Splat Feature Solver
Authors: Butian Xiong
Rong Liu
Kenneth Xu
Meida Chen
Andrew Feng
Venue: ICLR 2026 Poster (2026)
Keywords: Spalts
Feature Lifting
Solver
Optimization
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Feature lifting has emerged as a crucial component in 3D scene understanding, enabling the attachment of rich image feature descriptors (e.g., DINO, CLIP) onto splat-based 3D representations. The core challenge lies in optimally assigning rich general attributes to 3D primitives while addressing the inconsistency issues from multi-view images. We present a unified, kernel- and feature-agnostic formulation of the feature lifting problem as a sparse linear inverse problem, which can be solved efficiently in closed form. Our approach admits a provable upper bound on the global optimal error under convex losses for delivering high quality lifted features. To address inconsistencies and noise in multi-view observations, we introduce two complementary regularization strategies to stabilize the solution and enhance semantic fidelity. Tikhonov Guidance enforces numerical stability through soft diagonal dominance, while Post-Lifting Aggregation filters noisy inputs via feature clustering. Extensive experiments demonstrate that our approach achieves state-of-the-art performance on open-vocabulary 3D segmentation benchmarks, outperforming training-based, grouping-based, and heuristic-forward baselines while producing the lifted features in minutes. Demo Video, \textbf{Code} and \textbf{demo website} are all inside the supplementary.

Published as a conference paper at ICLR 2026
SPLAT FEATURE SOLVER
Butian Xiong', Rong Liu', Kenneth Xu², Meida Chen', Andrew Feng' 'University of Southern California, Institute for Creative Technologies University of Michigan, Ann Arbor
ABSTRACT
Feature lifting has emerged crucial component in 3D scene understanding, enabling the attachment of rich image feature descriptors (c.g. DINO, CLIP) onto splat-based 3D representations. The core challenge lies in optimally assigning rich general attributes to 3D primitives while addressing the inconsistency issues from multi-view images. We present a unified, kernel- and feature-agnostic for- mulation of the feature lifting problem as sparse linear inverse problem, which can be solved efficiently in closed form. Our approach admits provable upper bound on the global optimal eπrо under convex losses for delivering high qual- ity lifted features. To address inconsistencies and noise in multi-view observa- tions, we introduce two complementary regularization strategies to stabilize the solution and enhance semantic fidelity. Tikhonov Guidance enforces numerical stability through soft diagonal dominance, while Post-Lifting Aggregation filters noisy inputs via feature clustering. Extensive experiments demonstrate that our approach achieves state-of-the-art performance open-vocaben open-vocabulary 3D segmen- tation benchmarks, outperforming training-basee based, grouping- based, and heuristic- forward baselines while producing lifted features in minutes. Our code is available in the GitHub, We provide additional website for more visualization, as well as the video
INTRODUCTION
Recent advances in splat representations -ucch as 3D Gaussian Splatting (3DGS) Kerbl et al. 2023 2D Gaussian Splatting HHang et al. (2024), and Deformable Beta Splatting Liu et al. 2025 have enabled real-time, high-fidelity scene rendering by modeling geometry with compact, explicit primitives. These splat-based methods combine differentiable projection, alpha composit- ing, and efficient visibility-aware rasterization to preserve geometric detail and multi-view consis- tency, supporting applications ranging from style transfer Liu et al. (2024); Galerne et al. (2025) to
scene understanding Guo et al. (2024); Qin et al. (2024); Shi et al. (2024; ; Jun-Seong et al. (2025); }
Cheng et al. (2024): Cen et al. 2025 Dou et al. (2024); Gu al. (2024) Zuo et al. (2025 Peng
ett al. (2024b). Nevertheless, enriching these primitives with detailed descriptors -ucc as CLIP,
DINO, General ViT, and CNN features-remains challenging due to the inherent difficulty of co-
herently lifting 2D observations into consistent 3D representations.
To address this challenge, recent efforts have focused on lifting per-pixel semantic descriptors (e.g.. CLIP, DINO) onto 3D primitives, enabling semantic tasks such as segmentation and querying. Ex- isting semantic feature lifting methods broadly fall into three categories: training-basee optimization
Shi et al. (2024); Qin et al. (2024): Zhou et al. 2024);; Qiu et al. (2024): Zuo et al. (2025), which pioneered in embedding semantic onto 3D primitives via multi-view training; grouping baseed based asso- ciation Wu et al. (2025): ; Peng et al. (2024b: Gu et al. (2024); Liang et al. (2024). which improved efficiency through feature clustering; and heuristic forward methods Guo et al. (2024): [Josphh et al.)
(004); Dou et al. (2024); Chacko et al. (2025); Jun-Seong et al. (2025): Cheng al. (2024), which prioritize speed and directly project semantic features onto 3D primitives.
While existing methods have achieved promising results, a unified theoretical framework for fea- ture lifting remains underexplored, especially concerning the heuristic forward methods that bypass the training process. Building upon prior efforts. identify several open challenges that limit generalization and theoretical understanding. First, establishing a rigorous mathematical formula- tion for defining feature lifting could be beneficial enable formal analysis, generalization, and

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Published as a conference paper at ICLR 2026
Splats Regrocotatien
Eap
Saleada
Sharts
Fasere Faraniiur
Toned
Sensor Parameters
Tileen Gailease
Cuewrng
SAM Ope.1
Panchstion
Dunndraam Tasks Fusiiin Levdlokka
Prnsted
20 Guituity Segastishe
Figure 1: Overview of our Feature Lifting Framework. Our pipeline lifts dense 2D feature ob- servations (e.g.. MaskCLIP, DINO) onto general 3D splat representations by formulating the task as sparse linear inverse problem. The Solver incorporates Tikhonov Guidance to ensure numerical stability and Post-Lifting Aggregation to filter noisy inputs. The resulting lifted feature parameters enable high-fidelity downstream tasks, such as open- open-vocabulary 3D segmentation and localization.
optimization. Second, in the absence a formal definition, existing approaches currently lack the- oretical guarantees regarding the quality of the lifted features, leaving some uncertainty about their proximity to a globally optimal solution. Third, all aforementioned methods are exclusively focus on "SAM+CLIP" features and "3DGS" kernels, which may limit generalization across broader settings. Finally, most prior works do not explicitly account for the inherently noisy nature of collected data, where multi-view inconsistencies and observational noise can introduce ambiguity. Our formulation accounts for these challenges through theoretically grounded linear inverse framework.
Our key contributions are summarized below:
Propose the formulation of feature lifting sparse linear inverse problem, where each per-primitive descriptor is recovered via a global consistent solution to the system AX = B
Prove that, under convex losses and the assumption that our proposed linear system has unique solution, our solver admits provable upper bound on the global optimal error
Introduce two complementary modules to filter noisy input and stabilize the proposed linear system: Tikhonov Guidance and Post-Lifting Feature Refinement
Provide a generalized implementation for feature lifting to multiple primitive kernels and different dense features
Achieve state-of-the-art performance on the downstream task of open- open-vocabulary 3D se- mantic segmentation.
As illustrated in Figure our framework inputs precomputed splats, sensor parameters, and dense observations. These are mapped to the feature lifting equation A. B, where the Splats Sensor Matrix (A) is derived from the geometry and camera parameters, and the observations form the target vector (B). To solve for the feature parameters (X), we enhance stability by polarizing alpha val- ues to encourage diagonal dominance (Tikhonov Guidance) and employ Post-Lifting Aggregation to discard inconsistent masks. Our formulation the first to formalize the feature lifting problem as general linear inverse problem, and can therefore be applied across diverse splat primitives (c.g., 3DGS, 2DGS, Beta Splats) and dense feature modalities (e.g., CLIP, DINO, VIT, ResNet features). Moreover, it establishes mantic segmentation, outperforming existing training-based, grouping-basee and heuristic-forward baselines in mloUs.
sfate-of-the-ard downstream tasks such open- anccbbocayllary 3D
RELATED WORK
Prior feature- lifting techniques for 3D tasks can grouped into three families, each with distinct trade-offs between accuracy and efficiency.
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Published as a conference paper at ICLR 2026
Joint Training-based Methods such as LangSplat Qin al. (2024). LeGaussian Shi al. (024). FMGS Zuo et al. (2025), and SeatureSplats Qiu et al. (2024) jointly optimize scene geometry and high-dimensional feature embeddings to directly learn splat-wise semantic descriptors. While effective, end-to-end optimization over large descriptor sets and primitives can be computationally intensive, often requiring significant memory and training time. To alleviate resource demands, these approaches employ descriptor compression (c.g., PCA in LangSplat Qin et al. (2024), quantization in LeGaussian Shi et al. (2024), and deep auto-encoders FeatureSplats Qiu Qiu al. (2024)) or reduce the number of primitives (FMGS Zuo et al. (2025)). These strategies help manage resource usage, though they may introduce trade-offs in terms of geometric detail or feature precision.
Grouping-bard based Methods first extract 2D region or instance masks using models such as SAM Kirillov et al.] (023) and SAM2 Ravi al. (2024). Following that, each mask is linked to 3D Gaussians via lightweight training process. Finally, features are aggregated into 3D either by additional optimization or by direct unprojection Wu et al.] (2025); |Png et al.] (2024b); Gu et al.) (2024); Liang et al.] (2024); Cen et al. (2025). While these approaches reduce the cost of joint optimization, they still require one to two hours of scene-specific optimization. Furthermore, these methods depend SAM's per-view masks, while powerful, are designed primarily for instance segmentation and may not be directly suited for noisy, dense, pixel-wise feature lifting.
In particular, LAGA Cen al. (2025) per-view SAM masks Kirillov et al. (2023) and trains an affinity model to cluster 3ID Gaussian splats, subsequently associating splat clusters across views. However, this approach assumes that feature variance reflects true semantic differences and is there- fore view-dependent, introducing a dynamic K-means clustering step that adds complexity and may increase memory and computational requirements. In contrast, our analysis suggests that such dis- crepancies often stem from mask inaccuracies- another over- wer-segments and includes adjacent objects- matther than from genuine viewpoint changes. Our convex- regulaaree inverse problem solver suppresses this noise directly- requiring additional training, multi-level clustering algorithms, or view-dependent features assigned to one primitive.
as one mask isolating only the target while
Heuristic Forward Methods-e.g.. Argmax Lifting Chacko al. (025 Occam's ' LGS LGS Cheng et al. 2024), Semantic Gaussian Guo et al. (2024), gradient-guiedd splitting Joseph et al. (2024). Coseg- Gaussians Dou et al. 20244), ) and DrSplats Jun-Seong et al. (2025 are analytic and training-free, offer high efficiency and simplicity. However, they often lack formal mathematical foundation and sensitive to noisy inputs. Interestingly, three recent heuristic pipelines CosegGaussians Dou et al. 2024), Occam's LGS Cheng et al. (2024), and DrSplats Jun-Seong et al. indepe--nddy proposed the identical row-sum weighting rule (row-sum preconditioner), underscoring its broad practical effectiveness. However, while CosegGaussians applied the row-sum weighting scheme r; = E, Wi.jbj/ E, Wi,j it did so without an accompanying theoretical interpretation. Occam's LGS later offered a maximun-likelihodd interpretation of the same weighted-average rule but pro- vided no error bound. Dr. Splat simplifies the preconditioner further by summing only the top-k contributions per primitive, trading off some theoretical rigor for computational efficiency.
None of the three families of methods explicitly address that feature lifting is fundamentally sparse, row-stochastic, linear inverse problem subject to noise(has misleading masks) and in- completeness-ice. it is singular and requires careful regularization or preconditioning ensure stability and obtain a reliable solution approximation. Building on this observation, we model fea- ture lifting as linear system, which allows us derive theoretical bounds for any convex loss and demonstrate applicability across a range of embeddings (e.g., DINO, VIT, CNN) and splat's 's kemels.
3 FEATURE SPLAT SOLVER
In this section, we begin by formally defining the feature lifting problem, enabling the transfer of various downstream tasks into a mathematical framework. We then establish optimality bounds for the row-sum preconditioner under the linear inverse problem setting. Finally, derive two regularization terms to stabilize the solution in the presence of noise, particularly in downstream tasks such lifting SAM-generated masks embedded with CLIP features.
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Published as a conference paper at ICLR 2026
3.1 PROBLEM DEFINITION
3.1.1 SPLATS RENDERING
To justify formulating the Feature Lifting problem linear inverse problem, we first review the core splats rendering process. Most splats primitives, including planar 2D Gaussian Splats Huang et al. (2024), volumetric 3D Gaussian Splats Yu et al. (2024); Kerbl et al. (2023), and Deformable Beta Splats| Liu et al. (025), employ a fixed, depth-sorted alpha-blending pipeline. Concretely, for each viewing ray r, there is sequence of primitives ordered from front to back, with their respective contribution to the final color denoted as wp. The background color is Cp. The rendered ray color
C, is given below:
Wp op II
op), apdpr Op I+e-8
(1)
f=1
C, uw Co 1 11 C. up
P
Op and cp denote the opacity and color (or feature) of the p-th primitive. For fully opaque primitives (e.g., meshes under standard z- z-buffering), setting Vp. dp 1 reduces EquΩ to a simple depth test. Here, is the raw opacity term inputted into a sigmoid activation function to produce the final opacity. The primitive difference only affects the kernel function that calculates the 6pr of ray on primitive p. which is agnostic to the calculation of the final rendered color C(r). There are several notable properties:
Property 1. up is highly sparse in Cr
Property ww==1
Property 3. The rendered color C. is usually very close (i.e. PSNR is more than 24 according Yu et al. (2024): Kerbl et al. 20023); Liu al. (2025) to the given observation C, in the training data set.
The first property arises from the tile-based rendering design of Gaussian Splat: et al. (2023) Since the tile size is typically set to 16 x 16, most splats are excluded from rendering any given tile.
The second property is the row stochastic property. It is less than one because the standard alpha- blending heuristic of terminating ray integration once the composite opacity approaches one. It is close to one based on the assumption that scene geometry should block any further contribution from background color during training. practice, we randomize the background color during training, forcing splats to fully occlude the randomly colored background from all viewing directions. Further justification of this property can be found in the appendix G
The third observation is noted in recent splats training method Yu et al. (2024) Huang al. (2024)
Kerbl et al. (202)); Liu et al. (025). Those properties will be used to justify our formulation.
3.1.2
FEATURE LIFTING EQUATION
Here, we introduce the feature lifting equation.
= B, A RxP. R E B
is is the number rays in the observation, F' is the dimension of the observation data, and P is the number of primitives. Each row of A represents the observation Wp mentioned in Equ a particular ray r. Therefore, we have the following assignment:
AG Wrps = B C (ir,j=p))
(4)
Note how A becomes a fixed matrix once the geometry-related attributes are given. Likewise, B becomes fixed once the observation (Features such as CLIP, DINO, or other general features per pixel) has been given. The goal is solve x, or in other words, to determine the feature vector asso- ciated with each geometric primitive. We refer to the solution r as the lifted feature representation of primitive P and observations O.
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3.1.3 INVERSE PROBLEM
First, we ask whether Eauits solution, and, whether the given solution unique. In typical sronngg-where A E R with R > P- the system is overdetermined and generally inconsis- tent, meaning no exact X satisfies equation 3 Instead, we consider the least squares formulation (or more generally, a convex loss minimization problem):
X arg min ||AX -BIl
(5)
where the minimizer exists for any B and lies in the column space of A. In our context, Prop- erty 3 guarantees that real-world observations B such as RGB color, approximately lie within range(A) (A). As a result, the least-squares residual is small, and a near-exact lift exists. Intuitively, any observation derived from the same RGB signal should have a near-exact lift. From a semantic viewpoint, we also require one-to-one mapping. Each geometric primitive should admit a single descriptor, mirroring an ideal embedding (e.g. a perfect 3D CLIP) that assigns one feature per ob- ject. Thus, uniqueness in equation 5 is not just for mathematical convenience, but for the purpose of aligning with downstream task requirements. Any deviation from uniqueness signals is either due to noisy inputs or suboptimal solvers precisely the singular, and misleading-mar mask problem address through our convex regularization and preconditioning strategies.
When the observed signal varies smoothly with the camera parameters (intrinsics and extrinsics), the inverse problem satisfies the afore-mentioned three- pree-pronned criteria: a solution exists, is unique, and depends continuously noise- for example, if one view's segmentation mask captures only the noodles of a ramen bowl, while the next view's 's mask includes both the bowl and noodles-thh the resulting CLIP embeddings jump abruptly. In such cases, there is no exact solution. The optimal "solution" will be the least square "solution". our proposed solver then served as a bounded approximation to the least square solution. Our proposed regularizer will filter out the misleading signals.
the data. However, when the signal is discontinuous corrupted by
3.2 SOLVER
In this session, we will introduce solver under the well-posedness condition and give optimal upper bound of our solver. In our setting, the least-squares problem in Eq. equation 5 is convex,
so stochastic methods such as SGD provably converge the global minimizer Esser et al. (2010);
Saad (2003). However, cold-start training can be prohibitively slow. Prior works (e.g. C Chacko
al. 2225 Dou et al.) (2024); Jun Seong et al. (2025); Cheng et al. Joseph Joseph
al. (2024)
have explored efficient one-shot approximations that show practical value but do not offer formal guarantees. To address this, we introduce the row-sum preconditioner as a, closed-fore -oorm solver. We then develop an analytical framework that (i) quantifies its (1 + approooxxiitoo error under both L2 and general convex losses, and (ii) interprets the behavior of existing heuristics as special cases.
(AT = VD(ATA) x == D x D' (ATAA) AYB Ij-
E, Ag A.j
(6)
The proposed initial solution is given in Equ where D is the diagonal operator containing square roots of the row sums, and e is all-ones vector. The expression on the right-hand side is the element- wise formulation. We now proceed to analyze the optimality of the proposed solution.
((x) Σ
Σ
Aujz Bi
[(x) EΣ Agg ||=, B.ll
Jensen
An
((x) S ((x)
(8)
Here, we start with the original loss function L(x), and calculate surrogate loss function [(x). The norm ||- represents any convex loss function such as L1, L2, or a Huber loss. From Property we apply the Jensen's 's inequality. This means the surrogate loss function J is larger than L and serves as an upper bound for the true loss. For the sake of argument, we consider a special case where ||- Il is the 1.2 loss. If I attains minimum, it occurs where the gradient is zero, shown in Equ
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RGB
Ground Truth
Ours
DrSplat
bowl chopsticks
egg
wavy noodles kamaboko
onion segments com
nori
Figure 2: Qualitative comparison on the LeRF-OVS Ramen scene. We compare our method against DrSplats and the Ground Truth. As shown in the legend, distinct colors represent different semantic classes (e.g., egg, chopsticks). Our method performs better compared to recent SOTA Jun-
Seong et al. 2025 More qualitative result could be found in Fig. Fig. and Fig.
Therefore, we obtain an optimal solution on the surrogate loss function J.
0J
0J dx,
Σ, Agy B Σ, Aij
Σ Ang (z, BB),
(9)
We now define 3, which intuitively measures the dispersion of the lifted feature along a viewing ray at the global optimal lift. Suppose the optimal lift yields solution åt. We define 3 at Equ 11
As |
Bill.
14 Σ AgA
(10)
o:
0. = Σ Aij (A 13)
max
(11)
2. Pi
Property (Diagonal Dominance Reduces 3). If each row of A becomes increasingly diagonally dominant i.e., one entry in each row satisfies AT Ajj > A A all j-then the dispersion (3 is smaller. In other words, stronger diagonal dominance results in smaller beta.
Notice that usually x!  Therefore, x' is not optimal in J. By Equ 8 equation under the L.2 loss:
we have the following
((x') < J(x)s
(12)
I(t) = EE A Σ (1+ 3.) s
( (1+ ((x') S (1 3)L(E)
(13)
While our 1 -p--propxxiitnionnn is proven under the I,2 loss for any convex loss I(-) that is Lipschitz- smooth or strongly convex, the proposed solution is bounded above by function 3. This gen- eralizes the stability and approximation behavior of our method beyond the Euclidean norm. To be more specific, the Jensen equation always hold we are using any convex loss function. While is not strictly bounded by the + 3, one can always find finite transform of according to proposed loss function.
3 that is bounded
From the analysis, can conclude that the methods in Dou et al. 2024) Cheng et al. (024) also bounded by the 1 + 3 term. The method Chacko et al. (2025) is bounded when a To norm function is applied. The approach in JJseph et al. (2024) is bounded only when the input observations unit vectors. Jun-Seong et al. (2025) does not provide a theoretical bound, as it selects the top-K splats based solely on depth ordering.
Although our solver can lift any 2D feature into high- dimensional primitives, few benchmarks exist to evaluate such capability. We evaluate our approach on the LeRF-OVS Qin al. (2024) and 3D-OVS Liu al. (2023) datasets, using the segmentation masks annotated from Qin et al. (2024); Kerr et al. (2023). ) and report mean Intersection-ovee over-Union (mIoU) according to the protocols of Cen et al. (2025); Jun-Seong et al. (2025). As Dr. Splat's official code was not available at the time of writing, we follow the evaluation protocol provided by LAGA for consistency. CosegGS and Occam's LGS Dou et al. (2024); [heng et al. (0024), both based on the same naïve solver (Eqq. 6)). are represented here by single baseline. As shown in Tab we group the methods into four categories: 2D- and NeRe-based, training trining-based, grouping- based, and heuristic heward-llffing First, second, and third place in the benchmark are highlighted in light red, light pink, and light yellow, respectively. Results for the 3D-OVSLin et al. (2023) dataset is provided in the appendix

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3.3 REGULARIZER
We have shown that our solution is 3-bounded. However, because this approximation does not rely on any continuity assumptions, it can become quite coarse in the presence of strong noise. In particular, if the linear operator A is rank-deficient (or nearly so) and thus fails to satisfy continuity requirements, the resulting solution will be noisy. To address this, we introduce two regularization strategies: one to regularize the operator A itself, and another to filter the observations B. By removing noisy components and reinforcing diagonal dominance, our solver produces more stable feature-lifting results in downstream tasks.
3.3.1 TIKHONOV GUIDANCE
(163), we observe that emphasizing diagonal dominance helps mitigate noise from linear system A. Therefore, propose carefully designed regularizer applied during solving without sacrificing the RGB rendered result. Specifi- cally, we first convert Equ into fully diagonal row-sum version. Briefly speaking, stabilizing the linear system A A involves avoiding small eigenvalues. Mathematically, by adding a diagonal
According to property 4 and inspired by A. & V. (1977); A.
matrix, which is strictly non-singular to the original A " as shown in Equ 14 we obtain matrix Á with larger eigenvalues. Intuitively, one extreme way decrease the value of 3 would be to make splats either transparent, or fully opaque. In this extreme case, each row in Ā would contain only single non-zero entry with a value of one, yielding a globally optimal solution. We employed such regularization by carefully adjusting the opacity activation term during feature lifting. Compare to linear adjustment like original Tikhonov Regularizer, our method utilizes non-linear soft guidance without undermine the visual quality. We introduce more implementation details about the Tikhonov Guidance in the appendix B
min (IAi - b112 + [|M111
(14)
3.3.2 POST AGGREGATION FILTERING
Inspired by LAGA Cen et al. (225)). we cluster the lifted features to identify and remove noise from SAM-generated masks, as shown as Equ[T5] where -1 denotes unclassified splats, and K is the number of clusters. Unlike LAGA, which learns separate affinity features, we simply reuse the Tikhonov-Guided solution E from Eq. [14 as our clustering feature. This immediately assigns each splat to cluster. We then encode each Gaussian's cluster ID as one-hot signal and render this signal back to 2D. By applying an argmax operation, we recover a 2D mask for each cluster, establishing pixel- level correspondence between the clusters and the original SAM masks as shown in Equ 15 and Equ 15 (Note: Any orthogonal encoding mecoding-deooding System could be used here).
The remaining masks-denoted as Breare significantly more self-consistent and better aligned with the underlying decomposition of splat primitives. The visualization of the alignment is displayed in the technical appendix[[] This produces well-posed data set that further boosts downstream semannic-segmeetttiio and object-querying performance to state-of-the-art levels. In contrast to LAGA's complex view-dependent clustering, our simpler Post Aggregation Filtering approach re- veals that most apparent "view-dependent" variations stem from mask noise rather than useful multi- view information. Noisy masks can be found in Fig as well as Fig(7] We further provide many mis-leading masks' visualization and trust worthy masks in the appendix C.
7 Agg x (-1.... KJ", T= onchot(?) {0, (0
(15a)
K arg max( - e (-1,...,
(15b)
The function M identifies the binary mask corresponding to ray ry based on the original observation in B, and similarly finds the mask for the projected label associated with the same ray ry. More explicitly, the function M gathers all pixels within the same image that share the same label and constructs a binary mask. We then calculate the Intersection over Union (IoU) between each SAM mask and its corresponding cluster mask. Masks with an overlap below predefined threshold are discarded, as detailed in Equation 16
( Bj: IoU(m, 2 T, 0.
M(j, B) my E @R" M(j.k) = =mi "R" BJ=
otherwise.
(16)

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Published as a conference paper at ICLR 2026
Table I: LeRF OVS (left) vs. Multi-Feature & Ablation (right).
(ailoU comparison LeRl' OVS. symbol denotes results reported directly from the original papees, while I indicates results evaluated using their official implementations. Our mloU evaluation follows the LAG/Cen
(b]Multi Feature Comparison on Cosine-Smiilarit- evalinat the feature agnostic capability without Tikhomov guidunce, post- aggregation filtering, or automatic threshold selection. our method dense features generaledd by FeatUp [uu et all 20244 including features from DINO, DINOv2, CLIP, MaskCI.TP VT,, and ResNet. For fair comparison, we geometry provided by Giplar to obtain the geometry for all scenes. Notiee that SAM + OpenCLIP follow exactly LangSpla(Qin et
apply
2025) implementatiion. Fora fair com- parison, we use the same 3D Gaussian model as the lifting prim- nive, trained using the official repository provided by LAGACon ett al. (2025 The same truined model is used for LAGA, DiSplat, Occam LGS, our method
j evaluntion. F demotes Fig- urines. T Teatime, R Ramen, W Waldo kitchen. We use SAM+OpenCLIP for encoding for fair comparison
implemenntation.
Features/Scone
E.
T
R
W.
Mcan
Method/Seene
F
R.
W.
Mean
SAM+OpenCLLI Kinillv et
2023
89.3
90.7
90.6
91.0
90.4
LSeg'
al 2022
7.6
21.7
7.0 29,9
16.6
MaskC1 Dong Br 2023
92.4
94.0
94.5
94.7
93.9
LeRt
Kert
(2023
38.6
45.0
28.2
37.9
DINC Caroa et ai 2051
91.9
78.7
93.7
80.2
94.6
83.0
82.0
93.8
81.0
N2F2
Shalgul
202.
202.
47.0
69.2
56.6
47.9
54.4
DINOVZ Oxiinh er 22023
83.5
85.6
89.6
89.2
87.0
LangSplat
Qin at 2024
25.9
35.6
29.3
33.5
31.1
VIT DowoDirsss
2220
84.6 83.7
86.4
88.0
85.7
Ressectre et 2016
95.8
94.8
96.2
97.0
96.0
LeGaussian
31.2
17.6
17.3
SuperGueg
43.7
55.3
18.1
26.7
35.9
VLGS
Peng et al (204m
58.1
73.5
61.4
54.8
62.0
(c)Ablation Study. We evalunte the impact of each module on the T; denotes Tikhonov Guid- ance, P denotes Post Aggregation Filtering. and A represents Auto- matic threshold selection. The baseline correponnds to the row-sum formulation in Equ [8] To further understand which components is effactive provide full ablation study shown the appendix, TaN
LcRF data step-by-step
SAGA
Con
2023
36.2
53.1
14.4
OpenCaassiinn
Wu al
2025
61.1
59.1
29.2
31,9
45.3
GS Grouning"
Ye
2023
60.9
40.0
45.5
38.7
46.3
I.GAA
Cen et al
202
56.1
68.9
57.4
64.6
61.7
LAGA
Con ct
2025
64.1
70.9
55.6
65.6
64.0
Method
F
T
R
W
Mean
DiSplat Jun-Scong cl
2025
47.5
66.2
36.7
47.5
49.5
DiSplat Jun-Seong et
2025
53.4
57.2
24.7
39.1
43.6
Ours woo (T,PA)
60.1
68.3
55.3
47.7
57.8
OccamL
Cheny
60.1
68.3
55.3
47.7
Ours w/o (PA)
61.7
67.8
53.8
49.6
58.2
Ours wlo (T,A)
65.5
72.0
58.6
50.4
61.6
Occaml GS
Cheng
2024
58.6
70.2
51.0
65.3
61.3
Ours woo (A)
64.8
71.6
61.7
54.7
63.2
Ours
67.6
68.5
62.3
62.1
65.1
Qurs (full)
67.6
62.3
68.5
Table 2: Multi-Kernel and Runtime Comparison. Left: Multi- across different splats.
Right: end-to-end runtime.
(a)Mulii Kernel Comparison on mloU, For this comparison, we methed without Guidanne,,, Post Aggregation Fil- toring, or auto threshold selection to illustrate its kereel agnostic ca-
(b)Runtime Comparison. We compare the rumtime of our lifting method with LAGA and DrSplats, along with the ability preserve the full feature dimensionality. Here T, denotes Tikhonov Guidance. P denotes Post Aggregation Filtering. a single RTX 4090 GPU using CUDA Toolkit 12.8 for consistency. Notice that the runtime of lifting-bused methods seales lincarly with the number of views, whereas training- based and grouping croppingbussed bused methods are determined by predefined training steps. For DrSplats, report results using Top-40 follow their implementation.
pabiity. We evaluate performance using DBS, 2DGS, well as 3DGS, à represents the inri Kerbl al. 2023) implementation luned hyper parameters exactly according to LAGACen et al. (2025) re- lemsed code." represents Gspla[Tancik with no additional hyper parameters changed except set the back. ground color mndom.
timings are measured
(Tancik et al. (2023) implementation
Method
R
Mean
Method
Mean
DBS Lig 2025
50.8
51.2
61.3
53.2
w/o (T.P)
00:03:29
00:02:06
00:01:28
00:02:13
00:02:12
3DGS
2023
55.3
63.5
47.8
49.8
54.1
Ours wlo (P)
00:03:14
00:02:05
00:01:12
00:01:47
00:02:05
3DGS
Kerble (2025)
60.1
68.3
55.3
47.7
57.8
Ours full
00:05:22
00:02:37
00:1159
00:03:02
00:03:15
2DGS
Franng
2029
62.0
66.3
56.0
51.1
58.9
DeSplat
00:02:55
00:01:19
00:01:03
00:01-43
LAGA
01:43:33
01:23:22
01:20:48
01:30:16
01:29:30
3.3.3
AUTO THRESHOLD SELECTION
We observe that threshold selection can significantly alter the final result. Rather than manually choosing thresholds per object (as in Qin et al. (2024)) we leverage the high contrast of the raw attention map for automatic selection. As shown in Fig, 15 even though the ideal hard threshold for correctly isolating chopsticks shifts from 0.225 to 0.30 in the raw attention values, the first valley in the attention histogram remains clearly identifiable. We therefore derive our threshold directly from the histogram's 's local extrema. We first locate its largest peak and then take the adjacent, smaller valley as the threshold. Further details provided in the Appendix
4 EXPERIMENT
We demonstrate our kernel-agnostic capability with multi-kerne comparison Tab 2 In this study, the 2DGS implementation outperforms all other representations due to its specially designed kernel that encourages high opacity values, yielding a naturally lower / as result.
For downstream segmentation tasks, qualitative results in Fig 2 Fig Fig. 3 and Fig. 4 demonstrate that our method generates significantly clearer and more localized attention maps for object queries.
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Our Attention Maps
apple
dog
Mify
toy
Dr. Splat's Attention Maps
Ground fruth
Green apple
Jake the dog
Milly
apple
toy
Segmentation Mask Comparisons
Ground Truth
Ours
Dr. Splat
old camera
rubber duck with hat
green apple
jake the dag toy
clephant
duck with buay
waldo
pink ice cream
red apple
pirate
tesia door handle
chair
spanula
miffy
porcelain
Figure 3: Qualitative Comparison of Attention Maps and Segmentation Masks. We present qualitative comparison between proposed method (top row) and the baseline, Dr. Splat (middle row). The heatmaps visualize the model's attention response, or affinity feature projection, to various text prompts (e.g.. "Green apple," "Jake the dog." "Miffy"). The bottom compares the final semantic segmentation masks for the entire scene against the ground truth.
In contrast, while the baseline (Dr. Splat) identifies the general location of objects, its activations are more diffuse and less uniform. This lack of precision leads to lower performance in down- focused attention maps translate into segmentation masks that closely match the ground truth, exhibiting fewer false positives and less noise than the baseline. These qualitative observations align well with the quantitative mloU results reported in Table T
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To compare feature lifting quality more broadly, we project variety of descriptor:Fu al. (2024) MaskCLIP, CLIP. VIT. DINO, and BesNet-througe our solver (prior to any post-
aggregation filtering) and visualize the results using cosine similarity and PCA. Tab Fig and
Fig 14 show consistent improvement on current SOTA lifting methodsGiuo et al. (2024); Chacko
al. 22025). (see the [ for details). We avoid PSNR for evaluation since MSF-based metrics scale with the number of feature channels. For example, DINO features (384 channels) yield consistently lower PSNR than that of CLIP features (512 channels) despite having comparable perceptual quality. Instead, we demonstrate both quantitatively via cosine similarity as mentioned in T and qualitatively via PCA visualization that our lifted projections consistently outperform the raw descriptors, making direct PSNR comparisons potentially misleading. While we conduct experiments with different types of primitives-inchee feature descriptors we use only 3DGs as the standard primitive to ensure fairness.
2DGS, 3DGS, and DBS, for comparing
To compare runtimes, we report times for lifting, and post-processing using standard SAM+OPenCLIP the encoder mentioned in Tab Additionally, we perform further experi- ments using MaskCLIP as an encoder, which are included the appendix L The motivation behind this choice is that standard SAM+OpenCLIP typically takes approximately
hour pre-prceess the dataset, whereas MaskCLIP completes the same pre-processing task within minutes. Additional mIoU results for Mas
also provided in the appendix [ The splats training time per scene is roughly 20 minutes for the Gsplats Tancik et al. (2023) training pipeline and approximately 40 minutes for the Inria-based pipeline. Regarding memory consumption, our implementation can lift features with over 512 channels without encountering CUDA out-of-memory (OOM) errors. In contrast, in our testing environment, DrSplat's is implementation could only handle up to 32 channels before hitting memory limitations. Lifting-basse methods exhibit linear complexity with respect to the number of feature channels. view images, and witness splats per ray.
Finally, our ablation study isolates the impact of each component naive preconditioner, full Tikhonov (as shown in Table - post-aggregation filtering. We also examine implementation details, including feature scaling, multi-level SAM mask integration, and segmentation-threshee selection. All qualitative results and additional engineering notes are provided in the appendix
5 DISCUSSION
Our method provides a framework to distinguish meaningful 3D clusters from noise, offering a foundation for building more robust feature lifting pipelines in 3D scene understanding. In practice, the noises and inconsistency in sensing process also poses a challenge in feature lifting process. Our method addresses such issues via regularization and could inform the development of sensing mechanisms that yield more consistent observations.
From a theoretical standpoint, averaging features across views helps suppress view-dependent com- ponents while preserving view-independent structures. Such view dependence information can then be quantified by subtracting the lifted (3D) features from the original 2D features to obtain any structured residual patterns correspond to view-specific information.
Finally, while our method focuses on lifting dense features, it will also be feasible to lift sparse descriptors (e.g., SIFT) by embedding them into dense representation using auxiliary signals. That being said, visualizing sparse 3D splats remains an open challenge.
6 CONCLUSION
In this work, we formulate feature lifting as sparse linear inverse problem and derive a general approximation to its core equation. We prove that our solution achieves a globally bounded error. To further refine the reconstructed features, we introduce two complementary modules: (1) Tikhonov Guidance and (2) Post-Lifting Aggregation. Our implementation completes the lifting process in under 10 minutes.
The method is designed to be broadly applicable to any dense feature representation and splat-based kernel. Experiments multiple 3D semantic segmentation benchmarks demonstrate state-of-the- art performance. We also quantitatively evaluate the quality of lifted features using cosine similarity metrics to demonstrate the method's 's effectiveness across different feature descriptors. Together, the method provides a scalable and theoretically framework for enrichment of 3D representations with 2D dense features support scene understandings and other downstream tasks.
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7 ACKNOWLEDGMENT
The authors would like to thank our primary sponsors of this research: Mr. Clayton Burford of the Battlespace Content Creation (BCC) team at Simulation and Training Technology Center (STTC). This work is supported by University Affiliated Research Center (UARC) award 1991NNF14-D. 0005. Statements and opinions expressed and content included do not necessarily reflect the position or the policy of the Government, and no official endorsement should be inferred.
REFERENCES
N. Tikhonov A. On ill-posed problems. Matematicheskii Sbornik. Novaya Seriya, 61((03)(2)221- 223, 1963. In Russian.
N. Tikhonov A. and Y. Arsenin V. Solutions of Ill-Posed Problems. Winston & Sons, 1977.
Yash Bhalgat, Iro Laina, Joao F Henriques, Andrew Zisserman, and Andrea Vedaldi. N2f2: Hi- erarchical scene understanding with nested neural feature fields. In European Conference on Computer Vision, pp. 197-214. Springer, 2024.
Mathilde Caron, Hugo Touvron. Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 1660-9660, 2021.
Jiazhong Cen, Jiemin Fang, Chen Yang, Lingxi Xie, Xiaopeng Zhang, Wei Shen, and Qi Tian. Segment any 3d gaussians. arXiv preprint arXiv:23 /2.00:33/.000860. 2023.
Jiazhong Cen, Xudong Zhou, Jiemin Fang. Changsong Wen, Lingxi Xie, Xiaopeng Zhang, Wei Shen, and Tian. Tackling view-dependent semantics in 3d language gaussian splatting. In ICML, 2025.
Rohan Chacko, Nicolai Haeni, Eldar Khaliullin, Lin Sun, and Douglas Lec. Lifting by gaussians: A simple, fast and flexible method for 3d instance segmentation. arXiv preprint arXiv:2502.00173, 2025.
Jiahuan Cheng, Jan-Nico Zaech, Luc Van Gool, and Danda Pani Paudel. Occam's Igs: A simple approach for language gaussian splatting. arXiv preprint arXiv:2412.018077 2024.
Xiaoyi Dong, Jianmin Bao, Yinglin Zheng, Ting Zhang, Dongdong Chen, Hao Yang, Ming Zeng, Weiming Zhang, Lu Yuan, Dong Chen, al. Maskelip: Masked self-distillation advances con- trastive language-image pretraining. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 10995-11005, 2023.
Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11922 2020.
Bin Dou, Tianyu Zhang, Yongjia Ma. Zhaohui Wang, and Zejian Yuan. Cosseggaussians: Compact and swift scene segmenting 3d gaussians. arXiv e-prints, pp. arXiv-2401, 2024.
Emii Esser, Xiaoqun Zhang, and Tony F Chan. A general framework for class of first order primal- dual algorithms for convex optimization in imaging science. SIAM Journal on Imaging Sciences, 3(4):1015-1044 2010.
Stephanie Fu, Mark Hamilton, Laura Brandt, Axel Feldman, Zhoutong Zhang, and William Freeman. Featup: A model-agnostic framework for features at any resolution. arXiv preprint arXiv:2403. 10516, 2024.
Bruno Galerne, Jianling Wang, Lara Raad, and Jean-Michel Morel. Sgsst: Scaling gaussian splatting style transfer. In Proceedings of the Computer Vision and Pattern Recognition Conference, pp- 26535-2653 26544, 2025.
11

---

Published as a conference paper at ICLR 2026
Qiao Gu, Zhaoyang Lv, Duncan Frost, Simon Green, Julian Straub, and Chris Sweeney. Egolifter: Open-world 3d segmentation for egocentric perception. European Conference on Computer Vision, pp. 282-400. Springer, 2024.
Jun Guo, Xiaojian Ma, Yue Fan, Huaping Liu, and Qing Li. Semantic gaussians: Opca-vocybulary scene understanding with 3d gaussian splatting. arXiv preprint arXiv:2403.15624 2024.
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recog- nition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp- 770-778, 2016.
Binbin Huang, Zehao Yu, Anpei Chen, Andreas Geiger, and Shenghua Gao. 2d gaussian splatting for geometrically accurate radiance fields. In ACM SIGGRAPH 2024 conference papers, pp- 1-11, 2024.
Joji Joseph, Bharadwaj Amrutur, and Shalabh Bhatnagar. Gradient-driven 3d segmentation and affordance transfer in gaussian splatting using 2d masks. arXiv preprint arXiv:2409. 1681, 2024.
Kim Jun-Seong, GeonU Kim, Kim Yu-Ji, Yu-Chiang Frank Wang, Jaesung Choe, and Hyun Oh. Dr. splat: Directly referring 3d gaussian splatting via direct language embedding registration. arXiv preprint arXiv:2502.16652 2025.
Bernhard Kerbl, Georgios Kopanas, Thomas Leimkühler, and George Drettakis. 3d gaussian splat- ting for real-time radiance field rendering. ACM Trans. Graph., 12(4):139-1, 2023.
Justin Kerr, Chung Min Kim, Ken Goldberg, Angjoo Kanazawa, and Matthew Tancik. Lerf: Lan- guage embedded radiance fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 19729-19739, 2023.
Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander Berg, Wan-Yen Lo, et Segment anything. Proceed- ings of the IEEE/CVF International Conference on Computer Vision, pp. 4015-4026, 2023.
Boyi Li, Kiliin Q Weinberger, Serge Belongie, Vladlen Koltun, and René Ranftl. Language-driven semantic segmentation. arXiv preprint arXiv:2201.0335 2022.
Siyun Liang, Sen Wang, Kunyi Li, Michael Niemeyer, Stefano Gasperini, Nassir Navab, and Fed- erico Tombari. Supergseg: Open- 3d segmentation with structured super-gaussians, 2024. URL htt.t:::////// //tpivv///xvvvv.a/ org abs / 2412. 10231
Kunhao Liu, Fangneng Zhan, Jiahui Zhang, Muyu Xu, Yingchen Yu, Abdulmotaleb El Saddik, Christian Theobalt, Eric Xing, and Shijian Lu. Weakly supervised open-vocabulary segmen- tation. Advances in Neural Information Processing Systems, 36:53433-53456 2023.
Kunhao Liu, Fangneng Zhan, Muyu Xu, Christian Theobalt, Ling Shao, and Shijian Lu. Style- gaussian: Instant 3d style transfer with gaussian splatting. In SIGGRAPHI Asia 2024 Technical Communications, pp. 1-4. 2024.
Rong Liu, Dylan Sun, Meida Chen, Yue Wang, and Andrew Feng. Deformable beta splatting, arXiv 2025.
preprint arXiv:2501.
Maxime Oquab, Timothée Darcet, Théo Moutakanni, Huy Vo, Marc Szafraniec, Vasil Khalidov, Pierre Fernandez, Daniel Haziza, Francisco Massa, Alaaeldin El-Nouby, et al. Dinov2: Learning robust visual features without supervision. arXiv preprint arXhv:2304.0719.. 2023.
Qucheng Peng, Benjamin Planche, Zhongpai Gao, Meng Zheng, Anwesa Choudhuri, Terrence Chen, Chen Chen, and Ziyan Wu. 3d vision-language gaussian splatting. arXiv preprint arXiv:2410.07577. 2024a.
Yuning Peng. Haiping Wang, Yuan Liu, Chenglu Wen, Zhen Dong. and Bisheng Yang. Gags: Granularity feature distillation for language gaussian splatting. arXiv preprint arXiv:2412.136644 2024b.
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Published as a conference paper at ICLR 2026
Minghan Qin, Wanhua Li, Jiawei Zhou, Haoqian Wang, and Hanspeter Pfister. Langsplat: 3d lan- guage gaussian splatiing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 20051-20060, 2024.
Ri-Zhao Qiu, Ge Yang, Weijia Zeng, and Xiaolong Wang. Feature splatting: Language-driven physics-based scene synthesis and editing. arXiv preprini arXiv:2404.01223, 2024.
Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, al. Learning transferable visual models from natural language supervision. In International conference machine learning, pp- 9748-8763. PMLR, 2021.
Nikhila Ravi, Valentin Gabeur, Yuan-Ting Hu, Ronghang Hu, Chaitanya Ryali, Tengyu Ma, Haitham Khedr, Roman Rädle, Chloe Rolland, Laura Gustafson, al. Sam 2: Segment anything in images and videos. arXiv preprint arXiv:24088 2400.000000444 00714, 2024.
Yousef Saad. Iterative methods for sparse linear systems. SIAM, 2003.
Jin-Chuan Shi, Miao Wang. Hao-Bin Duan, and Shao-Hua Guan. Language embedded 3d gaus- sians for open-vocabulary scene understanding. Proceedings of the IEEF/CVE Conference on Computer Vision and Pattern Recognition, pp.
2024.
Matthew Tancik, Ethan Weber, Evonne Ng, Ruilong Li, Brent Yi, Terrance Wang, Alexander Kristoffersen, Jake Austin, Kamyar Salahi, Abhik Ahuja, et al. Nerfstudio: A modular frame- work for neural radiance field development. In ACM SIGGRAPH 2023 conference proceedings, pp. 1-12, 2023.
Yanmin Wu, Jiarui Meng, Haijie Li, Chenming Wu, Yahao Shi, Xinhua Cheng, Chen Zhao, Haocheng Feng, Errii Ding, Jingdong Wang, et al. Opengaussian: Towards point-level 3d caussian-based open vocabulary understanding. Advances in Neural Information Processing Sys-
tems, 37:19114-19138, 2025.
Mingqiao Ye, Martin Danelljan, Fisher Yu, and Lei Ke. Gaussian grouping: Segment and edit anything in 3d scenes. arXiv preprint urXiv:2312.0003 2023.
Zehao Yu, Anpei Chen, Binbin Huang, Torsten Sattler, and Andreas Geiger. Mip-splatting: Alias- free 3d gaussian splatting. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 19447-19456, 2024.
Shijie Zhou, Haoran Chang, Sicheng Jiang, Zhiwen Fan, Zehao Zhu, Dejia Xu, Pradyumna Chari, Suya You, Zhangyang Wang, and Achuta Kadambi. Feature 3dgs: Supercharging 3d gaussian splatting to enable distilled feature fields. In Proceedings of the IEEE/CVF Conference on Com- puter Vision and Pattern Recognition, pp. (167--2168,,,, 2024.
Xingxing Zuo, Pouya Samangouei, Yunwen Zhou, Yan Di, and Mingyang Li. Fmgs: Foundation model embedded 3d gaussian splatting for holistic 3d scene understanding. International Journal of Computer Vision, 133(2);611-66) 2025.
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Our Attention Maps
Chopsties
Egg
Karsbboko
toy
Dr. Splat's Attention Maps
Ground Truth
Bowl
Chopsicks
Egg
Napkin
Segmentation Mask Comparisons
Ground Truth
Ours
Dr. Splat
I'chopstickss, 1) ('eggg:
(bowf: 1)
('wavy noodles', 1)
('plate', 1)
('napkin',
("kamaboko,,
('anion segments!,
I'nerl,
('sake cup',
Figure 4: Attention Map Comparison: As demonstrated in the figures, our implementation pro- duces clearer attention maps and segmentation masks compared to Dr. Splat.
A MULTIMEDIA SUPPLEMENTARY
In the supplementary we submitted, we have additional embedding website. The website is local, needs to open it by uncompressing the website package and click the index.html. We have additional code zip file with detail README guidance. To preview the overall result, one can ckeck video
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RGB
Ours
DrSplat
GT
rubber duck hat
green apple jake dog toy apple
pikachu
waldo pirate hat
rubies cube toy elephant
porcelain hand
chopsticks egg
sake cup napkin
wavy noodles kamaboko
onion segments
tea a glass apple
yellow pouf shoep
three cookics
dalle brand
plate
4
plastic ladie
refrigcrator
pot
spatula
Figure 5: Additional Qualitative Segmentation Results. Scenes from top to bottom: Figurines,
Ramen, Teatime, and Waldo's Kitchen (LeRF-OVS dataset). Our method consistently produces sharper, less noisy segmentation masks compared to DrSplat and aligns closely with the Ground Truth.
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Ours
LAGA
Aedderd segtedde
Srar Fuz Sepresttts
/
well weaving
Figure 6: The left column shows the results from our method, while the right column (yellow- purple mask) shows the results generated by LAGA for the 3DOVS 'room' scene. Although the 3DOVS ground truth considers the wooden table as part of the wooden wall, our model able to clearly distinguish between the two. While LAGA's result appears achieve higher mloU this particular scene, it actually generates misleading masks.
B TIKHONOV GUIDANCE
First, let us discuss why Tikhonov regularization thcoretically important for stability, and why our system can become unstable. Instability arises when the matrix contains nearly identical rows. In our setting, adjacent pixels often undergo almost the same rendering and alpha-blending processes, leading to duplicated weights. Redundant rows with similar observation values typically pose no problem (as in the RGB domain), but if identical rows correspond to different observations, the system becomes singular and no exact solution exists. Even nearly identical rows introduce large errors in B due to near-singularity in A.
Mathematically, common remedy strengthen diagonal. Specifically, we convert Equa- tion Ginto fully diagonal, row-sum preconditioner by squaring the original weights. We then adjust the opacity activation term À by compressing the sigmoid function to polarize each splat's opacity. Because lifting is performed without modifying any geometry- does not compromise image- based evaluation metrics. We choose X = 1.2 for both the lifting
parameters, this approach equation and the attention-man map projection, shown by the results in Table
There are a few notes about the polarization. To be specific, after we get the original training figure, the first thing need to do is to convert it to Regularized version, by injecting our in this stage, we get a polarized alpha value. And after lifting, when we do the 3D) segmentation, or localization, can directly
the feature generated. But the challenge when we project the attention queried back to 2D to do the segmentation, what alpha should we use. Experiments shows that, using the same À the best for the 2D attention map generation.
1 1 -
Å.g Wijs Op
(17)
E, A3,Bi Ij
2 = D Aje x D(ATA)B
(18)
Σ, Ab,
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Good Masks
Bad Masks
Clustered Mask
Only
Overlapped
Figure 7: Here we display the figure for post lifting aggregation examples. The first row is displaying the right mask generated in the SAM, while the second row the mis-leading masks generated in the SAM model. We compare our clustered masks displayed in green with the SAM generated mask which displayed in red. And we will filter out the low yellow region (overlapping region) masks through mloU thresholding. This observation shows that view-dependent information might due to the mis-leading masks generated by SAM.
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2DGS Feature PCA/ RGB Renders
3DGS Feature PCA/ RGB Renders
Figure 8:
The left column shows the results obtained using Gsplat with 2D Gaussian Splatting (2DGS) for feature lifting, while the right column shows the results using Gsplat with 3D Gaussian Splatting (3DGS). appears that better reconstruction quality leads to improved PCA outcomes. The lifted features are based SAM-OpenCLIPP embeddings.
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C DENOISING PROPERTIES OF POST-LIFTING AGGREGATION
The Post-Lifting Aggregation module is a critical component for denoising input errors. It is effec- tive not only at resolving inconsistent segmentation masks but also at mitigating errors introduced by noisy camera poses.
IMPLEMENTATION
As described in the main paper, we first cluster the initial lifted features using HDBSCAN. Next, we project each 3D cluster onto all training image frustums to identify reliable 2D masks that over- Deaetioon-vve-Uniiio (loU) overlap above 75% are deemed
lap with the cluster. Masks with an reliable, while others are discarded during feature aggregation. Finally, we aggregate features only from these reliable masks masks-merging them into a single feature representation and assign this uni- fied feature to all splats within the corresponding cluster.
INTUITION
As noted in the "Tikhonov Guidance" section (Appendix B small noise in observa- tions maniifasnns nearly identical rows in the system matrix can lead to large errors. A straightforward remedy to identify and discard these unreliable observations.
Why is it safe to discard them? Recall our problem definition: "each primitive should admit single descriptor." Theoretically, nearly identical rows (rays hitting the same primitive) should yield nearly identical features. Discrepancies imply errors either from the solver corrupted observations. Since our queries rely on cluster-level attention scores, noise that affects a cluster uniformly (cluster- independent noise) merely shifts the score by constant without altering the relative ordering.
In contrast, cluster-dependent noise-often introduced by occlusions or semantic bleed from nearby objects (see Fig. distorts these scores. By generating a pseudo-mask for each cluster and com- puting its IoU against the original input masks, we can effectively filter out clusters where the pseudo-mask mask indicates unreliability.
Crucially, this mechanism makes our method extremely robust to noisy camera poses. Misaligned poses result low overlap between the projected cluster and the 2D mask, causing those corrupted observations to be automatically filtered out. We validate this robustness in the following experi- ments.
EXPERIMENTS
We first demonstrate robustness against inconsistent masks in Tab. and Tab. 4 Our aggregation module yields direct gain of 1.9% mloU even with accurate camera poses, simply by resolving mask inconsistencies.
To evaluate robustness against camera noise, we conducted a controlled experiment where artificially corrupted the poses of a random subset (N) of every 100 images in the training set. The splat geometry was fixed (trained clean poses). The noise injection was defined follows:
* Rotation: We added Gaussian noise with 1 to roll, pitch, and yaw.
Translation: We added Gaussian noise with a
scene scale
100
We then applied our solver to this noisy data. The quantitative results, presented in Tab. B demon- strate that our method maintains high performance even when significant fraction of poses corrupted. Additionally, we provide a qualitative comparison between results obtained from clean poses versus those with 50% pose corruption in Fig. 9
D TRAINING PIPELINE SETTING
Achieving high-quality reconstruction is not the primary focus of our study. While our code includes components for training, the reconstruction results less accurate compared to those obtained
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RGB
Clean
50/100
GT
rubber duck with hat
green apple
pikachu
waldo
rubies cube toy elephant
jake the dog toy statue
porcelain hand red apple
pirate hat
chopsticks egg
sake cup napkin
wavy noodles kamaboko
com onion segments
tcu glass apple
yellow pouf sheep
three cookies
dalle brand
plate
plastic ladle
refrigerator
pot
spatula
Figure 9: Qualitative robustness against noisy camera poses. The columns display (from left to right): the input RGB images, semantic segmentation results using clean camera poses, results with 50% of camera poses corrupted (50/100), and the Ground Truth (GT) segmentation masks. Although there is slight drop visual quality, our method maintains consistent segmentation performance even under severe pose noise.
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Table 3: Robustness against noisy camera poses. The first column indicates the number of images corrupted (per 100 images). The remaining columns report the downstream mloU scores. Note that cosine similarity is not used here because corrupted camera poses invalidate the ground truth projection alignment. Our method maintains high performance ( 65% mloU) even when up to 20% of camera poses are noisy, demonstrating significant robustness.
Corrupted Images (per 100)
Figurines
Ramen
Teatime
Waldo Kitchen
Mean
100/100
1.43
56.0
18.1
36.8
28.1
50/100
64.7
71.7
58.9
48.
60.8
20/100
72.1
63.3
69.1
55.2
65,0
10/100
68.8
64.8
63.9
57.4
63.7
3/100
65.6
64.2
63.4
59.5
63.2
2/100
66.9
64.2
63.4
59.1
63.4
1/100
66.2
63.0
64.7
59.8
63.6
0/100 (Clean)
67.6
68.5
62.3
62.1
65.1
Table Mean IoU (mloU%) on LeRF OVS for various methods. These are additional experimental results using our data for the ablation study. We use different backbones to train the splats and evaluate the resulting mloUs
Method
Figurines
Ramen
Teatime
Waldo Kitchen
Means
DrSplat (3D Query)
47.48
36.66
66.16
47.48
49.45
Gsplat (3DGS) Wio W/o (Threshokd 0.65)
55.30
47.81
63.48
49.78
54.09
Gsplat 2DGG Backbone W/o P W/o (Threshold 0.65)
62.00
56.04
66.34
51.07
58.86
Gsplat (3DGS) W/P w/o T (Threshold 0.65)
56.55
62.24
68.04
53.01
59.96
Gsplat (2DGS)
(Threshold 0.65)
67.83
60.20
66.96
60.62
Inria Trained Result Wio P. Naive (Wo Tikhonov) (Threshold)
60.06
55.30
68.33
47.73
57.85
Inria Trained Result Wo P. (Threshold-0.65)
61.30
54,20
67.60
45.01
57.03
Trained W/p
(1.2/1.2)
61.70
Inria Trained Result W/p w/ (Tikhonov square, sigmoid)
71.96
58.16
69.29
52.73
63.03
Inria Trained Result W/p (Threshold 0.65) W/T
64.76
61.70
71.63
54.71
63.20
Inria Trained W/p W/o Tikhonov Square, w/o sigmoid
65.45
58.55
72.04
61.61
Inria Trained W/p W/o (Tikhonov w/o squeer) hist selection
72.19
64.28
66.08
56.69
64.81
Inria Trained W/o T W/p W/ Dynamic Threshold
69.42
63.89
69.53
61.55
66.10
Inria Trained
W/ Dynamic Threshold
67.64
62.34
68.48
62.11
65.14
Table Effect of Tikhonov Guidance (Asquare/ Areg) on mloU (%). À Equ denotes the parameters used when solving the Feature Lifting Equation. When using text query generate the attention map, we apply À Proj to obtain the 2D attention map. The experiments show that setting both values to 1.2 yields optimal results.
À Equ / X Proj
Figurines
Ramen
Teatime
Waldo Kitchen
Means
0.5 1.0
59.93
53.77
66.43
41.32
55.36
0
62.77
54.02
67.38
43.90
57.02
1.0
61.30
54.20
67.60
45.01
57.03
1.1/1.1
61.59
53.96
68.93
47.72
58.05
1.2/
61.70
53.75
67.80
49.60
58.21
1.35 1.35
61.80
53.44
65.56
50.36
57.79
1.5
61.80
53.40
65.53
50.40
57.78
21

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Published as a conference paper at ICLR 2026
Table 6: Our methods generated masks versus LAGA generated mask on 3D-OVS dataset, mentioned in Fig room scene is not labeled correctly in ground truth, therefore, we provide two results
scene. The former one is the result measured original 3DOVS dataset, and the left one is the fixed results. In both comparison, we are at least the same compare to the current state of the method.
Methods
Bed
Bench
Lawn
Room
Sofa
Means
LAGA
84.9
83.3
93.6
93.1/86.2
76.5
86.3/84.9
Ours
90.2
93.2
89.0
85.5/92.7
73.6
86.3/87.7
Table 7: Weight Summation of each rows statistic property. In the Property assume that the row summation is I, and in the main thesis, we state that this property usually holds in the splats rendering. Here is experimental results regarding the final weight summation of each pixel. The number is with a %. The dataset we are using is LeRF
Method Metrics
Figurines
Ramen
Teatime
Waldo Kitchen
Means
3DGS(means) Black Background
99.49
97.92
99.40
99.86
99.17
3DGS(Std) Black Background
1.37
1.54
0.67
0.18
0.94
3DGS(mcans)
99.74
99.85
99.83
99.91
99.17
3DGS(Std)
0.01
0.04
0.02
0.05
0.04
2DGS(means)
99.86
99.46
99.83
99.91
99.77
2DGS(Std)
0.04
0.45
0.05
0.05
0.15
Table 8: Weight Summation of each rows statistic property. In the Property assume that the row summation is I, and in the main thesis, we state that this property usually holds in the splats rendering. Here is experimental results regarding the final weight summation of each pixel. The number is with %. The dataset we are using is 3DOVS
Methods
Bed
Bench
Lawn
Room
Sofa
Means
3DGS(means)
99.92
99.80
99.67
99.64
99.93
99.79
3DGS(Stt)
0.01
0.04
0.08
0.04
0.01
0.04
2DGa(means)
99.92
99.93
99.95
99.92
99.92
99.93
2DGS(Stt)
0.01
0.01
0.00
0.01
0.01
0.01
22

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Published as a conference paper at ICLR 2026
using the LAGA training code. Therefore, in the main comparison table, use LAGA's pre-trained model. For visualization experiments, we adopt the Gsplat implementation for both 2DGS and 3DGS ensure fair comparison. As shown in Fig [ the visualizations suggest that reconstruction
quality does influence the feature lifting results.
E LIFTING IMPLEMENTATION
Our code is publicly available in the supplementary material and on the project website. We adopt the original rendering pipeline for feature lifting, with a modification the final alpha-blending step: instead of projecting each splat's color into the 2D image, we back-project 2D feature information into the corresponding 3D splat feature and record the blending weights at runtime. This approach more memory memory-efficien efficient than DrSplats, which explicitly constructs pixel-to-spll correspondences. As result, DrSplats may encounter CUDA out-of of-morrry (OOM) errors when the maximum depth increases, whereas method is capable of handling significantly larger inputs. In principle, any 3D image produced by the rendering pipeline can lifted in a similar way by slicing its rendered features.
3D SEGMENTATION
For 3D segmentation, splats can be selected by comparing attention scores associated with target (' ("positive') words against those linked to background words. To avoid the complexity of explicit background-word selection, we compute direct attention scores for each splat and render them as one-dimensional features in the 2D image-thereby minimizing background interference. Since the raw attention scores typically fall outside the [0,1] interval, we rescale them for visualization and manual thresholding. However, during the dynamic threshold selection step, operate directly the un on-normalized attention scores to determine the optimal threshold. Further visualization results can be found in the appended video
G PROPERTY JUSTIFICATION
Recall from property 2 this property means for each ray, there should be nearly no influence of the background color. Let first justify why this property is necessary. If without the above property, even the optimized lift will depend on background feature. When we utilize random feature background, the error has lower bound which is the left out alpha for each ray. This justification will also hold true we are utilizing color as feature. To justify this property, we first scratch a theoretical proof, and then, we give out experimental results.
THEORETICAL
C₁ ~ u((1,11
(19)
C. Eupo + +1- Co
(20)
P
F
8
Σ Sp I(w) MMSEC,,
(21)
L(w) = Ecg (C,--C,)
(22)
Eog (E Up Cp - ()- c. P
(23)
Here we define the ground truth for per ray color as C, we use MSE as a loss function to calculate the loss between observed color and rendered color. The goal of the proof is show that under any gradient descent based method, if the loss converges, s approaches to one. Notice that here we define the background color Cý random background that has uniform distribution the normalized
23

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color definition. Let us take the stochastic gradient with respect to weight w, and the summation of weight s.
ØL
2(C, - C.) Ch)
(24)
Owl
0L
Σ
ÖL
2 - C.) Σ CCG
(25)
Ös
dui,
p
Here we substitute the residual back to the Equ 24
E
wp - Cr, Cr C,- = (1 s)c
(26)
p
0L
2 (s+ + (1-s) C)) E(G,- c
E
(27)
Ōs
When we expand the above equation, get the expectation of the gradient is the Equ
0L
E
= E 2 Σ cp-22 22 -(p-C))
Ös
(28)
(1 s) (s- (s- (C))]]
And apparently, we can get everything canceled out, except this term shown in Equ 29
ÖL
E
(s-1)0 1)o²
(29)
Therefore, to converge, 8 - must be zero, i.e. Σp up = Q.E.D. According to Property 3 usually have a converged system at least on RGB, therefore this property holds.
we
EXPERIMENTAL
To experimentally validate our theoretical prediction, we conducted the following experiment. We trained both 3D Gaussian Splats and 2D Gaussian Splats separately using random backgrounds, then computed the mean and variance their final alpha distributions. the mean exceeds a threshold vi 99.6 because color values quantized into 256
99.6, theory is confirmed. We selected levels, and additional floating-pott precision does not improve RGB rendering. For comparison, also ran the 3D Gaussian Splats experiment with black background. As shown in Tables 7 and g, the results align well with our theoretical proof.
(1 Quantize Scale 100 99.6
(30)
H FEATURE AGNOSTIC AND KERNEL AGNOSTIC
FEATURE AGNOSTICISM
Recall from Section 3.2 that our solver is proven be optimal under any convex loss function.
Theoretically, this guarantees tighter error bound compared to heuristic or optimization-basee based approaches such as Chacko al. (2025); Jun-Seong et al. (202):; Guo al. (2024); [Josehh et al.) 2024). While Table demonsttated that method consistently achieves cosine similarity above 80%, that result alone did not quantify our superiority over specific baselines.
To address this, we provide detailed comparison against current ceature-agnostic methods, specif- ically Guo et al. (2024); Chacko et al. (2025). We exclude Dr.Splat Jun-Seong et al. (2025) from this comparison because its pipeline necessitates compressing original features (c.g., 512 dimen- sions) down to -iw-eeenniionll subspaces (e.g., 32 dimensions). thereby losing feature generality. Similarly, grouping-basee methods excluded as they cannot operate without mask guidance. As
24

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RGB
Rendered
Observation
SAM+OpenCHL CLIP
Figure 10: Feature Map Comparison: This figure compares our rendered features against the ground truth 2D features. The ground truth visualization is generated by applying PCA the fea- ture maps extracted directly from the input image by the foundation model. The rendered fea- tures represent the PCA the features projected from our solved splats. These results demonstrate the SAM+OpenCLIP pipeline. Additionally, we compare our lifted result to current SOTA lifting method in Fig 13
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Published as a conference paper at ICLR 2026
RGB
Rendered
Observation
DINOV2
Figure 11: Feature Map Comparison: This figure compares our rendered features against the ground truth 2D features. The ground truth visualization is generated by applying PCA the fea- ture maps extracted directly from the input image by the foundation model. The rendered features represent the PCA of the features projected from our solved splats. These results demonstrate the DINOv2 pipeline. Additionally, we compare our lifted result to current SOTA lifting method in Fig 14
26

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Published as a conference paper at ICLR 2026
SAMOpenCLIP
DINOv2
Rendered Image
GT Image
Rendered Image
Image
Rendered Feature
GT Feature
Rendcred Feature
GT Feature
CLIP
ViT
Rendered Image
GT Image
Rendered Image
Image
Rendered Feature
GT Feature
Rendered Feature
GT Feature
MaskCLIP
ResNet
Rendered Image
GT Image
Rendered Image
Image
Rendered Feature
GT Feature
Rendered Feature
GT Feature
Figure 12: Further Visualization results, we are using Teatime, ramen, figurines, waldo kitchen re- sults from different scenes. More visualization results could be found in the supplementary materials
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Published as a conference paper at ICLR 2026
Ours
Semantic GS
ArgMaxLifting
Ope+O
Figure 13: Qualitative Comparison of Feature Fidelity: We visualize the principal components (PCA) of the lifted feature fields rendered into 2D using the SAM+OpenCLIP backbone. We compare our proposed method (left columns) against another optimization-basee Semantic Gaus- sian Guo et al. (2024) (middle column) and the heuristic Argmax Lifting Chacko et al. (2025) (right column). The input RGB and ground truth feature map are the same as the Fig 10 Our method recovers sharper object boundaries and more consistent internal feature representations (higher fi- delity), avoiding the floating Gaussian artifacts and the noise inherent in heuristic aggregation.
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Ours
Semantic GS
ArgMaxLifting
DINOv2
Figure 14: Qualitative Comparison of Feature Fidelity: We visualize the principal components (PCA) of the lifted feature fields rendered into 2D using the DINOv2 backbone. We compare our proposed method (left columns) against another optimization-based Semantic Gaussian Guo et al. (2024) (middle column) and the heuristic Argmax Lifting Chacko al. (2025) (right column). The input RGB and ground truth feature map are the same as the Fig 11 Our method recovers sharper object boundaries and more consistent internal feature representations (higher fidelity), avoiding the floating Gaussian artifacts and the noise inherent in heuristic aggregation.
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Table 9: Comparison of feature lifting fidelity (Cosine Similarity). Red indicates the best perfor-
mance (highest), Pink indicates the second best, and Green indicates the lowest performance. Our method consistently achieves the highest fidelity across all feature types.
Feature
Method
F
T
R
W.
Mean
Semantic Gaussian Guo et al. (0244)
80.7
83.1
83.7
85.2
83.2
SAM+OPenCLIP
Argmax Lifting Chacko et al. 2025
81.8
82.9
83.8
85.4
83.4
Kirillov al. 2023
Ours
89.3
90.7
90.6
91.0
90.4
Semantic Gaussian Guo al. 2024
90.6
93.0
94.0
93.1
92.8
MaskCLIP
Argmax Lifting Chacko et al. Ours
2025
91.3
92.3
93.3
94.2
92.8
Dong al. 2023
92.4
94.0
94.5
94.7
93.9
Semantic Gaussian Guo et al. 2024
90.4
92.8
94.1
93.7
92.8
CLIP
Argmax Lifting Chacko et al Ours
2025
90.8
91.6
93.4
94.3
92.5
Radford et al. (002
91.9
93.7
94.6
94.9
93.8
Semantic Gaussian Guo et al. Argmax Lifting Chacko Ours
(024)
72.5
76.5
81.3
75.2
76.4
DINO
2025
74.0
72.3
78.3
78.9
75.9
Caron et al. 202
78.7
80.2
83.0
82.0
81.0
Semantic Gaussian Guo et al. (024))
77.5
82.5
88.2
83.9
83.0
DINOv2
Oquab et al. 2023
Argmax Lifting Chacko et al. Ours
2025
80.2
79.6
87.2
87.3
83.6
83.5
85.6
89.6
89.2
87.0
Semantic Gaussian Guo al. (2024)
81.7
82.6
85.8
85.4
83.9
VIT
Argmax Lifting Chacko et al. 2025
81.6
77.8
83.7
86.2
82.3
Dosovitskiy et al. (2020
Ours
84.6
83.7
86.4
88.0
85.7
Semantic Gaussian Guo et al. Argmax Lifting Chacko et al. 2025
(0244
94.9
94.4
96.0
94.4
94.9
ResNet
94.8
93.1
95.1
96.5
94.9
He et al. (0016)
Ours
95.8
94.8
96.2
97.0
96.0
the high similarity range (80-90%) achieved by method represents signifi- cant improvement over these existing approaches.
shown in Table g
For qualitative feature visualizations, please refer Fig. 10 Fig.
and Fig. 12
Comparisons with
existing feature-agnostic methods, such as Chacko et al. 1205 Guo et al. 2024). are provided in
Fig. 13 and Fig.
KERNEL AGNOSTICISM
For multiple kernel feature visualization, one can check Fig appended video
There are plenty of the content in the
I
THRESHOLD
We can refer directly Fig. 15 The basic idea trace the gradient from top to bottom, then use the first local maximum and the preceding local minimum to determine the threshold. In this way, the threshold adapts dynamically and is independent of the background words.
30

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Attontion Mac Histogram: chopsticis
250030
200000
0.30
0.33
Map Histogram: egg
$3000
0.00
0.29 Value
Figure 15: This figure is from the Ramen scene in the LeRF dataset. The query word is "chopsticks" for the first row, and "eggs" for the second row. The first column represents the attention maps' histograms while the second column is the actual attention map. A simple gradient-based dynamic threshold selection strategy can be readily envisioned for downstream tasks such as 3D segmenta- tion.
31


Reviews:
[{"review_id": "bRqhtLKrrq", "reviewer": "Reviewer_u6Yd", "summary": "This paper addresses the feature lifting problem, which aims to transform vision foundation model features (e.g., DINO/CLIP) into Gaussian-splatting-based representations. The authors innovatively formulate this problem as a sparse linear inverse problem and propose a closed-form solver. In addition, they introduce two modules to suppress the noise inherent in foundation model features. Experimental results demonstrate the proposed method’s effectiveness and generalization across different Gaussian splatting kernels. Overall, the paper presents solid contributions both theoretically and practically.", "questions": "* In Figure 2, why are the segmentation boundaries so noisy? Moreover, for the two similar and adjacent eggs, why does the method only able to segment one of them?\n* According to Section 3.2, the solver is closed-form and enables one-shot estimation without iterative SGD. Theoretically, this should result in very fast inference, yet the runtime is still reported as 1–3 minutes. Could the authors clarify what factors contribute to this computational cost?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "* The paper formulates feature lifting as a sparse linear inverse problem and derives a closed-form solution, which is elegant and theoretically sound.\n* The mathematical derivations and reasoning are solid and well-motivated.", "weaknesses": "* The space allocation in the manuscript is unbalanced — too few visualizations are included in the main text, while most figures are deferred to the supplementary material. Moreover, some figure captions are vague.\n* The paper lacks discussion and comparison with feed-forward models related to VGGT, such as Anysplat, which can also lift DINOv2 features to Gaussian-splatting representations. Considering their feed-forward nature, such models are likely to offer faster runtime performance.\n* In Table 1 (b) and (c) lack highlighted numerical values, making it difficult to visually discern the performance trends.\n* The statement “Third, many existing methods are specialized for particular feature types or geometric kernels, which may limit generalization across broader settings” requires further clarification. Specifically, which feature types are those methods specialized for? It would also strengthen the paper to include visual evidence showing that the proposed approach generalizes better across diverse cases.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "UpDOEEQPej", "reviewer": "Reviewer_67o8", "summary": "This paper introduces Splat Feature Solver (SFS), a self-supervised framework designed to learn 3D scene representations using 3D Gaussian Splatting (3DGS) as the core rendering primitive.\nThe key idea is to reconstruct multi-view images from learnable Gaussian feature fields, optimizing both photometric and perceptual losses without camera supervision. The authors claim that the model learns geometry-aware features from raw multi-view imagery and achieves competitive results on downstream 3D tasks such as novel-view synthesis and depth prediction.", "questions": "1, How does SFS perform on unposed or pose-free datasets compared to pose-supervised ones?\n\n2, Could the authors provide any quantitative measure of learned 3D consistency (e.g., reprojection error or latent geometry alignment)?\n\n3, Are the improvements statistically significant across multiple runs?", "limitations": "", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1， The paper targets a highly relevant goal，efficient and scalable self-supervised 3D representation learning using Gaussian splatting, an area of growing academic and industrial interest.\n\n2，Compared to NeRF-style volumetric sampling, the splatting-based pipeline is computationally lighter and supports faster convergence. The engineering design is practical and well-motivated.\n\n3， The pipeline, loss functions, and training strategy are described with good clarity. Figures are intuitive and well-illustrated.\n\n4，Experiments across multiple datasets show consistent, if modest, improvements over previous self-supervised 3D baselines. Ablation results are included to demonstrate the influence of loss terms and feature solvers.", "weaknesses": "1, The method essentially reuses the existing Gaussian Splatting pipeline as a self-supervised pretext task, with minor modifications to the loss formulation. The “feature solver” concept adds no clearly new principle beyond standard photometric reconstruction with latent feature regularization. The contribution is incremental and primarily engineering-driven.\n\n2, The paper does not provide any analysis explaining why the proposed self-supervised optimization leads to meaningful 3D representations. There is no exploration of feature alignment, depth consistency, or the information content of Gaussian features. The claim of “self-supervised 3D understanding” is thus empirically unsubstantiated.\n\n3, Although the method is described as “self-supervised,” it implicitly assumes access to approximate camera poses or adjacency constraints during training. The paper does not clarify how SFS handles unposed or unordered images. True pose-free capability is not demonstrated.\n\n4, Reported performance gains over NeRF-based SSL or other Gaussian-based SSL approaches (e.g., GS3, UniSplat) are small (often <1% absolute improvement). Key comparisons to Pose-Free Gaussian Fields, PixelSplat, or DUSt3R are missing, leaving the evaluation incomplete.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "5BUjJ9k9cS", "reviewer": "Reviewer_djJk", "summary": "1 The paper formulates feature lifting in splat-based 3D representations as a sparse linear inverse problem AX=B , and proposes a closed-form row-sum preconditioner solver with a provable (1+β) -approximation error bound under convex losses.\n\n2 It introduces two regularization strategies—Tikhonov Guidance (to enhance diagonal dominance and numerical stability) and Post-Lifting Aggregation (to filter noisy SAM masks via clustering)—and evaluates the method on open-vocabulary 3D semantic segmentation using mIoU on LeRF-OVS and 3D-OVS benchmarks.\n\n3 Comprehensive ablation studies validate each component, and experiments across multiple splat kernels (3DGS, 2DGS, DBS) and feature backbones (CLIP, DINOv2, ResNet, etc.) demonstrate state-of-the-art performance with minutes-level runtime, confirming both effectiveness and generality.", "questions": "Similar to weakness.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 1, "contribution": 2, "strengths": "The paper presents a strong and cohesive contribution by formulating feature lifting in splat-based 3D representations as a sparse linear inverse problem with an original and theoretically grounded perspective that unifies and improves upon prior heuristic, training-based, and grouping-based methods. The proposed closed-form solver with a provable (1+β) -approximation error bound enhances both originality and technical quality, while the two lightweight yet effective regularization strategies (Tikhonov Guidance and Post-Lifting Aggregation) address real-world noise and inconsistency issues without sacrificing efficiency. The work is clearly presented with a logical flow from problem definition to theoretical analysis and extensive experiments across kernels, features, and benchmarks. Its significance lies in enabling fast, general, and high-fidelity semantic enrichment of 3D scenes—advancing open-vocabulary 3D understanding with practical impact and theoretical insight.", "weaknesses": "1 The paper lacks a clear and detailed pipeline diagram—Figure 1 is overly abstract and fails to illustrate concretely how high-dimensional features are assigned to Gaussian splats, making the core lifting mechanism hard to grasp.\n\n2 Despite claiming SOTA performance on LeRF-OVS, the paper provides minimal qualitative comparisons (only Figures 2 and 8, each against a single baseline), severely limiting confidence in the method’s robustness across diverse scenes.\n\n3 Table 1(b) reports cosine similarity across feature types but doesn’t link these metrics to downstream task gains, raising questions about its necessity.\n\n4 Additionally, the paper suffers from formatting issues. Such as overly large table captions, excessively long figure titles, and inconsistent font sizes in visuals—detracting from readability and professionalism.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)