Splat the Net: Radiance Fields with Splattable Neural Primitives
Authors: xilong zhou
Bao-Huy Nguyen
Loïc Magne
Vladislav Golyanik
Thomas Leimkuehler
Christian Theobalt
Venue: ICLR 2026 Poster (2026)
Keywords: neural rendering
radiance field representation
3DGS
NeRF
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Radiance fields have emerged as a predominant representation for modeling 3D scene appearance. Neural formulations such as Neural Radiance Fields provide high expressivity but require costly ray marching for rendering, whereas primitive-based methods such as 3D Gaussian Splatting offer real-time efficiency through splatting, yet at the expense of representational power. Inspired by advances in both these directions, we introduce splattable neural primitives, a new volumetric representation that reconciles the expressivity of neural models with the efficiency of primitive-based splatting. Each primitive encodes a bounded neural density field parameterized by a shallow neural network. Our formulation admits an exact analytical solution for line integrals, enabling efficient computation of perspectively accurate splatting kernels. As a result, our representation supports integration along view rays without the need for costly ray marching. The primitives flexibly adapt to scene geometry and, being larger than prior analytic primitives, reduce the number required per scene. On novel-view synthesis benchmarks, our approach matches the quality and speed of 3D Gaussian Splatting while using 10x fewer primitives and 6x fewer parameters. These advantages arise directly from the representation itself, without reliance on complex control or adaptation frameworks.

Published as a conference paper at ICLR 2026
SPLAT THE NET: RADIANCE FIELDS WITH SPLATTABLE NEURAL PRIMITIVES
Xilong Zhou*, Bao-Huy Nguyen*, Loic Magne, Vladislav Golyanik, Thomas Leimkühler, Christian Theobalt *Co-first. authors
Max Planck Institute for Informatics {xzhou, bnguyen @mpi-inf mpg- de
ABSTRACT
Radiance fields have emerged predominant representation for modeling 3D scene appearance. Neural formulations such as Neural Radiance Fields provide high expressivity but require costly ray marching for rendering, whereas primitive- based methods such as 3D Gaussian Splatting offer real-time efficiency through splatting, yet at the expense of representational power. Inspired by advances in both these directions, we introduce splattable neural primitives, a new volumetric representation that reconciles the expressivity of neural models with the efficiency of primitive-based splatting. Each primitive encodes a bounded neural density field parameterized by shallow neural network. Our formulation admits an exact analytical solution for line integrals, enabling efficient computation of perspectively accurate splatting kernels. As result, our representation supports integration along view rays without the need for costly ray marching, The primitives flexibly adapt to scene geometry and, being larger than prior analytic primitives, reduce the number required per scene. On novel-view synthesis benchmarks, our approach matches the quality and speed 3D Gaussian Splatting while using 10x fewer primitives and 6x fewer parameters. These advantages arise directly from the representation itself, without reliance on complex control or adaptation frameworks. The project page is https::///// /tts:///vaala /vcaiv........ www.mppppii inf www..pp.................. de/ jects /ectss/splaatte
INTRODUCTION
Radiance fields have become predominant representation for modeling 3D scene appearance. Unlike surface-based approaches, their volumetric formulation is compatible with the gradient- optimization routines employed during training from multi-view images. Neural representations, particularly Neural Radiance Fields introduced by |Mildenhall et al. (2020). offer unprecedented expressivity in encoding radiance fields. However, rendering image from volumetric scene representation is generally challenging: Volume rendering (Kajiya & Von Herzen 1984) requires the computation of costly integrals along view rays, typically solved using quadrature methods such as ray marching (Max 1995). As remedy, primitive- an efficient alternative. Popularized by 3D Gaussian Splatting (3DGS) (Kerbl al. 2023), these approaches model radiance fields using mixture of simple volumetric functions. The key to high rendering efficiency lies in the observation that these primitives can be easily projected onto the image plane, where they become 2D kernels that can be efficiently splatted. A prime example is the 3D Gaussian primitive used 3DGS, which reduces to 2D Gaussian splatting kernel (Zwicker al. 2001). Recently, a variety of functions have been explored as primitives (Mai et al.) (025 von Lützow Nießnner 2025 Hamdi et al. 22024 Held et al. 2025 Huang et al.) 2024), all relying on relatively simple analytical formulations, which widely considered essential for enabling efficient conversion into dieeddependent splatting kernels.
representations have emerged as
These developments have led to prevalent, somewhat dichotomous view of radiance field repre- sentations: Neural representations are expressive but come with the high cost of ray marching for rendering, whereas primitiye-based representations, though simpler and less expressive, offer more

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Published as a conference paper at ICLR 2026
Mom: 350MB
Mem: 84MB
PSNR: 30.31
PSNR: 31.82
Gaussian Primitives
#Primitives: 1.5M Neural Primitives
#Primitives: 220K
(b)
Figure 1: (a) Overview of volumetric splattable neural primitives. Fach primitive is spatially hounded by ellipsoid, and its density is parameterized as shallow neural network. (b) A real scene rendered using Gaussian primitives (left) and neural primitives (right). Our method achieves comparable PSNR to the Gaussian representation with fewer primitives, highlighting the expressivity of neural primitives.
efficient rendering through splatting. We challenge this common wisdom by introducing splattable neural primitives, offering both expressivity and real-time efficiency; see Fig. for an overview.
The central design ingredient of our primitives is a neural volumetric density field. Its density distribution is parameterized by shallow yet expressive neural network and is spatially bounded by an ellipsoid. This formulation admits an exact analytical solution for line integrals (Subr) 2021 Lloyd al. 2020), which enables efficient computation of a perspectively accurate image-space footprint, le., splatting kernel for rendering. Despite its neural representation, this enables integration of the density field along each pixel's view ray without the need for costly ray marching. Our primitives flexibly adapt scene geometry and, being typically larger than the analytic primitives employed in recent work, reduce the total number needed to represent a scene. This yields a highly favorable trade-off among quality, performance, and compactness in novel-view synthesis: We match the quality and speed 3DGS while using 10x fewer primitives and 6x fewer parameters. Crucially, these advantages result from the design of our representation itself, without requiring complex control or adaptation frameworks (Mallick et al. 2024 Fan et al. 2024). In summary, our contributions are:
A taxonomy of radiance field representations, highlighting a dichotomy between neural and splatting- approaches (Sec. (Sec.2.1).
A novel volumetric representation based on splattable neural primitives, bridging the gap between and leveraging the benefits of both neural and primitive- basee approaches (Sec. (3)
The application of the representation to novel-view synthesis, validating its practical effec- tiveness and efficiency: Neural primitives achieve real-time rendering speed and produce result quality comparable to 3DGS with a smaller memory budget (Sec.
2 BACKGROUND AND RELATED WORK
2.1 RADIANCE FIELD REPRESENTATION AND RENDERING
Radiance fields represent the appearance of a scene via a function Fø (x, - (a, c), which maps a spatial location x E IR3 and view direction d E S to volumetric density E R and an RGB color c E Rd Synthesizing an image from a radiance field involves emission-absorption volume rendering (Kajiya & Von Herzen 1984 along view rays r(f) + td, where o E R denotes the camera center, and E R4, parameterizes the ray. Specifically, each RGB pixel color C' E R3 is computed by evaluating the radiance field along its corresponding view ray:
C(r) (tr)=Jo -[" exp (-/. (-
(r())
(r(1)) (r()),
(1)
where t, and ty are near and far bounds, respectively. Recent years have seen considerable research devoted to the foundational question of how to best represent Fg. Representations can be arranged along an atomicity scale, from monolithic models that entangle all components in a single structure to modular formulations made up of many simple, spatially localized primitives (horizontal axis in
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b)
Neural Radiance
Miature of (laedaaei and 2011
Ours
Neuralit
InstantNGP
SD Gavasian pesi ai 2i0t
Plenneels
Neuol Radionce de
Penneek
Mixture of
20 Coussian Splatinng
Ours
Aromicity
InstaniNCP
Rendering::
Ray Marching Sumpling
Spiatting Avalyticintegrrni
Representation:
Neural
Natt-Neural
Figure 2: Positioning of our work relative hallmark radiance field representations. a) Overview of representa- tions organized along two central design dimensions: Atomicity (horizontal axis), spanning from monolithic (left) to distributed (right) representations; Neurality (vertical axis), ranging from non-neural (bottom) to fully neural (top) approaches. Dot color indicates the supported rendering algorithm. b) Illustration of the rendering algorithms associated with each representation. Our method is the only neural, primitive-based model that supports efficient splatting for sanderingttheeeee eliminating the need for costly ray marching-while retaining the flexibility of neural design.
Fig. Fi). In the following paragraphs, we briefly review the literature on radiance field representations along this atomicity scale, from monolithic to modular.
Neural Radiance Fields (NeRFs) (Mildenhall et al. 2020) represent Fe using a neural network. Numerous follow-up works (Barron et al. [222] Martin Brualla et al. (202]) extended and enhanced its capabilities. However, rendering an image from involves ray marching, that is, discretizing Eq. into finite sum of samples along each ray (Max 1995) (red dots in Fig. 2b):
N
4-1
C(r)
Σ exp
Σ 05 (1 -1-oa (1-exp(-o,)),)
(2)
where d; is the distance between adjacent samples. This rendering process is computationally expensive, as each sample entails a forward pass through the representation network. The pursuit of efficiency has motivated shift from monolithic to more distributed, explicit representations.
Prominent directions include the use of grids (Fridovich-
et al., 2022] Barron et al.) (023).
volumetric meshes (Govindarajan et al.) 2025). and neuro-explicit structures (Müller et al. 2022
Chan et al. [022] Reiser et al.][2021] all seeking trade-off's between computational cost and memory.
Sparse representations allow skipping of empty space (Lombardi et al. 2021 Liu al. 2020 Yu
ct al. 2021), reducing the number of samples during ray marching.
Taking a radically different approach by pushing atomicity the extreme, 3D Gaussian Splatting (3DGS) (Kerbl et al. (223)) represents Fg as an unstructured mixture of up to millions of 3D primitive functions. Each primitive, Pt, is specified by small set of parameters that determine its density distribution, (x),, along with appearance parameters that capture its view-dependent color, c; Rendering an image from this representation can be achieved through splatting, two-step process: In the first step, a; is projected to the image plane by integrating along the view ray r (blue lines in Fig. 2). yielding 2D opacity kernel
a; (r) = 1 - exp (-f- (r()))
In the second step, Eq. simplifies to highly efficient alpha blending of the 2D kernels:
i-1 -
C(r) ~
Σ (r()),(()) (EV(r)
II 1=1
(4)
where Af represents the indices of the depth-sorted primitives intersected by the view ray. Evaluating
Eq is generally non-trivial, but for 3D Gaussian primitives P., the footprint a; simplifies to 2D
Gaussian kernel under reasonable assumptions (Zwicker et al. 2001 Celarek et al., 2025). enabling
high rendering speed and supporting high-quality radiance fields with millions of Gaussians in 3DGS.
The 3D Gaussian is not the only primitive allowing efficient (approximate) conversion into a 2D
splatting kernel a. Recent work has explored a variety of primitive shapes (Mai et al. 2025 von
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Lützow & Nießner 2025 Hamdi al. 2024 Held al.
2025 Chen al. 2024 Li et al. 2025 Gu
et al. 2024| Hamdi et al. 2024 Talegaonkar et al. 2025 Liu et al. 2025). all relying on hand-crafted
representation introduces splattable neural primitives, greatly increasing modeling flexibility. Neural components have also been used in the context of primitive splatting. for example, by injecting structure into the representation (Lu et al. 2024) or enforcing spatial regularization (Mihajlovic et al., 22024, yet these methods ultimately splat Gaussian functions. To the best of our knowledge, are the first represent the volumetric kernel itself 1uff-i.c i.e., the density distribution as a neural network, making the primitive fundamentally neural rather than merely Gaussian with neural augmentations.
analytic kernels for efficient evaluation of Eq. []] In contrast,
2.2 INTEGRATION WITH NEURAL NETWORKS
Estimating integrals is common in visual computing. Feed-forward neural networks trained on the integrand can sometimes perform this task effectively. A notable class in this context is shallow neural networks with one hidden layer, which remain universal function approximators (Cybenko) 1989)
and can be integrated in closed form (Yan et al. 2013 Zhe-Zhao et al. 2006 Lloyd et al., 2020 Subr 2021). Our approach builds on this insight by modeling neural primitives that support -losed-form integration along view rays. In contrast, deep neural networks have also been applied to integral
computation via derivative graphs (Lindell et al. [202T] Teichert al. 2019), but their high evaluation
cost and difficulty in producing consistent integrals along arbitrary rays remain challenges.
METHOD
In this section, we first introduce our neural representation (Sec. 3.1 before explaining how to render images using this representation (Sec. 3.2). Finally, we discuss implementation details including population control strategy, network design, and training protocol (Sec. 3.3
3.1 REPRESENTATION
b)
fout
We parameterize Fe as a mixture of vol- umetric primitives (P.}. Each primitive occupies a volume bounded by an ellip- soid (Mai et al. 2025). which we denote as B (Fig. 3). This ellipsoid is defined by center XB RR3 scaling vector SB E IR along its principal axes, and a rotation quaternion qa E R In accor- dance with the radiance field formalism, each primitive must define spatially vary- ing density a and a view-dependent color c, described next. We define density field ox): B IR within the volume of the ellipsoid as
o
x
fin
B
Figure 3: a) Geometry of our representation for a single prim- itive. Analytic splatting kernels are computed by performing closed-form integration of a neural density field (green shape) along view rays (blue line). b) Architecture of our neural density field. Density o is a function of 3D spatial position
(x)
fo
x
X
(5)
|
where for is shallow neural network with one hidden layer of width N₂ and periodic activation (Sitz. mann et al. 2020) (Fig. 3D):
[x( = W2 (cos (wo (W1 (x) + b,))) + b2-
Here, W1 E N. and W2 E x are weight matrices, while by E N. and b E R are biases. Similar to Sitzmann et al. (202)). we use a fixed boosting frequency wg. which yields stable initialization. The network structure of Eq. addmits an interpretation analogous to Fourier series, where W1 and b, correspond to frequencies and phases, and W2 and b2 are amplitudes and offsets. The normalization by x and Sæ in Eq. 5 ensures that fa operates on centered and uniformly scaled domain. In the appendix, we also show proof-of-concept extensions of this model to higher-dimensions inputs, including time, which can be easily incorporated into model by augmenting the network's 's input dimensions. To represent view sie-ddependent color, we adopt the Spherical Harmonies basis.
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32Prims
128Prims
512Prims
8Prims
32Prims
128Prims
Neural Prim
Neural Prim
CT
1.7K *
6.9K
27.6K
1.7K
6.9K
Gaussian Prim
Gaussian Prim
448
1.8K
7.2K
112"
448"
1.8K
Figure 4: Demonstration of the expressivity of the proposed neural density field. We train both neural and Gaussian primitives on the leapor and leaf datasets using different numbers of primitives. For each example, we visualize the reconstructed density field and color-coded primitives, illustrating how these dllpsood-boundeer neural primitives are deformed to represent complex structures. denotes the total number parameters.
3.2 RENDERING
Images of our representation are rendered using an efficient splatting-basee approach. Specifically, for each primitive bounding ellipsoid B intersected by view ray r(t), we compute the entry and exit distances, Ii and fout along the ray via an analytic line-ellipsoid intersection. To obtain splatting kernel via Eq. 3 the crucial step is to evaluate the density integral along the view ray (blue line in Fig. 3):
leur a (o + td) dt = S (fom;; o, d) - (fin: o, d),
((imn fout, o, d) ==
where S(4 o, d) denotes the antiderivative with respect to of the function / >> a(o + (d), which depends parametrically on o and The equality follows from the fundamental theorem calculus. Based recent findings (Lloyd al. 2020 Subr 2021), derive dlseddform antiderivative for our density field:
S(t: o, d) = [22 Ø (wo Wi (d)) sin (wo (t Wi (d) + W1 (o) + b,)) + f. .2,
where 2 denotes elementwise division. Incorporating Eq. with the previous derivations yields the final splatting kernel
((r) = - 1-cppp ( max (0, (fmn fowt, o, o,d)))
where the additional clamping to zero ensures nonnegative accumulated density. The final pixel color determined using front-to-back compositing per Eq.
Discussion We emphasize the efficiency of evaluating the splatting kernel via Eq. which computes a closed-form integral along arbitrary view rays through the neural density field, thereby avoiding the computational cost of ray marching. In contrast to splatting based Gaussian rendering, relying on an affine approximation of the projection operator (Heckberl) 1989 Zwicker et al. 2004), our method yields perspectively accurate results. Note that the density directly, neither during training nor during view synthesis. Instead, all computations operate directly on its antiderivative S. Yet, in contrast to light-field-stlee approach that directly regresses integrated appearance (Sitzmann et al., (021), our method achieves multi-view consistency by construction. A detailed analysis of the computational cost of the integration procedure is provided in Appendix A
Eq. is never evaluated
3.3 IMPLEMENTATION DETAILS
Primitives We initialize W1 ~ ( and W₂ U (- / 6/No// ///////)))))) fol-
lowing Sitzmann et al. (2020). We set the number of hidden neurons N,, to 8 and the frequency

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Mem(0. 1MB)
Mem(2MB)
Unlimited
Ours
Keen (2 reMi) PAND. 2387
Noon (Paily POVR: ass
Menn (RAMB) PAND: 30:1
3DGS
Noon (0) (MB) PSNR: 22.39
Men axt8) PSND 2018
Men (S0MB) PENR: 3467
Ours
(UMMM)) PSNK 2235
(2N55 PaNie 20-33
MET (60MB) PANK 11:4
3DGS
Figure 5: Comparison of our method against 3DGS the synthetic dataset under different memory constraints.
multiplier w/ to 30. Similar to 3DGS, we employ four bands of Spherical Harmonics coefficients for color representation. Each neural primitive our system consists of 99 parameters in total, around 1.6x more than Gaussian primitives used in 3DGS. We provide detailed analysis of network configurations in Sec.
Population Control Population control is key factor the success of primitive-based methods. However, the 3DGS densification strategy is incompatible with neural primitive representations. To address this, we introduce a simple yet effective densification strategy. Unlike 3DGS, which uses the gradients of primitive screen- spaceesspeeeaaa locations as the criterion for densification, our approach relies on gradient magnitude of the network weights. Similar to 3DGS, we duplicate or split primitives when this gradient exceeds threshold. Primitives with low gradients are pruned. We do not use any opacity resetting.
Training We follow the same loss function 3DGS, and introduce geometric regularization term to penalize the extreme anisotropy in primitive shapes by minimizing the standard deviation of the components of the scale vector Sp. The effectiveness of this regularization is demonstrated in Sec. We implement all frameworks in PyTorch (Paszke et al. (017)) and CUDA. All models are trained on single NVIDIA A40 GPU and evaluated on an NVIDIA RTX 4090 for performance analysis. Due to the complex optimization landscape of neural fields, the convergence of our representation slower than couusian-bbssen one. We therefore extend training 100k iterations. Additional training details are provided in Appendix B
4 EVALUATION
In this section, we perform comprehensive evaluation of neural primitives on novel-view synthesis tasks. We first demonstrate the expressivity of the neural density field (Sec. 4.1 We then perform quantitative and qualitative analysis on synthetic datasets (Sec. (42) and real datasets (Sec. 4.3) using standard evaluation metrics: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM) (Wang et al. 2004), and Learned Perceptual Image Patch Similarity (LPIPS) (Zhang et al. 2018). Please refer to Appendix C for additional results.

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Published as a conference paper at ICLR 2026
Table 1: Quantitative comparison of method against 3DGS the Synthetic NeRF dataset under different
memory budgets. We evaluate image quality using three standard metrics: LPIPS, PSNR, and SSIM.
Mem (MB)
0.1
0.4
1.0
2.0
4.0
Unlimited
Method
3DGS
Ours
3DGS
Ours
3DGS
Ours
3DGS
Ours
3DGS
Ours
3DGS
Ours
PSNR
23.1
24.7
25.6
27.6
27.2
28.9
28.4
30.4
29.6
31.4
33.3
33.4
SSIM
.843
.879
.882
.916
.907
.932
.925
.948
.941
.956
.970
.967
LPIPS
.49
.161
.174
.097
.129
.073
.098
.051
.022
.039
.031
.032
3DGS
ConvSplat
GES
VoI3DGS
BetaGS
Ours
CT
Figure 6: Visual comparison of method against several rrmiiiveebbsed methods the novel-view synthesis task real scenes. We demonstrate that our neural primitives achieve high-fidelity results comparable to other approaches, requiring 10x fewer primitives and 6x fewer parameters.
4.1 PRIMITIVE EXPRESSIVITY
Leveraging a flexible neural density field and analytically exact integration, our method faithfully reproduces complex geometries with small number of primitives. To demonstrate this, we optimize varying numbers of neural and Gaussian primitives to approximate the density fields of several 3D geometries from multiple views. We visualize both the renderings and the color-coded primitives in Fig. 4 We observe that few neural primitives suffice to represent complex and diverse geometries, such as the teapot's curved handle, the smooth cut in the leaf, and the triangular leaf petiole. In contrast, Gaussian primitives are limited by their symmetric ellipsoidal shape and soft boundaries, making them unsuitable for accurately representing complex solid structures. For the toy examples of teapot and leaf in Fig. 4 neural primitives achieve superior performance while using 16x fewer primitives and xx fewer parameters than 3DGS.
4.2 SYNTHETIC SCENES
Protocol We compare our method with 3DGS on the Synthetic NeRF dataset (Mildenhall et al., 2020) across varying memory budgets. Specifically, we resample the original meshes to target vertex counts (200, 500, 1k, 2k, 5k, 10k, 20k) and use them initialize primitive positions for optimization, omitting primitive densification. We also include an "unlimited" setting, in which training follows the standard densification procedure with no primitive budget.
Results We report numerical results in Tab. I Our method outperforms 3DGS under limited memory budgets and achieves performance comparable to 3DGS when no memory constraints are imposed. Visual comparisons are shown in Fig. 5 For Ficus, single primitive already reconstruct
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Table 2: Numerical comparisons three real-scene datasets. For each method, indicate whether it is
splatting-bar (Spl.) and/or neural (Neu.). also report novel- wiew synthesis quality (PSNR1. SSIM LPIPS.). rendering speed (in frames per second), and memory usage (in MB).
Mip-NeRF360
Tanks & Temples
Deep Blending
Spl.
Neu,
PSNR
SSIM LPIPS FPS
Mem
PSNR
SSIM LPIPS
FPS
Mem
PSNR
SSIM LPIPS
FPS
Mem
Plen x v
23.08
.626
2.1k
21.08
.719
.379
13
2.3%
23,06
.795
2.7k
INGP
25.59
.699
.331
48
21.92
.745
.305
14
48
24.96
.817
.390
3
48
Mip360
x /
27.69
.792
.237
<1
9
22.22
.759
.257
<11
29.40 9
.901
.245
<1
9
3DGS
27.21
.815
.214
152
734
23.14
.841
.183
188
411
29.41
.243
154
676
26.91
.794
.250
279
377
23.35
.836
.198
372
222
29.68
.901
.252
289
399
BetaGS
x
28.75
.845
.179
71
356
24.85
.870
.140
119
200
30.12
.914
.236
91
343
ConvSplut
V
26.66
.769
.266
103
77
23.71
.842
.170
83
83
29.61
.901
.245
66
110
VoLDDG
27.30
.813
.209
124
703
23.74
.854
.167
168
255
29.72
.908
.247
156
844
TE3GGS
27.31
.001
.252
265
152
23.95
.837
.201
408
73
29.82
.904
.260
409
67
Ours
V
27.21
.791
.216
115
93
23.59
.846
.162
158
80
29.20
.892
.264
178
82
an entire leaf (highlighted by the white frame). Similarly, in Lego, neural primitives capture diverse geometries, such as the front shovel and the rear wheel. In contrast, Gaussian primitives perform poorly on these complex structures, particularly under tight budgets. We further analyze the impact of the primitive initialization strategy. Neural primitives with random initialization achieve an average PSNR of 33.36, which is comparable to 3DGS with random initialization (33.32) and to neural primitives with mesh-based initialization (33.40). This observation indicates that our representation behaves similarly to 3DGS across different initialization strategies.
4.3 REAL SCENES
Protocol For evaluation on real scenes, we follow established practice and use two scenes from Deep Blending (Hedman et al., 2018), two from Tanks Temples (Knapitsch al., 2017), and all scenes from the Mip-NeRF360 dataset (Barron et al. 2022). We compare against three method fami-
lies: (i) splatting-based approaches with analytic primitives 3DGS (Kerbl et al. 2023), GES (Hamdi et al. 2024), ConvSplat (Held et al. 2025), BetaGS (Liu et al., 2025), and VoL3DGS (Talegaonkar ct al. 2025); ; (ii) T-3DGS (Mallick et al. 2024). which provides a more sophisticated mechanism for
controlling the memory footprint of primitive- based-bbbdddeee representations; and (iii) monolithic representa-
tions- Plenoxels (Fridovich- Keil et al. 2022), INGP (Müller et al. 2022), and MipNeRF360 (Barron)
ett al. 2022). All experiments use the official code released by the respective authors. Since reproduced baseline results closely match those reported in the respective papers, we report the original numbers for consistency. For a fair comparison, all inference FPS values are measured single NVIDIA GeForce RTX 4090 GPU.
Results We summarize numerical results in Tab. 2 Our method achieves high-fidelity reconstruc- tions with image quality and runtime comparable to state-of-the-art splatting-based approaches with analytic primitives, while generally requiring substantially less memory. Compared to monolithic neural representations,
neural splatting- based representation is more than order of magnitude faster. While T-3DGS attains a similar trade-off, its control mechanisms are orthogonal to our contri- bution, which focuses the representation itself; "taming" neural primitives can be expected to yield significant gains as well. Fig. confirms that our reconstructions are on par with the state of the art. In particular, our approach accurately captures fine- grained, structured geometry, such the carpet region (highlighted in red) in the Kitchen and Bonsai scenes.
5 ABLATION STUDIES
Here, first investigate alternative neural integration strategy compatible with neural repre- sentation (Sec. 5.I). We then analyze the impact of the key parameters in our model formulation (Sec. 5.2 as well as the effect of the geometry regularization term (Sec. (.3
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Rendering
Color coding (final step)
Color codrncodiig (initial step)
Ours
Autoint
regularization
w/ larizaaiooo
Figure 7: We analyze (left) the effect of an alternative neural integration strategy, AutoInt Lindell et al. 2021 and (right) the effect of geometry regularization during training.
GT
N =4
N =8
N_=16
N =232
GT
N, =8
N,=16
wp-1
10
wg=30
Figure 8: We visualize the effect of network configuration (N, and wa) on the expressivity of our neural density field.
5.1 NEURAL INTEGRATION
AutoInt (Lindell al. 2021) is alternative approach for computing line integrals in neural field, which we compare in Fig. 7 left. Autolnt uses ray-based parameterization and applies automatic differentiation with respect ray depth during training obtain integral network. However, this induces view-dependent density, leading to inconsistencies across viewpoints. In contrast, our method models the density field with shallow network that depends only on 3D position, ensuring multi-view consistency.
5.2 PRIMITIVE NETWORK CONFIGURATION
We analyze how the number of hidden neurons (N,) and the frequency multiplier (wp) affect the expressivity of our neural representation. We vary N, E [4, 32] and wo E {1, 10, 30}, and run experiments
Snowflake using a single primitive and Leaf using eight primitives. As shown in Fig. 8 larger N, and higher wo better reproduce the Snowflake structure and the smooth contours of Leaf. Although N. 16 offers greater expressivity than in toy settings, this advantage diminishes on real scenes due to the difficulty of optimizing highly under-constrained problem.
We further analyze the effect of the network configuration on all MipNeRF360 scenes. To facilitate meaningful comparison, resume training from pretrained checkpoint and disable densification, thereby eliminating the influence of the number of primitives. We report PSNR values and memory footprint in Tab. 3 As wi increases from 0 to 50, the PSNR initially improves and reaches its peak for W/ = 30, after which it slightly declines. At Wh 30, increasing N, from to yields a larger quality improvement than increasing it from 8 to 16. However, the memory footprint from 8 to 16 significantly higher (37 MB) than that from to (19 MB). Balancing memory footprint and expressivity, set N, and we 30 the default configuration for all experiments.

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Published as a conference paper at ICLR 2026
Table 3: Ablation study of network configuration (N, and wa) all MipNeRF360 scenes. For each setup. report the memory footprint (in MB) and image quality (PSNR).
PSNR
N
Mem
10
Wi
30
Wp
73
26.35
27.29
27.33
27.12
92
26.32
27.42
27.54
27.41
16
129
26.19
27.46
27.62
27.55
5.3 GEOMETRY REGULARIZATION
Jointly optimizing millions of neural primitives in complex scenes highly under-constrained and prone to local minima, often resulting in extreme geometries, as shown in Fig. 7 right. We find that geometric regularization stabilizes training by penalizing elongated primitives. While numerical results remain similar, the regularization yields clear qualitative improvements.
6 DISCUSSION AND CONCLUSION
Our method is a novel radiance field representation that reconciles the expressivity of neural represen- tations with the efficiency splatting- -baed rendering techniques. We identify accurate density field integration a key factor for achieving high expressivity in novel-view synthesis. Inspired by neural radiance fields, we formulate each primitive as a shallow network, which enables exact integration by evaluating the analytical anti-derivative with only two queries, reducing the ray-marching burden. While such a network has comparably limited representational capacity, the primitive-base based approach mitigates the limitation by enabling collection of tiny primitives jointly reconstruct fine-grained scene details. This design provides both computational accuracy and efficiency. Furthermore, we show that ellipsoid-boundee renderer, achieving real-time rendering performance. Our experiments demonstrate that neural primi- tives produce high-fidelity results comparable to 3DGS while requiring 10x fewer primitives and 6x fewer parameters, and delivering 100x speedups over baasel-based methods. We believe that splattable neural representation opens new possibilities integrating neural-based representation with splatting- based rendering techniques.
neural primitives be integrated into differentiable splatting-base
Although neural primitives exhibit substantial expressivity with limited memory resources, the com- plexity of the optimization landscape for millions of networks occasionally introduces convergence difficulties, hindering the expressivity of neural representations and slowing down convergence, For instance, the MipNeRF360 dataset, neural primitives require average wall-clock training time of 2.5 hours, which upproximately 2.5x longer than 3DGS. A promising avenue for future research to develop effective optimization training strategies, such the stochastic preconditioning technique (Ling et al.] 2025). to fully unleash the expressivity of neural primitives and accelerate convergence. Moreover, our neural density field is independent of the improvement strategies for the color field and densification in 3DGS, making it theoretically compatible with such techniques. For example, the error-guiie prror-guided adaptive densification strategies (Rota Bulò al. 2024 Mallick et 2024) could be readily adapted to our framework. Spatially-varying textured primitives (Chao et al. 2025) could also be integrated with the proposed neural density field. Exploring such integrations remains an interesting future research direction.
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In this Appendix, we present detailed analysis of the integration cost (Appendix A the hyperpa- rameters in the novel view synthesis task (Appendix BB, and additional numerical and visual results for both the synthetic and real datasets (Appendix C In Appendix [ we also demonstrate two applications of our neural representation: dynamic scene representation and relighting.
A INTEGRATION COST
Table 4: Comparison of GPU profiling metrics in Nsight Compute.
Metric
3DGS
Ours
Compute (SM) Throughput [%]
84.52
80.02
Memory Throughput [%]
53.09
80.02
Executed Instructions [inst] 868,881,013
3,406,837,112
Goal We conduct comprehensive analysis of the computational overhead of neural and Gaussian primitives, from macro to micro-level evaluations on a single NVIDIA GeForce RTX 4090 GPU. We begin by evaluating the total rendering time under the same primitive budget, which provides the computational cost of the full rendering pipeline, including preprocessing, primitive sorting/tiling, integration, and alpha blending. We then analyze the computational cost in the render kernel function, which consists of the integration and blending processes. Finally, we focus on the integration step, decomposing into the floating point (FP) operation level.
Protocol We perform computation analysis on a set of 100k primitives with random positions inside a volume and other random properties (MIP weights for neural primitives, opacities for gaussians) using our method and 3DGS, under the camera configurations of the synthetic NeRF dataset. We report FPS for total rendering time, similar to other 3DGS-based approaches. And we rely on Nsight Profiling to evaluate the render kernel function, providing compute and memory throughput, and executed instructions. We additionally manually decompose the integration process into floating-point (FP) operation level and report the FLOP number.
Analysis - FPS Neural primitives achieve an FPS of 218.87, which is approximately 2.5x slower than 3DGS (546.54). This gap is expected, as neural primitives require additional computation, including the MI.P query, integration, and ray/ellipsoid intersection. In real scenes, our method needs 10x fewer primitives, which balances computational complexity with the number of primitives, enabling real-time performance.
Analysis Nsight We report the Nsight profiling results by monitoring the render kernel function in Tab. [......a which consists of integration and alpha blending steps. Since our method and 3DGS employ the same alpha blending structure, the performance difference solely comes from the integration part. Both 3DGS and our method rely heavily on GPU compute (84.52% vs. 80.02%). Unlike 3DGS, which keeps its parameters in shared memory, our implementation must repeatedly access global memory for MIP weights, resulting in a higher memory throughput of 80.02%. The total number of executed instructions for neural primitives is 3.4 x 10 approximately four times higher than that of 3DGS (8.7 108).
Analysis FLOP We further decompose the integration process and provide a FL.OP-based analysis focused on the integration step. Using heuristic operation costs, where basic arithmetic, division, and exp/sin operations are assigned costs of I, 4, and 30, respectively, 3DGS requires approximately 43 FLOPs per integration, whereas method requires roughly 769 FLOPs.
Summary Importantly, although neural primitives yield higher computational costs across FPS, Nsight, and FLOP-basel analysis, method requires roughly 10x fewer primitives to represent the same scene as 3DGS. As result, the overall rendering speed during inference remains over 100 FPS, which is comparable to 3DGS and ensures real-time performance.
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GT
8Prims
32Prims
128Prims
GT
8Prims
32Prims
128Prims
Neural Prim
Neural Prim
432'
1.7K
6.9K
432"
1.7K
6.9K
Caussian Prim
Gaussian
112"
1.8K *
112
448
1.8K
Figure 9: Demonstration of the expressivity of the proposed neural density field. We train both neural and Gaussian primitives on the drill gun and banana under different numbers of primitives. For each example, we visualize the reconstructed density field and color-coded primitives, illustrating how neural primitives are trained represent complex structures. denotes the total number of parameters.
GT
Me 1MB)
Mem(2MB)
Unlimited
Men (nnesay PSMR, 2022
Men (2MB) PSNR, 2667
Men PSNR
PSNB 2
USAIB)
Men OLESMRI PSNR 242
Mon (2M5) PSNR 2016
Men (SMM)) PSWR 30
MER (EMM PSNR:: 28-34
Mam (MB PANR: 30A
AAR (PAAA))) PSNU 36 T0
ERAND 25208-2122
Sam Pias) PSN 2026
PSNK
Figure 10: More visual results the Synthetic NeRF dataset under limited and unlimited memory hudgets.
B HYPERPARAMETERS
We train all scenes using the Adam optimizer (Kingma & Ba 2015 with learning rate of 10 for the MLP. For the datasets BlenderNeRF, Mip-NeRF360, Tanks Temples, and Deep Blending, we adopt the following learning rate hyperparameters: primitive means (1.6 x 10 10-4), scales (5 x 10 10-3). quaternions (10 110-3), and SH coefficients (2.5 x 10 Population control is governed by a growing scale threshold of 10-2 and pruning scale threshold of 0.5.
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3DGS
ConvSplat
GES
Ours
GT
Figure 11: More visual comparison real datasets.
Table 5: PSNR scores of each scene in the Blender Synthetic Dataset.
Chair
Drums
Ficus
Hotdog
Lego
Materials
Mic
Ship
3DGS 500 Prims 22.91
19.09
22.39
25.55
20.99
22.99
27.59
23.32
Ours 200 Prims
24.60
20.27
23.87
29.37
22.56
24.20
28.39
24.23
3DGS 10k Prims
29.19
23.56
29.68
32.31
26.72
27.28
31.19
27.03
Ours Prims
31.24
24.67
32.86
34.71
29.33
28.06
34.01
28.26
3DGS nolimit
35.83
26.15
34.87
37.72
35.78
30.00
35.36
30.80
Ours nolimit
34.58
26.13
34.81
37.38
35.41
30.91
36.16
31.44
For Mip-NeRF360, Tanks Temples, and Deep Blending, M...--graieett-aaee densification and pruning are performed every 500 iterations between 1k and 15k, using thresholds of 10-4 and 2 x 10 respectively. In contrast, BlenderNeRF uses slightly lower thresholds (10-5 and 10-9) and the densification routine is executed more frequently, every 200 iterations, starting 1 and continuing until 20k.
C MORE RESULTS
C.I NUMERICAL RESULTS
BlenderNeRF Synthetic Dataset Our neural primitive requires 41 parameters from its 8-neuron MLP. 10 from geometry (3 for means, scales, and 4 for quaternion), and 48 from SHs, in total 99 parameters, 1.68x more than 3DGS parameters (59). We report per-scene image metries (PSNR, LPIPS, and SSIM) in Tab.5 Tab. Ø and Tab. under different memory budgets. For a fair comparison, we constrain the number primitives in our system to half that 3DGS and report numerical results under this setting. As shown in these three tables, the first two double rows exhibit apple-to-apple comparison between 3DGS and our method under the same memory budget. Neural primitives outperform Gaussian primitives consistently, highlighting the expressivity of our representation. The last double rows in the three tables evaluate the performance of the two representations under unlimited memory budgets.
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Table 6: SSIM scores of each scene in the Blender Synthetic Dataset.
Chair
Drums
Ficus
Hotdog
Lego
Materials
Mic
Ship
3DGS 500 Prims
0.8564
0.8065 0.8769
0.8873
0,7819
0.8489
0,9282
0.7638
Ours 200 Prims
0.8890
0.8608
0.8983
0.9391
0.8247
0.889
0,9439
0.7893
3DGS 10k
0.9420
0.9124
0.9585
0.9578
0.8946
0.9242
0.9738
0.8393
Ours 5k
0,9635
0.9343
0.9777
0.9722
0,9373
0.0471
0.9866
0.8677
3DGS nolimit
0.9878
0.9548
0.9870
0.9852
0.9820
0.9600
0,9927
0.9070
Ours nolimit
0,9856
0.9475
0.9841
0.9838
0.9808
0.9632
0.9910
0.8993
Table 7: LPIPS scores of each scene in the Blender Synthetic Dataset.
Chair
Drums
Ficus
Hotdog
Lego
Materials
Ship
3DGS 500
0.2247
0.310
0.150
0,219
0.309
0.256
0.147
0,383
Ours 200
0.1359
0.220
0.089
0.093
0,200
0.1328
0.0968
0.3182
3DGS 10k
0.0813
0.121
0.038
0,072
0.131
0.098
0.034
0.208
Ours 500
0.0385
0.043
0.015
0,0293
0,0467
0.0472
0.0130
0.1453
3DGS nolimit
0.010
0.037
0.011
0.020
0.017
0.038
0.006
0.109
Ours nolimit
0.014
0.047
0.016
0.020
0.017
0.032
0.008
0.100
present the per-scene performance metrics of our neural primitives, including PSNR, SSIM, LIPS, the number of primitives, and the associated model memory footprint.
Real Datasets Tables
and
C.2 VISUAL RESULTS
Toy Examples We provide additional visual comparisons of our method and 3DGS on two toy examples (drill gun and banana). As shown in Fig. neural primitives exhibit significantly greater expressivity than 3DGS, achieving reconstructions with superior quality using fewer primitives and parameters. In contrast, 3DGS struggles to capture solid density fields, sharp edges, and smooth contours in both drill gun and banana.
Synthetic and Real Results In Fig. 10 we demonstrate additional visual results on the synthetic NeRF dataset, evaluated on the models optimized under varying memory budgets. Moreover, we provide comparison and visual results on additional real scenes in Fig.
D APPLICATIONS
In addition the novel view synthesis task, show that neural primitives can be readily adapted into other multimodal tasks, such as dynamic and relighting, by introducing an additional input channel the density field or incorporating neural color field.
D.1 VOLUMETRIC DYNAMIC NOVEL VIEW SYNTHESIS
Method The zero-order Spherical Harmonics (SH) coefficient of each primitive is modeled as function of time & expressed as summation of polynomial function and a Fourier series, similar to Lin et al. (2024):
S(G)) So + P.(E)) + Fi(E))
(10)
where Sy denotes the zero-order SH coefficient. The polynomial function is defined as:
Pr.(E)) = Σ a,ci
(11)
and the Fourier series component is given by:
Fi(E)) = Σ (b, cos(iEE) + sin(iE)))
(12)
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Table 8: Novel view synthesis results in Mip-NeRF360 dataset
Mip-NeRF360
Avg
Bicycle
Bonsai
Counter
Flower
Garden
Kitchen
Room
Stump
Treehill
PSNR
24.28
32.61
29.44
20.46
27.03
31.82
31.85
24.73
22.64
27.21
SSIM
0.7028
0,9467
0.9140
0.5497
0.8421
0.9291
0,9295
0.6862
0.6169
0.7907
LPIPS
0,2658
0.1540
0.1643
0.3390
0.1319
0.1112
0,1750
0,2780
0.3249
0.2160
Prims
3 10
1.9 10
1.7 x 10
2.5 10
2.6 10
2.2 x 102
1.7 10
3.3 10
2.8 x 102
2.4 x 10
Mem (MB)
116.25
73.30
66.22
93.55
97.32
84.10
65.22
124.15
104.59
91.63
Table 9: Novel view synthesis results in Tank& Temple and Deep Blending datasets.
Tamp&Temple Temple
Avg
Deep Blending
Avg
Train
Truck
Playroom
Drjohnson
PSNR
21.98
25.19
23.58
29.62
28.78
29.29
SSIM
0.8175
0,8780
0.8478
0.8955
0.8886
0.8921
LPIPS
0.1864
0.1330
0.1597
0,2626
0,2661
0,2644
Prims
2.2 x 10
2.0 x
2.1 x 10
x 10
2.7 10
2.2
Mem (MB)
84.66
74.43
79.55
60.90
102.74
81.82
where ag b;, C. E I.. In our experiments, we set both and n to 4.
We begin by uniformly sampling 100, 000 primitives within the volume's bounding box and train the system over 100, 000 iterations. The densification process starts at iteration 1, 000 and continues until iteration 30, 000, executed at intervals of 500 iterations. Similar to static scene configurations, all hyperparameters remain the same.
Data setup We evaluate our method the dynamic volumetric novel view synthesis setting using a synthetic dataset, including four volumetric effects from J Each effect is recorded by 40 cameras on the upper hemisphere to capture temporal evolution, with 38 cameras for training and for testing. The Colorful Smoke and Ground Explosion scenes contain 128 and 130 timesteps per camera, while Dust Tornado and Smoke Fire each have 100 timesteps per camera.
To reconstruct the temporal evolution of the volumetric effects, adopt Eulerian approach by incorporating an additional temporal variable & E [0, 1] for timestamp into our neural density field.
Training
The temporally and spatially variant density field ox, Ex) now is:
fo (x, = W2 cos(wg) (x)) + & W + b,) + b
(13)
where learnable temporal weight W, e No, Furthermore, the zero-order SH coefficients for each primitive are modeled as a function of time & by expressing them as the sum of a polynomial function and Fourier series.
Results Fig. 13 shows the visual results of our representation. By introducing an additional dimension, system effectively captures the temporal evolution of the volumetric effects.
D.2 RELIGHTING
Method Unlike novel view synthesis, where color is represented as SH coefficient, in relighting task, the primitive color per view ray is formulated as a combination of constant color Ca. and neural color function of 3D position view direction d and light direction d:-
Các + c(x, d. d:),
(14)
To smoothly adapt the relighting application neural representation, incorporate per- primitive color network field, where the light direction is computed relative to the center of each primitive.
19

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Published as a conference paper at ICLR 2026
Ours
GT
Figure 12: Relighting results under OLAT illumination using neural primitives.
Dataset and Training Setup We conduct relighting application One-Light-at-a- Time (OLAT) datasets provided by Bi et al. (2024): Kang et al. (2019), including: (1) rendered images of synthetic NeRF scenes, and (2) rendered images of real captures.
We show relighting results in Fig. 12 Our relighting strategy can achieve decent image- based rendering without requiring intrinsic properties, capturing specular reflection (fabrics example provided in Fig. 12 and complex self-shadowing (refer to hotdog in Fig. 12 and lego scene in Fig. 1
Results
20

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Published as a conference paper at ICLR 2026
Timestep 20
Timestep 30
Timestep 40
Timestep 50
Timestep 60
GT
Ground Explosion
Ours
GT
Smoke Fire
Ours
GT
Colorful Smoke
Ours
GT
Dust Tornado
Ours
Figure 13: We demonstrate our results for volumetric dynamic view synthesis. By introducing an additional time dimension & our neural primitives can reconstruct the scene's evolution and synthesize coherent results for volumetric dynamic
21


Reviews:
[{"review_id": "ZcsIikAtaI", "reviewer": "Reviewer_4maN", "summary": "This paper introduces \"splattable neural primitives,\" a novel radiance field representation that combines the expressivity of neural networks with the rendering efficiency of primitive-based splatting. Each primitive is an ellipsoid-bounded volume with a shallow neural network defining its density field, enabling exact analytical integration along view rays. The method achieves real-time rendering performance comparable to 3D Gaussian Splatting (3DGS) while using significantly fewer primitives (10×) and parameters (6×), demonstrating strong results on synthetic and real-world novel-view synthesis benchmarks.", "questions": "1. Scalability & Robustness: Given the optimization difficulties mentioned, how does the method scale to extremely large, unbounded outdoor scenes? Are there specific types of scenes or geometries where the neural primitives consistently fail or underperform?\n2. Integration Cost: The paper emphasizes \"exact\" and \"efficient\" integration. What is the precise computational overhead of evaluating the analytical anti-derivative compared to a single 3D Gaussian splatting kernel? A breakdown of rendering time (integration vs. blending) would clarify the practical trade-offs.", "limitations": "", "rating": 4, "confidence": 2, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. Novel Representation: The proposal of fundamentally neural primitives with closed-form ray integration is a conceptually clean and innovative contribution. It successfully bridges the gap between expressive neural fields and efficient splatting-based rendering, a notable advance in the field.\n2. Empirical Efficiency: The method demonstrates compelling practical benefits, matching 3DGS's quality and speed while drastically reducing primitive and parameter counts. This efficiency is directly attributed to the representation's inherent expressivity, not external control mechanisms.", "weaknesses": "1. Optimization Challenges: The paper acknowledges slower convergence and difficulties in optimizing millions of neural primitives due to a complex loss landscape. This suggests the method may be less robust or more sensitive to training configurations compared to established baselines like 3DGS.\n2. Limited Ablation on Real Scenes: While toy examples (e.g., Snowflake, Leaf) effectively showcase expressivity, the ablation studies on network width and regularization lack depth for complex real-world scenes. The claimed expressivity advantage is not fully quantified or visually demonstrated on challenging benchmarks.", "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": "98WvRK62Y1", "reviewer": "Reviewer_FKH4", "summary": "This paper introduces splattable neural primitives, a hybrid radiance field representation designed to unify the expressivity of neural radiance fields with the efficiency of splatting-based rendering. Each primitive is represented as an ellipsoid-bounded neural density field, parameterized by a shallow sinusoidal network that admits a closed-form integral along view rays. This analytical formulation eliminates the need for expensive ray marching while retaining multi-view consistency. Experiments on both synthetic and real-world datasets demonstrate that the proposed approach achieves comparable or superior performance to 3D Gaussian Splatting (3DGS), requiring ten times fewer primitives and fewer parameters overall.", "questions": "1. How does performance vary with different configurations of network width and frequency? \n\n2. The scalability of the method for very large scenes is insufficiently discussed, how does runtime and memory usage scale with the number of primitives in such scenes?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The proposed formulation is conceptually sound and well motivated. Representing volumetric primitives as shallow neural fields bounded by ellipsoids provides an elegant way to connect neural and analytic splatting methods under a single theoretical framework.\n\n2. The analytical derivation of the antiderivative for the density field is mathematically consistent and efficiently implemented, offering a clear path to rendering without ray marching.\n\n3. Experimental results indicate that the proposed neural primitives maintain strong image quality under strict memory constraints, remaining both compact and efficient.", "weaknesses": "1. The overall training process is more complex, requiring more iterations and careful convergence control due to the optimization of numerous small neural modules.\n\n2. While the ablation studies illustrate the role of model parameters, a more detailed analysis of trade-offs between expressivity, convergence, and stability would have strengthened the paper’s argument.\n\n3. The impact of network width or frequency choices on quality and efficiency remains underexplored in the ablation section.", "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": "Wt9PdDaH2g", "reviewer": "Reviewer_ByAG", "summary": "The paper proposes splattable neural primitives: volumetric, ellipsoid-bounded primitives whose density is represented by a shallow neural network with periodic activation. A key technical claim is a closed-form antiderivative for line integrals through the neural density, which yields a perspectively accurate splatting kernel and thus avoids ray marching while retaining neural expressivity. Empirically, on synthetic and real novel-view synthesis benchmarks, the method targets the quality/speed of 3D Gaussian Splatting (3DGS) while using ~10× fewer primitives and ~6× fewer parameters, attributing the gains to the representation itself rather than to heavy control frameworks.", "questions": "How robust is training to different initializations (e.g., sparse SfM points, noisy/sparse seeds, or purely random placements/shapes)? Can you report quantitative results (PSNR/SSIM/LPIPS, convergence rate) and qualitative failure modes across several inits on both synthetic and real scenes? (This would mitigate concerns about mesh-based seeding.)\nThe authors extend training to 100k iterations due to slower convergence. Can you share wall-clock training time comparisons and memory bandwidth/throughput metrics vs. 3DGS?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "This paper introduces a neural primitive whose volumetric density is learned via a one-hidden-layer MLP, yet remains analytically integrable along rays. This bridges the perceived “neural vs. primitive” dichotomy and is, to my knowledge, a first in making the primitive itself neural while still splatting.\nThe analytical formulation is clearly spelled out (ray–ellipsoid intersection, anti-derivative, front-to-back alpha compositing), and the implementation details include population control (split/duplicate/prune via weight-gradient magnitudes) and geometric regularization to avoid degenerate ellipsoids.\nAblations probe network width/frequency and the effect of regularization; comparisons to an alternative neural integration strategy (AutoInt) clarify multi-view consistency benefits.", "weaknesses": "1. While the representation is new, final image quality/speed sometimes appears comparable to strong modern 3DGS variants that incorporate compression/regularization/adaptive control (e.g., BetaGS, T-3DGS, structured/linear kernels), some of which achieve very low memory or high FPS. A more direct, apples-to-apples model-size / memory / bandwidth comparison to these compression-oriented pipelines would clarify the net practical advantage. (Table 2 partially covers this, but a focused compression study would help.)\n2. Adding per-primitive neural components (albeit shallow) complicates implementation relative to purely analytic Gaussians, which map naturally to existing graphics pipelines and hardware rasterization paths. This may limit industrial adoption unless the benefits (fewer primitives, comparable speed) translate into easier deployment (e.g., on mobile/embedded) than a tuned Gaussian pipeline. A short discussion of engine integration, batching, and runtime kernels would strengthen practical significance. (Authors do note PyTorch/CUDA implementation.)\n3. On the synthetic dataset, initializing primitive positions from resampled ground-truth meshes risks leaking geometry and may overstate robustness; a stronger setting would evaluate multiple non-oracle inits (sparse SfM points, random, noisy depth). The paper acknowledges slow convergence vs. Gaussians and extends training, which heightens the importance of init robustness.\n4. It may be worth to consider augmenting each primitive with a small learnable feature vector as additional input to the MLP to further boost expressivity under fixed primitive counts; this could bridge to richer local modulation without exploding primitive numbers.", "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": "mHX7e0eFVW", "reviewer": "Reviewer_awhh", "summary": "The paper proposes Splat the Net, a unified representation that integrates the expressivity of neural radiance fields with the real-time rendering efficiency of splatting-based approaches. Each primitive in the proposed framework defines a bounded neural density field represented by a shallow sinusoidal network, for which the authors derive a closed-form solution to line integrals along view rays.\nThis analytic construction practically allows accurate, differentiable rendering without ray marching. The approach achieves state-of-the-art visual quality on multiple benchmarks, such as NeRF Synthetic, Mip-NeRF360, and Tanks & Temples, while requiring an order of magnitude fewer primitives and parameters than 3D Gaussian Splatting.", "questions": "Given that training is more computationally demanding than purely analytic splatting, are there potential strategies—such as improved initialization, parameter sharing, or adaptive optimization—that could help accelerate convergence?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The proposed framework is novel and well-explored. By introducing neural primitives that can be analytically integrated and splatted, the authors effectively bridge two traditionally separate families of radiance field models.\n2. The resulting design reconciles neural expressivity with analytic efficiency, achieving a favorable trade-off between compactness, rendering quality, and runtime.\n3. The paper provides extensive experiments across synthetic and real benchmarks, complemented by ablations and visual comparisons that clearly support the claims.", "weaknesses": "1. The reliance on per-primitive neural parameters may constrain the method’s scalability and practicality, particularly in memory-limited environments.\n2. While the experimental results are comprehensive, the paper could be further strengthened by a brief discussion of scenarios where the proposed neural primitives may be less effective, which would help clarify the scope and robustness of the approach.", "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)