Quantifying and Alleviating Co-Adaptation in Sparse-View 3D Gaussian Splatting
Authors: Kangjie Chen
Yingji Zhong
Zhihao Li
Jiaqi Lin
Youyu Chen
Minghan Qin
Haoqian Wang
Venue: NeurIPS 2025 poster ()
Keywords: gaussian splatting; sparse-view reconstruction; co-adaptation;
Primary area: applications
TL;DR: This paper introduces the concept of co-adaptation in 3D Gaussian Splatting, analyzes its impact on rendering artifacts, and proposes strategies to reduce it.

Abstract: 3D Gaussian Splatting (3DGS) has demonstrated impressive performance in novel view synthesis under dense-view settings. However, in sparse-view scenarios, despite the realistic renderings in training views, 3DGS occasionally manifests appearance artifacts in novel views. This paper investigates the appearance artifacts in sparse-view 3DGS and uncovers a core limitation of current approaches: the optimized Gaussians are overly-entangled with one another to aggressively fit the training views, which leads to a neglect of the real appearance distribution of the underlying scene and results in appearance artifacts in novel views. The analysis is based on a proposed metric, termed Co-Adaptation Score (CA), which quantifies the entanglement among Gaussians, i.e., co-adaptation, by computing the pixel-wise variance across multiple renderings of the same viewpoint, with different random subsets of Gaussians. The analysis reveals that the degree of co-adaptation is naturally alleviated as the number of training views increases. Based on the analysis, we propose two lightweight strategies to explicitly mitigate the co-adaptation in sparse-view 3DGS: (1) random gaussian dropout; (2) multiplicative noise injection to the opacity. Both strategies are designed to be plug-and-play, and their effectiveness is validated across various methods and benchmarks. We hope that our insights into the co-adaptation effect will inspire the community to achieve a more comprehensive understanding of sparse-view 3DGS.

Quantifying and Alleviating Co-Adaptation in Sparse-Vit View 3D Gaussian Splatting
Kangjie Chen'*
Yingji Zhong? Minghan Qin'
Zhihao Li
Jiaqi Lin'
Youyu Chen'
Haoqian Wang"
Tsiinguua University
HKKUST
HHuawei Noah's Ark Lab
*Harbin Institute of Technology
Abstract
3D Gaussian Splatting (3DGS) has demonstrated impressive performance in novel view synthesis under dense-vier settings. However, in sparse- sparse-view scenarios, despite the realistic renderings in training views, 3DGS occasionally manifests appearance artifacts in novel views. This paper investigates the appearance artifacts in sparse-view 3DGS and uncovers a core limitation current approaches: the optimized Gaussians are overly-entangled with another aggressively fit the training views, which leads to a neglect of the real appearance distribution of the underlying scene and results in appearance artifacts novel views. The analysis is based on a proposed metric, termed Co-Adaptation Score (CA), which quantifies the entanglement among Gaussians, i.e., co-adaptation, by computing the pixel-wise variance across multiple renderings of the same viewpoint, with different random subsets of Gaussians. The analysis reveals that the degree of co- adaptation is naturally alleviated as the number of training views increases. Based on the analysis, we propose two lightweight strategies to explicitly mitigate the co- adaptation in sparse-vies view 3DGS: (1) random gaussian dropout; (2) multiplicative noise injection the opacity. Both strategies are designed be plug-and-play and their effectiveness is validated across various methods and benchmarks. We hope that our insights into the co-adaptation effect will inspire the community to achieve more comprehensive understanding of sparse-view 3DGS.
Introduction
Recent advances 3D Gaussian Splatting (3DGS) [1] have demonstrated remarkable capabilitics for photorealistic novel view synthesis in dense-view settings. However, under sparse-view supervision, 3DGS often suffers significant performance degradation in novel view rendering, manifesting as artifacts caused by incorrect geometry or appearance distribution due to limited supervision from training views. Existing works mainly improve sparse-view 3DGS through geometry regularization, such monocular depth constraints [2, 3, 4, 7, 8, 9], matching-based point initialization [10], and dense point initialization [11, 12]. Although these methods achieve improvements by enhancing geometric accuracy, few have investigated appearance artifacts in sparse-viet 3DGS. These artifacts, often overlooked, are common in novel view rendering and typically manifest as occasional color cefiiers-coloy not belonging to the scene-as as illustrated in Figure 1. In this paper, focus on analyzing and mitigating appearance artifacts in the novel view rendering of sparse-view 3DGS.
We begin analysis by revisiting the rendering characteristics of 3DGS. In the splatting process, each pixel receives contributions from multiple Gaussians projected onto its corresponding tile on the
* This work done while he intern Huawei.
Conreponndng author. E-mail: wanghaoqian anw.asignninnninnuaa... edu, cn
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Why do we see colors that don't belong to the scene?
Gread Toch
S0GS Render
3ICS Rriseer
Goord
SPGSS
Figure I: Appearance artifacts in sparse-view 3DGS. In novel view rendering, the optimized 3DGS occasionally produces colors that do not match the scene's true appearance distribution.
image plane [1]. This effective appearance modeling under dense-view settings. However, it also introduces potential entanglement between Gaussians, especially when they are jointly optimized to fit overlapping pixel regions in the training views. In sparse-view scenarios, such entanglement becomes problem- atic-muliiple Gaussians with divergent colors may aggressively collaborate fit limited training pixels, ignoring the true underlying appearance distribution. Here, we refer to this entanglement as co-adaptation 3DGS, and hypothesize that appearance artifacts sparse-view novel view synthesis are closely related to excessive co-adaptation.
composition is fundamental characteristic of 3DGS, enabling
To validate our hypothesis, propose metric quantify the level of co-adaptation across Gaussians, namely the Co-Adaptation score (CA). Specifically, we randomly select subsets Gaussians using dropout and render the same target view multiple times. The CA score is computed the average per per-pixel variance across these renderings. In the appendix, we further provide a theoretical derivation showing that the CA score directly reflects the coupling between the color and opacity attributes of Gaussians. Empirically, we observe that the CA score decreases as the number of training views increases. This suggests that the degree of co-adaptation in 3DGS tends to be naturally suppressed as the training data becomes denser. This observation inspires us to further investigate whether explicitly reducing co-adaptation in sparse-view 3DGS can improve novel view rendering quality.
To mitigate co-adaptation in viee 3DGS, we propose two simple yet effective strategies. (1) apply dropout during training by sampling subset of Gaussians, disrupting excessive entanglement among Gaussians. (2) We inject multiplicative noise into the opacity parameters throughout training, perturbing each Gaussian's 's contribution to the rendered pixel. Unlike perturbing position color, which can harm convergence, or perturbing scale, which tends to cause blurring, opacity noise provides softer, more targeted regularization by destabilizing the reliance structure among co-adapted splats. Both strategies are plug-and- hlug-and-play. and their effectiveness is validated across various methods and benchmarks in the experiment section.
To summarize, our contributions are as follows: (1) We analyze the source of appearance artifacts and identify the entanglement among Gaussians as the performance bottleneck for sparse-view 3DGS. (2) We propose a metric of Co-Adaptation Score (CA), to quantitatively measure the entanglement among Gaussians in sparse-view 3DGS. (3) Based on the analysis and the proposed metric, further propose two plug-and and-play training strategies that can suppress co-adaptation among gaussians, i.c. random gaussian dropout and multiplicative noise injection, whose effectiveness is validated across various methods and benchmarks.
Related Work
3D Gaussian Splatting under Sparse Views. Recent studies have explored a variety of strategies to improve 3D Gaussian Splatting (3DGS) [1] under sparse-view supervision. Some approaches [2, 3,

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5, 6, 7, 8, 9] incorporate external geometry priors, typically from monocular depth estimators [13, 14]. to enforce multi-view depth consistency and enhance geometric fidelity. Other works [15, 16, 17, 18, 19, 20, 21J leverage generative priors from diffusion models to synthesize plausible unseen views or guide view-dependent effects. In addition, other methods [10, 22, 23] introduce self-supervised or physically motivated regularization strategies, such opacity decay, innocular-guided photometric consistency, and dual-model co-regularization, to suppress floating artifacts and improve geometric consistency. Additionally, a separate line of work [4, 6, 24, 25, 26, 27, 28, 29, 30] departs from per-scene optimization by training neural predictors across large-scale data to directly infer 3DGS representations from sparse imputs. Recent works [31, 32] have also explored dropout- based strategies for improving sparse-view 3DGS performance. While both of them report clear improvements, they attribute the effectiveness of dropout to empirical factors-
reducing overfitting through fewer active splats [31], or enhancing gradient flow to distant Gaussians [32]. In contrast, our work identifies and formalizes co-adaptation suppression the key underlying mechanism, offering more principled explanation for why dropout benefits sparse-view generalization in 3DGS.
Co-Adaptation in Neural Networks. Co-adaptation describes the tendency of neurons in neural networks to become overly dependent during training, leading to overfitting and poor generalization. This issue was first highlighted by Hinton et al. [33], who proposed Dropout to mitigate such dependency by randomly deactivating neurons. Subsequent stochastic regularization methods [34, 35, 36, 37, 38, 39, 40] further promote feature diversity through randomization, consistency enforcement, or latent-space mixing. Beyond empirical methods, theoretical studies [41, 42, 43] have analyzed co- adaptation's 's negative impact generalization, linking it to sharp loss minima [41], low sensitivity to perturbations [42], and poor uncertainty estimation [43]. While these insights have been validated in classification and regression tasks, their implications for structured prediction like 3D reconstruction remain underexplored. Our work extends this investigation to 3D Gaussian Splatting, revealing similar interdependencies among spatial Gaussians and showing that dropout and opacity noise effectively mitigate co-adaptation under sparse-view supervision.
3 Co-Adaptation in Gaussian Splatting
In this chapter, we investigate co-adaptation in 3D Gaussian Splatting (3DGS) [1], which significantly affects generalization under sparse-view settings. First, we explain co-adaptation in 3DGS and analyze why excessive co-adaptation leads to artifacts in novel view synthesis. Then, we propose metric to quantify co-adaptation via variance across dropout-rendered outputs. Based on this metric, make empirical observations about co-adaptation in 3DGS. Finally, introduce two simple strategies to explicitly mitigate co-adaptation: dropout regularization and opacity noise injection.
3.1 Characterizing Co-Adaptation
Unlike explicit spatial representations [44, 45, 46] that define fixed scene geometry. 3DGS represents scenes as a set of view-dependent Gaussians without explicit surface definitions. This allows 3DGS to model flexible, cally, 3DGS renders images by projecting 3D Gaussians onto the image plane and blending their contributions using differentiable alpha compositing, The color of each pixel u is computed as:
appearance-driverr representations that adapt to different viewpoints. Specifi-
i-1
C(u) Σ SEATUa)
C: 04 (1-1aj)
(1)
j=1
where (u) denotes the set of Gaussians projected to pixel u, sorted by depth. Each or is the projected opacity of the i-th Gaussian, serving as its blending weight. As shown Equation 1, the perceived color C'(u) depends on the specific combination of Gaussians (u)) along the rendering ray. While this cooperative blending mechanism makes 3DGS highly effective in fitting the appearance of training views, its optimization objective focuses solely on minimizing the discrepancy between the rendered images and the ground-truth views. Specifically, 3DGS optimizes the Gaussian set G to minimize the reconstruction loss over training views Virsin
G arg min
Σ C()(G),),To))
G
DE Vinin
where R(g, v) represents the rendered image from view using G, and T, is the ground-truth image. The loss L supervises only the rendered outputs, without imposing any explicit internal constraints
3

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(a) dense views
(b) thin artifacts
(c) thick artifacts
(d) wrong color
Figure 2: Visualization of 3DGS behaviors under different levels of co-adaptation. Thin gray arrows indicate training views, bold arrows indicate novel view. Green arrow denotes correct color prediction, while red indicates color errors. (a) Simulates a 3DGS model trained with dense views, where Gaussian ellipsoids contribute evenly to pixel color across views, resulting accurate rendering from the novel view. (b)()(d) Simulate various cases of 3DGS trained under sparse-view settings. (b) and (c) show that co-adaptation in the training views where Gaussians contribute unequally to pixel colors results in thin and thick artifacts under novel views. (d) shows highly co-adapted case where multiple Gaussians with distinct colors collectively overfit single grayscale pixel in the training view, resulting in severe wrong color artifacts under the novel view.
on the Gaussian parameters such as position, shape, color, opacity. As result, multiple Gaussians can casily form tightly coupled combinations to each pixel the training views. This dependency becomes especially problematic under sparse-view supervision (see Figure 1), where the model tends to overfit fragile Gaussian configurations that fail to generalize to novel views.
Figure 2 further illustrates this phenomenon, showing how diverse Gaussians with different colors collaborate to reproduce grayscale pixels training views, yet produce inconsistent colors unseen views. We refer to this phenomenon as co-adaptation. To systematically understand and mitigate this effect, it is essential to establish a quantitative metric that captures the severity of co-adaptation.
3.2 Quantifying Co-Adaptation
To quantitatively analyze co-adaptation in 3D Gaussian Splatting, we define a co-adaptation score for each target viewpoint. The key idea that if set of Gaussians are overly dependent on each other, then randomly removing part of them during rendering will lead to unstable outputs. Specifically, we randomly drop 50% of the Gaussians and render the target view using only the remaining ones. We repeat this process multiple times and measure the variance across the rendered results.
randenly select Camscians
visible
US seboct
sibat
sbsak
render
CA
Var(
Figure 3: Illustration of Co-Adaptation Score (CA) Computation. Higher CA scores indicate more inconsistent renderings, suggesting stronger co-adaptation effects. Lower CA scores reflect more stable and generalizable representations.
To focus on regions where Gaussians contribute meaningfully, we define the visible region as the set blending weight exceeds a threshold of 0.8 in each rendering.
of pixels whose accumulated The final co-adaptation score computed as the average pixel-wise variance within the intersection of these visible regions across all K random dropout renderings. Formally, the score for given viewpoint v defined as:
CA(c) =
Σ uEft
Var (10)
Ω
where (k) denotes the color at pixel u in the k-th dropout-rendered image. To ensure that comparisons
are made over consistently visible regions, we define Ω. = n an (k)
> 0.8) denotes the set

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DNGaussian
Binocular3DGs
GS Count PSNR
0.0022
Test Extrapoction
Tist Extrop diatin Text Inter citerpoliion Thu View
20
0.0365
Than View
Test Interpo alion
0.0020
Na aap ZOUR cdll
3.0263
Score
0.0015
2:30
0.0355
0.0016
LOoK
Count
02920
0.0034
70k
Bino Count
DNCS Aug
0.0345
0.0012
40k-
Dino Aup
-20
12 35
30
12
155
30
3
6
10
Numberrn of Vieae
Number Vieeo
Number
(b)
Figure 4: Comparison of co-adaptation strength (CA), GS count and reconstruction quality un- der varying numbers of training views. (a-b) CA measured as pixel-wise variance for DNGaussian and Binocular3DGS on three target view types: extrapolation (far), interpolation (near), and training. (c) Gaussian count (left axis, in thousands) and average PSNR (right axis, in dB) for both methods. All plots are shown functions of input view counts, based on the LLFF "flower" scene.
CHCeaar
DiGzazer-
Eboocda 20G5
0.000
5
0000
5.00
Figure 5: Training dynamics of co-adaptation strength (CA) and reconstruction quality (PSNR) across different LLFF seenes. CA score (left axis) and PSNR (right axis) over training iterations for DNGaussian and Binocular3DGS on the "flower" and "orchids" scenes of the LLFF dataset.
of commonly visible pixels, and Olu (Ax) = EiEN as [1 aa-a) az)) is the accumulated alpha via
front-to-bace compositing .V1 represents the ordered list of Gaussians contributing to pixel u in the k-th rendering, sorted by depth and blended using front-to-back alpha compositing. A higher (A()) score reflects stronger co-adaptation, as the rendered appearance becomes more sensitive to which Gaussians are selected. We further provide a theoretical derivation in the appendix, showing that (A(v) directly reflects the coupling between the color and opacity attributes of Gaussians.
Empirical observations on Co-Adaptation score (CA) in sparse-view 3DGS. We summarize three empirical phenomena observed during sparse-view 3DGS training:
1) Increased training views reduce co-adaptation. Figure 4 shows that co-adaptation scores drop consistently as the number of training views increases, for both DNGaussian [2] and Binocu- lar3DGS [10]. While DNGaussian uses random initialization with a relatively stable Gaussian count in LLFF scenes [47], Binocular3DGS leverages pre-trained keypoint matcher [48] to generate denser initializations with more views. Despite these differences, both methods demonstrate that increasing view counts weakens co-adaptation and improves generalization.
2) Co-adaptation temporarily weakens during early training. Figure 5 shows the evolution of co-adaptation scores during training. analyze both DNGaussian and Binocular3DGS on two LLFF scenes, tracking CA scores training and novel test views. In the early stages-typically the first few thousand iterations CA scores drop sharply as the model rapidly fits visible content. Afterwards, scores stabilize and oscillate within fixed range. Notably, Binocular3DGS shows secondary increase co-adaptation after 20k iterations, coinciding with the introduction of warp- based supervision on novel views. This supervision likely introduces geometric mismatches, reinforcing undesired dependencies among Gaussians and causing the observed rise in CA.
3) Co-adaptation is lower at input views than novel views. Across nearly all scenes and training iterations (see Figure 5), co-adaptation scores at input (training) views remain consistently lower than those novel (test) views. This indicates that co-adaptation is more easily suppressed under familiar viewpoints, while novel views tend to retain stronger entanglements among Gaussians.
Inspired by these empirical findings, we investigate whether suppressing co-adaptation in 3DGS can enhance rendering quality for novel views.
5

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3.3 Strategies for Alleviating Co-Adaptation
We explore two regularization strategies to mitigate excessive co-adaptation in 3D Gaussian Splatting. First, we adapt dropout [33. 49] to randomly mask subsets of Gaussians during rendering, reducing over-reliance on fixed combinations. Second, inspired by noise-based regularization [50]. we inject Gaussian noise into opacity parameters, encouraging more flexible Gaussian contributions. Both techniques aim to enhance generalization by loosening overly rigid dependencies between Gaussians.
Dropout Regularization. Dropout is a classical regularization technique that mitigates neural network overfitting by randomly disabling subset of model components during training. Inspired by this idea, we apply a random dropout strategy to the Gaussian set during 3DGS training. At each iteration, every Gaussian has a probability p of being temporarily dropped:
Girain = {g E G 2gg =}, 2g ~ Bernoulli(1 pp)
(4)
where 9 denotes the full set of Gaussians, and 2n is binary random variable indicating whether Gaussian g is retained (z,- 1) dropped (2,, 0) during training. Each 2g is independently sampled from a Bernoulli distribution with retention probability 1 - p. The rendered image using the surviving subset Guain is then supervised against the ground truth of the corresponding training view. At test time, all Gaussians are used, but we scale their opacities to match training-tinn tamiing-time expectations:
lest = (1- g
og
train
Vg E G.
(5)
Opacity Noise Injection. Besides dropout, we explore injecting stochastic noise into Gaussian opacity to reduce co-adaptation. Unlike dropout, which removes entire Gaussians, opacity noise slightly perturbs each Gaussian's 's contribution, improving robustness to varying blending. We also tested adding noise to different parameters: 3D position noise caused instability and blur; SH coefficient noise had little effect, SH only affects color, not visibility or Gaussian count per pixel; scale noise also reduced co-adaptation but introduced blur with limited quality improvement.
Our final formulation focuses opacity:
opacity <- opacity (1+c), e~ c0
(6)
Discussion. (1) Dropout mechanism forces each ray to remain accurately supervised even when part of its contributing Gaussians are randomly omitted. As a result, the model learns to avoid over-reliance on fixed Gaussian configurations, nearby Gaussians along the ray tend acquire similar color and opacity characteristics, making them mutually substitutable. Therefore, dropout effectively alleviates excessive co-adaptation in Gaussian Splatting. Furthermore, since some Gaus- sians may be randomly dropped during training, the remaining ones tend to grow larger to maintain consistent surface coverage. This encourages the model to represent the scene using larger Gaussians, which helps reduce geometric inconsistencies and surface gaps, especially in sparse-viee view settings. By disrupting such entanglements, dropout enhances both appearance and structural generalization. (2) Opacity noise encourages nearby Gaussians along a ray to exhibit consistent color and trans- parency characteristics, making them less dependent on specific groupings. By weakening such over-specialized configurations, this strategy improves generalization under sparse-view conditions.
4 Experiments
4.1 Experiments Setup
We conduct experiments on three datasets: LLFF [47], DTU [51], and Blender dataset [52]. Following prior works [10, 53, 54, 55], we use 3 training views for LLFF and DTU, and 8 views for Blender. Test views follow prior settings [10, 53, 54, 55]. Input images are downsampled by factor 8 for LLFF, for DTU, and 2 for Blender, relative to their original resolutions.
Datasets.
Baselines. We conduct experiments on 3D Gaussian Splatting (3DGS) [1], DNGaussian [2], FSGS [3],
CoR-GS [22], and Binocular3DGS [10]. Our two proposed strategies, dropout regularization and opacity noise injection, are applied to each method to evaluate their effectiveness. Ablation studies are primarily conducted on Binocular3DGS. We follow the official implementations for all baselines. On LLFF, our reproduced results for DNGaussian and CoR-GS slightly differ from the reported values. For Blender, DNGaussian uses different training settings for different scenes, while we adopt unified setup for fair comparison, which leads to lower results. We also re-run Binocular3DGS with

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Table 1: Quantitative Comparison on LLFF and DTU Datasets. We evaluate five sparse-vien -iew 3DGS- based methods with and without our proposed co-adaptation suppression strategies, dropout regularization and opacity noise injection. We report PSNR, SSIM, LPIPS, and Co-Adaptation scores (CA) on both training and novel views to assess reconstruction quality and co-adaptation reduction.
Method
Seeting
(1FF((47)
[TT]S1]
PSNR
SSIM
1.PIPS
Train CA
Text CA
SSIM
1.PIPS
Train CA
Text CA
SUGIS 111
baseline
19.36
0.681
0.252
0,007543
0.008206
17:30
0.824
0.152
0.002096
0.00280
w/ dropeut
20.20
0.691
0.211
0.001752
D.002540
17.75
0.850
0.125
0.000757
0J002263
w/ opacity noise
19.91
0.676
0.221
0.001531
0.002300
17.27
0.839
0.140
0.001203
0,002290
DNCousian [2]
haseline
18.03
0.509
0.205
0.007234
0.007665
18.91
0.790
0.176
0,005113
0.005744
w/ drupout
19.43
0.623
0.302
0,003222
0.003821
19.86
0.828
0.149
0.001201
0.001917
opacity noise
0.008
0.294
0.045077
0.0050771
0.001011
0.0022411
FSGS [3]
baseline
0,001500
0,004558
0.00206
w/ dropous
0.716
0,009300
01802205
17.86
0.838
0.153
0.001057
0J8022766
w/ opecity noise
20.59
0.706
0.210
0.001666
0J002020
17.81
0.834
0.156
0.001096
0JII2245
CoR-GS (27)
buxeline
20.17
0,703
0.202
0,005025
0.005159
19.21
0.853
0.119
0,001090
0
w/ drapeut
21.64
0.712
0.217
0.001442
0.001617
19.94
0,868
0.118
0.009378
0.008611
w/ opacity noise
20.28
0.705
0.302
0.003731
0.003867
19:54
0.862
0.115
0.005558
0.0038 4
Binocular2DGS [10]
baseline
21.44
0.751
0.168
0,001845
0.001951
20.71
0.862
0.111
0.001399
0.001579
w/ drupout
22.12
0.777
0.154
0.000655
000979
21.00
0.875
0.108
0.000752
0.001146 146
opucity noise
22.12
0.780
0.00660
O. 0.000762
01001:366
0.001548
22.11
0,000663
0.800762
0.009736
0,001143
1DGS
dropost
openity nomeo
Grornd
deopount
opacity
Figure 6: Visual comparison on the LLFF dataset based on 3DGS and Binocular3DGS. Suppressing co-adaptation reduces color noise and improves scene geometry and detail quality.
white backgrounds to align with other methods. Baseline results in Table 2 are reported as original / reproduced, showing the original paper values and our re-implementation under the unified setup.
Metrics. To evaluate the rendering quality under novel views, we compute standard image quality metrics including average PSNR (peak -ngiie-t-noisee ratio), SSIM [56], and LPIPS [57] on each dataset. To assess the impact of different strategies on co-adaptation, we additionally report Co- Adaptation Score (CA) (Section 3.2) computed on both training views and novel test views.
Implementation Details. To ensure consistent scaling when comparing co-adaptation scores, we adjust the drop ratio during CA computation to account for training-time dropout. Specifically, in the absence dropout in training, CA is measured by randomly discarding 50% of the contributing Gaussians. When dropout with rate p (e-g. p = 0.2) used in training, we instead discard 2 (i.e., 60%) of the Gaussians during CA computation in test time.
1-p
4.2 Comparative Analysis of Co-Adaptation Suppression
(1) Analysis of Quantitative Results on Co-Adaptation and Rendering Quality. We evaluate the impact of our proposed dropout and opacity noise strategies across five DDGG-basee methods in sparse-vier -iew settings. As shown in Table 1, both strategies effectively reduce the Co-Adaptation Scores (CA) on both training and novel views across LLFF and DTU datasets, confirming their ability to mitigate over co-adaptation. We further observe that dropout generally outperforms opacity noise in improving rendering quality, consistently achieving higher PSNR and lower LPIPS in almost all tested settings. This suggests that dropout not only reduces co-adaptation but also better preserves novel view fidelity than opacity noise. However, applying both strategies together does not lead
7

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Table 2: Quantitative comparison on Blender dataset for input views. We evaluate three sparse-ieww 3DGS- based methods with and without our proposed Co vo-adaptation suppression strategies.
Method
Settng
PSNR1
SSIM
LPIPS
Train CA
Test CA 1
3DGS [1]
haseline
23.54
0.881
0,095
0.004247
0.0039377
dropout
0,001805
0,002015
w/ opacity noise
23.65
0.884
0.094
0.003167
0.0031366
DNGaussian [2]
baseline
24.31 23.41
0.886
0.879
0.088/0.097
0.004352
0.004947
drrpouu
23.98
0,089
0,001973
0.002585
w/ opucity noise
23.43
0,878
0.097
0,004282
0.004922
BinocularSDSS [10]
baseline
24.71 /23.81
0.872 0.889
0.101 00.993
0.001776
0.00198]
dirpouu
24.24
0.001
0.001539
w/ opacity moise
24.24
0,894
0.092
0,0010338
0.001179
3005
BineelbeaDes
Ground Truth
Beadine
wi dhspout
upacity noisc
Ground Truth
Baseline
wi diopour
wi opacily
Figure 7: Visual comparison on DTU and Blender datasets based on 3DGS and Binocular3DGS. Suppressing co-adaptation leads to clearer appearance representation in novel view rendering.
to further improvements beyond using either strategy alone, indicating they address the same issue without additive benefits. Table 2 extends the comparison to the Blender dataset, where experiments are conducted on 3DGS, DNGaussian, and Binocular3DGS. On Blender, both strategies reduce CA, but the 3DGS baseline shows higher training-vies CA than novel- -view CA, likely due to the ting-shaped object- scene structure and denser 8-view coverage. Random initialization and lack of geometric constraints in 3DGS may further blur the distinction between training and novel views.
(2) Visual Improvements on Gaussian Point Clouds and Rendering Quality, We further provide visual comparisons on LLFF, DTU, and Blender datasets. Specifically, Figure 6 presents results on the LLFF dataset, while Figure shows side-by-side comparisons on DTU and Blender datasets. These visualizations highlight improvements by strategies LLFF, DTU, and Blender, showing reduced artifacts and clearer structures for both 3DGS and Binocular3DGS. As shown in Figure 6, both strategies effectively suppress the colorful speckle artifacts commonly observed in baseline 3DGS renderings, while also improving the spatial coherence of the reconstructed scenes. Compared to baseline 3DGS, Binocular3DGS starts with denser, keypoint- guidddd initialization, which already reduces such artifacts. Nevertheless, applying our strategies further improves the rendered results, producing more complete object appearances for example, clearer flower petals in the flower and orchids scenes, and sharper boundaries in the trex scene. We emphasize that while Binocular3IDGS produces fewer visible artifacts, co-adaptation remains underlying challenge affecting generaliza- tion to novel views. Colorful speckles are merely one extreme symptom of this issue. Our strategies consistently reduce these artifacts and improve rendering quality across both baselines. Additionally, Figure 7 demonstrates that these benefits generalize to DTU and Blender datasets. On DTU and Blender, dropout and opacity noise lead to clearer and more stable structures.
4.3 Ablation Studies of Regularization Strategies
(1) Training Dynamics Comparison. Fig- ure 8 compares the training dynamics of Binocu- lar3DGS baseline with our Dropout and Opacity Noise Injection strategies on flower and orchids scenes. Both strategies reduce the CA scores of training and testing views, making the dy- namics smoother than the baseline. Although the baseline shows a sharp CA increase around 20k iterations due to adding a warp-based pho- tometric loss, the two strategies help suppress this spike, especially on the flower scene where
Figure 8: Training dynamics (CA and PSNR) com- parison of Baseline and w/ two training strategies. significant rise is observed. On the orchids scene,
8

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Table Ablation study on the dropout probability p in Binocular3DGS on the LLFF dataset.
Dropout p
PSNR t
SSIM f
I.IPS
Train CA 4
Test CAA 4
0.0 (Baseline)
21.440
0.751
0.168
0.001845
0.001951
0.1
21.901
0.768
0.157
0.000995
0.001066
0.2
22.123
0.777
0.154
0.000875
0.000978
22.037
0.777
0.156
0,000848
0.000951
0.4
22.025
0.775
0.158
0.000849
0.000926
0.5
21.927
0.773
0.163
0.000871
0.000982
0.6
21.793
0.768
0.170
0.000848
0.000978
Table 4: Comparison of different rendering strategies for Binocular3DGS trained with dropout
probability = 0.2 on the LLFF dataset. Baseline: Training and Rendering without dropout. A: Single random dropout rendering. B: Averaging multiple random dropout renderings (five times). C: Using all Gaussians with opacity scaled by (1 p).
Strategy
PSNR
SSIM
LPIPS
Train CA
Test CA
Baseline
21.440
0.751
0.168
0.001845
0.001951
A
21.977
0.769
0.162
0.000875
0.000978
B
22.124
0.776
0.157
0.000875
0.000978
C
22.123
0.777
0.154
0.000875
0.000978
only slight increase remains. In addition, both strategies improve PSNR over the baseline, showing their effectiveness in stabilizing training and enhancing reconstruction quality.
(2) Ablation on Dropout Probability p and Rendering Strategies. Table 3 presents the ablation study on different dropout probabilities p. We observe that setting p to 0.2 achieves the best overall reconstruction quality metrics. Although this setting yields the lowest trainingvview CA score, the testing-viers view CA is not minimized, suggesting that CA score not strictly monotonic with reconstruction quality. Extremely low CA scores do not necessarily guarantee better rendering results once a certain threshold is reached. In addition, we evaluate three rendering strategies under the same dropout- trained model in Table 4. Strategy A applies random dropout inference with probability p. Strategy B performs multiple stochastic dropout renderings and averages the results. Strategy C scales the opacity of all Gaussians by (1 p) and renders the image in single pass. Our experiments show that Strategy C achieves the best quality-efficiency trade-off with single-pass rendering, while Strategy B performs similarly but five times slower.
(3) Ablation on Opacity Noise Scale a. Table reports the ablation study on different opacity noise scales We observe that 0.8 achieves the best reconstruction quality. Increasing gradually reduces both training and testing CA scores. However, when a goes below 0.8, the reconstruction quality starts to degrade, despite further reductions in CA. This again confirms that lower CA does not always improve rendering quality beyond a certain point.
Table 5: Ablation study on the noise scale applied opacity the LLFF dataset.
(Noise Scale)
PSNR
SSIM
LPIPS
Train CA
Test CA
(Baseline)
21.440
0.751
0.168
0.001845
0.001951
0.1
21.647
0.757
0.165
0.001409
0.001511
0.2
21.864
0.764
0.161
0.001 126
0.001239
0.3
21.942
0.769
0.158
0.000959
0.001074
0.4
22.065
0.774
0.155
0.000859
0.000964
0.5
22.072
0.776
0.154
0.000861
0.000968
0.6
21.999
0.777
0.155
0.000794
0.000895
22.076
0.777
0.155
0.000712
0.000798
0.8
22.119
0.780
0.155
0.000660
0.000762
0.9
22,059
0.779
0.157
0.000589
0.000693
1.0
22.053
0.779
0.159
0.000560
0.000640
5
Conclusion
In this paper, we introduce the concept of co-adaptation 3D Gaussian Splatting (3DGS) [1] and reveal its link to appearance artifacts under sparse-view settings. We propose the Co-Adaptation Score (CA) metric to quantify this effect and show that higher view density naturally reduces co-adaptation. Motivated by this, we propose two simple strategies-dropou regularization and opacity noise injection- that effectively mitigate co-adaptation and improve sparse-view novel view synthesis. We hope our findings inspire future work on mitigating co-adaptation in learned 3D representations.

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Acknowledgement
This work was supported by the Shenzhen Science and Technology Project under Grant (CC100220018100000004 KJZ222024009331322100011
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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
The abstract and introduction clearly state the problem of co-adaptation in sparse-view view 3DGS, introduce the CA metric, and summarize the proposed mitigation strategies, all of which are supported by the main content and experiments.
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Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [Yes]
Justification: We provide a formal expansion of the Co-Adaptation Score (CA) in the supplemental material, showing its direct connection to the correlation between the color and opacity parameters of Gaussians, where lower CA indicates weaker co-adaptation and higher CA indicates stronger co-adaptation.
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A Appendix Supplemental Material
A.1 Theoretical Analysis of Co-Adaptation Score
Note. In the main paper, CA is reported as the average pixel-wise variance over the commonly visible region of entire image. Here, for clarity, derive the formula for single pixel
We begin by formalizing how random dropout perturbs the rendered color. Under a dropout mask 2 (21,-.., 2n) e where each 2; 1] independently indicates whether Gaussian is kept- the color at pixel u is
(())(u)=
E :EN(1)
24 ag (1-1zaa))
(7)
jei
Here (u) is the depth-sorted list of Gaussians projecting to pixel C and a, the color and opacity of Gaussian i, and the product term is the usual front-to-back transmittance. The Co-Adaptation Score measures how much (u) fluctuates as we sample different masks:
CA(u) = Var, Varz(C(*) (C())())
(8)
large variance indicates that dropping subset of Gaussians greatly alters the pixel color, i.e. that Gaussians have become overly co-dependent. To see how CA depends on the individual parameters, we apply first-order expansion of the transmittance:
I[ (()=))))) ~
Σ
Oj.
(9)
jKl
Substituting back and discarding second-order (and higher) interactions yields
(x2)
(u)
Σ 24 aa -
Σ
2
C2
aq
Ezjas
(10)
jei
In this approximation, the dominant term is the simple sum of active contributions. Neglecting the smaller second term, the variance becomes
CA(u) x Varz Σ 21 c2 c3:))
(11)
Since each 24 is Bernoulli random variable with success probability Pr[z; = 1] = 1 - p, where denotes the dropout probability, its first and second moments are given by
E[=,] p, Var(z;) = =p(1- p)-
(12)
As the dropout decisions 24 are independent across different Gaussians, we can derive the variance of the total weighted sum of Gaussian contributions pixel follows:
Var Σ 2aaa) = Var(z)) (,) = p(1 - p) E()
(13)
Hence, we obtain a simplified expression for the Co-Adaptation Score (CA) at pixel u:
CA(u) = p(1 p)
Σ (EN(a)
(c a.)
(14)
This final form shows that the CA score grows proportionally with the sum of squared weighted color-opacity terms across all Gaussians contributing pixel u, scaled by the dropout-related variance factor p(1 - p). It quantitatively captures how variations in both color and opacity among Gaussians manifest co-adaptation under random dropout perturbations.
Equation 14 highlights several key insights: (1) Dependence on opacity and color: Gaussians with large CjO, terms contribute more significantly to the CA score. When these contributions are similar or redundant, the resulting variance-and thus co-adaptation- low. (2) Effect of dropout rate: The multiplicative factor p(1 p(1-p) p) reaches its maximum at 0.5, justifingg our choice to adopt this value in practice to enhance the sensitivity the CA metric. (3) Regularization implications: Perturbations to C (e.g., via noise injection or dropout) reduce the magnitudes of the summation terms, leading to lower CA scores and implicitly mitigating excessive interdependence among Gaussians.
In summary, this theoretical analysis substantiates the CA score principled indicator of color- opacity coupling strength under dropout perturbations, thereby providing a foundation for the design of our co-adaptation suppression strategies.
21

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spacciy
Figure 9: Visual comparison on the LLFF dataset based on 3DGS. Suppressing co-adaptation reduces color noise (see the changes in the GS point cloud) and improves scene geometry and detail quality.
Ground Truth
Raseline
w/ dropout
w: opacity noise
Ground Truth
Baseline
dropouu
wi opacity nolse
Figure 10: Visual comparison the DTU dataset based on 3DGS. Suppressing co-adaptation leads to more consistent scene fusion across views, resulting in clearer structure and more accurate details.
A.2 Extended Qualitative Results
We present additional qualitative results on the LLFF [47], DTU [51], and Blender [52] datasets to further illustrate the visual improvements brought by co-adaptation suppression strategies.
We first examine the LLFF dataset, where improvements are clearly observed both in rendered images and Gaussian point clouds. As shown in Figure 9, our methods yield point clouds that are cleaner and more geometrically coherent. The baseline 3D Gaussian Splatting (3DGS) [1] often produces scattered, colorful speckles, which are significantly suppressed after applying our co- adaptation regularization. These visual improvements in point clouds directly lead to better rendering in novel views. For instance, in the trex scene, fossil bones exhibit high-frequency flickering and speckling in the baseline, which are clearly alleviated with our methods. In the flower scene, petals and leaves display incorrect colorization under novel views, while the regularized versions better preserve the natural appearance. Similarly, the fern scene, severe color inconsistencies appear on the pole, ground, and leaf textures under the baseline, but these are significantly reduced when co-adaptation is suppressed. Overall, the results suggest that reducing co-adaptation enhances both structural consistency and appearance fidelity in sparse-view 3DGS.
LLFF.
DTU. On the DTU dataset, we observe that both co-adaptation suppression strategies significantly enhance structural coherence and reduce visual artifacts in sparse-view 3DGS. As illustrated in
22

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Ground Truth
Raseline
w/ droooout
w/ ogacitt noise
Ground Truth
Baseline
w/ dropout
w/ opacity noise
Figure 11: Visual comparison on the Blender dataset based on 3DGS. Suppressing co-adaptation reduces floating artifacts and enhances the completeness and clarity of fine structures.
3DGS
DNGaussian
FSGS
Binocular3DGS
dropout
wi' opacity noise
Ground Truth
Figure 12:
Visual comparison LLFF dataset across multiple methods, using Binocular3DGS as the baseline. Suppressing co-adaptation further reduces colorful speckle artifacts and floating noise, while enhancing the completeness and structural coherence of the reconstructed geometry.
Figure 10, suppressing co-adaptation leads to improved fusion across views, enabling more accurate and consistent detail reconstruction. In the scene containing multiple stacked boxes, our methods help preserve fine-scale textual details on the box surfaces, with the characters on packaging appearing noticeably clearer compared to the baseline. In the scene with the red ball, our regularization strategies substantially reduce the bright floating speckles that frequently appear in front of the camera, especially the lens center, leading to cleaner and more complete object reconstruction. Furthermore, in the scene featuring a small pink pig plush toy, the eyes the pig-barely visible in the baseline-are are successfully reconstructed under novel views when using either of suppression methods. These improvements confirm that controlling co-adaptation strengthens the model's 's ability to render fine geometric and appearance details in complex real-wo weal-world scenes.
Blender. On the Blender dataset, we observe consistent improvements rendering quality and structural fidelity when applying co-adaptation suppression strategies. As shown in Figure 11, both dropout and opacity noise help reduce subtle artifacts and enhance reconstruction realism under sparse- view supervision. In the chair and drums scenes, novel view renderings generated with methods
23

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Table 6: Ablation study on the noise scale applied scale parameters in Binocular3DGS on the LLFF dataset. We use multiplicative noise with different Ø values and evaluate the impact on rendering quality and co-adaptation.
Scale Noise o
PSNR t
SSIM
LPIPS
Train CA +
Test CA +
0.0 (Baseline)
21.440
0.751
0.168
0.001845 845
0.001951
0.1
21.551
0.755
0.166
0.001520
0.001682
0.2
21.760
0.760
0.161
0.001326
0.001432
0.3
21.724
0.762
0.161
0,001148
0.001238
0,4
21,690
0.762
0.161
0,001075
0.001237
0.5
21.674
0.765
0.159
0,001009
0.001091
0.6
21.685
0.766
0.159
0.000927
0,001014
0.7
21.597
0.762
0.162
0.000945
0.001012
exhibit fewer detail-related artifacts, particularly around fine structures such as chair legs and drum edges, resulting in more accurate geometry and cleaner appearance. In ficus scene, both strategies significantly improve the photorealism of the reconstructed flowerpot, leading to more consistent shading and geometry that better match the true scene layout. Additionally, in the hotdog scene, we observe a clear reduction in floating speckle artifacts outside the object boundaty-espeecilll near the sausage and tray demomsttrttrinnnggggg the effectiveness of co-adaptation suppression in eliminating non-semantic visual noise. Together, these results highlight the generalizability of our techniques to synthetic datasets with complex textures and fine-scale geometry.
Method Comparison. Figure 12 presents a visual comparison across multiple 3DGS methods, using Binocular3DGSS [10] as the baseline. Binocular3DGSS is strong baseline with geometry-awan initialization, yet our co-adaptation suppression strategies (dropout and opacity noise) still lead to noticeable improvements. In the flower scene, existing sparse-view approaches exhibit occasional color speckles and geometry gaps; applying our methods further reduces these artifacts and yields more complete, coherent novel view reconstructions.
A.3 Exploration of Noise Injection on Different Gaussian Attributes
Beyond the opacity noise experiments presented in the main paper, we further explore noise injection on other Gaussian parameters, including the scale, position, and SH (spherical harmonics) coeffi- cients. These experiments aim to analyze whether perturbing other parameters can also suppress co-adaptation and improve rendering quality under sparse- sparse-view settings.
Scale Noise Injection. We first examine the effect of injecting multiplicative noise into the scale parameters of Gaussians. Similar to opacity noise, we apply multiplica- tive perturbation as follows:
$ s= s-s-(1+
E~,,0))"
(15)
where denotes the original scale and a is the noise strength. The results of this experiment are summarized in Table 6. Compared to the Binocular3DGS baseline, scale noise yields limited improvements in overall reconstruc- tion metrics such as PSNR, SSIM [56], and LPIPS [57]. However, it reduces the co-adaptation strength (CA) on both training and novel views, indicating that scale per- turbation helps decouple Gaussian interactions to some extent. This finding aligns with our visual observations in Figure 13, where scale noise improves scene-level geo- metric coherence in some cases, but introduces mild local blurring in object details. The observed trade-off can be explained by the functional role of scale in Gaussian rendering: perturbing scale slightly alters the spatial support of Gaussians, which may improve coverage and fusion in sparse-view settings, but risks oversmoothing fine structures. As a result, while scale noise contributes to better scene fusion in some examples, it reduces local detail sharpness, leading to modest overall gains.
Baseline
w/ scale noise
Visual comparison of scale noise effects in Binocular3DGSS.
Figure 13:
Position Noise Injection. For position parameters, we introduce additive noise scaled by the nearest- neighbor distance of cach Gaussian, which perturbs their spatial locations and disrupts alignment
24

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Table Ablation study of position and SH noise injection on the LLFF dataset. Position noise is added as Gaussian noise scaled by nearest-neighbor distance; SH noise is applied multiplicatively.
Noise Scale
PSNR
SSIM
LPIPS
Train CA
Test CA
0.0 (Baseline)
21.440
0.751
0.168
0.001845
0.001951
Position Noise (additive)
0.1
21.093
0.742
0.171
0.001701
0.001812
0.3
20.760
0.726
0.182
0.001594
0,001730
0.5
20.540
0.715
0.189
0.001653
0.001733
SH Noise (multiplicative)
0.1
21.475
0.749
0.171
0.001769
0.001876
0.3
21.391
0.750
0.170
0.001633
0.001753
0.5
21.390
0.751
0.168
0.001799
0.001906
Table 8: Ablation study different SH orders used in 3DGS under sparse-view settings on the LLFF dataset. We evaluate rendering quality and co-adaptation across SHO to SH3.
SH Order
PSNR
SSIM f
LPIPS
Train CA L
Test CA
19.293
0.652
0.235
0.006736
0.007259
19.239
0.651
0.234
0,007087
0.007587
2
19.377
0.657
0.229
0.007167
0.007858
(Baseline)
19.357
0.651
0.232
0.007543
0.008206
with the image plane. Even under small perturbations, this leads to degraded convergence and blurred geometry sparse-view training. Although a coarse-to-fine training strategy can somewhat stabilize optimization, its effect overall reconstruction quality remains limited.
SH Noise Injection. For SH parameters, we apply multiplicative noise in the form c. (1 + e) with e ~ NN0, to perturb the directional color components. However, since SH parameters do not affect the spatial configuration of Gaussians along ray, they do not influence the contribution weights of Gaussians during the alpha blending process. As a result, SH noise has limited effect on alleviating co-adaptation. While may seem intuitive that perturbing SH and opacity could yield similar regularization effects-since both influence final pixel colors-their impact on rendering differs fundamentally. Opacity noise directly modifies the weight assigned to each Gaussian during alpha blending, thereby altering the effective contribution and even the number of Gaussians used to render a pixel. This enables opacity noise to disrupt the co-adapted structure more substantially. In contrast, SH perturbation only changes the emitted color of each Gaussian without modifying its blending weight, thus providing limited relief against co-adaptation.
A.4 Extended Ablation on SH Orders
To investigate whether the choice of SH (spherical harmonics) order plays a significant role in co-adaptation, conduct a controlled ablation study using SH orders from 0 to 3 in vanilla 3DGS training under sparse-view view settings. The quantitative results are shown in Table 8, and corresponding qualitative comparisons of Gaussian point clouds visualized in Figure 14.
Renders
Point Cloodss
Ground Truth
SHO
SHI
SH2
SH3
Figure 14: Visualization of Gaussian point clouds under different SH orders on the LLFF flower scene. SHO yields cleaner points, while higher SH orders occasionally introduce more color speckles.
25

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We observe that lower SH orders, especially SHO, tend to yield slightly lower co adaptation scores and cleaner Gaussian point distributions. contrast, SHI to SH3 occasionally produce localized color speckles, but these artifacts appear stochastically-wittoee For example, SHI may exhibit more noticeable artifacts than SH2 certain training runs. Overall, the differences in co-adaptation strength across SHO to SH3 remain relatively minor, and the emergence of appearance artifacts is not strongly determined by the SH order. These findings suggest that while SH complexity may influence directional appearance expressiveness, it is not dominant factor in controlling co-adaptation or mitigating color artifacts in sparse-view 3DGS.
a consistent correlation to SH order.
A.5 Gaussian Count Comparison
To supplement our main experiments, we provide a detailed comparison of the final average number of Gaussians under different training strategies on the LLFF dataset. Specifically, we compare vanilla 3DGS and Binocular3DGS baselines with our proposed dropout and opacity noise regularization strategies. Results are summarized in Table 9,
Table 9: Final Gaussian count and performance metrics under different strategies on LLFE
Setting
PSNR 1
SSIM
LPIPS
Train CA 1
Test CA
Final Count
3DGG [J]
0.651
0.232
0.007543
0.008206
111137
dropout
20,20
0.691
0.211
0.001752
0,002340
115046
w/ opacity noise
19.91
0.676
0.223
0.001531
0.002300
98356
Binocular3DGS [10]
21.44
0.751
0.168
0.001845
0.001951
102021
dropout
0.777
0.154
0.000875
0.000978
122340
w/ opacity noise
22.12
0.780
0.155
0.000660
0,000762
104832
These results show that our method does not improve the CA-score by duplicating Gaussians. The final Gaussian count remains comparable to, or even lower than, the vanilla baselines. This supports that the improvements in CA metrics reflect genuine regularization effects on opacity and color distributions, rather than degenerate collapse of the representation space.
A.6 Exploration of a Color Variance Metric (CV)
To further understand how our proposed dropout and opacity noise strategies influence color distribu- tion, introduce auxiliary metric measure the variance of rendered colors while decoupling it from opacity variations. Specifically, we adopt pixel-wise color variance formulation that weighs contributing colors o; using their rendering compositing weights w;, defined as:
i-1
10;
0;
II j=1
o5)
(16)
We compute the color variance of each pixel using the following formulation:
E, E. WhC;
2
Var(c)
(17)
E, W/ Σ W3
This formulation reflects the variance of color contributions that decoupled from the opacity aggregation behavior during splatting. Averaging the per-pixel variance over the entire image yields global color variance metric (CV).
Table 10 reports the CV metric, co-adaptation scores (CA), and final Gaussian statistics under different regularization strategies. The experiments are conducted the LLFF dataset using both the vanilla 3DGS and Binocular3DGS baseline.
Table 10: Color variance (CV) and co-adaptation score (CA) under different strategies on LLFE
Setting
PSNR f
Train CA J
Test CA
Train CV
Test CV +.
Final GS Count
GS Radius
Binocular3DGS [10]
21.44
0.001845
0.001951
0.2496
0,2563
102021
21.38
w/ dropout
22.12
0.000875
0.000978
0.0992
0.1065
122340
35,93
w/ opacity noise
22.12
0.000660
0.000762
0.0476
0.0534
104832
31.64
26

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We observe that both dropout and opacity noise substantially reduce the proposed CV metric and the CA score. The opacity noise achieves the lowest CV. In contrast, dropout occasionally results in slightly larger Gaussians, which may contribute to marginally higher CV and CA.
Additionally, have also experimented with alternative regularization scheme that explicitly aligns the color directions of Gaussians (after normalization) with the ground truth ray direction. However, this strict constraint significantly degraded rendering quality, likely due to the loss of flexibility in 3D Gaussian expression.
A.7 Comparison with Alternative Strategies for Reducing Co-Adaptation
To better situate our proposed methods within the broader landscape of appearance artifact mitigation and generalization enhancement in sparse-viers view 3DGS, we additionally compare with three alternative strategies that are known or expected to influence model co-adaptation behavior. All comparisons are conducted based on the Binocular3DGS baseline and evaluated on the LLFF dataset.
Baseline w/ Scale Noise: We inject multiplicative noise into the scale parameters of Gaussians during training. This strategy introduces spatial variation and slightly perturbs the scale consistency across views, which can act as a regularizer against overfitting and co-adaptation.
We apply pixel-wise absolute gradient accumulation for Gaussian densification, replacing the standard gradient used in vanilla 3DGS. This method promotes the preservation of fine structures and reduces appearance artifacts, which may help alleviate view-specific co-adaptation.
Baseline w/ AbsGS [58]:
Baseline w/o Opacity Decay [10]: We remove the default multiplicative decay applied to Gaussian opacity parameters (x0.995 per iteration). Without this decay, redundant Gaussian opacities tend to maintain, causing higher co-adaptation scores, reduced sparsity, and more pronounced floating artifacts.
Table Il summarizes the comparison results across several quantitative metrics, including rendering quality (PSNR, SSIM, LPIPS) and co-adaptation strength (Train/Test CA).
Table 11: Comparison of different strategies for mitigating co-adaptation and improving rendering quality on LLFF.
Setting
PSNR 1
SSIM 1
LPIPS
Train CA |
Test CA
bascline [10]
21.44
0.751
0.168
0.001845
0.001951
w/ dropout
22.12
0.777
0.154
0.000875
0.000978
w/ opacity noise
22.12
0.000660
0.000762
w/ scule noise
21.68
0.766
0.159
0.000927
0.001014
w/ AbsGS [58]
21.61
0.754
0.163
0.001446
0.001593
w/o opacity decay [10]
20.26
0.708
0.202
0.004413
0.004830
We observe that dropout and opacity noise yield the lowest co-adaptation scores and the best rendering metrics overall. Scale noise also helps mitigate co-adaptation to some extent, while AbsGS provides balance between detail preservation and regularization. In contrast, removing the opacity decay results in a substantial increase in co-adaptation scores and degrades rendering quality.
These results provide empirical evidence that multiple strategies-boll architectural and regularization- based-aaeeaoo.. can influence co-adaptation behavior in 3DGS. Our proposed dropout and opacity noise methods remain the most effective among them in reducing co-adaptation.
A.8 Impact on Geometry Reconstruction
Beyond the improvement in appearance fidelity, also assess whether our proposed regularization strategies enhance the quality of geometry reconstruction in sparse view settings. To this end, we compare the predicted depth maps from trained 3DGS models against pseudo ground-truth depth maps gained under an 18-view denser configuration on the LLFF dataset.
We evaluate the quality of depth using the following standard metrics:
27

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AbsRel: Mean absolute relative error between predicted and reference depths.
RMSE:
Root mean squared error, capturing the overall deviation.
MAE:
Mean absolute error, measuring absolute differences in depth.
Log10:
Logarithmic error, which is more sensitive to errors in distant regions.
Table 12: Depth quality under sparse-view settings (LLFF, 3 views).
Setting
AbsRel L
RMSE
MAE
Log10
haseline [2]
0.0732
4.2785
2.5802
0.0314
w/ dropout
0.0676
4.1048
2.4258
0.0295
w/ opacity noise
0.0651
3.9182
2.2923
0.0276
We observe that both dropout and opacity noise consistently improve geometry prediction quality across all four metrics, with opacity noise showing the strongest impact.
A.9 Exploration of Advanced Dropout Strategies
To further investigate how to suppress co-adaptation more effectively in sparse-view 3DGS reconstruc- tion, we explore several targeted dropout strategies beyond uniform random dropout. All experiments conducted using the LLFF dataset and the Binocular3DGS baseline. Below, summarize the design and evaluation three dropout variants.
Concrete Dropout. We implement a variant of Concrete Dropout [59] by learning per-Gaussian dropout probability p: 1). During training, we sample soft mask z; using the Binary Concrete distribution:
2, Sigmoid (Log(p)) - log(1 1 p.) + log(u:) - log(1 (1- - 21)
U(0, 1)
(18)
where T = 0.1 a temperature hyperparameter. The final Gaussian opacity is updated as 03 + 0 (1 2))
This method allows end-to-end learning of dropout uncertainty. However, under sparse-viet view settings, we find that the soft mask introduces insufficient regularization, resulting in significant degradation.
Density-based Dropout. We hypothesize that Gaussians in dense spatial regions more likely to over co-adapt. Hence, we compute nearest-neighbor density scores and assign dropout probabilities proportionally. Specifically, we assign higher dropout rates to denser regions and lower rates to sparser ones. Dropout rates are linearly mapped from 0.2 (sparsest) to 0.5 (densest).
Although this strategy introduces a more selective regularization mechanism and achieves noticeable improvement over the baseline, it leads to a larger number of remaining Gaussians compared to random dropout. Moreover, it does not yield a clear advantage in rendering quality and in some cases even underperforms the uniform random dropout strategy.
Geometry-aware Dropout. To account for high-order geometric co-adaptation, we estimate local geometric complexity by computing structural variation among each Gaussian's nearest neighbors. However, the computational cost of this strategy approximately O(N3) for N Gaussians renderss infeasible practice. Thus, we omit this strategy from ablation studies.
Table 13: Comparison of dropout strategies on LLFF using the Binocular3DGSS baseline.
Setting
PSNR 1
SSIM t
LPIPS 1
Train CA
Test CA +
Final GS Count
baseline
21.44
0.751
0.168
0.001845
0.001951
102021
w/ random dropout
22.12
0.777
0.154
0.000875
0.000978
122340
w/ concrete dropout
20.88
0.731
0.205
0.004680
0.005320
22959
w/ density-hased dropout
22.05
0.773
0.158
0.000478
0.000536
150968
w/ geometry- dropout
Too costly; computational complexity estimated ((Na)
As shown Table 13, while concrete and density-based dropout offer additional perspectives on targeted regularization, experiments show that uniform random dropout remains the most effective
28

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and practical solution under sparse-vies view conditions. Geometry-ane aware strategies may hold future potential, but their high computational overhead limits immediate applicability.
A.10 Exploration of Multi- Learning
To further explore the impact of multi-view learning under sparse-view 3DGS settings, we imple- mented the official MVGS [60] using input views. As shown in Table 14, the MVGS model yields significantly degraded performance across all image quality metrics under sparse-view input, suggesting its lack of adaptation to sparse supervision.
Table 14: Sparse-view MVGS performance on LLFF.
Method
PSNR f
SSIM
LPIPS
MVGS [60]
15.45
0.507
0.362
We further added a simple multi-viww training module on top vanilla 3DGS, synchronizing three views per iteration (MV=3). This accelerates convergence due stronger multi-vies view gradients, but also results in aggressive Gaussian densification and a sharp rise in co-adaptation, as indicated by the co-adaptation scores.
We assess this integration under different training iterations (Ik, 3k, 5k, 10k), as shown Table
Table 15: Impact of multi-view (MV=3) learning on sparse-view 3DGS under different training iterations.
Setting
PSNR
SSIM f
LPIPS
Train CA |
Test CA |
GS Count (Avg.)
3DGS (10k)
19.36
0.651
0.007543
0,008206
111137
MV (10k)
18.75
0.639
0.245
0.016841
0.024286
1144360
MV (5k)
18.97
0.646
0.240
0.018252
0.022790
635671
w/ MV (3k)
19.41
0.665
0.228
0.01 1994
0.013679
259014
w/ MV (IK)
19.55
0.656
0.292
0,008352
0.008635
22910
While multi-view supervision introduces stronger signals and faster convergence, does not consis- tently reduce co-adaptation scores sparse-view artifacts. These findings suggest that multi-view strategies require additional regularization mechanisms to be effective under sparse-view reconstruc- tion settings. Nevertheless, the direction remains promising for future exploration.
A.11 Extended Experimental Details
To ensure fair comparisons, we adopt unified parameter settings across all scenes within each dataset. For example, while the original DNGaussian [2] uses different training configurations for each Blender scene, we apply a consistent setup across all scenes. Binocular3DGGS is retrained using white backgrounds to match other methods, as its original results were obtained using black backgrounds. For co-adaptation suppression, we use a fixed dropout probability of 0.2 across all methods and datasets, based ablations conducted Binocular3DGSS. Because each method learns distinet opacity distribution, we tune the opacity noise scale individually for each method within |0.05, 0.8) and fix it across all scenes in the same dataset. For CA score computation, we randomly drop 50% of the contributing Gaussians for each view and calculate the pixel-wise variance across multiple renderings. The number of training iterations for each baseline follows its official implementation.
A.12 Future Work and Broader Impact
While our study primarily focuses on quantifying and alleviating co-adaptation in 3D Gaussian Splatting (3DGS), the underlying analysis and methodology hold broader implications for 3D representation learning. The core idea of leveraging tropout-inspired regularization provides a simple yet powerful lens for understanding and mitigating undesirable dependencies among Gaussian primitives.
Specifically, our findings suggest several promising directions for future exploration:
29

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Point Initialization and Densification. The quantification of co-adaptation may inspire new initialization or adaptive densification strategies that enhance convergence stability in sparse-view 3DGS training.
Per-Gaussian Feature Learning. Extending co-adaptation analysis to learn better per- Gaussian semantic appearance embeddings could improve tasks such 3D segmentation, object retrieval, or open-vocabulary scene understanding [28, 61, 62, 63, 64].
Generalizable 3D Representations. The insight into co-adaptation may help build 3D representations that generalize better across novel views, modalities, or domains, thus benefiting reconstruction, editing, and generation tasks.
Adaptive and Intelligent Regularization Strategies. Building upon our exploration of dropout- based mechanisms, future work could investigate more targeted and adaptive strategics for better co-adaptation alleviating and novel view synthesis generalizability.
In summary, while dropout serves as the conceptual inspiration, our work goes beyond a direct adaptation. By uncovering and formalizing the co-adaptation phenomenon in 3DGS, we offer new perspective that may benefit wide range of point-based 3D learning frameworks. We hope this direction will stimulate further research robust, interpretable, and generalizable 3D representations.
A.13 Limitations
Although our proposed strategies-randon Gaussian dropout and opacity noise injection-effectivet) reduce co-adaptation and enhance novel view synthesis under sparse supervision, we observe that overly suppressing co-adaptation does not always yield further improvements in rendering quality, As evidenced in our ablation studies, rendering performance tends to plateau or even degrade once co-adaptation scores fall below certain threshold. This suggests that co-adaptation is not inherently harmful; rather, it constitutes essential aspect of 3DGS, facilitating cooperation among Gaussians to model fine- fine-grained appearance and geometry. The negative effects of co-adaptation primarily emerge under sparse-view training. where excessive entanglement can lead to artifacts overfitting. Consequently, while moderate suppression beneficial for improving generalization, excessive suppression may compromise the model's capacity to accurately fit scene content, ultimately limiting expressiveness. Our goal is thus not to eliminate co-adaptation entirely, but to selectively mitigate its detrimental forms. Future work may consider adaptive suppression mechanisms that dynamically balance generalization and representational fidelity.
30


Reviews:
[{"review_id": "Jn0bEoqFZL", "reviewer": "Reviewer_S997", "summary": "his paper points out that the appearance artifacts in sparse-view 3DGS from excessive entanglement (co-adaptation) among Gaussians. That is, Gaussians form strong dependent relationships to fit the training views, ignoring the real appearance distribution of the scene. Therefore, Co-Adaptation Score (CA) is proposed to quantify the degree of entanglement among Gaussians by calculating the pixel-wise variance of rendering results from different Gaussian subsets under the same viewpoint. Experiments show that the CA score naturally decreases as the number of training views increases. The author also proposed two strategies, random gaussian dropout and opacity noise injection, to mitigate the problem.", "questions": "Please refer to the Strengths And Weaknesses section.", "limitations": "Yes.", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n1. This paper establishes a connection between the sparse-view artifacts observed in 3D Gaussian Splatting (3DGS) and the co-adaptation effect. The proposed Co-Adaptation (CA) metric offers a quantifiable tool for analyzing this phenomenon.\n\n2. The paper introduces two simple yet versatile mitigation strategies that are compatible with various 3DGS variants. Both quantitative metrics (PSNR, SSIM, LPIPS) and qualitative results demonstrate that these strategies effectively reduce CA scores and alleviate artifacts.\n\nWeaknesses:\n1. The core idea draws inspiration from dropout, which is conceptually straightforward. As a result, the level of novelty appears limited.\n\n2. Although the paper introduces a new method aimed at improving the generalization ability of 3DGS under sparse-view settings, the overall improvement is relatively modest.\n\n3. The authors state that combining both proposed strategies does not lead to further improvement, but they do not provide experimental evidence to support this claim.\n\n4. Since the dropout strategy improves generalization by reducing the number of Gaussians during rendering, it would be helpful to compare this approach with directly reducing the number of points at initialization to verify whether similar benefits can be achieved.\n\n5. While the focus is on sparse-view training, the paper lacks evaluation under extremely limited-view settings (e.g., 1–2 input views), which would help better assess the robustness of the proposed strategies under severe data scarcity.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank you for the time and effort dedicated to reading our paper and providing constructive feedback. We have carefully considered your concerns and respond to them point by point below.\n\n---\n\n**W1: The core idea draws inspiration from dropout, which is conceptually straightforward. As a result, the level of novelty appears limited.**\n\n**A1:** While dropout is a well-established concept in neural networks, its application in 3D representation learning remains underexplored. More importantly, our work does not simply reuse dropout, but leverages it to **reveal and mitigate a unique co-adaptation phenomenon in 3D Gaussian Splatting (3DGS)**—a problem that, to our knowledge, has not been previously formalized. We believe this insight may help the community better understand the distinctive behaviors of 3DGS, and potentially inspire further studies on point initialization, densification, per-Gaussian feature learning (e.g., for semantic tasks), and more generalizable 3D representations beyond specific view settings. In this sense, our contribution extends beyond the method itself and offers a new perspective for future exploration.\n\n**W2: Although the paper introduces a new method aimed at improving the generalization ability of 3DGS under sparse-view settings, the overall improvement is relatively modest.**\n\n**A2:** We acknowledge that our proposed methods—random Gaussian dropout and opacity noise injection—are simple by design. However, they are highly practical and lightweight, making them easy to plug into existing sparse-view 3DGS frameworks to improve novel view generalization with minimal overhead. Our focus is on **addressing appearance artifacts caused by over co-adaptation**, a pervasive issue in sparse-view settings that has been largely overlooked. Despite their simplicity, the improvements are not negligible: quantitative results demonstrate reliable gains across several 3DGS baselines, and more importantly, qualitative comparisons reveal visibly cleaner point cloud geometry and significantly reduced color noise. We kindly refer the reviewer to Supplementary Figure 1 for a clearer illustration of the benefits.\n\n**W3: The authors state that combining both proposed strategies does not lead to further improvement, but they do not provide experimental evidence to support this claim.**\n\n**A3:** We respectfully clarify that our paper includes quantitative and qualitative evidence supporting this claim. In Table 1 of the main paper (last row), we show results on the LLFF dataset using the Binocular3DGS baseline, where applying both strategies together achieves metrics similar to using either one individually. Additionally, in the DTU dataset, the results with both strategies (as shown below) remain comparable to single-strategy settings, reinforcing our observation:\n\n| Setting  | PSNR ⬆️ | SSIM ⬆️ | LPIPS ⬇️ | Train CA ⬇️ | Test CA ⬇️ |\n|----------|--------|--------|---------|-------------|------------|\n| w/ both  | 21.05  | 0.875  | 0.109   | 0.000736    | 0.001143   |\n\nThis supports our point that while the two strategies are effective, they both address the same underlying co-adaptation issue, and thus do not provide additive improvements when combined. Furthermore, in nearly all qualitative comparisons, we separately present the results of applying either random Gaussian dropout or opacity noise injection. The visual improvements—such as clearer geometry and reduced artifacts—are highly similar across both cases, further suggesting that the two strategies address the same underlying co-adaptation issue.\n\n**W4: Since the dropout strategy improves generalization by reducing the number of Gaussians during rendering, it would be helpful to compare this approach with directly reducing the number of points at initialization to verify whether similar benefits can be achieved.**\n\n**A4:** To address this suggestion, we conducted a controlled comparison experiment by directly varying the number of initialization Gaussians in the DNGaussian framework. Specifically, we modified the `num_pts` parameter in the initialization code, which controls the total number of Gaussian points prior to training.\n\nAs shown in the table below, we evaluate performance across different initialization sizes using the LLFF dataset. We find that simply reducing the number of initialization points (e.g., 10, 30, 50, etc.) does not replicate the generalization benefits brought by our random Gaussian dropout strategy. Although reducing initial points can slightly lower CA and the final Gaussian count, it leads to worse PSNR, SSIM, and LPIPS.\n\nIn contrast, applying dropout during training (row *50 w/ dropout*) yields:  \n- Highest PSNR (19.43) and SSIM (0.623)  \n- Lowest Train/Test CA scores  \n- A relatively compact final Gaussian count\n\nThis demonstrates that **dropout offers more than static reduction**—it provides dynamic regularization that actively suppresses co-adaptation and improves generalization under sparse views.\n\n### Initialization Comparison on LLFF (DNGaussian baseline)\n\n| **N**               | **PSNR ⬆️** | **SSIM ⬆️** | **LPIPS ⬇️** | **Train CA ⬇️** | **Test CA ⬇️** | **Final GS Count (Avg.)** |\n|---------------------|-------------|-------------|--------------|------------------|------------------|----------------------------|\n| 10                  | 18.37       | 0.571       | 0.331        | 0.007134         | 0.007515         | 39006                      |\n| 30                  | 18.68       | 0.588       | 0.307        | 0.007179         | 0.007695         | 43743                      |\n| 50                  | 18.93       | 0.599       | 0.295        | 0.007234         | 0.007645         | 45835                      |\n| **50 (w/ dropout)** | **19.43**   | **0.623**   | 0.302    | **0.003242**     | **0.003821**     | 42113                      |\n| 70                  | 18.85       | 0.591       | 0.297        | 0.007157         | 0.007646         | 48655                      |\n| 90                  | 18.75       | 0.592       | 0.295        | 0.007268         | 0.007703         | 51494                      |\n| 100                 | 18.84       | 0.594       | 0.293        | 0.007191         | 0.007721         | 52152                      |\n| 500                 | 18.72       | 0.584       | **0.291**    | 0.007232         | 0.007955         | 97329                      |\n| 1000                | 18.73       | 0.571       | 0.296        | 0.007488         | 0.008277         | 160211                     |\n\n> *Note: The `num_pts` is controlled via `num_pts = int(pcd_shape.max() * N)` in code; the row **50 (w/ dropout)** shares the same initial Gaussian count with N=50 but applies dropout during training.*\n\n**W5: While the focus is on sparse-view training, the paper lacks evaluation under extremely limited-view settings (e.g., 1–2 input views), which would help better assess the robustness of the proposed strategies under severe data scarcity.**\n\n**A5:** To address this concern, we conduct additional experiments on DNGaussian under extremely sparse settings with only 1–2 input views on the LLFF dataset. As shown in the table below, both of our proposed regularization strategies improve performance even under extremely limited-view conditions.  \n\n| Views          | PSNR ⬆️ | SSIM ⬆️ | LPIPS ⬇️ | Train CA ⬇️ | Test CA ⬇️ |\n|----------------|--------|--------|---------|-------------|------------|\n| 1              | 12.30  | 0.287  | 0.520   | 0.009779    | 0.010383   |\n| w/ dropout     | 12.35  | **0.303**  | 0.529   | **0.004436**    | **0.005119**   |\n| w/ opacity noise | **12.45**  | 0.294  | **0.511**   | 0.005078    | 0.005712   |\n| 2              | 16.06  | 0.457  | 0.381   | 0.008123    | 0.008865   |\n| w/ dropout     | **16.78**  | **0.495**  | **0.379**   | 0.003641    | 0.004900   |\n| w/ opacity noise | 16.58  | 0.488  | 0.384   | **0.002952**    | **0.003880**   |\n| 3              | 18.93  | 0.599  | 0.295   | 0.007234    | 0.007645   |\n| w/ dropout     | **19.43**  | **0.623**  | 0.302   | **0.003242**    | **0.003821**   |\n| w/ opacity noise | 19.15  | 0.608  | **0.294**   | 0.004507    | 0.005071   |\n\n---\n\nWe hope the above response sufficiently addresses your concerns. If you have any further concerns or suggestions, we sincerely welcome your continued comments and discussion. Thank you again for your valuable feedback and time."}, {"review_id": "JhU6RNQja3", "reviewer": "Reviewer_jvPz", "summary": "This paper studies how different Gaussians co-adapt during training which can cause appearance artifacts when rendering from views not seen during training. The authors thoroughly analyze the phenomenon, which is especially prevalent in the few-view setup. \nA metric, the co-adaptation (CA) score is proposed to measure this dependency, and it is defined by rendering views multiple times while randomly dropping some of the Gaussians and computing the variance. Two different methods are proposed to lower the CA score during training, and this is observed to also improve the rendering metrics of the test views.", "questions": "- A simple way to game the metric (i.e. achieving low training CA) is to simply duplicate each Gaussian N times with opacities scaled such that the total transmittance through all N duplicates is the same as the transmittance through the original one. For a large enough N this will result in a low variance when dropping each of the N gaussians with some probability, and hence a low CA. Was any behaviour like this observed? Specifically, what was the average number of Gaussians for the different datasets and methods (i.e. the rows in Table 1) after training with and without the proposed extra components (dropout and opacity noise)? \n- Were any alternative measures tried that just measured variance in colors $c_i$, attempting to decouple it from however the opacities change? A straight-forward way would be to measure the variance of $c_i$ per pixel weighted proportionally to its rendering weight $\\alpha_i \\prod_{j=1}^{i-1}(1 - \\alpha_j)$. How does this variance change with dropout or opacity noise compared to the baselines?\n- Another way of thinking about how Gaussians should represent a scene is that rather than striving to have multiple redundant low opacity blobs (as in this paper - low CA is correlated with small alpha’s and that it should be robust to dropping random Gaussians) is to consider Gaussians as approximating e.g. a mesh with one or very few high opacity non-redundant Gaussians on the surfaces. Though in this way, a low CA is not desirable, but rather an overparametrization. Maybe a better way is to enforce a few high density Gaussians on surfaces, and then a large alpha will suppress colors that are off. Do you have any opinion about if/why the proposed CA-score is a better way of thinking than this?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The authors analyse the reason for appearance artifact for novel view synthesis with Gaussian splatting, especially prevalent in the sparse view setup, and suggest that the issue is that multiple Gaussians co-adapt during training. The authors propose a metric by rendering multiple times while applying dropout to the Gaussians.\n- The most important result is that the proposed methods to reduce CA score, in addition to indeed reducing the CA score, furthermore consistently improve the renderings of the test views.\nThe analysis of the CA score is mostly thorough and it is analysed in multiple aspects, e.g. the training dynamics and dependence on e.g. number of views or properties such as the degree of the spherical harmonics. It is also tested for multiple (5) baseline methods for Gaussian splatting.\n\nWeaknesses:\n- There are some limitations of the proposed metric. As shown in the supplementary, a low score is connected to having many Gaussians with low opacities as well as low variance in color ($CA \\approx p(1-p) \\sum_i (c_i \\alpha_i)^2$, eq. (8) in the supplementary), and this is insufficiently investigated in the paper. Specifically, the coupling between colors and opacities makes it unclear if a low value is due to low variance in color or many low opacity Gaussians. Please see the items under the questions section.\n- There are some straight-forward visualisations that are missing. For instance, plotting the CA score per pixel along with the renderings in e.g. fig. 6 or 7 would be informative to see for which pixels or regions there is low or high co-adaptation. Another less direct option would be e.g. the average or maximum alphas per pixel for the closest Gaussians, since the CA score is closely related to the average $\\alpha_i c_i$ as shown in the supplementary.", "was_revised": true, "final_justification": "The authors provided detailed answers to all my questions. The extra experiments regarding numbers of Gaussians and color variance strengthen the paper, since it shows that the lowered CA score depends mostly on reduced variance in colors and that the number of Gaussians per scene is roughly the same when training with dropout. I keep the borderline accept rating.", "rebuttal": "We sincerely thank you for the thoughtful and in-depth feedback. Your insightful questions and constructive suggestions—particularly regarding the limitations and alternative formulations of the CA score—have been invaluable in helping us further refine both the theoretical and practical aspects of our work. Below, we address each of your concerns in detail and discuss the directions your comments have inspired.\n\n---\n\n**W1 and Q1:** The reviewer is concerned that the reduction in CA-score (Co-Adaptation score) observed after applying the proposed dropout and opacity noise strategies might be an artifact. Specifically, they suspect that our method could be “gaming” the CA metric by duplicating each Gaussian into multiple low-opacity ones, which artificially reduces color variance under dropout. They request evidence that such duplication behavior is not occurring, and ask for the average number of Gaussians across all settings.\n\n\n**Response:** We sincerely thank the reviewer for this insightful concern. To directly address this, we report the **final average number of Gaussians** trained under all settings (vanilla 3DGS, Binocular3DGS, and our proposed strategies). As shown in the table below, the number of Gaussians remains largely consistent across methods, and in some cases (e.g., 3DGS + opacity noise), the count is even slightly lower:\n\n| Setting             | PSNR ⬆️  | SSIM ⬆️ | LPIPS ⬇️ | Train CA ⬇️ | Test CA ⬇️ | Final GS Count (Avg.) |\n|---------------------|--------|--------|--------|------------|-----------|------------------------|\n| 3DGS                | 19.36  | 0.651  | 0.232  | 0.007543   | 0.008206  | 111137                 |\n| w/ dropout          | 20.20  | 0.691  | 0.211  | 0.001752   | 0.002340  | 115046                 |\n| w/ opacity noise    | 19.91  | 0.676  | 0.223  | 0.001531   | 0.002300  | 98356                  |\n| Binocular3DGS       | 21.44  | 0.751  | 0.168  | 0.001845   | 0.001951  | 102021                 |\n| w/ dropout          | 22.12  | 0.777  | 0.154  | 0.000875   | 0.000978  | 122340                 |\n| w/ opacity noise    | 22.12  | 0.780  | 0.155  | 0.000660   | 0.000762  | 104832                 |\n\nThese results indicate that our method does not reduce the CA-score by duplicating Gaussians, as the final point count remains comparable or even lower. This supports the validity of CA as a meaningful metric and reflects genuine improvements in opacity and color distribution. We will include these results in the revised version to further clarify this point.\n\n---\n\n**W2:** Missing co-adaptation score map visualizations. The reviewer points out that our paper lacks visualizations of co-adaptation (CA) scores, and suggests providing per-pixel CA heatmaps or related indicators such as alpha distributions to better illustrate regions of high or low co-adaptation.\n\n**Response:** We thank the reviewer for the valuable suggestion. We agree that CA visualizations can offer intuitive insight into how co-adaptation varies spatially. Preliminary visualizations indicate that regions with high CA scores often align with geometrically complex areas and tend to have more densely packed or overlapping Gaussians. In the revised version, we will include per-pixel CA score heatmaps overlaid with rendered views (e.g., Figure 6 or 7).\n\n---\n\n**Q2:** Were any alternative measures tried that just measured variance in colors $c_i$, attempting to decouple it from however the opacities change? A straightforward way would be to measure the variance of $c_i$ per pixel weighted proportionally to its rendering weight $w_i = \\alpha_i \\cdot \\prod_{j=1}^{i-1}(1 - \\alpha_j)$. How does this variance change with dropout or opacity noise compared to the baselines?\n\n**Response:** Thank you for the insightful suggestion. We have implemented the proposed alternative variance measure in our CUDA rendering kernel by computing, for each pixel, the **weighted variance** of contributing color values $c_i$, using their compositing weights:\n\n$$\nw_i = \\alpha_i \\cdot \\prod_{j=1}^{i-1}(1 - \\alpha_j)\n$$\n\nSpecifically, we compute the per-pixel variance of the color parameters ${c_i}$, which can be derived as follows:\n\n$$\n\\mathrm{Var}(c) = \\frac{\\sum_i w_i c_i^2}{\\sum_i w_i} - \\left( \\frac{\\sum_i w_i c_i}{\\sum_i w_i} \\right)^2\n$$\n\nThis formulation reflects the variance of color contributions decoupled from however the opacities change. We compute the **color variance metric (CV)** by averaging the per-pixel variance of the color parameters ${c_i}$ over the entire rendered image.\n\nThe results are summarized below:\n\n| Setting           | PSNR ⬆️ | Train CA ⬇️ | Test CA ⬇️ | Train CV ⬇️ | Test CV ⬇️ | Final GS Count (Avg.)  |  GS Radius (Avg.)  |\n|------------------|----------|---------------|--------------|------------------------|-----------------------|---|---|\n| baseline          | 21.44     | 0.001845      | 0.001951     | 0.2496                 | 0.2563                | 102021 | 21.38 |\n| w/ dropout        | 22.12     | 0.000875      | 0.000978     | 0.0992                 | 0.1065                | 122340 | 35.93 |\n| w/ opacity noise  | 22.12    | 0.000660      | 0.000762     | 0.04760                | 0.0534                | 104832 | 31.64 |\n\nWe observe from the above results that both dropout and opacity noise significantly reduce the **color variance metric (CV)** and **co-adaptation score (CA)**. The CV reduction from dropout is weaker than that from opacity noise, possibly because dropout tends to produce slightly more Gaussians with larger scales after training. This leads to a higher color variance.\n\nWe would also like to share a related experiment we previously explored: instead of computing the CV metric, we once tried adding a weak constraint during training by aligning the color directions (after normalization) of all Gaussians with GT pixel color along the same ray. However, even with very small loss weights, this significantly degraded the rendering quality. We believe this is because such constraints overly limit the expressive power of 3DGS, where color co-adaptation is part of its inherent flexibility.\n\nThank you for raising this insightful point. We will incorporate the implementation details of the CV metric, the associated experimental findings, and our related exploratory attempts into the revised version of the manuscript.\n\n---\n\n**Q3:** **On whether enforcing fewer high-opacity Gaussians is a better representation approach than minimizing CA-score.**\n\n**Response:** Thank you for this insightful perspective. We agree that, in theory, having a few high-opacity Gaussians located precisely on surfaces is an ideal and compact representation. However, under sparse-view settings, achieving such configurations is extremely difficult. In practice, we observe that surface Gaussians tend to be more concentrated and have relatively higher opacities, but not necessarily fewer in number.\n\nMore importantly, unlike traditional mesh or point cloud representations, co-adaptation is an inherent property of 3DGS. That is, multiple Gaussians collaboratively contribute to the color fitting along a ray, which reflects a key feature of the 3DGS representation. In this context, our proposed Co-Adaptation (CA) score offers a principled way to quantify how strongly Gaussians rely on each other in the rendering process. We believe that CA provides a more faithful and flexible characterization of this intrinsic cooperative behavior, rather than imposing strict sparsity or singular high-opacity constraints, which may undermine the expressive power of the 3DGS framework.\n\nThat said, we also acknowledge the potential value in exploring more **compact and cohesive representations** that retain the high expressiveness of 3DGS while naturally reducing unnecessary co-adaptation. Developing such representations—ones that maintain structural efficiency without over-constraining the cooperative dynamics—could be a promising direction for future research.\n\n---\n\nWe hope our response has addressed your concerns accurately and respectfully, and that we have not misunderstood the valuable perspective you intended to convey. If you have further thoughts or suggestions, we would be truly happy to continue the discussion. Thank you again for your thoughtful and inspiring feedback."}, {"review_id": "FU1n3G48Ue", "reviewer": "Reviewer_AmxR", "summary": "The paper presents a systematic analysis and improvement of appearance artifacts in 3D Gaussian Splatting for novel view synthesis under sparse-view settings. The authors find that existing 3DGS methods are prone to co-adaptation among Gaussian points during sparse-view training, which leads to abnormal artifacts when rendering from novel viewpoints. To address this, the authors introduce the Co-Adaptation Score (CA) as a metric to quantify the dependencies between Gaussians, and proposes two plug-and-play regularization strategies—Random Gaussian point dropout and opacity noise injection—to effectively suppress co-adaptation. These strategies enhance the model’s generalization and rendering quality for unseen views. Experimental results demonstrate that these methods significantly reduce artifacts and improve synthesis performance.", "questions": "See in the weakness part.", "limitations": "yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths:\nThe authors systematically analyze the appearance artifact problem in novel view synthesis of sparse-view 3D Gaussian Splatting, clearly identifying the co-adaptation among Gaussians as a performance bottleneck. They propose a quantitative metric, the Co-Adaptation Score (CA), providing a tool for quantifying and analyzing this issue. The methods are simple and effective, introducing two plug-and-play regularization strategies—Random Gaussian point dropout and Opacity noise injection. The proposed methods are easy to integrate into existing 3DGS frameworks and can effectively suppress co-adaptation, thereby improving the model's generalization ability and rendering quality for novel views.\n\nWeaknesses:\n- The paper mainly focuses on its own proposed strategies, with limited horizontal comparison and discussion with other existing methods for mitigating appearance artifacts or improving generalization.\n- It is unclear whether the proposed methods are effective for geometry reconstruction based on GS under sparse-view settings.", "was_revised": true, "final_justification": "The author's response has addressed my concerns, so I have decided to accept the paper.", "rebuttal": "We sincerely thank you for taking the time to read our paper and for your valuable comments. We truly appreciate your positive assessment of our work. Below, we address the two weaknesses you mentioned.\n\n---\n\n**W1: The paper mainly focuses on its own proposed strategies, with limited horizontal comparison and discussion with other existing methods for mitigating appearance artifacts or improving generalization.**\n\n**A1:** Thank you for pointing out this limitation. In addition to our two proposed strategies we conducted further experiments with **three additional strategies** to better situate our method within the broader context. All results are based on the same baseline implementation (Binocular3DGS [1]) on LLFF:\n\n- **baseline + scale noise**: We inject multiplicative noise into the scale parameters of Gaussians during training. This scale noise also helps mitigate co-adaptation in sparse-view 3D reconstruction to some extent, leading to improved rendering quality.\n- **baseline + AbsGS [2]**: Applies pixel-wise absolute gradient accumulation for densification instead of standard gradient in vanilla 3DGS, which enhances fine details and reduces artifacts. The introduction of AbsGS also helps alleviate co-adaptation to some extent and improves rendering quality.\n- **baseline w/o opacity decay [1]**: We remove the default opacity decay strategy (a per-iter multiplicative factor 0.995 applied to all Gaussian opacities). Without this regularization, the co-adaptation score increases significantly, causing visible floater artifacts and worse rendering quality.\n\n| Setting                    | PSNR ⬆️ | SSIM ⬆️ | LPIPS ⬇️ | Train CA ⬇️ | Test CA ⬇️ |\n|---------------------------|--------|--------|---------|------------|-----------|\n| baseline [1]                 | 21.44  | 0.751  | 0.168   | 0.001845   | 0.001951  |\n| w/ dropout                | 22.12  | 0.777  | 0.154   | 0.000875   | 0.000978  |\n| w/ opacity noise          | 22.12  | 0.780  | 0.155   | 0.000660   | 0.000762  |\n| w/ scale noise    | 21.68 | 0.766  | 0.159   | 0.000927   | 0.001014  |\n| w/ AbsGS [2]      | 21.61  | 0.754  | 0.163   | 0.001446   | 0.001593  |\n| w/o opacity decay [1]| 20.26  | 0.708  | 0.202   | 0.004413   | 0.004830  |\n\n**W2: It is unclear whether the proposed methods are effective for geometry reconstruction based on GS under sparse-view settings.**\n\n**A2:** Thank you for pointing out this important aspect. To evaluate how our proposed strategies affect geometry reconstruction under sparse views, we compare the depth maps predicted by trained 3DGS models against pseudo ground-truth depth under an 18-view setting on LLFF.\n\nWe use four common metrics:\n\n- **AbsRel**: Measures the average relative error between the predicted and ground-truth depths.\n- **RMSE**: Reflects the overall deviation between depth predictions and ground truth.\n- **MAE**: The average of absolute differences between depth predictions and ground truth.\n- **Log10**: Measures logarithmic error, which better captures errors in farther regions.\n\nThe results are summarized below:\n\n| Setting            | AbsRel ⬇️ | RMSE ⬇️ | MAE ⬇️ | Log10 ⬇️ |\n|--------------------|-----------|--------|--------|----------|\n| baseline [3]           | 0.0732    | 4.2785   | 2.5802   | 0.0314   |\n| w/ dropout         | 0.0676    | 4.1048   | 2.4258   | 0.0295   |\n| w/ opacity noise   | 0.0651    | 3.9182   | 2.2923   | 0.0276   |\n\nAs shown, both strategies consistently improve geometric accuracy across all metrics. In addition to these quantitative results, Supplementary Figure 1 provides visual comparisons of the reconstructed 3D point clouds. We observe significantly clearer structures, reduced color noise, and better point coherence.\n\nWe appreciate the reviewer’s suggestion and will include more depth and geometry quality comparisons in the revised paper.\n\n\n\n**Reference**  \n[1] Han, Liang, et al. \"Binocular-guided 3d gaussian splatting with view consistency for sparse view synthesis.\" Advances in Neural Information Processing Systems 37 (2024): 68595-68621.   \n[2] Ye, Zongxin, et al. \"AbsGS: Recovering fine details in 3D Gaussian Splatting.\" Proceedings of the 32nd ACM International Conference on Multimedia. 2024.     \n[3] Li, Jiahe, et al. \"Dngaussian: Optimizing sparse-view 3d gaussian radiance fields with global-local depth normalization.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2024.\n\n---\n\nWe sincerely thank you again for your positive evaluation and recognition of our work. We hope the above responses have resolved your concerns. If you have any further questions or suggestions, we are more than happy to continue the discussion."}, {"review_id": "3yNFw4K9KP", "reviewer": "Reviewer_jEws", "summary": "This paper focuses on sparse view reconstruction. To be specific, they investigate the appearance artifacts in sparse-view 3DGS. These artifacts is generated due to the nature of volume rendering in 3DGS. The authors propose a Co-Adaptation Score to measure the difference between real appearance distribution and renderings. The authors propose two strategies to mitigate the co-adaptation in sparse-view 3DGS: (1) Gaussian dropout; (2) noise injection for opacity. The experiments show the effectiveness of the proposed method.", "questions": "In Figure 3, to the images in Var(), why are they all the same?\nIn Table 1, why are there no results of Binocular3DGS on DTU?", "limitations": "The novelty is quite limited. Also, the proposed method can be more clearly explained. \nI am very interested in whether multi-view learning can improve sparse view reconstruction or not.\nI anticipate an innovative 3D Gaussian filtering technique for sparse view reconstruction.\nAlthough our current score is low, I would like to raise my score if authors address my concerns.", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "# Strengths\n1. This paper is well organized and easy to follow.\n\n2. This paper proposes a co-adaptation concept for sparse view reconstruction, which aims to quantify the difference between the real appearance distribution and Gaussian renderings.\n\n3. The proposed metric well reflects the drawbacks of existing methods.\n\n# Weakness\n\n1. In Figure 4, the column c can be divided into two parts to make it clearer.\n\n2. In Figure 5, the legends are too small to read.\n\n3. The description of Opacity Noise Injection is unclear. For example, in Eq. 6, how to define $\\sigma$? Moreover, the authors have introduced that different noise acting on different 3D Gaussian attributes have different impacts. Why do authors only inject noise into opacity? In theory, I think the noise should be very small, otherwise, it will degrade rendering results. Furthermore, the final opacity should be in the range [0, 1]. These details are not mentioned.\n\n4. The proposed Dropout Regularization is confusing to me. Why randomly dropout but not find unreasonable 3D Gaussians and drop them? In theory, a tailored filtering method would be more effective and interesting, not randomly removing.\n\n5. Overall, the novelty of this paper is quite limited. Although I recognize the findings of the co-adaptation concept, the proposed two regularization methods are too simple and easy. \n\n6. To the sparse view reconstruction, multi-view learning [1] may be a good way to mitigate the co-adaptation problem.\n\n[1] https://arxiv.org/abs/2410.02103", "was_revised": true, "final_justification": "The rebuttal is clear and successfully addresses my concerns.", "rebuttal": "We sincerely thank you for the thoughtful and constructive feedback. We're encouraged by your recognition of our co-adaptation concept and metric, and truly appreciate your openness to raising the score upon clarification. Below we address each concern in detail.\n\n---\n\n**W1: In Figure 4, the column c can be divided into two parts to make it clearer.**\n\n**A1:** We appreciate the suggestion. In the revised version, we will clearly separate the DNGaussian and Binocular3DGS results in subfigure (c) of Figure 4 to improve readability and visual clarity.\n\n**W2: In Figure 5, the legends are too small to read.**\n\n**A2:** We agree the legends in Figure 5 are too small due to layout compression. We will enlarge them and adjust the layout in the revised version for better readability.\n\n**W3: The description of Opacity Noise Injection is unclear ...**\n\n**A3:** Thank you for these detailed questions. Our responses are as follows:\n\n(1) How is the noise scale parameter $\\sigma$ in Eq. 6 defined?\n\nWe set $\\sigma$ to 0.8 in our experiments. Related ablation results can be found in Table 5.\n\n(2) Why only inject noise into opacity? \n\nWe tested noise injection on multiple Gaussian attributes:\n\n- **Opacity:** Multiplicative noise effectively reduces co-adaptation and improves novel view quality without degradation.\n- **Scale:** Helps generalization but may cause blurring with excessive noise.\n- **Position (xyz):** Additive noise, scaled by local nearest-neighbor distance, often causes training divergence due to geometric instability.\n- **SH coefficients:** No significant improvement observed.\n  \nWe highlight opacity noise due to its best performance. More results are in Supplementary Section C.1.\n\n(3) Should the noise be small? \n\nYes for position; even small noise is harmful. Opacity is more tolerant—$\\sigma = 0.8$ works well (Table 5), despite being relatively large.\n\n(4) Should final opacity be clamped to [0, 1]? \n\nYes. Opacity is clamped to [0, 1] after noise injection. We will clarify this in the revised version.\n\n**W4: .. Why randomly dropout but not find unreasonable 3D Gaussians and drop them? ..**\n\n**A4:** This is an excellent suggestion. We would like to clarify first that the goal of our dropout regularization is not to prune Gaussians, but to regularize the model to alleviate co-adaptation, particularly under sparse-view settings. Nevertheless, we have also explored more targeted dropout strategies beyond random dropout, including:\n\n(1) **Concrete Dropout [1]** \n\nIn our implementation, each 3D Gaussian is assigned a learnable dropout probability $p_i$ in the range (0, 1). During training, we adopt the Binary Concrete distribution [1] to make the dropout process differentiable. Specifically, for each Gaussian, we sample a uniform variable $u_i$ from $Uniform(0, 1)$ and compute a soft mask $z_i$ as:\n\n$z_i = Sigmoid\\left(\n\\frac{\n\\log(p_i) - \\log(1 - p_i) + \\log(u_i) - \\log(1 - u_i)\n}{\n\\tau\n}\n\\right)$\n\nwhere $\\tau$ is the temperature parameter (we use $\\tau = 0.1$). This soft mask controls the probability of dropping each Gaussian. The final opacity $o_i$ is updated as:\n\n$o_i \\leftarrow o_i \\cdot (1 - z_i)$\n\nThis formulation enables end-to-end training while softly dropping out Gaussians based on learned uncertainty. Additionally, we add a weak regularization term to the loss to avoid $p_i$ collapsing to extreme values (close to 0 or 1), which improves stability and preserves the intended randomness. However, concrete dropout did not yield the expected gains. We suspect that the soft mask lacks sufficient regularization strength under sparse data, leading to unstable learning and weak suppression of co-adaptation. See results in the table below.\n\n\n(2) **Density-based Dropout**  \n\nWe adapt dropout probabilities based on Gaussian point density. Specifically, we compute the nearest-neighbor distance for each Gaussian and rank all Gaussians accordingly. Points in denser regions are assigned higher dropout probabilities, as over co-adaptation is more likely in such areas. In contrast, sparse regions are less prone to overfitting and thus have lower dropout rates. In practice, we set dropout probabilities to range from 0.2 (sparsest) to 0.5 (densest) via linear mapping.\n  \n(3) **Geometry-aware Dropout**  \n\nWe hypothesize that Gaussians in geometrically complex regions are more vulnerable to over co-adaptation and thus require stronger regularization. To approximate local complexity, we evaluated structural variation across each Gaussian’s nearest neighbors. However, this approach involves computing high-order geometric relationships across multiple neighbors for every point, resulting in prohibitive computational cost—approximately $\\mathcal{O}(N^3)$ for $N$ Gaussians. Due to this inefficiency, we ultimately did not include this variant in our ablation studies.\n\n### Comparison of Various Dropout Strategies\n\nWe present a comparative study of the dropout strategies described above, based on the LLFF dataset and the Binocular3DGS baseline.\n\n| Setting   | PSNR ⬆️ | SSIM ⬆️ | LPIPS ⬇️ | Train CA ⬇️ | Test CA ⬇️ | Final GS Count (Avg.) |\n|-|-|-|-|-|-|-|\n| baseline  | 21.44   | 0.751   | 0.168 | 0.001845  | 0.001951    | 102021 |\n| w/ random dropout   | 22.12   | 0.777   | 0.154    | 0.000875     | 0.000978    | 122340  |\n| w/ concrete dropout    | 20.876  | 0.731   | 0.205    | 0.004680     | 0.005320    | 22959   |\n| w/ density-based dropout | 22.05   | 0.773   | 0.158    | 0.000478     | 0.000536    | 150968  |\n| w/ geometry-aware dropout | –  | –  | –  | –  | – | –  |\n\n>*Note for geometry-aware dropout. Too costly: computational complexity estimated as $\\mathcal{O}(N^3)$.*\n\nFrom the results above, we observe that random dropout achieves the best overall performance across metrics. Nevertheless, more targeted dropout strategies remain a promising direction for future research. Our exploration of more targeted dropout strategies (e.g., gradient-based) will be included in the revised version of the paper.\n\n\n**W5: Overall, the novelty of this paper is quite limited ...**\n\n**A5:** We appreciate the reviewer’s acknowledgment of the co-adaptation finding. While the proposed regularization strategies—random Gaussian dropout and opacity noise injection—are intentionally simple, their novelty lies not in algorithmic complexity but in their ability to uncover and alleviate a previously unformalized problem in 3DGS: over co-adaptation under sparse-view settings. To our knowledge, this phenomenon has not been explicitly studied in the 3DGS literature. Our work offers a new lens to examine and improve generalization in sparse-view 3D reconstruction, and we believe this conceptual contribution can spark further research in more adaptive view-independent 3D representations, better initialization or densification schemes, or point-level semantic reasoning with splats. Despite their simplicity, the methods yield measurable improvements (both quantitative and qualitative) with negligible overhead. We hope this balance between effectiveness and simplicity may benefit the community in both research and practice.\n\n\n**W6: To the sparse view reconstruction, multi-view learning (MVGS) may be a good way to mitigate the co-adaptation problem.**\n\n**A6:** We thank the reviewer for the insightful suggestion regarding multi-view learning (MVGS). We implemented the official MVGS under sparse-view settings (3 views) and observed a significant performance drop—likely because MVGS was designed for dense-view reconstruction and lacks sparse-view adaptation.\n\nTo further assess this, we added a same multi-view learning module atop vanilla 3DGS, training with three synchronized views per iteration. This setup accelerates convergence—likely due to stronger gradients—but lacks regularization, leading to overfitting, degraded performance, and a rapid increase in Gaussian count due to aggressive densification.\n\nSupplementary sparse-view MVGS results are shown below:\n\n| Method | PSNR ⬆️ | SSIM ⬆️ | LPIPS ⬇️ |\n|-|-|-|-|\n| MVGS  | 15.45 | 0.507 | 0.362 |\n\nTo further evaluate the integration of multi-view learning (MV=3) into sparse-view 3DGS, we present results at different training iterations (1k, 3k, 5k, 10k):\n\n| Setting  | PSNR ⬆️ | SSIM ⬆️ | LPIPS ⬇️ | Train CA ⬇️ | Test CA ⬇️ | GS Count (Avg.) |\n|-|-|-|-|-|-|-|\n| 3DGS (10k)| 19.36   | 0.651   | 0.232 | 0.007543     | 0.008206 | 111137 |\n| w/ MV (10k) | 18.75 | 0.639| 0.245| 0.016841|0.024286 | 1144360 |\n| w/ MV (5k)  | 18.97 | 0.646| 0.240| 0.018252|0.022790 | 635671 |\n| w/ MV (3k)  | 19.41| 0.665| 0.228| 0.011994|0.013679| 259014 |\n| w/ MV (1k)  | 19.55 | 0.656| 0.292| 0.008352| 0.008635 | 22910 |\n\nWhile multi-view supervision accelerates early convergence, it does not reduce CA scores or sparse-view artifacts. This suggests multi-view learning needs further regularization for sparse views, and the direction remains promising.\n\n**Q7: In Figure 3, to the images in Var(), why are they all the same? In Table 1, why are there no results of Binocular3DGS on DTU?**\n\n**A7:** We recommend the reviewer to zoom in and examine the rendered images in Figure 3 more closely. Although they may appear visually similar at a glance, each image is rendered from a different Gaussian subset and contains observable differences, especially in opacity distribution and fine structural details within the same regions. We will consider enlarging the images in the final version to make such differences more clearly visible.\n\nBinocular3DGS (w/ both) on DTU is omitted in Table 1 as we used LLFF to show both strategies are similarly effective. Below are DTU results under joint training.\n\n| Setting | PSNR ⬆️ | SSIM ⬆️ | LPIPS ⬇️ | Train CA ⬇️ | Test CA ⬇️ |\n|-|-|-|-|-|-|\n| w/ both | 21.05 | 0.875 | 0.109 | 0.000736 | 0.001143 |\n\n**Reference**  \n[1] Gal, Yarin, Jiri Hron, and Alex Kendall. \"Concrete dropout.\" Advances in neural information processing systems 30 (2017).\n\n---\n\nWe hope our reply addresses your concerns and welcome any further discussion~"}]

Author rebuttal:

Meta-review: The paper proposed to analyze the source of appearance artifacts and identify the entanglement among Gaussians as the performance bottleneck for sparse-view 3DGS. It further proposed a metric of Co-Adaptation Score to measure the entanglement among Gaussians in sparse-view 3DGS. It also proposed two plug-and-play training strategies that can suppress co-adaptation among gaussians.

The paper was reviewed by four reviewers in the community. The authors provided rebuttal and there had been discussions among the authors and the reviewers. The rebuttal and the following discussions succefully addressed most of the issues from the initial reviews where the reviewers acknowledged the improvement. Afterward, the recommendations from the reviewer were Borderline accept, Accept and Strong Accept. Reviewer S997 was with an initial Borderline Reject rating while the authors addressed most of the comments. 

Given the consistent ratings, I would like to accept the paper. While the reviewers are consistent with the contributions from the paper, the authors are requested to revise the paper correspondingly.
Decision: Accept (poster)