.1]
27.304
0.862
0,113
5.225
0.066
6.92%
[0.200.5.0.11
GS18
[0.1.15]
0.2
27.298
0.862
0.113
5,363
0.069
-4.47%
10.1.1771
10.5.0.11
GS19
[0.1.15]
0.2
27.234
0,861
0.114
4.652
0.061
-1.11%
[0.1.3]
10..00...0.11
GSS
[0.1.15]
0.2
10.13.7]
27.352
0,863
0.112
5.548
0.069
-1.17%
GS6
[0.1.30]
1.0
[0.1][0.1]
27.263
0,862
0.112
5,877
0.162
4.68%
GS9
SISSGS2
27.438
0.864
0.123
2.076
0.006
-6.00%
GS7
SISSGSS
27.590
0.864
0.127
1.983
0.005
-64.%
GS10
SISSGSI
27.370
0.863
0.122
2.145
0.016
-6188
GS8
SISSGS2
27.170
0.862
0.124
2.075
0.012
-63.0%
Table 18: Quantitative results in Garden from MipBerf-360 with different components for 3DGS- MCMC pipeline. AIU definitions follow the table description above (Table 17). For RSR, the sampler defaults to uniform (interval 100) except SISS. R denotes the form of regularization, its hyperparameter, and max corresponds to C2 in the paper; other parameters remain default. 0 in SISSMC1 denotes using 01 = 02 = 0 here.
cite
Sparse
ATU PrOAIU/RAIU
RSR
R.
An/max.
R.
A./max,
PSNR
SSIM
LPIPS
Nalm
Na/m
A A.
MCI
L1
0.01/.
L1
0.01/
27.862
0.879
0.094
5.466
0.433
-2.63%
MC2
L.I
0.01/-
T.1
0.01/-
27,889
0.878
0.096
5.785
0.115
3.04%
MC3
V
[0.1.30]
0.1/0.1
LI
0.01/-
L1
0.01/
27.896
0.878
0.095
5.770
0.13
2.77%
MC4
[3,30]
0.1/0.1
SISSMCI
0.01/-
0.089
0.23%
V
[26.30]
SISSMCI
DAR
9/10
25.235
0.107
0.55%
MC6
V
[26,30]
0.01/1
SISSMC2
DAR
0.001/10
DAR
5/10
24.993
0.825
0,149
5.651
0,249
0.65%
MC18
S
LI
0,011-
LI
0.014
28.010
0.882
0.090
5.726
0,174
1.99%
MC19
SISSMCI
L1
0014
LI
0.014
28.028
0.882
0.089
5.705
0.195
1.62%
MC20
SISSMC2
L.
0011
0,014
27.877
0.879
0.094
5.714
0,186
1.78%
MC9
SISSMCT
DAR 0.001/-
LI
0.01A
28.057
0.882
0.093
5.632
0,268
0..2%%
MC10
SISSICI
0.001/10
0.01/
0.088
5.752
2.24%
MC11
SISSMC2 DAR 0.001/10
LI
0.01A
28.065
0.884
0.088
5.740
0,160
2.24%
MC12
SISSMCI DAR 0.001/5
LI
0.01/
28.072
0.884
0.088
5.756
0.144
2.52%
MC13
SISSIII DAR
0,001/1
T.I
0.011-
28.021
0.883
0.089
5,807
0.093
3.43%
MC14
SISSMCI DAR 0.001/10
DAR
0:001/10
28.045
0.833
0.088
5.805
0.095
3.40%
MCIS
SISSICI 0.001/10
DAR
0.001/1
28.018
0.088
0.104
3.24%
MC16
SISSMII 0.001/10
DAR
10
0.088
1.97%
MC17
/
SISSMCI DAR 0.001/10
DAR
10-P/10
28.104
0.884
0.088
5.726
0.174
1.99%
MC?
SiSSMC2 DAR 0.001/10
DAR
10
5/10
28.109
0.884
0.088
5.714
0,186
1.78%
MC8
SISSMC3 DAR
0.001/10
DAR
P01P/10
28.144
0.885
0.088
5.687
0.213
1.30%
29

---

Published as a conference paper at ICLR 2026
K.4 STUMP FROM MIPNERF-360
Table 19: Quantitative results in Stump from MipBerf-360 with different components for vanilla 3DGS pipeline. For AIU, the brackets denote its active iteration range (e.g., [15,30] means 15k-30k iterations). ProAIU is the sampling probability of primitives, and JJAU constrains the extra update step applied to sampled primitives. [-I[-] denote the scale value and the iteration at which it takes effect. For example, 1.5.0.1](0.11. means JAIU = 0.5 after 0. iterations, 1/ATI = 0.1 after 3k, and VJAI 0 before 0.1k. In Ours, AdamW-GS uses the same configuration but different StSS settings. Sparse denotes using Sparse Adam or Adam, and Half means using Adam in densification but Sparse Adam P-Op. RSR here means only adding RSR to the pipeline.
cite
Sparse
AIU
ProATU
NATC
noise
reset
Ours
PSNR
SSIM
LPIPS
N_/m
Na/m
AN,
GS1
26.606
0.772
0.216
4.542
0.252
GS2
26.511
0.762
0.233
3.751
0.026
-17.4%
GS3
Half
26.730
0.774
0.215
4.774
0.029
5.10%
V
SiSSGS RRSR
0.782
0,210
-19.7%
GS4
Halt
[15,30]
[0.11[15]
26.710
0.773
0.215
4.928
8.49%
GS15
Half
[15.30]
1.0
[0.11115]
26.759
0.774
0.214
4.59
0,270
1.18%
[0.1.15]
10.1110.11
0.766
9.51%
GS17
[0.1.7]
0.2
[0.5][0.1]
26.475
0.764
0.227
5.010
0.030
10.3%
[0.200.5.001]
GS18
[0.1.15]
0.2
26.611
0.768
0.224
4,811
0.026
5.94%
10.1..71
[0.5.0.1|
GS19
[0.1.15]
0.2
26.633
0.767
0.226
4,830
0.026
6.34%
[0.1.3]
JO..U.S.00111
GS5
10.1.15
[0.1.3.7]
26.630
0.767
0.224
5.165
0.026
13.7%
G86
[0.0030]
1.0
[0.1][0.1]
26.601
0.768
0,222
5:274
0,125
16.1%
GS9
SISSGS2
27.175
0.796
0.211
2.894
0.014
.3.35%
GS7
SISSGSS
27.271
0.798
0.211
2.677
0.009
-41.0%
GS10
SISSGS1
27.033
0.800
0.206
2.567
0.023
-43.5%
0.800
0,206
-45.6%
Table 20: Quantitative results in Stump from MipBerf-360 with different components for 3DGS- MCMC pipeline. AIU definitions follow the table description above (Table 19). For RSR, the sampler defaults to uniform (interval 100) except SISS. R denotes the form of regularization, its hyperparameter, and max corresponds to C2 in the paper; other parameters remain default. 0 in SISSMC1 denotes using 01 = 02 = 0 here.
cite
Sparse
ATU
PROATC/MAIU
RSR
R.
An/max.
R.
Aa/max.
PSNR
SSTM
L.PISS
N./m
Nylm
A N,
MC1
0.017
1.1
0.01/-
27.204
0.805
0.183
4.245
0.555
-6.53%
MC2
0.012-
1.1
0.11-
27.293
0.805
0.182
4.718
0.082
3.84%
MC3
[0.1.30]
0.1/0.1
LI
0.01A
L.1
0.01/-
27.273
0.805
0.182
4.698
0.102
3.43%
[3,30]
0.1/0.1
SISSMCI
0.012
0.01/-
27.131
0.806
0.177
4.535
0.265
-0.154%
126,301
SISSMCI DAR
0.001/10
5/10
20.854
0.179
1.73%
MC6
[26.30]
0.01/1
SISSMC2
DAR
0.001/10
DAR
10
9/10
25.509
0.782
0.195
4.615
0.185
1.60%
MC18
SISSMCT
0.014-
0.01/-
27.064
0.805
0.179
4.620
0.180
1.71%
MC19
SuSSMC
L1
0,012-
0,01/
27.172
0.807
0.176
4.631
0.169
1.93%
MC20
SISSMC2
0,100
0014
27.170
0.796
0.190
4.673
0.127
2.88%
MC9
SUSSMCI
DAR
0.011--
L1
0,011-
26.943
0.796
0.191
4.620
0.180
1.71%
SISSMCI
DAR 01110100
0.01/
0.800
0.087
3.76%
MC11
SUSSMC2 DAR 0001/10
0.01/-
27.064
0.803
0.176
4.705
0.095
3.58%
MC12
SuSSMC
DAR 0,00/55
0,01/-
27.070
0.799
0.179
4.712
0.088
3.74%
MC13
SISSMCI
DAR 0,001/1
1.1
0.01/-
26.853
0.793
0.184
4.741
0.059
4.38%
MC14
SUSSMCI DAR 0.001/10
DAR
0.001/10
26.966
0.797
0.180
4.724
0.076
4,00%
SiSSMCI DAR 0.001/10
0.001/1
27.108
0.801
0.177
4.717
0.083
3.85%
SiSSMCI 0.001/10
1/1
27.088
0.178
0.117
3.10%
MC17
SiSMCI DAR 0,01/100
10 9/10
27.101
0.802
0.178
4,681
0.1
3.06%
MC7
ScSSMC2 DAR 0.001/10
DAR
10
5/10
27.159
0.805
0.175
4.673
0.127
2.88%
MC8
SUSSMC3 DAR
0.001/10
DAR
10
P/10
27.245
0.808
0.174
4.650
0.150
2.37%
30

---

Published as a conference paper at ICLR 2026
K.5
TREEHILL FROM MIPNERF-360
Table 21: Quantitative results in TreeHill from MipBerf-360 with different components for vanilla 3DGS pipeline. For AIU, the brackets denote its active iteration range (e.g., [15,30] means 15k-30k iterations). ProAIU is the sampling probability of primitives, and IJAU constrains the extra update step applied to sampled primitives. [-I[-] denote the scale value and the iteration at which it takes effect. For example,
1.,.011110.1.3. means JAIU = 0.5 after 0.1k iterations, 1/ATI: = 0.1 after 3k, and VJAI 0 before 0.1k. In Ours, AdamW-GS uses the same configuration but different StSS settings. Sparse denotes using Sparse Adam or Adam, and Half means using Adam in densification but Sparse Adam P-Op. RSR here means only adding RSR to the pipeline.
cite
Sparse
AIU
PROATO
NATU
noise
resct
Ours
PSNR
SSIM
LPIPS
N₂/m
Na/m
AN,
GS1
22.534
0.633
0.326
3,547
0.228
GS2
22.477
0.629
0.340
2.701
0.027
-2388%
GS3
Half
22.558
0.634
0.327
3,820
0.031
7.69%
GS0
SISSGS! RSR
22.447
0.320
2,887
0.016
-18.6%
GS4
Halt
[15330]
0.5
[0.1
22.538
0.633
0.327
3.732
0.052
5.21%
GS15
Hall
[15,30]
1.0
[0.1]115]
22.577
0.634
0.325
3,726
0.083
5.04%
GS16
10.1.151
0.5
[0.1110.11
-1.66%
G817
[0.1.7]
0.2
10.5][0.1]
22.633
0.631
0.335
3.304
0.029
6.85%
[0.2.0.5.00.]
GS18
[0.1,15]
0.2
22,509
0.631
0.334
3,490
0.030
-1.60%
[0.1.1.7]
10.5.0.11
GS19
[0.1.15]
0.2
22.537
0.630
0.335
3,131
0.026
11.7%
[0.1.3]
10..D....0..1
GSS
10.1.15)
0.2
[0.1337]
22.558
0.631
0.334
3.553
0.029
0.169%
G86
[0.1,30]
1.0
[0.1][0.1]
22.484
0.631
0.331
4.074
0.080
14.8%
G89
SISSGS2
22.791
0.646
0.322
2.616
0.003
26.25.
GS7
SISSGIS
22.691
0.644
0.328
2.553
0.002
.28.0%
GS10
SISSGSI
22.905
0.650
0.322
2.335
0.006
-34.1%
SI5SGS2
0.005
137.1%
Table 22: Quantitative results in TrecHill from MipBerf-360 with different components for 3DGS- MCMC pipeline. AIU definitions follow the table description above (Table 21). For RSR, the sampler defaults to uniform (interval 100) except SISS. R denotes the form of regularization, its hyperparameter, and max corresponds to C2 in the paper; other parameters remain default. 0 in SISSMC1 denotes using 01 = 02 = 0 here.
cite
Sparse
ATU PrOAIU/RAIU
RSR
R.
An/max.
R.
A./max,
PSNR
SSIM
LPIPS
N.lm
Na/m
A.a
MCI
L1
0.01/.
L1
0.01/
22,894
0.655
0.310
3.329
0.37
-6.14%
MC2
L.I
0.01/-
T.1
0.01/-
23.023
0.659
0.300
3.621
0.079
2.08%
MC3
V
[0.1.30]
0.1/0.1
LI
0.01/-
L1
0.01A
23.012
0.658
0,302
3.612
0.088
1833%
MC4
[3,30]
0.100.1
SISSMCI
0.01/-
V
[26.30]
DAR
9/10
1.94%
MC6
V
[26.30]
0.01/1
SISSMC2
DAR
0.001/10
DAR
P/10
22.715
0.660
0,268
3.622
0.078
2.11%
MC18
S
LI
0,014-
LI
0.014
22.930
0.663
0.291
3,591
0,109
1.21%
MC19
SISSMCI
L1
0014
LI
0.014
22.918
0.663
0.285
3.580
0.120
0.93%
MC20
SISSMC2
L.
0010
0,014
22.953
0.654
0.312
3.323
0.377
-6.32%
MC9
SISSMCT DAR 0.001/-
LI
0.01A
MC10
SISSMCI
0.001/10
0.270
3.653
2.98%
MC11
SISSMC2 DAR 0.001/10
LI
0.01A
22.740
0.660
0.268
3.654
0,046
3.01%
MC12
SISSMCI DAR 0.001/5
LI
0.01/
22.684
0.655
0.271
3.654
0.046
3.01%
MC13
SISSIII DAR
0,001/1
T.I
0.014-
22,533
0.652
0.274
3.663
0.037
3.27%
MC14
SISSMCI DAR 0.001/10
DAR
0.001/10
22.690
0.655
0.270
3.663
0.037
3.27%
MCIS
SISSICI 0.001/10
DAR
0.001/1
0.270
3.661
3.21%
MC16
SISSMII 0.001/10
DAR
10
0.270
3.638
2.56%
MC17
/
SISSMCI DAR 0.001/10
DAR
110P/10
22,806
0.658
0.270
3.639
0.061
2.59%
MC?
SiSSMC2 DAR 0.001/10
DAR
10
1/19
22,836
0.661
0.268
3.637
0.063
2.53%
MC8
SISSMC3 DAR
0.001/10
DAR
10-P/10
22.866
0.662
0.265
3.630
0.07
2.34%
31

---

Published as a conference paper at ICLR 2026
6.6 ROOM FROM MIPNERF-360
Table 23: Quantitative results in Room from MipBerf-360 with different components for vanilla 3DGS pipeline. For AIU, the brackets denote its active iteration range (e.g. [15,30] means 15k-30k iterations). ProAIU is the sampling probability of primitives, and NAIU constrains the extra update step applied to sampled primitives. [-][-] denote the scale value and the iteration at which it takes effect. For example, [0.5,0.1][0.L]
means 7AI 0.5 after 0.1k iterations, 7ATU = 0.1 after 3k, and VJAIU = 0 before 0.1k. In Ours, AdamW-Cr uses the same configuration but different StSS settings. Sparse denotes using Sparse Adam Adam, and Half means using Adam in densification but Sparse Adam in P-Op. RSR here means only adding RSR to the pipeline.
cite
Sparse
AIU
PROATU
MAIC
noise
Ours
PSNR
SSIM 0.920
LPIPS
N,im
Na/m
A.N
GS1
31,500
0.221
1.374
0.202
GS2
31.096
0.917
0.231
1,131
-17.6%
GS3
Hall
31.607
0.921
0.220
1.537
0.041
11.8%
GS0
SISSGSI
31,541
0.921
0,220
0.994
0.017
-28.8%
GS4
Hall
[15,30]
0.5
[0.5
31.719
0.921
0.220
1.496
0.111
8.87%
GSIS
Half
[15.30]
1.0
[0.1][15]
31.614
0.921
0,220
1.466
0.113
6.69%
GS16
[0.1.151
0.5
10.11]0.11
31.389
0.919
0,228
1.447
0.034
5.31%
GS17
[0.1.7]
0.2
[0.5][0.1]
[0.2,0.5.0.1]
GS18
[0.1,15]
0.2
31.379
0.918
0.227
1,473
0.037
7.20%
[0.1.1.]
[0.5,0.11
GS19
10.1.15]
0.2
[0.1.3]
[0.8.0.5.0.1]
GS5
[0.1.15]
0.2
31,509
0.919
1.504
0.036
9.46%
[0.1.3.7]
G56
[0.1.30]
[0.1]]0.1]
31,259
1.549
0.066
12.7%
GS13
SISSGS3
31.768
0.920
0,227
0.617
0.006
55.1%
GS7/GS8
SiSSGSI
31.741
0.921
0.222
0.624
0.005
-4.66
GS14
StSSGS4
31,753
0.920
0,222
0.632
0.005
-54.0%
Table 24: Quantitative results in Room from MipBerf-360 with different components for 3DGS- MCMC pipeline. AIU definitions follow the table description above (Table 23). For RSR, the sampler defaults to uniform (interval 100) except StSS. R denotes the form of regularization, its hyperparameter, and max corresponds to C, the paper; other parameters remain default. in StSSMC1 denotes using 01 a2 = 0 here.
cite
Sparse
AIU
PROASU/RATU
RSR
R.
A./max,
R.
A./max,
PSNR
SSIM
LPIPS
N./m
Na/m
AN
MCI
0.01/-
LI
0.017-
32.03
0.927
0210
1,320
0.250
-3.93%
MC2
L1
0.01/-
L1
0.01/-
32.417
0.929
0.209
1.472
0.098
7.13%
MC3
[0..300
0.100.1
0.011-
L1
0.01/-
32.493
0.930
0.207
1.438
0.132
4.65%
MC4
[3.30]
0.1/0.1
SISSMCI
0.01/-
L1
0.01/-
32.498
0.930
0.204
1.351
0.219
-1.67%
MC6
[26,30]
0.01/1
SISSMII
DAR
0.001/10
DAR
10
9/10
19.068
0.734
0.387
1,505
0.065
9.53%
MC18
SISSMCT
L1
0,01/-
L1
0.01/-
32,328
0.929
0.207
1.428
0.142
3.93%
SISSMCI
0,000
32.514
0,930
MC20
SiSSMC2
L.1
0010
1.1
0.11/-
31.179
0.922
0.213
1.126
0.444
-18.4%
MC9
SESSMCI DAR 0.001--
0.01/-
32.498
0.930
0.204
1,351
0.219
-1.67%
MC10
SISSMI
32.600
1.536
MCL1
SISSMC2 DAR 0.001/10
L1
0.01/-
32,542
0.933
0.197
1.535
0.035
11.7%
MC12
SISSMCI DAR 0.01/5
32.611
0.933
0.197
1,536
11.7%
MC13
SiSSMII DAR 0.00/11
L1
0.01/-
32.317
0.932
0.7
1,546
0.024
12.5%
MC14
SISSMCI DAR 0.001/10
DAR
0.001/10
32.547
0.933
0.195
1,528
0.042
11.2%
MC15
SISSMC
32.586
0,933
0.196
1.528
11.2%
MC16
SISSMCI DAR 0.001/10
10
71
32.647
0.933
0.197
1,515
0.055
10.2%
MCBMC?
StSMMI DAR 0.001/10
DAR
10 9/10
32.651
0.933
0.19
1,515
0.055
10.2%
MC21
SISSMC2 DAR 0.001/10
DAR
101
32.647
0.933
0.197
1,512
0.058
10.0%
32

---

Published as a conference paper at ICLR 2026
K.7 COUNTER FROM MIPNERF-360
Table 25: Quantitative results in Counter from MipBerf-360 with different components for vanilla 3DGS pipeline. For AIU, the brackets denote its active iteration range (e.g., [15,30] means 15k-30k iterations). ProAIU is the sampling probability of primitives, and NAIU constrains the extra update step applied to sampled primitives. [-][-] denote the scale value and the iteration at which it takes effect. For example, [0.5,0.1][O..]
means 7AI 0.5 after 0.1k iterations, 7ATU 0.1 after 3k, and VJAIU = 0 before 0.1k. In Ours, AdamW-Gs uses the same configuration but different StSS settings. Sparse denotes using Sparse Adam Adam, and Half means using Adam in densification but Sparse Adam in P-Op. nSB here means only adding RSR to the pipeline.
cite
Sparse
AIU
PIOAJU
NATU
noise
Ours
PSNR
SSIM
LPIPS
N./m
Na/m
A.N
GSI
29.046
0.909
0.201
1.092
0.097
GS2
28,979
0.907
0.205
1.005
0.034
-7.96%
GS3
Half
29.065
0.909
0.201
1.115
0.076
2.10%
GS0
V
SISSGS
29.026
0.909
0.202
0.768
0.011
-30.6%
GS4
Halr
[15.30]
0.5
[0.]][15]
29,060
0.909
0.201
1.124
0.067
2.93%
GS15
Half
[15.30]
1.0
[0.1](15]
29.079
0.909
0.201
1.067
0.116
-2.28%
GS16
V
[0.1.15]
0.5
[0.11
28.947
0.908
0.204
1.163
0.035
6.50%
GS17
[0.1.7]
[0.5][0.]]
[0.200.5.00.]
GS18
[0.1.15]
0.2
29.010
0.908
0.203
1.199
0.036
9.97%
[0.1.1.7]
10.5,0.11
GS19
[0.1.15]
[0.1.3]
[0.8.0.5.0.1]
GS5
[0.1.15]
0.2
28. 28.998
0.908
0.202
1,221
11.81%
[0.1.3.7]
GS6
[0.1,30]
1.0
[0.1][0.]]
0.908
0.202
1.257
GS13
SISSGS3
29.084
0.907
0.204
0.579
0.005
46.9%
GS7/GS8
SiSSGSI
292
0.907
0.206
0.535
0.004
-51.0%
G4
SISSSS4
29.077
0.907
0.203
0.535
0.003
-51.0%
Table 26: Quantitative results in Counter from MipBerf-360 with different components for 3DGS- MCMC pipeline. AIU definitions follow the table description above (Table 25). For RSR, the sampler defaults to uniform (interval 100) except StSS. R denotes the form of regularization, its hyperparameter, and max corresponds to C, the paper; other parameters remain default. in StSSMC1 denotes using 01 a2 = 0 here.
cite
Sparse
AIU
PROASU/RATU
RSR
R.
A./max,
R.
A,/max,
PSNR
SSIM
LPIPS
N./m
Na/m
AN
MCI
0.01/-
LI
0.017-
29,229
0.944
0.195
1,084
0.106
-0.73%
MC2
L1
0.01/-
L1
0.01/-
29.180
0.912
0.198
1.148
0.042
5.12%
MC3
[0..300
0.100.1
0.011-
L1
0.01/-
29.194
0.914
0.196
1.140
0.05
4.39%
MC4
[3.30]
0.1/0.1
SISSMCI
0.01/-
L1
0.01/-
29.345
0.916
0.190
1.098
0.092
0.54%
MC6
[26,30]
0.01/1
SISSMII
DAR
0.001/10
DAR
10
9/10
28.791
0.916
0.186
1.148
0.042
5.12%
MC18
SISSMCT
L1
0,01/-
L1
0.01/-
29.274
0.914
0.196
1.160
0.03
6.22%
SISSMCI
0,000
29.291
0.916
0.191
MC20
SiSSMC2
L.1
0010
1.1
0.11/-
29.069
0.911
0.199
0.967
0.223
-11.4%
MC9
SESSMCI DAR 0.001--
0.01/
29.075
0.910
0.202
1.13
0.060
3.47%
MC10
SISSMI
0,001/10
0.01/
29,476
0.919
0.184
1.172
MCL1
SISSMC2 DAR 0.001/10
LI
0.01/-
29.495
0.919
0.183
1.171
0.019
7.23%
MC12
SISSMCI DAR 0.01/5
0.01/
29,470
0.919
0.184
1,143
0.047
4.67%
MC13
SiSSMII DAR 0.00/11
L1
0.01/-
29.450
0.919
0.183
1,181
0.009
15%
MC14
SISSMCI DAR 0.001/10
DAR
0.001/10
29.455
0.919
0.182
1.172
0.018
7.32%
MC15
SISSMC
29.486
0.919
0.183
0.019
MC16
SISSMCI DAR 0.001/10
10
71
29.475
0.919
0.184
1,163
0.027
6.50%
MCBMC?
SISMMI DAR 0.001/10
DAR
10
9/10
29,515
0.919
0.183
1.163
0.027
6.50%
MC21
SISSMC2 DAR 0.001/10
DAR
101
29.506
0.919
0.184
1.161
0.029
6.31%
33

---

Published as a conference paper at ICLR 2026
K.8 KITCHEN FROM MIPNERF-360
Table 27: Quantitative results in Kitchen from MipBerf-360 with different components for vanilla 3DGS pipeline. For AIU, the brackets denote its active iteration range (e.g., [15,30] means 15k-30k iterations). ProAIU is the sampling probability of primitives, and NAIU constrains the extra update step applied to sampled primitives. [-][-] denote the scale value and the iteration at which it takes effect. For example, [0.5,0.1][O._]
means 7AI 0.5 after 0.1k iterations, 7ATU 0.1 after 3k, and VJAIU = 0 before 0.1k. In Ours, AdamW-Cs uses the same configuration but different StSS settings. Sparse denotes using Sparse Adam Adam, and Half means using Adam in densification but Sparse Adam in P-Op. RSR here means only adding RSR to the pipeline.
Sparse
AIU
PROATU
MAIU
Ours
PSNR
SSIM
LPIPS
N,/m
Na/m
A.N
GSI
31.505
0.928
0.127
1.699
0.116
31.053
0.926
0.131
1.621
0.036
-4.59%
GS3
Hall
31,564
0.929
0.127
1.774
0.040
4.41%
GS0
SISSGS RER
31,072
0.922
0.133
0.930
0.013
-45.2%
GS4
Hall
[15.30]
0.5
10.11|15
31.531
0.929
0.127
1.721
0.089
1.29%
GSIS
Half
[15,30]
[0.1][15]
31,509
0.929
0.127
1.602
0.237
-5.00%
GS16
[0.1.15]
0.5
10.1110.11
31.110
0.926
0.130
1.766
0.035
3.94%
[0.1.7]
[0.5][0.]]
31.389
1.740
0.037
[0.200,,00.1]
GS18
[0.1.15]
30.997
0,926
0.129
1.769
0.035
4.12%
[0.1.1.7]
10.5.0.11
[0.1.15]
31,330
0.129
1.724
[0.1.3]
[0.800.500.]]
[0.1.15]
0.2
31.355
0.927
0.129
1.772
0.036
4.29%
[0.1.3.]]
[0.1.30]
[0.
31.404
0.928
0.128
1,782
0.069
GS13
SISSGS3
31,770
0.927
0.131
0.692
0.005
-5..3%
GS7/GS8
SISSGSI
31.728
0.927
0.132
0.667
0.004
.60.7%
GS14
SISSGS4
31,741
0.926
0.133
0.667
0.004
-60.7%
Table 28: Quantitative results in Kitchen from MipBerf-360 with different components for 3DGS- MCMC pipeline. AIU definitions follow the table description above (Table 27). For RSR, the sampler defaults to uniform (interval 100) except StSS. R denotes the form of regularization, its hyperparameter, and max corresponds to C, the paper; other parameters remain default. in StSSMC1 denotes using 01 a2 = 0 here.
cite
Sparse
AIU
PrOASU/MATU
RSR
R.
A./max,
R.
A./max,
PSNR
SSIM
LPIPS
N./m
Na/m
AN
MCI
0.01/-
LI
0.017-
32.173
0.933
0.122
1.661
0.149
-2.23%
MC2
L1
0.01/-
L1
0.01/-
32.079
0.934
0.122
1.753
0.057
3.17%
MC3
[01.300
0.100.1
0.011-
0.01/-
32.286
0.934
0.122
1.743
0.067
2.58%
MC4
[3.30]
0.1/0.1
SISSMCI
0.01/-
L1
0.01/
31,765
0.909
0.137
1.681
0.129
-1.05
MC6
[26,30]
0.01/1
SISSMII
DAR
0.001/10
DAR
10
9/10
21.787
0,820
0.234
1,729
0.081
1.76%
MC18
SISSMCT
L1
0,01/-
L1
0.01/-
32,363
0,346
0.120
1.72
0.09
1.23%
SISSMCI
0,000
32.289
0.119
1.714
MC20
SiSSMC2
L.1
0014
1.1
0.11-
31,924
0.931
0.124
1.495
0.315
-12.0%
MC9
SESSMCI DAR 0.001--
0.01/-
32.342
0.934
0.121
1,703
0.107
2.35%
MC10
SISSMI
32.570
1.765
MCL1
SISSMC2 DAR 0.001/10
L1
0.01/-
32,397
0.935
0.118
1,763
0.047
3.76%
MC12
SISSMCI DAR 0,01/5
32.443
0.936
1,767
MC13
SiSSMI DAR 0.00/11
L1
0.01/-
32.458
0.935
0.118
1,786
0.024
5.1%
MC14
SISSMCI DAR 0.001/10
DAR
0.001/10
32,466
0.936
0.117
1,766
0.044
3.94%
MC15
SISSMC
32.173
0.935
0.118
1.766
3.94%
MC16
SISSMCI DAR 0.001/10
10
32.521
0,936
0.117
1,756
1.756
3.35%
MCBMC?
StSMMI DAR 0.001/10
DAR
10 9/10
32,546
0.937
0.117
1.755
1.755
3.29%
MC21
SISSMC2 DAR 0.001/10
DAR 10
111
32.298
0.936
0.117
1.753
0.057
3.17%
34

---

Published as a conference paper at ICLR 2026
K.9 BOSAI FROM MIPNERF-300
Table 29: Quantitative results in Bosai from MipBerf-360 with different components for vanilla 3DGS pipeline. For AIU, the brackets denote its active iteration range (e.g. [15,30] means I 15k-30k iterations). ProAIU is the sampling probability of primitives, and TJATU constrains the extra update step applied to sampled primitives. [-][-] denote the scale value and the iteration at which it takes effect. For example,
means 7AIU 0.5 after 0.Ik iterations, 7AIU 0.1 after 3k, and YAAIU = 0 before 0.1k. In Ours, AdamW-GS uses the same configuration but different StSS settings. Sparse denotes using Sparse Adam Adam, and Half means using Adam in densification but Sparse Adam in P-Op. RSR here means only adding RSR to the pipeline.
Sparse
AIU
PROATU
MAIU
Ours
PSNR
SSIM
LPIPS
N,/m
Ng/m
A.N,
GSI
32.269
0.943
0.207
1.159
0.115
31.610
0.216
1.230
0.016
6.12%
GS3
Half
32.325
0.943
0.206
1.256
0.017
8.36%
GS0
SISSGSI nsn
32.284
0.942
0.205
1,003
0.011
-13.4%
GS4
Hall
[15.30]
0.5
10.11115
32.382
0.943
0.206
1,230
0.037
6.12%
GSIS
Half
[15,30]
[0.1][15]
32.406
0.943
0.206
1.208
0.072
4.22%
GS16
[0.1.15]
0.5
[0.1][0.1]
32.243
0.942
0.209
1,360
0.016
17.3%
[0.1.7]
10.511.111
0.208
1.353
0.017
16.7%
[0.20.,,0..1]
GS18
[0.1.15]
32.293
0,943
0.208
1.370
0.015
18.2%
[0.1.1.7]
10.5.0.11
[0.1.15]
32.260
1,283
[0.1.3]
[0.800..00.1]
[0.1.15]
[0.1.3.7]
32,260
0.208
1.378
0.016
18.8%
[0.1.30]
10.111.111
32.251
0,942
0.208
1.428
0.034
GS13
SISSGS3
32,409
0.942
0.204
0,807
0.004
-30.3%
GS7/GS8
SISSGSI
32.251
0.942
0.205
0.747
0.004
33.55%
GS14
SISSGS4
32.279
0.206
0.735
0.003
-36.5%
Table 30: Quantitative results in Bosai from MipBerf-360 with different components for 3DGS- MCMC pipeline. AIU definitions follow the table description above (Table 29), For RSR, the sampler defaults to uniform (interval 100) except SiSS. R. denotes the form of regularization, its hyperparameter, and max corresponds to C. the paper; other parameters remain default. 0 in SISSMCI denotes using 01- 02 0 here.
cite
Sparse
AIU
PROATV/AAU
RSR
R.
Amaxa,
R,
A,/max,
PSNR
SSIM
LPIPS
N,/m
Na/m
A.
32.572
MC2
Ll
0.01/-
L.1
0.01/-
32.508
0.945
0.203
1,200
0.070
3.53%
MC3
[0.1.30]
0.170.1
0.011-
L1
0.01/
32.588
0.946
0.202
1.19]
0.079
2.76%
MC4
[3_30]
0.1/0.1
SISSMC1
32.742
-2.50%
MC6
[26.30]
0.01/1
SISSMCI
DAR
0.001/10
DAR
10-2/10
29.919
0.922
0.213
1.204
0,066
3.88%
MC18
SESSMCI
L1
0,01/
LI
0.01/-
32.527
0.946
0.201
1,205
0.065
3.96%
MC19
SUSSMC1
0011
0.01/-
32.645
0,947
0.199
1,201
0.069
3.62%
MC20
SISSMC2
0,01/
0.01/
32.417
0,944
0.204
0.959
0,311
-17.2%
MC9
SiSSMCI DAR 0.017-
1.1
0.017
32,513
01943
0.206
1.184
0.086
2.15%
MC10
SiSSMII DAR 0001/100
0,014-
33.006
0,950
0.191
1,221
0.049
5.34%
MCII
ScSSMC DAR 0.001/10
0.01/-
32,990
0.950
0.189
1.234
0,036
6.47%
MC12
SiSSMC1 DAR 0001/5
L1
0.01/-
32,990
0.950
0.189
1.237
0.033
6.72%
MC13
SISSMCI DAR 0.00/11
0.01/
32,921
0,950
0.190
1,252
8.02%
MC14
SISSMC1 DAR 0.001/10
DAR
0.001/10
32.916
0.950
0.189
1.235
U.037
6.38%
MCIS
SISSMCI
0.001/1
32.906
0,950
0.189
1.232
MC16
SISSMCI
10 1/1
32,990
0,950
0.190
MCR/MC7
SISSMCI DAR 0.001/10
DAR
9/10
33.022
0,950
0.190
1.220
0.050
5.26%
MC21
SrSMCC DAR 0.001/10
DAR 10 9/10
33.007
0.950
0.190
1,219
0.051
5.17%
35


Reviews:
[{"review_id": "y9ONp5mROi", "reviewer": "Reviewer_A2qo", "summary": "This paper revisits optimization in 3D Gaussian Splatting and argues that standard practice (Adam + synchronous updates) introduces two harmful couplings: (i) update-step coupling that rescales optimizer states and updates invisible primitives, and (ii) gradient/regularization coupling that makes effective weight decay depend on Adam’s second moment. It decomposes the training recipe into three parts: Sparse Adam, Re-State Regularization, and Decoupled Attribute Regularization, and then re-couples the beneficial pieces into AdamW-GS. Across vanilla 3DGS and 3DGS-MCMC, the paper reports consistent quality gains and meaningful wall-clock savings. Their method also reduces redundancy while improving rendering performance.", "questions": "I am having a hard time connecting the cits (e.g., GSs, MCs, Ours) when reading the paper. Primarily, I need to frequently read the Appendix and identify the differences in the configuration. It would be better to provide a clearer explanation or include the difference in the table consistently.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* This paper pinpoints that Adam synchronously updates even invisible primitives, rescaling their moments and changing attributes despite zero gradients (coined Implicit Update). Such a study helps the understanding of the 3DGS Optimization procedure. \n* On outdoor scenes, the method reduces primitives by 48.4% while improving PSNR by +0.2 dB and SSIM by +0.01; on indoor scenes, it removes 50% of primitives while still gaining +0.1 dB PSNR, unlike MaskGaussian, which removes 61% but drops PSNR by 0.1 dB. The proposed approach strikes a better balance. Further, Table 4 (Deep Blending, Tanks & Temples) shows that AdamW-GS surpasses vanilla baselines.\n* Time-cost breakdowns show large step-time and total runtime reductions compared with baselines.", "weaknesses": "* The comparison emphasizes MaskGaussian (and RePR), but omits other density-control splatting methods (Compact3DGS, Deformable beta splatting) cited in related work. Without matched-budget comparisons on the same scenes, it’s hard to evaluate the reported ~48–50% primitive reductions with small PSNR/SSIM gains compared with various baselines.\n* All the per-scene tables report single PSNR/SSIM/LPIPS numbers with no error bars or seed variance, so it’s unclear whether gains are stable across runs or due to initialization. Given the small rendering quality gap compared with the baselines, it is necessary to have the error bars (at least with several examples) to understand the significance of the improvements.\n* Most results emphasize vanilla 3DGS and 3DGS-MCMC setups on standard static benchmarks; there’s little evidence for large-scale indoor scans, or outdoor long-range sequences where visibility patterns and sparsity differ. A dedicated failure case section will help to further study the method.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "snX1aq08Yk", "reviewer": "Reviewer_AiQe", "summary": "The paper re-examines optimization in 3D Gaussian Splatting (3DGS) and argues that two kinds of coupling: (i) update-step coupling from synchronous Adam that induces \n\"implicit updates\" on invisible primitives, and (ii) gradient coupling where regularization gradients are mixed into Adam's moments. It proposes a three-part redesign: Sparse Adam for view-conditioned updates, Re-State Regularization (RSR) to periodically rescale moments, and Decoupled Attribute Regularization (DAR) that removes $\\nabla R$ from moment updates and applies a preconditioned, clipped regularization step. The recoupled system (\"AdamW-GS\") is shown to improve PSNR while reducing total runtime.", "questions": "+ The \"hand-crafted\" StSS schedule  is the method's most significant liability. How sensitive is the performance to this schedule? Could authors provide additional experiments on different scenes with the same schedule?\n\n+ The paper notes that Sparse Adam alone degrades performance, and the RSR component is required to \"fix\" it. This suggests a tight, possibly brittle, inter-dependency. How robust is the method to the RSR hyperparameters? If the $\\alpha$ values are slightly misconfigured, does the optimization fail entirely?\n\n+ Regarding the ablation studies for DAR, it remains unclear whether the observed benefits stem from DAR's adaptive mechanism (i.e., scaling by $\\sqrt{\\hat{v}}$) or simply from its resultant effective magnitude. Please include baselines where (a) L1 and (b) constant-penalty (AdamW-style) are tuned to match DAR's average/max regularization step (with and without $C_t$), to rule out scale effects.\n\n+ Given that the noise-based exploration mechanism is scene-dependent and can be harmful, what alternative exploration strategies could be integrated? Could the RSR's moment-rescaling be adapted to also induce exploration (e.g., by adding noise during rescaling) rather than just activating regularization?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "+ The motivation is well-explained, and provides carefully analysis (with figures and measurements) to show the synchronous Adam rescales moments even with zero gradients, producing implicit updates.\n+ Sparse Adam + RSR + DAR is easy to implement, integrates with both vanilla 3DGS and 3DGS-MCMC\n+ Experimental results show AdamW-GS improves quality and cuts runtime", "weaknesses": "+ The proposed AdamW-GS optimizer is far more complex to tune than the standard Adam. It introduces numerous new hyperparameters, such as moment scaling factors ($\\alpha_1$, $\\alpha_2$) for RSR 15, and regularization scales ($\\lambda$) and clipping values ($\\mathcal{C}_t$) for DAR 16. This may pose challenges to directly applied hyper-parameter settings on MipNerf360 to other scenes.\n\n+ Related to first point, the crucial RSR component relies on a \"hand-crafted\" milestone-based schedule (StSS) to function. This schedule is manually designed for the test datasets (see Fig. 6) and is unlikely to generalize to new scenes or datasets without being re-tuned\n\n+ The claim of removing primitives \"without introducing additional pruning components\" is nuanced. The method works by aggressively pushing opacity below the existing 1/255 threshold, at which point the original 3DGS rendering pipeline already excludes them.\n\n+ Some important ablations are missing. For example, the contribution of DAR is not isolated in the ablation studies. To prove DAR’s advantage isn’t just a scale/clip effect, the paper should include step-size-matched baselines (e.g., L1 with λ tuned to match DAR’s average regularization step; AdamW-style constant penalty with matched effective step). Current comparisons don’t fully disentangle mechanism vs magnitude.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "C5OMIl7Pg9", "reviewer": "Reviewer_odb6", "summary": "The authors analyzed Adam optimizer for the problem of 3DGS optimization, provided several observations and modifications on the optimizer to be more effective, summarized as AdamW-GS. Specifically, they made the observation that the previously proposed sparse Adam is effective at eliminating dead gaussians, but also lead to performance degradation. To resolve this, they have proposed steps such as Re-State Regularization (RSR) and Decoupled Attribute Regularization (DAR). RSR aims at better activating regularization by rescaling the moment, by introducing two additional scaler. DAR aims to decouple the main objective function (photometric loss) and regularization (on opacity and scale), such that they do not influence each other and cause over/under regularization. Experiments demonstrate that AdamW-GS consistently improves reconstruction/NVS results compared to 3DGS/3DGS-MCMC.", "questions": "See Weakness - how would authors propose for tuning the additional hyperparameters in practice?\n\nSince Taming 3DGS is extensively referenced, has it been properly compared to this work?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The authors tackle an important problem in determining the appropriate optimization function on the problem of 3DGS reconstruction. While 3DGS has been influential, the optimization behavior can easily get stuck either due to overfitting/floaters or underfitting (blobs). \n\nThe proposed AdamW-GS shows consistent improvements compared to 3DGS and 3DGS-MCMC, with faster training process and fewer (dead) gaussian primitives. \n\nI am not an expert in optimization, but the experiments, observations, and modifications seem reasonable and generalizable enough to me.", "weaknesses": "The modification in AdamW-GS introduces additional hyperparameters, with no obvious intuition in how to adjust them. The RSR parameters, for example, are obtained through grid search. While observations show that the regularization term is sometimes over/under effective, it is unclear to me how to determine over/under fitting based on a single run and tune hyperparameters accordingly. \n\nI find the table listing of MC1, MC2, etc. to be confusing and difficult to cross reference and understand what the authors are doing.\n\nA few papers on automated efficient 3DGS may be worth citing:\n\nPUP-3DGS (Hanson et al., CVPR25) - determines dead gaussians/gaussians with low contribution to loss\nLP-3DGS (Zhang et al. NIPS24) - automatically reduces gaussian counts during training, similar to AdamW-GS\n3DGS-LM (Höllein et al. ICCV25) - Optimization with Levenberg-Marquardt instead of Adam", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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:

Decision: Accept (Poster)