BeyondMix: Leveraging Structural Priors and Long-Range Dependencies for Domain-Invariant LiDAR Segmentation
Authors: Yujia Chen
Rui Sun
Wangkai Li
Huayu Mai
Si Chen
Zhuoyuan Li
Zhixin Cheng
Tianzhu Zhang
Venue: NeurIPS 2025 poster ()
Keywords: LiDAR  Segmentation
Unsupervised Domain Adaption
Primary area: applications
TL;DR: In this work, we address unsupervised domain adaptation  for LiDAR segmentation by introducing BeyondMix, a framework that overcomes critical limitations in existing mix-based methods.

Abstract: Domain adaptation for LiDAR semantic segmentation remains challenging due to the complex structural properties of point cloud data. While mix-based paradigms have shown promise, they often fail to fully leverage the rich structural priors inherent in 3D LiDAR point clouds. In this paper, we identify three critical yet underexploited structural priors: permutation invariance, local consistency, and geometric consistency. We introduce BeyondMix, a novel framework that harnesses the capabilities of State Space Models (specifically Mamba) to construct and exploit these structural priors while modeling long-range dependencies that transcend the limited receptive fields of conventional voxel-based approaches. By employing space-filling curves to impose sequential ordering on point cloud data and implementing strategic spatial partitioning schemes, BeyondMix effectively captures domain-invariant representations. Extensive experiments on challenging LiDAR semantic segmentation benchmarks demonstrate that our approach consistently outperforms existing state-of-the-art methods, establishing a new paradigm for unsupervised domain adaptation in 3D point cloud understanding.

BiyondMix: Leveraging Structural Priors and Long-Range Dependencies for Domain-Invariant LiDAR Segmentation
Yujia Chen!.2, 1.2 Rui Sun', Wangkai Li!.__ Huayu Mai Si Chen'2, Zhuoyuan Li
Zhixin Chengl., Tianzuu Zhang
University of Science and Technology of China
National Key Laboratoray of Deep Space Exploration, Deep Space Exploration Laboratory
'Shenzhen International Graduate School, Tsinghua University (yujia_chen, issunrui, lwklwk, mai556, sa23010094, thengzhixin]ee @mail. ustc. edu. en, tzzhang @ ustc.edu.cn
Abstract
Domain adaptation for LiDAR semantic segmentation remains challenging due the complex structural properties of point cloud data. While mix-based paradigms have shown promise, they often fail fully leverage the rich structural priors inherent in 3D LiDAR point clouds. In this paper, we identify three critical yet underexploited structural priors: permutation invariance, local consistency, and geometric consistency. We introduce BeyondMix, a novel framework that har- nesses the capabilities State Space Models (specifically Mamba) construct and exploit these structural priors while modeling long-range dependencies that transcend the limited receptive fields of conventional voxel-based approaches. By employing space-filling curves to impose sequential ordering point cloud data and implementing strategic spatial partitioning schemes, BeyondMix effectively captures domain-invariant representations. Extensive experiments challenging LiDAR semantic segmentation benchmarks demonstrate that our approach consis- tently outperforms existing state-of-the-ard methods, establishing a new paradigm for unsupervised domain adaptation in 3D point cloud understanding.
Introduction
LiDAR sensors maintain operational integrity under adverse conditions 41
64 20
where camera-
based perception fails. Semantic segmentation enables critical scene understanding for autonomous navigation safety [46]] 39 (7). Despite significant advancements through deep learning methodolo-
62 D. LiDAR segmentation requires extensive annotated datasets substantial challenge given the prohibitive resource requirements for manually labeling point clouds comprising about 10Sh points per scan. While synthetic data provides readily available annotations, it introduces domain shift, violating the i.i.d. assumption between training and deployment distributions in sta- tistical learning theory [58), consequently degrading model performance. Unsupervised domain adaptation (UDA) techniques have been extensively studied to address this issue by transferring knowledge from labeled source domain to unlabeled target domain, and improve the model's s performance on the target dataset without requiring additional annotations. The unstructured nature of LiDAR point clouds coupled with challenges in designing effective alignment methodologies renders UDA for LiDAR segmentation particularly difficult.
gies [16] 33
79
*Corresponding author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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mloU
180 degree
Category Semantic Integrity
Azimuthal Consistancy
Begin
End
+7.1
Region
Order
20
Region
End
Begin
10
Spatial Region Integrity
Permutation Invariance
Spurderoey
Tarerfosy
Renbomdar
Condis
PatarMaa
LaterMia
Bepandibii
Local
Consistency
Geometric Consistency
(a)
(b)
Properties
Category Semantic Integrity
Azlimuthal Semantic Consistency
Spatial Region Integrity
Permutation Invariance
Geometric Consistency
Consistency
Feasibility Mix
V
N
V
Previous
Effective Receptive
Field
x
Feasibility of Mix
V
v
Ours
Effective Receptive
V
N
Field
(c)
Figure 1: (a) Performance comparison across diverse mixing methodologies. (b) Schematic illus- tration of distinct structural priors. (c) Comparative analysis of properties between our proposed approach and existing methods.
In previous work, the Mix- paradigm 48 19
has gained prominence due to algorithmic
simplicity and empirical efficacy. These approaches generate intermediate domains by strategically combining source and target distributions, thereby smoothing decision boundaries and facilitating fea- ture disentanglement [56). Mix-based paradigm encompass various integration criteria: CoSMix [48] leverages semantic labels, PolarMix (68) utilizes azimuth angles, and LaserMix incorporates inclination patterns for source-target domain fusion.
As illustrated Figure | (a), which empirically validates the efficacy of structured Mix-based paradigms, we observe that naive random mixing of source-target domains results in substantial performance degradation. This deterioration occurs because the destruction intrinsic geometric structure prior fundamentally compromises representational learning, rendering models incapable of extracting meaningful discrininative features. example, when automobile and architectural elements are randomly mixed, their intersecting regions confound class-specifit feature learning processes. We find that existing approaches leverage different structural priors: (I) category semantic integrity (CoSMix 48) ), (2) azimuthal semantic Consistency(Polarl/
(68)) and (3) spatial regioin 19 However, the inherent structural priors 3D LiDAR point clouds extend
ntegrity(LaserMix
significantly beyond these three isolated dimensions, presenting substantial unexplored potential.
Through theoretical analysis, we uncover that previous paradigm have overlooked three critical structural priors, as illustrated in Figure (b): (1) Permutation Invariance Prior, whereby point cloud representations should remain consistent regardless of acquisition trajectory or scanning order
43 (e.g., different angular perspectives or sampling paths), preserving invariance to permutation operations. (2) Local Consistency Prior, whereby point cloud features should maintain consistency across different local spatial partitions [63] 22), independent of acquisition perspective artificially defined spatial segmentation schemes; and (3) Geometric Consistency Prior, whereby LiDAR point cloud geometric structures (surface curvatures, normal vectors) should maintain stability under various processing operations [29] 71], with remaining points preserving critical geometric information even under partial masking. However, these three struetural priors intuitively resist straightforward implementation through mix-based paradigm like previous work.
In addition, autonomous driving LiDAR datasets typically comprise hundreds of thousands of points per sean. The predominant methodology employs voxelization with U-Net architectures, wherein predictions for each voxel depend on its surrounding neighborhood defined by the network's

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receptive field representnnin careful balance between computational efficiency and performance. Our analysis demonstrates that Mix-based operations attain effectiveness by integrating scans from both the source and target domains, thereby ensuring that voxels receive informative signals from both domains within their receptive fields. When receptive fields encompass cross-domain contextual information, as illustrated in Figure 2 Point A, the model is constrained from relying solely on Nomain-speccinee cues, fundamentally promoting the learning of domain-invariant representations. We provide a theoretical justification in the Appendix. However, current mix-based methodologies suffer from a critical limitation: their sparse mixing patterns result in numerous voxels possessing receptive fields confined to single domains, significantly constraining the adaptation capacity of UDA frameworks. We conduct an exemplary analysis of LaserMix [9] which, despite achieving the most comprehensive mixing strategy and superior performance, still exhibits the aforementioned limitation. When LaserMix partitions scans into 2-6 regions based on inclination angle, each region spans approximately 360-1,300 voxels within the 4,000-voxels coordinate space. However, mainstream UNet architectures maintain receptive fields of merely 230 voxels, consequently resulting in numerous voxels being unable to simultaneously capture information from both domains. Similar observations have been documented across alternative mixing methodologies [48] [68]. As illustrated in Figure 2 Point B's receptive field fails to encompass both domains, fundamentally impeding the learning of domain-invariant representations.
Remarkably, we observe that recent advances in the State Space Model. SSMs [10] and Mamba [8] have emerged as promising architectural paradigms for sequence modeling, ow- ing to their robust long-range model- ing capabilities, and linear-time com- plexity. The Mamba architecture ne- cessitates the transformation of un- ordered 3D LiDAR data into struc- tured point sequences while preserv- ing spatial proximity relationships. Our investigation reveals a twofold ad- vantage: (1) Mamba's 's diverse scan- ning methodologies can potentially address the limitations inherent in mix-based approaches by construct- ing varied structural priors and effec- tively leveraging these priors. (2) Its sequential processing paradigm cou- pled with linear time complexity for modeling long-range dependencies en- ables comprehensive exploration of structural priors, thereby significantly expanding the effective receptive field, as illustrated by Point C in Figure
Beam 1
Beam 2
Beam
Beam 4
Receptive Field
Target Domain
Source Domain
Longrange Dependencies
Point
Polnt
Area
Area 2
Point C
Area
Area 4
Figure 2: Comparative Analysis of Receptive Fields Across Different Methodologies. Point A illustrates a receptive field containing only single domain, while Point B shows receptive field spanning both domains. Point C demonstrates the implementation of SSMs, which effectively leverage long- range dependencies between points, resulting an expansive receptive field.
In this work, we introduce BeyondMix, which leverages Mamba to construct structural priors be- yond the capabilities of existing mix-based methods while simultancously exploiting long-range dependency modeling to transcend limited voxel receptive fields for enhanced domain-invariant representation learning-ee as illustrated in Figure (c). Specifically: space-filling curves provide an established mechanism for imposing sequential ordering on point cloud data by mapping multidimen- sional space to mic-dimnnioona sequences while maintaining locality properties. Two predominant
Haaaaches-Hlbbeee curves [13] and Z-order curves [34] [34]-serve serve distinct computational purposes:
Hilbert curves optimize range queries, while Z-order curves facilitate hierarchical indexing (visu- alization analysis in Appendix). (1) Diverse space-filling curves induce different spatial proximity relationships that inherently satisfy permutation invariance prior requirements.
(2) Leveraging the local semantic similarity property of LiDAR point clouds [19] we implement both cylindrical partitioning (via inclination angles) and rectangular partitioning (via Z-axis coordinates) for each scan. These different sub-region divisions enable the construction of local consistency prior. (3) Recognizing that scans with varying densities maintain invariant structural properties, we formulate geometric consistency prior.
3

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Sourse Domain
Additional Structural Priors
Est
stu
Apermstation
Permutation Imariance Prior
y
Shored
Shored
Hilbert CUPVER
Z- Z-arder curves
4
Mixed Domain
Liocat
stu
D stua
Local Coniistincy
milx
Feature
y
EMA updiate
AMAA update
Reclangulee Pertiion
Cyfindrical Partition
Target Domain
Aggameiric
toe
D tea
Geomebik Consistency
Density
Input x²
Prediction/...:))
(Pseudo) Label y
07
Figure 3: BeyondMix overview. For labeled source domain data x² and mixed domain data m compute supervised loss L and Lmix through the student network fstu, while for unlabeled target data w', we compute adaptive loss L via both student fstu and teacher Stea networks. Additionally, we design three additional structural priors: (1) Permutation Invariance Prior across different Lidar point orderings, (2) Local Consistency Prior between various structural partitioning schemes, and (3) Geometric Consistency Prior across different point density distributions.
Our contributions can be summarized as: (1) Problem Identification (WHY): We provide a dual- perspective analysis of existing mix-based methods in UDA for LiDAR point cloud segmentation, revealing insufficient exploitation and utilization of structural priors; (2) Methodology Design (WHAT)): We propose BeyondMix, leveraging Mamba construct structural priors beyond mix-based methods while thoroughly exploiting long-range dependencies to overcome limited voxel receptive fields; (3) Implementation (HOW): Extensive experiments demonstrate that BeyondMix consistently achieves SOTA performance on two challenging LiDAR semantic segmentation benchmarks.
Related Work
UDA for Point Cloud Segmentation. UDA for point cloud semantic segmentation follows two main paradigms: (1) Range-view methods that address domain shift in 2D projections, evolving from Cycle-GAN techniques (ePointDA (77)) and geodesic alignment (SqueezeSegV2 (65) to
domain-specific knowledge extraction (Gated [45] CCL (2 and (2) 3D-based methods operating
directly point clouds through density normalization (C&L 70
PCT
[69] statistical alignment
(DGT 773 and domain-invariant feature learning (59 61 72 73
78
68
19
48 This latter category
encompasses three key approaches: adversarial training methodologies (ADVENT (59, FADA (61].
MRNet (78)) using discriminator networks to align feature representations: prototype guidance techniques (PMAN 722) PCAN (73)) that extract source domain prototypes to enhance target domain learning; and mixup strategies (CoSMix [48), PolarMix [68], LaserMix [1]] that integrate domains through various criteria. While mix- methods effectively construct intermediate domains and partially leverage structural priors, their efficacy remains fundamentally constrained by insufficient exploration and utilization of the complete prior space available in LiDAR point cloud representations.
More related work is provided in the Appendix.
3 Method
In this section, we first formalize the standard self- self-training paradigm for 3D UDA semantic segmen- tation and Mamba, respectively (.I). Then, we introduce our new 3D LiDAR UDA framework, BeyondMix, novel approach that thoroughly exploits and leverages structural priors unattainable by previous mix-based methods, while alleviating the limited receptive field issues inherent in prior approaches (Sec 3.2p. Finally, we provide comprehensive details regarding training and inference
procedures (Sec 3.2 The overall framework of our proposed approach is illustrated in Figure 3

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3.1 Preliminaries
Self- Self-Training (ST) for 3D UDA semantic segmentation. Due to its empirical efficacy and con- vergence stability, the self-training paradigm has emerged the predominant framework for 3D unsupervised domain adaptation tasks. For a labeled source LiDAR point cloud scan x², we employ the standard cross-entropy loss function to derive precise semantic segmentation predictions for each individual voxel:
N Σ E
--
vi log Pi.ke
(I)
where K denotes the total number of semantic classes, ye represents the ground truth semantic label, and P, represents the classcconditional probability prediction for the i-th voxel across the K semantic categories.
For an unlabeled target domain scan x", we leverage pseudo-labeling as a supervised learning strategy to facilitate domain adaptation:
K
C' ΣΣ N
of Po
(2)
The pseudo-labels are generated by the teacher network ftea. yielding the network's class-conditional probability output threshold 7 to filter these pseudo-labels, selecting only the most reliable pseudo- -anuutt-nnttations:
P. (x.). We then apply a confidence thresholding mechanism with a predefined
arg max p! (x+), if if P! (xx) 2
0.
(3)
0.
otherwise
where T E [0, 1] is a confidence threshold. The teacher network's 's weights are dynamically updated through Exponential Moving Average (EMA) strategy implemented by the student network s ensuring smooth and stable knowledge transfer: = the momentum coefficient, and 0 represents the network parameters, denotes the current training iteration, and val represents the update interval.
0tea= af t-vel + (1 -c , a E [0, 1) is
Mamba. The SSMs is initially introduced the field of control engineering to model dynamic systems. Specifically, the SSMs in deep learning encompass three key variables: the input zx(), the latent state representation l()), and the output v(4. The system can be defined as follows:
h' (t) = (h(t) + Br(t), v(t) = Ch'
(4)
where A represents the state transition matrix that describes how the system states volve, B denotes the control matrix that describes the influence of the inputs the states, and C defines state impact on outputs. To handle discrete-time sequence data inputs. the Zero-Order Hold typically used:
he Ah + Bæ, 3+ = Ch., A (xp((A)) = (AA) "(exp( (AA) I)AB,
(5)
where A represents the temporal discretization interval. However, due to the linear time invariant nature of SSM, the parameters (A, A. B, C) remain fixed across all time steps, which limits the expressive capacity of SSM. To overcome this limitation, Mamba [8] introduces a hardware-aware scan algorithm to achieve near-linear complexity and selection mechanism that treats the parameters (A, B. C) as functions of the input, effectively transforming the SSM into time- time-varying model:
h Φx (s.)), + d (x:) 4+ éc (z., h,,
(6)
where (xx)), (5(2)) (x.) and ( denote the parameter matrices are dependent on the inputs It.
3.2 BeyondMix
BeyondMix selects the most prevalent mixing strategy LaserMix 119 to generate mixed scans and labels by combining source and target domain data, thereby constructing mix-based structural priors:
N
K
miz LLasrMix((" ,a"), mix LaserMix(yy v²), Cmis
maz log Pe,k
(7)
where Lmix is the cross-entropy supervision error for the mixed scan. The discriminative feature representation F E MCC (whose spatial proximity relationships still preserve the 3D structure) is then obtained by processing the mixed sean mix through the encoder network, where M is the num- ber of features and C is the feature dimension. To further enhance the learning of domain invariant domain-invariant
5

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representations in discriminative features, we propose three key structural priors beyond conventional mixing approaches- permmttttne invariance, local consistency, and geometric consisteney- -whle si- multaneously modeling long-range dependencies through efficient sequence processing mechanisms.
Permutation Invariance Prior. Diverse space-filling curves, due to their different computa- tional approaches to spatial proximity, induce different 1D sequential arrangements that inher- ently satisfy permutation invariance prior requirements [42 43]. Simultaneously, their sequen- tial ordering thoroughly leverages structural prior cues and explores long-range dependencies. Specifically, let TH {I,...,M. M) 7 {l....,M M} be the Hilbert curve permutation [13 and Tz (I,...,,i + {I,... M) be the Z-order permutation [34]. By applying the Hilbert and Z-order permutations тh and zz we obtain the reordered features F'H- F[TH]] and F'z F F[TZ)),
respectively. For each ordered sequence, the Mamba processes the features sequentially to generate permutation-ssenitivee features:
On = M(Fn) E RRX Oz = MMF2) R MxC.
where .M()) represents the Mamba model. To enforce consistency across differentially ordered input features, we employ inverse mappings of the original permutations, thereby reconstructing representations in the default ordering for equivariance constraints: Ön On [ and Öz Ozl perrutation is then formulated as the mean squared error (MSE) between corresponding features across sequences:
Epermutation = 1100 - =2
(9)
The spatial distribution of objects and backgrounds in real-world LiDAR scans exhibits pronounced spatial correlations and semantic regularities [63] 23 19]. Specifically, the semantic composition of LiDAR point clouds demonstrates strong locality- based patterns, wherein ob- jects and backgrounds within proximal spatial regions tend to share characteristic semantic attributes. For instance, close-range areas of the LiDAR scan predominantly manifest road-like semantics, while distant regions typically encompass more complex urban landscape elements such as buildings and vegetation. Moreover, near-ground spatial zones predominantly feature road and sidewalk semantics, with minimal representation of elevated structures like buildings. This indicates that 3D LiDAR point clouds possess distinct height and range attribute priors, which encourages us to leverage structural priors for partitioning point cloud scans. However, regardless of the partitioning approach, LiDAR point cloud features should maintain consistency. Therefore, we construct local consistency priors and adopt two partitioning strategies: first, using the Z-axis to leverage category height attributes for division; second, using elevation angle to partition based on category-to-sente -o--sssos distance attributes.
Local Consistency Prior.
First, we employ elevation angle 0 and Z-axis height = as primary stratification mechanisms for segmenting the discriminative feature representation F E Mx into distinct cylindrical and rectangular regions. We accomplish this by quantizing 0; and z; into disjoint intervals. The cylindrical partitioning is defined as: R. = {F. @! @'im I 0, < 6 )maa) },1
1..... I,, where Ciin and 6 define the angular bounds of the 1-th region. Similarly, the rectangular partitioning is formulated as: R [F; 2 S 2; < > /. 1,.... V. where 2 and = define the height bounds of the v-th region. Subsequently. we implement Region wiise Hilbert Ordering within each segmented region, employing a Hilbert curve-based approach to systematically arrange features while preserving intra-region spatial proximity and geometrie relationships. We then concatenate these ordered subregions according their regional sequence generate distinct permutation schemes aT and TV that encode different structural priors. Applying these permutations yields reordered feature representations F,,- = F' y.. and Fy = ]- Following Equation g we generate permutation- sensitive features O,, and Ov. To establish local consistency prior, we map these features back to the default ordering through inverse permutation: Ö, On [m and Ōy Oz(mm²'. The local consistency prior loss is formulated as follows:
Liscal = |1o, - -9.--Or1'
(10)
Geometric Consistency Prior. Despite their sparsity and lack of ordering, 3D LiDAR point clouds
exhibit strong geometric redundancy due to underlying surface continuity. Point clouds typically
form coherent structures with local smoothness and global consistency, enabling reliable inference
of original geometry even from partially masked representations 42, 29, 7I]. We leverage this
property to establish geometric consistency priors through masking operations. We generate a density version f by applying a random binary mask Mask E (0.1)MM
F- [A Maski 1},
where Mask; ~ Bernoulli(1 p).
(11)

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Table 1: Comparison results of SynLiDAR -
SemanticKITTI adaptation in terms of mloU. The highest scores for each semantic class are highlighted using a color-coding system: Source only results marked in yellow, Target only results in gray, and the overall best performance metrics in blue.
Methods
m
CM
bicele
mo.ll
truck
oth-v
pars
mwccls
200d
sidew.
other S.
build
lense
vegel
60T.
pole
traf.
only Targel only
20.4
35.9
7.5
10.7
0.6
13.3
21.8
29.6
62.9
30.3
14.1
60.4
96.2
17.6
55.9
79.5
51.4
65.5
84.9
2.8
93.2
38.5
79.8
1.9
90.4
57.3
86.8
65.4
72.7
64.3
43.2
AdaptSegNet
57
27.9
52.1
10.8
11.2
2.6
9.6
15.1
35.9
2.6
62.2
10.4
41.3
0.1
58.1
17.1
68.0
38.4
38.7
35.9
20.4
CLAN
17.5
71.7
37.7
19.8
ADVENT
59
30.5
59.9
13.8
14.6
3.0
8.0
17.7
45.8
3.0
67.6
11.3
45.6
0.1
61.7
15.8
72.4
41.5
47.0
34.5
15.3
FADA 61
25.6
49.9
6.7
5.1
2.5
10.0
5.7
26.6
2.3
65.8
10.8
37.8
60.3
21.5
60.4
37.2
31.
35.4
17.4
MRNet 78
28.3
49.5
11.0
12.2
2.2
8.6
16.0
46,4
2.7
60.0
10.5
41.9
0.1
55.1
16.5
68.1
38.0
40.7
36.5
20.8
PMAN 72
33.7
71.0
14.
24.8
1.6
23,6
61.1
5.5
75.3
10.5
$4.1
0.1
47.9
174
69.6
38.6
61.5
37.0
18.6
CoSMix 48
29.9
56.4
10.2
20.8
2.1
13.0
25.6
41.3
67.4
43.4
0.0
57.9
12.2
68.4
44.8
35.0
42.1
17.0
PolarMix
[8
31.0
76.3
8.4
17.8
3.9
6.0
26.6
40.8
15.9
70.3
0.0
44.4
0.0
68.4
14.7
69.6
38.1
37.1
40.6
10.6
LaserMix
19
77.6
13.6
PCAN 773
37.0
85.0
17.5
27.4
10.4
11.9
27.5
63.7
2.6
78.1
13.5
50.1
0.1
68.5
20.0
76.2
41.3
45.7
41.0
21.8
73
92.9
17.3
49.2
83.3
MeyondMix (Ours)
17.1
68.2
BeyondMixt+ (Ours)
46.2
94.0
15.1
47.2
17.6
16.5
55.2
59.9
6.8
87.0
24.1
69.3
0.0
79.3
14.7
81.8
61.0
62.8
53.3
32.1
+23.8
and p E [0, 1) is the subsampling rate. We then apply Hilbert curve ordering to generate density- sensitive feature representations O and Ó:
M
=M((F) E MxC. Ō= RR where M'
Σ
Mask..
(12)
For the computation of geometric consistency loss, consider only the unmasked portions of the representation, thereby ensuring that the loss function evaluates only regions with reliable geometric information. Let {il Mask; = 1} be the index of unmasked points. We define the masked subset of O as Oz = {O, i I}. The loss is computed as:
M' Σ
Cgoametric
1
00
(13)
M
Training and Inference. The total loss for our training given by:
Lioral L + L + Xmixkmix + Aprior (Cperrmtationnn + Liocal Lgeameeric),
(14)
where Amiz and Aprior are the balancing coefficients for the loss. For inference, we only use the original network structure.
Expansion to other Mix-based methods. Existing mix-based methods each possess distinct struc- tural priors. Thoroughly exploiting and leveraging diverse range of structural priors can significantly enhance model performance. Based on this insight, we extend BeyondMix to BeyondMix++, which randomly selects from various existing mixing strategies when generating intermediate domains, including CoSMix [48) LaserMix [19, and PolarMix (68).
Experiments
4.1 Experimental Setup
Datasets. We utilize three common LiDAR datasets, performing two synthetic-to-real UDA tasks. (1) SynLiDAR (69] is synthetic dataset containing 198,396 point clouds with 32 semantic classes across 13 sequences. It simulates Velodyne HDL-64E LiDAR sensor. We follow the authors' in- structions (69 and use 19,840 point clouds for training and 1.976 validation. (2) SemanticKITTI 2 a real-world dataset collected in Karlsruhe, Germany, featuring 28 semantic classes. It was captured using Velodyne HDL-64E LiDAR sensor. We use sequences 00-10 (19,130 scans) for
training, while sequence 08 (4,071 scans) serves validation. (3) SemanticPOSS [37] consists of
7

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Table 2: Comparison results of SynLiDAR - SemanticPOSS adaptation in terms of mloU. The highest scores for each semantic class are highlighted using a color-coding system: Source only results marked in yellow, Target only results in gray, and the overall best performance metrics in blue.
Methods
mloU
bi.elst
car
trunk
veget.
traf:
pole
garh
build.
come.
fence
biccle
ground
Source only
38.3
47.2
43.6
37.8
70.3
11.1
33.8
19.5
67.9
11.2
19.9
9.6
77.9
47.8
Target only
57.3
61.6
75.1
48.4
77.9
47.7
37.8
29.9
77.8
37.7
51.2
54.9
81.2
63.9
Net
39.3
43,9
48.2
39.0
69.6
15.5
33.6
21.3
64.3
12.7
25.0
11.6
76.0
49.9
CLAN 32
39.5
43,9
46.6
71.0
15.1
34.3
20.4
9.5
23.2
12.0
75.1
51.3
ADVENT
59
40.1
44.6
47.6
40.1
71.2
15.6
35.6
22.0
68.4
10.6
25,9
10.4
76.7
52.3
FADA
37.6
39.6
41.2
69.2
16.3
32.1
67.9
22.0
13.0
71.4
47.9
MRNei 78
39.4
43.5
47.2
39.1
70.4
15.5
32.8
22.0
66.1
13.2
24.2
11.2
76.8
50.0
PMAN
46.5
52.6
61.5
75.1
18.8
36.5
21.4
74.7
25.8
73.7
CoSMix [S
44.6
53.6
47.6
44.8
75.1
16.8
37.9
25.3
72.7
19.9
39.7
10.8
80.0
56.5
PolarMix
32.6
39.1
11.9
10.7
79.0
LaserMix 19
45.5
58.4
61.3
47.7
69.0
21.9
39.5
30.9
61.0
16.1
36.5
7.1
79.5
62.6
73
48.6
37.5
23.9
76.9
41,9
11,9
79.1
DGTSST
50.8
55.1
70.7
46.1
74.2
30.1
36.3
44.1
81.0
4.3
62.8
10.3
78.5
67.2
BeyondMix (Ours)
52.9
57.6
68.5
46.2
76.9
32.1
39.2
40.5
79.9
21.4
62.7
12.8
79.7
67.1
ReyondMixs+ (Ours)
53.7
59.1
48.0
76.9
37.4
38.5
42.8
81.0
21.5
61.6
14.7
79.3
67.3
+15.4
+11.9
+26.2
+10.2
+6.6
+26.3
+4.7
+23.3
+13.1
+10.3
+41.7
+5.1
+1.4
19.4
2.988 annotated real-world point clouds with 14 semantic classes, collected Peking University, China, using a Pandora 40-line LiDAR sensor. We use sequence 03 for validation and all remaining sequences for training.
Evaluation protocol. Following virtual-to-real adaptation protocols established in previous works 699 48 731, we conduct two UDA experiments: SynLiDAR - SemanticPOSS (mapping to 14 segmentation classes) and SynLiDAR + SemanticKITTi (mapping to 19 segmentation classes). We adopt the widely accepted Intersection over Union (IoU) metric for semantic segmentation assessment. The IoU is calculated separately for each semantic category, providing class-specific insight into segmentation quality.
Our implementation framework leverages Py Torch 38] and MinkowskiEngine (5), running single NVIDIA RTX A6000 GPU with 48GB VRAM. The semantic segmentation backbonn employs a U-Net architecture MinkUNet34. For structural priors and Long-Range de- pendencies, adhered the default configuration with the Mamba architecture parameterized as follows: input dimension of 256, hidden state dimension of 256, convolutional kernel width of 4, and expansion factor of 2. In alignment with established practices in recent literature [88] 72 73),
Implementation.
we utilize raw X coordinates as the primary input features. Our processing pipeline maintains a consistent voxel size of 0.05m while accommodating variable point cloud densities without explicit size constraints. The optimization process employs the Adam optimizer [7 with a starting learning rate of 2.5e-4, governed by polynomial decay schedule with power coefficient 0.9, Comprehensive experimental configuration details are available in the Appendix.
4.2 Comparative Study
We conduct comprehensive experiments to evaluate the performance of domain adaptation from SynLiDAR to SemanticK/TTI and SemanticPOSS datasets. The mloU and per-class IoU scores are reported in Tables [
and 2 Qualitative Results can be found the Appendix.
Quantiative Results: (1) SynLiDAR - SemanticKITTI Adaptation. Our proposed BeyondMix++ achieves state-of-the-art performance with an mloU of 46.2%, surpassing all baseline methods by a significant margin (+23.8% over the source-only model). Notably, BeyondMix++ demonstrates exceptional improvements in challenging categories such as car (+58.1 person (+41.9%), and highlighting its robustness in adapting to diverse object scales and geometries. Compared to the recent DGT-ST (73), BeyondMix++ attains consistent gains across 13 out of 19 classes. (2) SynLiDAR + SemanticPOSS A Adaptation. BeyondMix++ achieves an mloU of 53.7%, outperforming existing methods by up to +8.2% (vs. LaserMix (9)). Remarkably, our method exhibits superior generalization on sparse objects(e.g. traffic-sign). Furthermore, BeyondMix++ significantly narrows the performance gap between source-only and target-only models, indicating its capability to achieve more effective domain invaarianniaiiantt representation learning.
road

---

4.3 Ablation Study
Without loss of generalizability, we stick with SynLiDAR semanticKITTI in our ablations. More ablation studies are presented the Appendix.
The Effect of Components. To validate the effectiveness of the proposed components in Beyond- Mix++, we conduct a systematic ablation study by progressively integrating different loss functions.
Using the self-training-basee DGT-ST 773 as our baseline, as shown Table 3 we observe that employing the mixed method mix yields 1.0% improvement. Exploring and constructing different structural priors through Lpermutation Clocal, and C Cgcometric contributes improvements
Table 3: Comparative study of different components.
# Lmix Epermutation Liocal Egeametuic ml)U(%)
43.1
(2)
44.1 (+1.0)
of 1.4%, 1.6%, and 1.3% respectively, indicating
(3)
(+1.4)
that each structural prior can help with domain-
(4)
44.7 (+1.6)
invariant representation learning. The pair-
(5)
43.4 (+1.3)
wise combinations of these components yield
(6)
45,4 (+2.3)
stronger gains (1.9-2.7%) demonstrating syn-
(7)
45.8 (+2.7)
ergistic effects in feature representation. Our
45.0 (+1.9)
full method ultimately achieves a substantial
performance of 46.2% mloU, representing sig- nificant gain of 3.1% over the baseline. These
(9)
46.2 (43.1)
results confirm the complementary nature of our proposed components in helping the model learn more comprehensive domain-invariant representations under different structural priors, through Permutation Invariance Prior, Local Consistency Prior, and Geometric Consistency Prior.
Table 4: Compari- son between differ- ent cylindrical parti-
Table 5: Compari- son between differ- ent rectangular parti- tioning region num- ber M.
Table 6: Compari- son between differ- ent Mask Ratios.
Table 7: Comparison between differ- ent mix strategies.
CosMix PolarMix LiserMix
mlol((%)
tioning region num-
45.1 (-1.1
ber L.
Mask %)
mloU(%)
(2)
44.8 (-144)
Num L
ml)
Num M
mloU(%)
40
45.9
(-0.3)
(3)
45.4
45.4 (-0.8)
45.3
50
46.2
(4)
45.7 (40.5)
45.6 (-0.6)
3
46.2
60
45.5 (-0.8)
(5)
46.0 (-0.2
5
46.2
4
46.0 (-0.2)
70
44.9 (-1.3)
(6)
v
45.9 (-0.3)
45.7(-0.5)
5
45.8 (-0.4)
80
44.3 (-1.9)
46.2
The Effect of Local Consistency Prior. Tables4and evaluaae different partitioning configurations for our Local Consistency Prior. The optimal setup combines 5 cylindrical regions and rectangular regions, achieving an ideal balance between segregating semantically distinct areas while preserving contextual information within regions. This configuration provides the best partitioning of spatial correlations and semantic regularities, helping the model improve UDA performance.
The Effect of Geometric Consistency Prior. Table reeveals that 50% mask ratio achieves optimal performance (46.2% mloU) for density consistency regularization. A lower ratio (40%) shows minor degradation (-0.3%) due to insufficient density variation, while higher ratios (60-80%) cause increasingly significant performance drops (-0.8% to -1.9%) as excessive point removal compromises structural information. The 50% mask ratio effectively balances creating meaningful density variation while preserving sufficient structural context for learning density-inds invariant representations across different geometric structure prior.
The Effect of Mix Strategies. As shown in Table 7 individual strategies show limited effectiveness: LaserMix (45.4%), CosMix (45.1 1%), and PolarMix (44.8%) each capture different domain-invarian features but with performance gaps. Dual combinations demonstrate complementary benefits: Cos- Mix+LaserMix (46.0%), PolarMix+LaserMe form individual approaches. The integration all three strategies achieves optimal performance (46.2% mloU), confirming that our BeyondMix++ successfully leverages the diverse structural priors and strengths of each mixing method to capture a more comprehensive range of domain-invarian features for robust LiDAR semantic segmentation.
(45.9%), and CosMix+PolarMix (45.7%) all outper-

---

Conclusion
BeyondMix addresses fundamental limitations in LiDAR segmentation domain adaptation by inte- grating three previously overlooked structural priors permutation invariance, local consistency, and geometric consistency- with Mamba's sequential processing. Our approach overcomes conventional receptive field constraints while effectively modeling Long-range dependencies, achieving state-of- the-art performance across benchmarks and highlighting the critical importance of structural priors in cross-domain representation learning.
Acknowledgements
This work was partially supported by the National Key R&D Program of China (Grant No. 2024YFB3909902), and the Youth Innovation Promotion Association of the Chinese Academy of Sciences (CAS).
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A Theoretical Insight
In our main text, we discuss that within the context of unsupervised domain adaptation, when a point's receptive field spans across two domains in the mixed images generated by the mix operation, the model can effectively learn aomain-invariant features for this point. Conversely, if a point's receptive field is confined entirely within single domain, the model struggles learn domain-invariam invariant features for that point. We now provide a detailed proof to support this claim.
We formulate our unsupervised domain adaptation framework as follows. We define the source domain Xr and target domain Ar, with a shared feature space 2 S B Our model architecture consists of two key components: feature extractor f X - Z that maps input data to the feature space, and classifier h 2 + y that performs the classification task. The learning objective combines for supervised learning on source domain, and the domain alignment loss Laligu minimize the discrepancy between feature distributions of the source and target domains. For I, E N₂ and I, E Nr, generate a mixed sample:
loss functions: the cross-entropy loss Lce
Tmir Ar + X)21, X Beta(o, (9).
(15)
where Beta(a; (8) indicates that the random variable follows a Beta distribution with parameters a and
We prove two claims: 1. Forward Proposition: a receptive field spans both domains (i.e. covers regions from both I. and zy, Coomain-invarian features are learned. 2. Reverse Proposition: If receptive field covers only a single domain, domain-invariant features cannot be effectively learned.
1. Proof of Forward Proposition: Cross-Domain Receptive Fields Enable Domain- Invariant Features
For a mixed sample, the gradient of the loss w.r.f. feature extractor parameters 0y is:
dLmin (Ccn()((()))).)) + A) &aatinn (f (zzz), f(x)) ,
(16)
08,
We observe that the first term (X-weighted) enforces sensitivity to source domain labels, while the second term ((1 - weweithte enforces aligument between target and source features. The combined gradient forces Oy to satisfy constraints from both domains, thereby driving the learning of Nomain-invarian patterns. This can be understood through minimizing (2; d) (where d denotes the domain label). The mix operation effectively disrupts domain-specific information, leading to:
potormation-thhorelll lens: maximizing cross-domain mutual information [(z; v) while
[(;; d) < H(d) (dl2)) 0,
(17)
where implies domain-invariant representations. Therefore, cross-domain receptive fields enable the model learn domain-invariant features.
2.Proof Reverse Proposition: Single-Domain Receptive Fields Fail to Learn
Features
E (0, 13 (no mixing), gradients depend solely on one domain:
ac (L.)()((())))..)) 28
A x=
DE ((()))
(18)
00,
==
60
Source-only training (A = 1): Overfitting to Nomain-speciine features (e.g., textures) degrades target general- ization.
Target-only training 0): Lack of supervision leads to trivial alignment (e.g.. feature collapse).
Due to domain shift (P(y)æ.) P(ylæx)). single momae- training causes:
[(x.) # fxx.) even y.- y/.
(19)
which results in misaligned distributions. The Maximum Mean Discrepancy (MMD) between domains remains: MMD(Z., Z.) [[ (o(2)) E., [d(=)]]l where maps a reproducing kernel Hilbert space. Therefore, single-domain receptive fields fail learn domain-invarian invarian features.
(20)
B
More Related Works
Point Cloud Semantic Segmentation. Point cloud semantic segmentation has evolved through three primary
representation paradigms: (1) Projection- based approaches like MVCNN [5]] and RangeNet++ [33 utilize
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CNN architectures via 2D mapping but sacrifice geometric detail: (2) Voxel-based methods improve compu- lational efficiency through regular grid processing, as demonstrated by MinkowskiNet [5]. TANet BT, and Cylinder3D 80]: and (3) Point-based networks enable end-to-end processing of raw point clouds, progressing from PointNct (42 through PointNet++ (43), DGCNN [63] Point Transformer (76), and PointNeXt [44], cach enhancing local geometric modeling capabiliitiss This work employs MinkowskiNet as its backbone architecture due its optimal balance between computational efficiency and segmentation accuracy.
State Space Models. State Space Models (SSMs) have evolved into powerful sequence modeling tools, progress- ing from S4 [TO]. which established HiPPO-based long-range dependency modeling, through computational refinements S4D [T] DSS [] and S5 49 culminating Mamha ( with its data-dependent state dynamies and hardware-ane aware design. In computer vision, SSMs have demonstrated remarkable versatility: Vision Mamba [30] pioneered pure SSM architectures for image tasks, VM-UNet [47) adapted them for medical image segmentation. while S4ND 35] and Motion Mamba (75 extended their application
multi-dimensional data and action recognition. Recent advances including PointMamba (28), PCM (74,, and Mamba3D [12] have successfully adapted Mamba to unordered point cloud data. Our work further extends this trajectory by demon- strating SSMs' effectiveness in unsupervised domain adaptation for LiDAR 3D point clouds, outperforming previous approaches in addressing domain shift challenges.
Multi-modal UDA methods for Point Cloud Segmentation. Unlike previous 2D unsupervised domain adapta- tion approaches 4 26 [7] [ 24 25] for segmentation tasks [54] 52 [3)) unsupervised domain adaptation
(UDA) for semantic segmentation has garnered significant scholarly attention, particularly regarding the principled exploitation and fusion of multimodal information streams for cross cross-domain generalization. Seminal investigations [21 60) explored the utilization of auxiliary modalities such as depth depth- available exclusively during source domain training to facilitate adaptation of 3D semantic segmentation frameworks. Subsequently, xMUDA [14] established paradigmatic approach by enforcing cross-modal consistency constraints, therehy enabling bidirectional knowledge transfer between image and point cloud representations to enhance domain generalization capabilitiis. Further advancements to this paradigm [5] incorporated sophisticated cross-modal fusion mechanisms and contrastive learning objectives to optimize representation alignment across both modali- ties and domains. Contemporary research has extended these foundational approaches through integration of advanced vision architectures and refined fusion methodologies. For instance, [40] incorporates the Segment Anything Model [8] (SAM) to augment 2D modality representations, consequently enhancing 3D segmentation performance through more effective cross-modal knowledge transfer. The authors of [67] propose a sequen- tial fusion-thoe then-distillation framework, which first aligns 2D and 3D feature representations within shared latent manifold before employing positive distillation techniques to preserve complementary modality-speeific information during the adaptation process. Furthermore, [50] introduces an adaptive regularization framework for modality-guidedd feature fusion, facilitating dynamic and contextually appropriate integration of visual and geometric information under domain distribution shifts.
C More Implementation Details
Our implementation framework leverages PyTorch (38) and MinkowskiEngine [. running on single NVIDIA RTX A6000 GPU with 48GB VRAM. The semantic segmentation backbone employs U-Net architecture MinkUNet34. For structural priors and Long-Range dependencies, we adhered to the default configuration with the Mamba architecture parameterized as follows: input dimension of 256, hidden state dimension of 256, convolutional kernel width of 4, and expansion factor of 2. In alignment with established practices in recent literature [8 72 [73] we utilize raw XYZ coordinates as the primary input features. The critical hyperparameters a and val configured 0.99 and 100, respectively. Our processing pipeline maintains a consistent voxel size of 0.05m while accommodating variable point cloud densities without explicit size constraints. The training regimen incorporates a comprehensive suite of data augmentation techniques. including random rotational transformations, Gaussian noise perturbation. coordinate jittering, and other enhancement strategies. The optimization process employs the Adam optimizer [17 with starting learning rate of 2.5c-4. governed by polynomial decay schedule with power coefficient 0.9. The network undergoes training for 100,000 iterations with each batch containing 2 samples. The loss function coefficients Xmiz and Aprior are set to and 0.01, respectively. The downsampling rate p is configured at 50% while the number of cylindrical partitions and rectangular partitions V are set to 3 and 5, respectively. When implementing BeyondMix++ with CosMix integration, which originally generates bidirectional mixed domains (source-> target and target->source) we randomly select a single directional transformation for intermediate domain generation to maintain computational efficiency while preserving adaptation benefits.
D Space-filling Curve
To more intuitively observe the impact of different space- filling curves on spatial proximity, we visualize the Hilbert curve and Z-order curve as shown in Figure (a), (b). (e) and (I) with dimensions of three and two, respectively. Z-order curves are renowned for their computational efficiency, while Hilbert curves are
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(a) Hilbert curve in 3D space
(b) Hilbert curve in 2D
(c) Points in 2D space
(d) Reordering points along Hilbert
N
N
(h) Reordering points along z- order
(e) Z-order curve in 3D space (f) Z-order curve in 2D space
(g) Points in 2D space
Figure 4: Space-filling curves.
distinguished by their Seeality-preservinn property. For clarity of demonstration, we present our analysis in 2D. The spatial proximity in point clouds can be effectively preserved through point cloud serialization. whereby points that adjacent in sequences maintain their neighborhood relationships in the point cloud representation. Figure 4 (c) and (g) illustrate randomly distributed points, which are subsequently sorted using the Hilhert curve and Z-order curve as shown in Figure (d) and (h). As observed, consistent with previous research findings (36), the Hilhert curve demonstrates superior spatial proximity preservation compared to the Z-order curve.
E
Pseudo Algorithm
Algorithm|] ppreentss the comprehensive training procedure of proposed BeyondMix++ framework for LiDAR semantic segmentation under unsupervised domain adaptation. The algorithm operates on teacher-student architecture (self-training paradigm), processing both source domain data with ground truth labels and unlabeled target domain data. For each training batch, we first compute supervised segmentation loss on source data and adaptation loss using paaher--eneratee pseudo-labels on target data. The core of BeyondMix++ is constructing three additional structural priors: (1) Permutation Invariance Prior, whereby point cloud representations should remain consistent regardless of acquisition trajectory or scanning order 42 43
(e-g.. different angular
perspectives or sampling paths), preserving invariance to permutation operations. (2) Local Consistency Prior, whereby point cloud features should maintain consistency across different local spatial partitions [63 23)
independent of acquisition perspective artificially defined spatial segmentation schemes; and (3) Geometric Consistency Prior, whereby LiDAR point cloud geometric structures (surface curvatures, normal vectors) should maintain stability under various processing operations (29 7 with remaining points preserving critical geometric information even under partial masking. However, these three structural priors intuitively resist straightforward implementation through mix-based paradigm like previous work. These components collectively form the total loss, which works alongside traditional mixing loss guide the student network's training. The teacher network parameters are periodically updated through exponential moving average (EMA) of student network weights, ensuring stable knowledge transfer. This unified approach effectively leverages Mamba to fully explore and utilize structural prior cucs and expand receptive fields and enhance the ability to extract domain-invarian representations from unstructured 3D LiDAR point cloud data.
F
More Metrics
We adopt the widely accepted Intersection Union (IoU) metric for semantic segmentation assessment. IoU is calculated separately for each semantic category, providing class caas--peecific insight into segmentation quality. To obtain holistic view of model performance, we derive the Mean Intersection over Union (mloU) by averaging these individual class IoU values. This comprehensive measurement effectively captures both the precision and consistency of our segmentation results across the entire spectrum of semantic categories.
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CoSMi
LaserMii
DGT-557
Bevundbiast (Ours)
Goound Truth
Figure 5: Qualitative results of UDA segmentation for SynLiDAR SemanticKITTI and SynLiDAR
+ SemanticPOSS tasks. Boxes highlight some regions of interest.
BryandMic++ (Ours)
Senwedkerm
SeorebicKET
SenmndeeOess
Figure 6: Error Map of UDA segmentation for SynLiDAR SemanticKITTI and SynLiDAR SemanticPOSS tasks. Boxes highlight some regions of interest. The binary visualization scheme employs red coloring highlight misclassified points, whereas gray regions represent accurate predictions.
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Algorithm Pseudo algorithms of BeyondMix++.
1: Inputs:Source Domain D {(=;y")) Target Domain DD {x²)
2: Define: Student Network fatw. Teacher Network ftea. Momentum Coefficient a, Update interval eal
3: Output: Student Network fatu
4: for each batch of (x", yy" in DS, x' in D For brevity. do
5: # Source Domain:
6: Calculate L for fatu by Eq. (1)
> Source loss
7: # Target Domain:
8:
Obtain pseudo-labels from Jr by Eq. (3)
9: Calculate L' for Stea by Eq. (2)
D. Target loss
# Mixed Scan:
11:
Calculate Lmix for fetu h g by Eq. (7)
Mix loss
12:
# Permutation Invariance Prior:
13:
Calculate permutation--sesittve features OH and Oz by Eq. (8)
14:
Calculate Epermutation for fetu by Eq. (15)
b Permutation Invariance Prior loss
15:
# Local Consistency Prior:
16:
Calculate permutation-sensae sensitive features OL and Oy by Eq. (8)
17:
Calculate Liocal for ftu by Eq. (10)
Spatial Consistency loss
18:
# Geometric Consistency Prior:
19:
Calculate permutation-sensitvv features O and Ô by Eq. (12)
20:
Calculate Lgeametric for fata by Eq. (13)
Density Consistency loss
21:
# Training:
22:
Calculate total loss:
23:
Liotal = L + L. + >mmia Liii + Aprior (Epormutation + Liocal + ggoometrie); by Eq. (14)
24:
Gradient backward Lrotal for sts
Update student model
25:
# EMA Update:
if Interval val: then
27:
geea = affea i-vol + a) Update teacher model
28:
end if
29:
end for
Table 8: Ablation studies of EMA coefficient a.
Table 9; Ablation studies of Threshold т.
EMA
mloU(%)
Threshold 7
mIoU(%)
0.5
45.6 (-0.6)
0.5
45.4 (-0.8)
0.7
45.9(-0.3)
45.8(-0.4)
0.9
46.0(-0.2)
0.7
46.2
0.99
46.2
0.8
45.9 (-0.3)
0.999
45.8 (-0.4)
0.9
44.9 (-1.3)
G More Qualitative Results
To further validate the effectiveness of proposed BeyondMix++ framework, present qualitative segmenta- tion results both source and target domains. ( representative examples that demonstrate superior cross-domain generalization capabilities of our approach compared to baseline methods. first row featuring SemanticKITTI scenes, BeyondMix++ produces significantly more accurate and consistent sidewalk segmentation. The baseline method erroneously classifies portions of terrain as sidewalks. while approach correctly delineates the boundary between these semantically similar but functionally distinet classes. The second row demonstrates BeyondMix++'s superior performance on terrain classification within SemanticKITTI. Our method correctly identifies terrain regions that are misclassified by the baseline approach, particularly in areas where terrain meets boundaries. In the SemanticPOSS visualizations (third row), Be- yondMix+ ++ achieves substantially more accurate segmentation of vegetation and other-vehicle classes. The baseline method exhibits fragmented predictions and class confusion these categories, whereas approach produces coherent and semantically consistent segmentations. The fourth row further validates BeyondMix++3s cross-domate generalization capabilities, where correctly segments vegetation and sidewalk regions in Se- manticPOSS that are severely misclassitied by baseline approaches. The baseline exhibits notable confusion between vegetation and sidewalk- common challenge in domain adaptation for LiDAR segmentation. These
25

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qualitative results collectively demonstrate that BeyondMix++ effectively leverages different structural priors learn domain-invarian features. The State Space Model architecture enhances BeyondMix+++ ability expand receptive fields and extract robust features from unstructured 3D point cloud data. By incorporating Permutation, Local, and Geometric consistency prior mechanisms, our approach successfully captures long-range contextual information and geometric relationships that remain stable across domains, leading to more accurate and consistent segmentation across different LiDAR sensor configurations and environmental conditions.
H More Error Map Results
In Figure 6. we present additional visualization results with corresponding error maps for the SynLiDAR + SemanticKITTI and SynLiDAR - SemanticPOSS adaptation scenarios, comparing our BeyondMix++ approach with CoSMix 48 I LaserMix [19). and DGT-ST ?3
The error maps clearly demonstrate that BeyondMix++ produces significantly fewer misclassifications compared to alternative methods, underscoring the effectiveness of our proposed approach in cross-domain LiDAR semantic segmentation.
Table 10; Comparison between different co-
Table 1I: Comparison between different co- efficient Auni-
efficient Amiz.
Amiz
ml)
Xani
mloU(%)
0.5
45.5 (-0.7)
0.1
44.4 (-1.8)
0,8
45.8(-0.4)
0,05
45.2(-1.0)
46.2
0.01
46.2
1.2
46.1(-0.1)
0.001
45.5 (-0.7)
I More Ablation Study.
Confidence Threshold. Table 2 presents our ablation study on the confidence threshold т. which plays a critical role in pscudo-label generation for unsupervised domain adaptation. Our experiments demonstrate that r=0.7 achieves optimal performance (46.2% mloU), establishing quality and quantity. Lower threshold values (0.5 and 0.6) result in decreased performance (-0.8% and -0.4% respectively), indicating that excessively lenient thresholds introduce noisy pseudo-labels that adversely affect training. Conversely, higher threshold values (0.8 and 0.9) also lead to performance degradation (-0.3% and -1.3% respectively), with particularly significant drop at 7=0.9. This suggests that overly strict thresholds discard potentially useful supervision signals from moderately confident predictions. The sharp performance decline with 7=0.9 (-1.3%) is especially noteworthy, indicating that excessively high confidence thresholds severely limit the number of available pscudo-labels, significantly hampering the model's ability to adapt to the target domain. These results confirm that 7=0.7 provides the optimal trade-off between pseudo-label precision and recall, enabling effective knowledge transfer in our BeyondMix++ framework for LiDAR semantic segmentation under domain shift conditions.
effective balance between pseudo-label
EMA. Table g presents our ablation study the Exponential Moving Average (EMA) coefficient a, which controls how quickly teacher model incorporates updates from the student model. We observe that a=0.99 achieves optimal performance (46.2% mloU), establishing an effective balance between stability and adaptability in teacher-student knowledge transfer. Lower a values (0.5, 0.7, and 0.9) show progressively increasing performance (-0.6% -0.3%, and -0.2% respectively), indicating that faster teacher updates compromise model stability by introducing excessive fluctuations during training. Conversely, an extremely high value (0.999) also results in performance degradation (-0.4%), suggesting overly conservative teacher updates fail to effectively incorporate emerging domain knowledge. These results confirm that a=0.99 optimally balances stability and adaptability in the teacher-student framework, enabling effective knowledge distillation for unsupervised domain adaptation in LiDAR semantic segmentation. This finding aligns with our theoretical understanding that the teacher model must maintain sufficient consistency while gradually incorporating valuable representations learned by the student model.
Balancing Coefficients. Table 10 shows Amazz = 1.0 yiclds optimal performance (46.2% mloU). Lower values (0.5, 0.8) reduce performance by 0.7% and 0.4%, suggesting insufficient mixed-domain learning, while a higher value (1.2) shows minimal impact (-0.1%). This suggests the model exhibits robustness to small increases in this coefficient, with balanced value of 1.0 providing optimal regularization. For Aprior (Table [T). the optimal value is 0.01. Larger values 10.1, 0.05) significantly degrade performance (-1.8%. -1.0%) by overemphasizing consistency constraints, which can overshadow the primary segmentation objective. Conversely, a smaller value (0.001) also reduces performance (-0.7%) as the regularization becomes too weak to effectively guide domain- invariant feature leamning. These findings confirm that proper balance between loss components (Amix L.0.
26

---

Aprior = 0.01) is crucial for effective domain adaptation and diverse structural prior cues, well as maximizing the extraction of domain-invariant features across different receptive fields.
Different Long-range Modeling Methods. To comprehensively validate approach, evaluated alternative long-range dependeney modeling techniques, including the widely adopted Point Transformer v3 (PTv3) [66], which implements attention mechanisms within locally grouped point cloud sequences. Our analysis revealed that the standard PTv3 implementation constrains the receptive field to 1024 points, which proves insufficient for our application domain. As demonstrated in our main text, the minimum requisite receptive field exceeds 1300 points (potentially substantially more, contingent upon mixing strategies and scanning methodologies). Mamba, conversely, exhibits an unbounded receptive field, rendering it particularly suitable modeling the long-rane dependencies essential to our task domain. The quantitative experimental results presented in Table ?? substantiate our theoretical assertions. Furthermore, Pamba establishes that "SSM can process the entire point cloud of 100,000+ points expeditiously without subdivision and model uncompressed long- range dependencies. affirming that "SSM demonstrates superior suitahility compared transformer architectures for extracting long-term dependencies." This aligns precisely with our requirements, as each scan our outdoor LiDAR datasct comprises over 100,000 points. While we implemented PTv3 with parameter setting of P = 2048, the quadratic computational complexity inherent to transformer architectures rendered the processing speed prohibitively inefficient for practical deployment.
Table 12: Comparison between Different Long-range Modeling Methods.
Method
mIoU (%)
PTv3 (P=1024)
45.6
Mamba
46.2
J Limitations
Despite the demonstrated effectiveness of BeyondMix, several limitations warrant acknowledgment. First, the sequential transformation of 3D point clouds introduces computational overhead that may impact real-time performance in resource-constrained autonomous systems. Second, while our approach leverages three key structural priors, additional Nomain-specifer priors may exist that could further enhance performance. Third, the elfectiveness of our method may vary across different sensor configurations and point cloud densities, potentially requiring domain-specific adjustments. Finally, our current implementation primarily focuses semantic segmentation tasks, and its generalizability other point cloud understanding tasks, such object detection instance segmentation, requires further investigation.
K Broader Impacts
BeyondMix contributes advancing autonomous driving technologies by enhancing LiDAR semantic segmen- tation capabilities across diverse environmental conditions. This advancement has potential societal benefits, including improved transportation safety, reduced accidents, and enhanced mobility for individuals with dis- abilitics. However, the deployment of such technologies raises important ethical considerations regarding privacy, security, and the potential for algorithmic bias. Additionally, autonomous systems become more prevalent, careful consideration must be given to their environmental impact, including energy consumption and electronic waste. encourage research community to address these broader implications while advancing the technical capabilities of domain adaptation methods for 3D perception systems.
27


Reviews:
[{"review_id": "24pE5UnPRE", "reviewer": "Reviewer_cNXC", "summary": "This paper proposes BeyondMix, a novel framework that harnesses the capabilities of State Space Models (specifically Mamba) to construct and exploit these structural priors while modeling long-range dependencies that transcend the limited receptive fields of conventional voxel-based approaches.", "questions": "1. Figure 1(c) is confusing. What's the difference between the symbol \"-\" and \"x\"? Could the author provide a detailed explanation? It would be best for the author to provide the strategies adopted by the specific method.\n2. Line 247, BeyondMix++ randomly selects from various existing mixing strategies. Could the author present the result of each mixing strategy? And which strategy best fits the proposed BeyondMix.", "limitations": "yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strength:\n1. This paper identifies three critical yet underexploited structural priors: permutation invariance, local consistency, and geometric consistency.\n2. Excellent work. The experiment is complete and sufficient. Writing and drawing are clear and easy to understand. \n\nWeakness:\n1. Some multi-modal UDA methods for point cloud segmentation also needs to be discussed in related work.", "was_revised": true, "final_justification": "Thanks for authors' rebuttal. I haven't found any evidence to lower the rating. I will keep the initial rating.", "rebuttal": "We sincerely appreciate your thorough review and constructive feedback on our manuscript. We are particularly grateful for your recognition of our work as **\"excellent\"** and your acknowledgment that our experimental validation is **\"complete and sufficient\"** with **\"clear and comprehensible\"** illustrations and exposition.\n\nWe see that your main concerns are further explanation of the certain ambiguous aspects in our manuscript. All your comments are addressed point by point in the following. **Please feel free to use the discussion period if you have any additional questions.**\n\n---\n\n## Q1:\nSome multi-modal UDA methods for point cloud segmentation also needs to be discussed in related work.\n\n## A1:\n We appreciate your valuable feedback. **We have supplemented our related work section with multimodality discussions and will incorporate this content into our final manuscript.**\n\nUnsupervised domain adaptation (UDA) for 3D semantic segmentation has garnered increasing academic attention, particularly regarding the exploitation of multimodal information streams. Seminal investigations [1, 2] explored the utilization of auxiliary modalities such as depth—available exclusively during source domain training—to facilitate adaptation of 3D semantic segmentation frameworks. Subsequently, xMUDA [3] established a paradigmatic approach by enforcing cross-modal consistency constraints, thereby enabling bidirectional knowledge transfer between image and point cloud representations to enhance domain generalization capabilities. Further advancements to this paradigm [4] incorporated sophisticated cross-modal fusion mechanisms and contrastive learning objectives to optimize representation alignment across both modalities and domains.\nContemporary research has extended these foundational approaches through integration of advanced vision architectures and refined fusion methodologies. For instance, [5] incorporates the Segment Anything Model (SAM) to augment 2D modality representations, consequently enhancing 3D segmentation performance through more effective cross-modal knowledge transfer. The authors of [6] propose a sequential fusion-then-distillation framework, which first aligns 2D and 3D feature representations within a shared latent manifold before employing positive distillation techniques to preserve complementary modality-specific information during the adaptation process. Furthermore, [7] introduces an adaptive regularization framework for modality-guided feature fusion, facilitating dynamic and contextually appropriate integration of visual and geometric information under domain distribution shifts.\n\n\n\n[1] Spigan: Privileged adversarial learning from simulation. ICLR, 2019\n\n[2] Dada: Depth-aware domain adaptation in semantic segmentation. ICCV, 2019.\n\n[3] xMUDA: Cross-modal unsupervised domain adaptation for 3D semantic segmentation. CVPR,2020\n\n[4]Cross-modal learning for domain adaptation in 3D semantic segmentation. TPAMI, 2022\n\n[5]Learning to adapt sam for segmenting cross-domain   point clouds. ECCV 2024\n\n[6]Fusion-then-Distillation: Toward Cross-modal Positive Distillation for Domain Adaptive 3D Semantic Segmentation. TCSVT 2025\n\n[7]Exploring Modality Guidance to Enhance VFM-based Feature Fusion for UDA in 3D Semantic Segmentation. CVPR 2025\n\n---\n\n## Q2:\nFigure 1(c) is confusing. What's the difference between the symbol \"-\" and \"x\"? Could the author provide a detailed explanation? It would be best for the author to provide the strategies adopted by the specific method.\n\n## A2:\nWe apologize for any confusion and will address this issue in the final manuscript.\n\nIn our notation, **\"-\"** denotes structural priors **not previously explored** in the literature, specifically permutation invariance, local consistency, and geometric consistency. The **\"x\"** symbol indicates structural priors that **cannot be implemented using mix-based methodologies.**\n\nExisting mix-based approaches each leverage a single structural prior:\n\n- **Cosmix** utilizes **Category Semantic Integrity**  by employing semantic category instances as the minimal mixing unit(illustrated in Fig. 1(b), first diagram)\n- **Polarmix** implements **Azimuthal Semantic Consistency** by extracting and rotationally mixing points of identical semantic classes (depicted in Fig. 1(b), second diagram)\n- **Lasermix** enforces **Spatial Region Integrity** by partitioning scenes according to inclination patterns (shown in Fig. 1(b), third diagram)\n\n\nThese methodologies are limited by their singular focus on one structural prior and insufficient receptive field capacity.\nOur approach incorporates both mix-compatible priors and those incompatible with mixing techniques. The additional 3 structural priors we adopt are:\n\n- **Permutation Invariance** (Fig. 1(b), fourth diagram): Ensures consistency across different scanning orders representing varied observational perspectives (e.g., top-down versus bottom-up)\n- **Local Consistency**(Fig. 1(b), fifth diagram): Leverages statistical partitioning. For instance:\n   - Cylindrical partitioning recognizes proximity-based semantic patterns (objects near sensors are typically\" car\"or \"motorcycle\"  while distant points often represent \"vegetation\")\n   - Rectangular partitioning utilizes Z-axis coordinates (lower values correspond to\" road\" while higher values indicate \"buildings\")\n\n- **Geometric Consistency** (Fig. 1(b), sixth diagram): Maintains consistent geometric representations across varying LiDAR point densities.\n\nAdditionally, our method models long-range dependencies, substantially expanding the receptive field and addressing the domain-invariant feature learning limitations in unsupervised domain adaptation caused by restricted receptive fields.\n\n---\n\n## Q3:\nLine 247, BeyondMix++ randomly selects from various existing mixing strategies. Could the author present the result of each mixing strategy? And which strategy best fits the proposed BeyondMix.\n\n## A3:\nAs demonstrated in **lines 329-336 of the main text and in Table 7**, we systematically evaluated the performance gains achieved by integrating BeyondMix with previous mixing strategies (CosMix, PolarMix, LaserMix) and their combinations. Our experiments reveal that when combining BeyondMix with individual mixing methods, LaserMix achieves the highest performance (45.4%). We attribute this to **LaserMix's more comprehensive structural priors and effective cross-domain receptive field construction**. When pairing BeyondMix with two mixing methods simultaneously, the CosMix+LaserMix combination yields the best results (46.0%). This can be explained by the operational similarities between PolarMix and LaserMix—**both involve radius-based manipulations relative to the central point, albeit through different mechanisms**—making CosMix+LaserMix a more complementary pairing. The integration of all three strategies achieves optimal performance (46.2%), confirming that our BeyondMix++ successfully leverages the diverse structural priors and strengths of each mixing method to capture a more comprehensive range of domain-invariant features for robust LiDAR semantic segmentation.\n\n**Table 7: Comparison between different mix strategies.**\n\n| #   | CosMix | PolarMix | LaserMix | mIoU (%)        |\n| --- | ------ | -------- | -------- | --------------- |\n| (1) | ✔      |          |          | 45.1 (**−1.1**) |\n| (2) |        | ✔        |          | 44.8 (**−1.4**) |\n| (3) |        |          | ✔        | 45.4 (**−0.8**) |\n| (4) | ✔      | ✔        |          | 45.7 (**−0.5**) |\n| (5) | ✔      |          | ✔        | 46.0 (**−0.2**) |\n| (6) |        | ✔        | ✔        | 45.9 (**−0.3**) |\n| (7) | ✔      | ✔        | ✔        | **46.2**        |"}, {"review_id": "Tds2ipYa6V", "reviewer": "Reviewer_ymd8", "summary": "This paper introduces BeyondMix for UDA in LiDAR semantic segmentation. The main contribution is the utilization of a State Space Model (Mamba) to process point cloud features. By employing space-filling curves (e.g., Hilbert and Z-order curves) to serialize 3D point clouds, the method satisfies Mamba's requirement for sequential input. They also construct 3 structural priors: Permutation Invariance, Local Consistency, and Geometric Consistency. In addition, the authors propose leveraging Mamba's powerful long-range dependency modeling capabilities to capture context from across the entire point cloud scene.", "questions": "I would ask the authors to please provide a response addressing the weaknesses I have outlined to help resolve my concerns. If the authors can clarify these issues in their rebuttal, I will consider raising my score.", "limitations": "yes", "rating": 3, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths\n﻿\n1. The paper identifies two main weaknesses in existing methods: \"insufficient use of structural priors\" and \"limited receptive fields.\" To address these limitations, the paper proposes using the Mamba model to unify the solutions to both problems—modeling long-range dependencies and constructing new structural priors. \n﻿\n2. The paper resolves the challenge of processing unordered point clouds with Mamba by using space-filling curves and further leverages different serialization and partitioning schemes to construct priors. This design is highly innovative.\n\n3. The paper is well-written and easy to understand. The results also demonstrate the effectiveness of the proposed method.\n﻿\n﻿\nWeaknesses\n﻿\n1. To construct the various structural priors, the method requires multiple serializations of the features and repeated forward passes through the Mamba model. This may introduce considerably higher computational complexity than baseline methods. The paper lacks a quantitative analysis of runtime evaluation (e.g., inference time and FLOPs).\n\n2. It's common for UDA methods like DACS, DAFormer, and DGT-ST to use a combination of source loss (L s) and mixed-sample loss (L mix). If L mix is already being used to adapt to the target domain, why is the separate target loss, L t, also necessary?.\n\n3. The Mamba model captures long-range dependencies along the 1D path (\"flatten\" a 3D structure into a 1D sequence), but its ability to capture complex 3D spatial relationships that do not lie on this path may be weaker. This could lead to the loss of critical spatial information.\n\n4. The method enforces \"equivariance\" on intermediate features by inverse-mapping the Mamba outputs back to their original order. However, the ultimate goal for segmentation is to achieve \"invariance\" in the final prediction. \n\n5. The proposed Permutation Invariance and Local Consistency priors all work by altering the processing order of points and then enforcing consistency on the feature representations. It seems to be be conceptually overlapping.", "was_revised": true, "final_justification": "According to the author's rebuttal, I tend to maintain the score.", "rebuttal": "We sincerely appreciate your time and effort in reviewing our manuscript. We are particularly grateful for your recognition that our work, BeyondMix, is **\"highly innovative,\"** **\"well-written and easy to understand,\"** with **\"effective results.\"**\n\nWe acknowledge your primary concerns regarding the missing comparisons and additional issues you highlighted.  All your comments are addressed point by point in the following. **Please feel free to use the discussion period if you have any additional questions.**\n\n---\n\n## Q1:\nTo construct the various structural priors, the method requires multiple serializations of the features and repeated forward passes through the Mamba model. This may introduce considerably higher computational complexity than baseline methods. The paper lacks a quantitative analysis of runtime evaluation (e.g., inference time and FLOPs).\n\n## A1:\nWe appreciate your suggestion regarding runtime evaluation. Below, we provide a comprehensive analysis of computational requirements including GPU memory utilization, per-iteration runtime, and FLOPs for both training and inference phases.\n\n\n\nDuring the **training stage**, the incorporation of long-range modeling mechanisms inevitably introduces additional computational overhead. However, this increase remains **relatively modest** due to the **near-linear complexity (approximately O(n))** of our Mamba-based implementation.\n\n**For inference**, our method employs a **standard network architecture without auxiliary modules** , resulting in computational requirements comparable to baseline approaches.\n\nAs demonstrated in Table R1, BeyondMix++ exhibits **identical GPU memory consumption, per-iteration runtime, and FLOPs during inference** compared to baseline methods such as LaserMix and DGT-ST. Notably, our approach achieves substantial performance improvements (+10.2% over LaserMix and +3.1% over DGT-ST) while incurring only **acceptable additional training overhead**, highlighting the favorable efficiency-performance trade-off of our proposed framework.\n\n**Table R1: Quantitative Analysis of Computational Overhead**\n\n| Method | GPU Memory (Train / Infer, GB/GB) | Time per Iteration (Train / Infer, iteration/s, scan/s) | FLOPs (Train / Infer, G/G) |\n|----|---|---|--|\n| **LaserMix** | 17.81 / 2.5 | 0.92 / 6.96 | 65.10 / 32.95 |\n| **DGT-ST** | 14.72 / 2.5 | 0.95 / 6.95 | 63.68 / 32.95 |\n| **BeyondMix++（Ours）** | 22.39 / **2.5** | 0.67 / **6.95** | 76.84 / **32.95** |\n\n---\n\n## Q2: \nIt's common for UDA methods like DACS, DAFormer, and DGT-ST to use a combination of source loss (L s) and mixed-sample loss (L mix). If L mix is already being used to adapt to the target domain, why is the separate target loss, L t, also necessary?.\n\n## A2: \nThank you for raising this important question regarding the necessity of target loss ($L_t$) in mix-based methods. We have conducted thorough investigations into this matter.\n\nWhile 2D UDA methods such as DACS and DAFormer employ loss functions formulated as $L_s+L_{mix}$, the discussion and empirical evaluation of mixing strategies in 2D domain are relatively limited. Given that our proposed approach falls within the 3D methodological framework, we primarily focus our investigation on 3D LiDAR-based techniques when examining domain adaptation strategies:\n\n- CosMix performs mutual mixing of source and target domains without intermediate forms, utilizing a total loss function of $L_{s->t}+L_{t->s}$ as defined in Equation 5 of the original paper.\n- PolarMix is primarily a data augmentation method without explicit specification regarding target loss utilization.\n- LaserMix, the current state-of-the-art mixing approach, incorporates a comprehensive loss function (Equation 9 of the original paper): $L_s+L_{mix}+L_{mt}$ , where $L_{mt}$ represents the target loss. **Their ablation studies in Table 3 (experiments (2) and (3) of the original paper demonstrate that removing target loss results in approximately 3% mIOU degradation.**\n- DGT-ST follows LaserMix's framework with a total loss function (Equation 15 of the original paper): $L_s+L_{mix}+L_{sac}$ , where $ L_{sac}$ is defined in Equation 12 of the original paper as essentially a target loss, albeit with unique teacher-student network input designs. **Their ablation studies in Table 5 of the original paper confirm that eliminating $ L_{sac}$ causes a 1.1% mIOU performance drop.**\n\nOur experimental results in Table R2 similarly indicate performance degradation when target loss $ L_t$ is removed from BeyondMix++. We posit that mix methods effectively learn cross-domain commonalities, while target loss $L_t$ enables focused learning of target domain-specific  3D knowledge, thereby enhancing model performance in the target domain.\n\n\n**Table R2：Comparative Analysis of Target Loss $L_t$**\n\n| Method          | mIoU (%)|\n| - | ---- |\n| W/O  $L_t$  | 45.3 |\n| W / $L_t$   | **46.2** |\n\n---\n\n##  Q3:\nThe Mamba model captures long-range dependencies along the 1D path (\"flatten\" a 3D structure into a 1D sequence), but its ability to capture complex 3D spatial relationships that do not lie on this path may be weaker. This could lead to the loss of critical spatial information.\n\n## A3:\nYour observation regarding the potential loss of 3D spatial relationships when flattening 3D structures into 1D sequences is valid. **However, our approach serves as a complementary component to existing methods rather than a replacement.** Our framework preserves the original spatial relationship learning while introducing additional structural priors that were previously underexplored.\n\nSpecifically, we model long-range dependencies that prior approaches have neglected. By employing different sequential orderings, each capturing distinct spatial adjacency patterns and structural priors, our method effectively extracts domain-invariant features at individual spatial points—a critical aspect in unsupervised domain adaptation tasks.\n\nThe diverse sequential representations enable the capture of complementary structural information while maintaining the integrity of the original spatial context, thereby enhancing the model's capacity to learn transferable features across domains without compromising spatial understanding.\n\n---\n\n## Q4: \nThe method enforces \"equivariance\" on intermediate features by inverse-mapping the Mamba outputs back to their original order. However, the ultimate goal for segmentation is to achieve \"invariance\" in the final prediction.\n\n## A4:\nOur approach can be elucidated through two principal perspectives:\n\n(1) **Intermediate feature equivariance facilitates terminal invariance.** Numerous classical paradigms, particularly consistency regularization frameworks, leverage data augmentation operations such as mixup and cropping to induce equivariance in the feature space while imposing invariance constraints in the prediction manifold. This methodology enhances model robustness against such augmentations, enabling the acquisition of more discriminative representations and consequently improving model efficacy.\n\n(2) Within the context of UDA for 3D segmentation tasks, an idealized model equipped with perfect structural priors would exhibit invariance to diverse structural perturbations (e.g., heterogeneous scanning methodologies). Previous approaches frequently induce equivariance to structural perturbations, primarily due to the insufficient incorporation of structural priors. We address this limitation by integrating previously neglected structural priors (including Permutation Invariance, Local Consistency, and Geometric Consistency) prior to intermediate feature representation learning. **This strategic integration alleviates equivariance effects, amplifies the encoder's invariance to structural perturbations, and constructs a substantially more robust model.** The resultant performance improvements are empirically substantiated in Table 3 of the main text.\n\n---\n\n## Q5:\nThe proposed Permutation Invariance and Local Consistency priors all work by altering the processing order of points and then enforcing consistency on the feature representations. It seems to be be conceptually overlapping.\n\n## A5:\nWe would like to further clarify the distinction between these two structural priors.\n\n**Permutation Invariance** leverages different space-filling curves (H-curve, Z-curve) to create diverse scanning sequences. Intuitively, this enables the modeling of long-range dependencies from different perspectives (e.g., top-down versus bottom-up approaches). This structural prior can be conceptualized as consistency across **different viewpoints**, ensuring feature representations remain invariant despite changes in observation sequence.\n\n**Local Consistency** priors utilize statistical partitioning based on **local characteristics**. For instance:\n\n- Cylindrical partitioning recognizes that objects proximal to LiDAR sensors frequently belong to categories like \"car\" or \"motorcycle,\" while distant points often represent \"vegetation\" (as validated in the LaserMix).\n- Rectangular partitioning leverages the global Z-axis coordinate as a discriminative metric, where lower Z-values typically correspond to \"road\" classes, while higher Z-values frequently indicate \"building\" structures.\n\nBy implementing various local partitioning schemes, we generate distinct sub-regions within which we apply sequential ordering. This approach effectively preserves local consistency priors and enhances the model's ability to capture domain-invariant features within contextually similar regions.\n\nConsequently, Permutation Invariance and Local Consistency priors leverage fundamentally distinct structural information, enabling complementary feature representation learning across different organizational hierarchies of the LiDAR data."}, {"review_id": "7WnJOH9Qso", "reviewer": "Reviewer_H4Er", "summary": "This paper introduce BeyondMix, which harnesses the capabilities of State Space Models (specifically Mamba) to construct and exploit these structural priors while modeling long-range dependencies. It tries to transcend the limited receptive fields of conventional voxel-based approaches. The suggested method has been validated to be effective.", "questions": "1. The Mamba model in the paper is only used as an auxiliary supervision module during the training phase. Has consideration been given to directly decoding Mamba features for classification during inference? Will this design have better results.  \n2. The receptive field at point B in Figure 2 contains two types of domains, but line 76 in the text states that they are not included;", "limitations": "The authors discussed their limitations of their work.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**  \n1. This paper introduce BeyondMix, which leverages Mamba to construct structural priors beyond the capabilities of existing mix-based methods while simultaneously exploiting long-range dependency modeling to transcend limited voxel receptive fields for enhanced domain-invariant representation learning.  \n2. This paper introduces the Mamba model and solves the problem of different feature expressions caused by uneven LiDAR density to a certain extent by constructing geometric consistency priors.  \n**Weaknesses**  \n1. The permutation invariant prior module only selects two specific sorting sequences and learns to make their representations in the Mamba space approach each other, rather than making their representations similar in any sorting. Therefore, whether it can be called \"permutation invariant\" remains to be considered.  \n2. The meaning of figures 1 (b) and (c) is unclear, especially the table in (c) is difficult to understand.", "was_revised": true, "final_justification": "Thanks for the authors' rebuttal. I haven't found any evidence of rating reduction and I keep the initial positive rating.", "rebuttal": "We greatly appreciate your time and thoughtful assessment of our manuscript. We are particularly grateful for your recognition that our BeyondMix approach effectively **addresses the challenges of cross-domain feature representation in LiDAR-based applications**.\n\nWe have carefully considered your primary concerns regarding your specific areas of interest and the inadvertent errors in our manuscript. In the following sections, we address each of your comments systematically to improve the clarity and accuracy of our paper. **Please feel free to use the discussion period if you have any additional questions.**\n\n---\n\n## Q1:\nThe permutation invariant prior module only selects two specific sorting sequences and learns to make their representations in the Mamba space approach each other, rather than making their representations similar in any sorting. Therefore, whether it can be called \"permutation invariant\" remains to be considered.\n\n## A1:\n We apologize for any confusion regarding our methodology. While numerous space-filling curve algorithms exist, we deliberately selected two of the most widely adopted implementations—H-curve and Z-curve—to generate diverse sequential representations. Our approach specifically aims to ensure that feature representations across these different scanning orders exhibit proximity in the Mamba embedding space.\nFor clarity, we will revise our terminology to **\"H-Z permutation invariance\"** to explicitly indicate the two specific space-filling curves employed in our framework. This modification will be incorporated in subsequent versions of the manuscript to enhance precision and prevent misinterpretation.\n\n---\n\n## Q2:\nThe meaning of figures 1 (b) and (c) is unclear, especially the table in (c) is difficult to understand.\n\n##  A2:\nWe apologize for any confusion and will address this issue in the final manuscript.\n\nIn our notation, \"-\" indicates structural priors not previously explored in existing methods, specifically permutation invariance, local consistency, and geometric consistency. The \"x\" symbol denotes structural priors that fundamentally cannot be implemented through mix-based approaches.\n\nCurrent mix-based methodologies each leverage a single structural prior:\n\n- **Cosmix** employs **Category Semantic Integrity** by utilizing semantic category instances as the minimal mixing unit (illustrated in Fig. 1(b), first diagram)\n- **Polarmix** implements **Azimuthal Semantic Consistency** by extracting and rotationally mixing points of identical semantic classes (depicted in Fig. 1(b), second diagram)\n- **Lasermix** enforces **Spatial Region Integrity** by partitioning scenes according to inclination patterns (shown in Fig. 1(b), third diagram)\n\nThese methodologies are limited by their singular focus on one structural prior and insufficient receptive field capacity.\nOur approach incorporates both mix-compatible priors and those incompatible with mixing techniques. The additional 3 structural priors we adopt are:\n\n1. **Permutation Invariance** (Fig. 1(b), fourth diagram): Ensures consistency across different scanning orders representing varied observational perspectives (e.g., top-down versus bottom-up)\n2. **Local Consistency**(Fig. 1(b), fifth diagram): Leverages statistical partitioning. For instance:\n   - Cylindrical partitioning recognizes proximity-based semantic patterns (objects near sensors are typically\" car\"or \"motorcycle\"  while distant points often represent \"vegetation\")\n   - Rectangular partitioning utilizes Z-axis coordinates (lower values correspond to\" road\" while higher values indicate \"buildings\")\n3. **Geometric Consistency** (Fig. 1(b), sixth diagram): Maintains consistent geometric representations across varying LiDAR point densities.\n\nAdditionally, our method models long-range dependencies, substantially expanding the receptive field and addressing the domain-invariant feature learning limitations in unsupervised domain adaptation caused by restricted receptive fields.\n\n---\n\n## Q3:\nThe Mamba model in the paper is only used as an auxiliary supervision module during the training phase. Has consideration been given to directly decoding Mamba features for classification during inference? Will this design have better results.\n\n## A3:\nWe acknowledge the suggestion regarding direct decoding of Mamba output features. As empirically demonstrated in Table R1, this approach induces substantial performance degradation. Our comprehensive analysis elucidates several contributing factors:\n\nDuring the training phase, our architecture leverages Mamba to process intermediate-layer features, establishing structural priors and effective receptive fields that constrain our encoder toward learning more discriminative and domain-invariant representations. However, Mamba transforms these intermediate features into an alternative high-dimensional alignment space that is fundamentally incongruent with the original feature manifold.\n\n**This transformed representation space lacks decoder-specific optimization, as the decoder was not trained to process features from this alternative embedding space.** Consequently, the semantic decoding process fails to effectively interpret these representations, resulting in substantial performance deterioration.\n\nThese empirical findings substantiate that our architectural design—utilizing Mamba as a constraint mechanism during training rather than as a feature extractor during inference—constitutes the optimal configuration for cross-domain feature learning in LiDAR semantic segmentation.\n\n**Talbe R1: Comparative Analysis of Decoding Features.**\n| Decoding Features|mIoU (%)|\n| -- | -------- |\n| MAMBA-Processed Features       | 34.8     |\n| Original Intermediate-layer Features | **46.2** |\n\n\n---\n\n## Q4:\n The receptive field at point B in Figure 2 contains two types of domains, but line 76 in the text states that they are not included\n\n## A4:\nWe sincerely apologize for the confusion caused by **our inadvertent error**. Thank you for bringing this issue to our attention. We incorrectly reversed the labels of point A and point B in Lines 64 and 76 of our manuscript.\n\nFor clarification, the caption of Figure 2 contains the correct description. We will rectify this error in the subsequent version of our manuscript to ensure consistency throughout the document."}, {"review_id": "mNiWLbTEB9", "reviewer": "Reviewer_6p4o", "summary": "This paper addresses unsupervised domain adaptation (UDA) for LiDAR semantic segmentation by improving upon existing mix-based strategies. The proposed method, BeyondMix, introduces a framework that explicitly models three structural priors: permutation invariance, local consistency, and geometric consistency. These priors are used to preserve intrinsic structure in point cloud data across domains. To enhance the model’s ability to capture long-range dependencies, BeyondMix leverages State Space Models, specifically Mamba, applied to sequentially ordered point cloud representations via space-filling curves. Experiments on SynLiDAR to SemanticKITTI and SemanticPOSS benchmarks show that BeyondMix achieves state-of-the-art cross-domain segmentation performance compared to prior methods.", "questions": "1. What are the runtime and memory overheads introduced by BeyondMix, particularly due to Mamba and the multiple auxiliary losses? \n2. Have you tested or considered BeyondMix under real-to-real domain shifts (e.g., SemanticKITTI → SemanticPOSS)? Would the same priors and Mamba integration apply effectively?\n3. Could you report per-class IoU in the ablation studies? This would help determine whether specific object categories benefit more from certain structural priors.\n4. Could you clarify how Mamba is integrated into your architecture (e.g., at voxel level or raw sequence)? Additionally, how does your use of Mamba compare in motivation and performance to recent long-range modeling methods such as PointTransformer v3? A conceptual and empirical contrast would help clarify the choice.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n1. The paper precisely identifies the limitations of existing mix-based UDA methods for LiDAR segmentation, particularly their underutilization of structural priors and limited receptive fields. It then formulates a method that directly addresses these issues through principled design.\n2. BeyondMix introduces three underexplored structural priors of permutation invariance, local consistency, and geometric consistency formalized as loss functions. These are combined with a state-space sequence model (Mamba) using space-filling curves, enabling long-range context modeling across unordered point clouds.\n3. The method achieves state-of-the-art results on two challenging UDA benchmarks (SynLiDAR → SemanticKITTI and SemanticPOSS), with significant mIoU gains across multiple semantic classes and domains.\n4. The paper includes extensive ablations showing the individual and combined benefits of each structural prior and Mamba integration, supporting the effectiveness and complementarity of its components.\n\n**Weaknesses:**\n1.  The method involves non-trivial additions (Mamba, multiple loss terms), but the paper does not report training/inference time or memory usage, leaving concerns about practical efficiency unaddressed.\n2.   All experiments are from synthetic to real. The paper does not examine real-to-real domain adaptation or more diverse shifts (e.g., different sensor types), which narrows its generalization claims.\n3.  The ablation study reports only overall mIoU, without showing per-class performance. This prevents analysis of which semantic classes benefit from each structural prior.\n4. The main text lacks sufficient discussion of alternative long-range modeling methods, particularly recent transformer-based architectures like PointTransformer v3. These are only briefly mentioned in the appendix. The absence of conceptual or empirical comparison weakens the justification for using Mamba and diminishes clarity on architectural novelty.", "was_revised": true, "final_justification": "The rebuttal has satisfactorily addressed my main concerns regarding computational overhead, real-world domain shift performance, and the rationale for using Mamba. The clarifications, together with the additional per-class ablation results, have resolved my doubts about the effectiveness and generalization ability of the proposed method. I therefore maintain my positive recommendation.", "rebuttal": "Thank you for your thorough review and thoughtful assessment of our manuscript. We appreciate your recognition that our work, BeyondMix, **successfully identifies the fundamental limitations of existing mix-based UDA methods**, provides **comprehensive ablation studies**, and achieves **state-of-the-art performance metrics.** \n\nWe acknowledge your primary concerns regarding the need for further clarification of certain aspects of our methodology. In the following response, we address each of your comments systematically to provide the requested explanations and clarifications. **Please feel free to use the discussion period if you have any additional questions.**\n\n---\n\n## Q1:\nWhat are the runtime and memory overheads introduced by BeyondMix, particularly due to Mamba and the multiple auxiliary losses?\n\n## A1:\nBelow, we provide a comprehensive analysis of computational requirements including GPU memory utilization, per-iteration runtime, and FLOPs for both training and inference phases.\n\nDuring the **training stage**, the incorporation of long-range modeling mechanisms inevitably introduces additional computational overhead. However, this increase remains **relatively modest** due to the **near-linear complexity (approximately O(n))** of our Mamba-based implementation.\n\n**For inference** , our method employs **a standard network architecture without auxiliary modules**, resulting in computational requirements comparable to baseline approaches.\n\nAs demonstrated in Table R1, BeyondMix++ exhibits **identical GPU memory consumption, per-iteration runtime, and FLOPs during inference** compared to baseline methods such as LaserMix and DGT-ST. Notably, our approach achieves substantial performance improvements (+10.2% over LaserMix and +3.1% over DGT-ST) while incurring only **acceptable additional training overhead**, highlighting the favorable efficiency-performance trade-off of our proposed framework.\n\n**Table R1: Quantitative Analysis of Computational Overhead**\n\n| Method | GPU Memory (Train/Infer, GB/GB) | Time per Iteration (Train/Infer, iteration/s, scan/s) | FLOPs (Train/Infer, G/G) |\n|-|-|-|-|\n| **LaserMix** | 17.81/2.5 | 0.92/6.96 | 65.10/32.95 |\n| **DGT-ST** | 14.72/2.5 | 0.95/6.95 | 63.68/32.95 |\n| **BeyondMix++（Ours）** | 22.39/**2.5** | 0.67/**6.95** | 76.84/**32.95** |\n\n---\n\n## Q2:\nAre you tested or considered BeyondMix under real-to-real domain shifts (e.g., SemanticKITTI → SemanticPOSS)? Would the same priors and Mamba integration apply effectively?\n\n## A2: \nIn accordance with established research paradigms [CosMix, PolarMix, LaserMix, DGT-ST], we construct UDA frameworks spanning synthetic-to-real scenarios (Syn→SK, Syn→SP), capitalizing on the availability of synthetic annotations. This virtual-to-real generalization framework aligns more closely with practical deployment scenarios. Furthermore, to substantiate the generalization of our methodology, we present **real-to-real adaptation results (SP→SK)** in Table R2. For **cross-modal sensing evaluation**, we establish an SK (rotating LiDAR with 64 beams)→PGT configuration, leveraging the PandarGT (PGT, a solid-state front-facing LiDAR with 150 beams) from Pandaset. As empirically demonstrated in Table R2, our approach consistently attains state-of-the-art performance metrics. This uniform superiority across synthetic-to-real, real-to-real, and cross-sensor domain adaptation paradigms corroborates the robust generalization capacity of our proposed methodology.\n\n**Table R2: Comparison Results of Other Settings**\n\n|Setting/Methods| **Source only** | **Target only** | **LaserMix** | **DGT-ST** | **BeyondMix++ (Ours)** |\n|-| -|- |-|-|-|\n| SemanticPOSS → SemanticKITTI (SP→SK) |22.5| 60.4| 29.5 | 38.1| **42.0**|\n| SemanticKITTI → PandarGT (SK→PGT) |27.5|78.2| 49.2| 52.5| **60.7**|\n\n---\n\n## Q3:\nCould you report per-class IoU in the ablation studies? This would help determine whether specific object categories benefit more from certain structural priors.\n\n## A3: \nAs requested, we provide a comprehensive per-class performance analysis from our ablation study in Table R3.\n\nUpon incorporating $L_{permutation}$, we observe significant improvements in the \"sidewalk\", \"road\", \"person\", and \"pole\" categories. This enhancement can be attributed to the distinct characteristics of our space-filling curves. The Hilbert curve constructs a continuous path traversing 3D voxels with strong locality preservation, resulting in more comprehensive modeling of relatively small local objects such as \"person\" and \"pole\". Conversely, the Z-curve's horizontal continuity properties offer advantages in modeling planar categories like \"sidewalk\" and \"road\".\n\nWhen $L_{local}$ is introduced, substantial performance gains emerge in the \"car\", \"motorcycle\", \"vegetation\", \"road\", and \"building\" categories. This aligns with our local consistency structural priors, where cylindrical partitioning recognizes that objects proximal to LiDAR sensors typically include \"car\" and \"motorcycle\" instances, while distant points frequently represent \"vegetation\". Additionally, rectangular partitioning effectively preserves local features by leveraging the observation that \"building\" structures typically appear at higher elevations while \"road\" surfaces are situated at lower positions. These experimental results corroborate our theoretical framework.\n\nThe addition of $L_{geometric}$ yields balanced improvements across all categories, indicating that geometric consistency across varying point densities serves as a universal constraint applicable to diverse semantic classes.\n\n**Table R3: Ablation Study of Per-class Performance.**\n\n|Methods|mIoU|car|bi.cle| mt.cle | truck | oth-v. | pers. | bi.clst | mt.clst | road | parki. | sidew. | other-g. | build. | fence | veget. | trunk | terr. | pole | traf. |\n|--|--|-|-|-|-|-|-|-|-|-|-|--|--|-|-|-|--|-|--|-|\n| $BaseLine$ |43.1 |92.9 |17.3|43.4|15.0 |6.1|49.2 |54.2 |4.2|86.4 |19.1 | 62.3 | 0.0 | 78.2 | 9.2 | 83.3 | 56.0 | 59.1 | 51.2 | 32.3 |\n| $+L_{mix}$ |44.1 |92.4 |17.9|42.9| 16.6 |13.5|52.1|53.9|6.6|86.3 |21.5 | 59.9 | 0.0 | 77.9 | 14.4 | 79.8 | 57.5 | 59.7 | 52.4 | 32.6 |\n| $+L_{mix}+L_{permutation}$ |44.5|92.8 |17.5| 44.8 |16.1|10.2 |54.5 | 55.7 | 5.5 | 87.1 | 21.1 | 66.4 | 0.0 | 78.0 | 13.2 | 80.4 | 57.7 | 60.5 | 52.9 | 31.2 |\n| $+L_{mix}+L_{local}$ | 44.7 | 93.9|17.4 |47.2|17.3|10.7|53.6| 55.9|6.7| 87.2 | 20.7 | 65.3 | 0.0 | 79.1| 10.3|80.9| 58.3 | 61.1 | 52.5 | 30.6 |\n| $+L_{mix}+L_{geometric}$ |43.4|92.6|16.9 | 43.1|15.9 |8.8| 49.5| 54.6|5.6| 86.1 | 20.0 | 63.2 |0.0|77.5|9.3|79.9| 57.4| 60.4 | 52.7 | 30.9 |\n| $+L_{mix}+L_{permutation}+L_{local}$ |45.4 | 93.9 |15.1| 46.2 |16.7|13.3| 55.5 | 57.2 | 6.6 |86.5| 24.0| 68.0 |0.0| 78.8| 14.1 | 81.7 | 59.3 | 61.2 | 53.2 | 32.1 |\n| $+L_{mix}+L_{local}+L_{geometric}$ |45.8| 94.4| 15.2 |46.9| 17.1 |15.7| 54.9 | 59.8 | 6.7 | 86.3| 22.4| 67.4 |0.0| 79.2| 13.7 | 82.1 | 60.6 | 62.3 | 53.0 |32.0|\n| $+L_{mix}+L_{permutation}+L_{geometric}$ |45.0|93.7|14.8| 45.5 | 16.9| 15.2 | 54.7 | 57.0 |6.9| 85.9| 22.3 |67.9| 0.0| 78.6 | 11.9 | 80.4 | 60.5 | 59.2 | 52.0 | 31.9 |\n| $+L_{mix}+L_{permutation}+L_{local}+L_{geometric}$ | 46.2 | 94.0 |15.1 | 47.2 | 17.6 | 16.5 |55.2|59.9|6.8 |87.0| 24.1 | 69.3 | 0.0 | 79.3 | 14.7 | 81.8 | 61.0 | 62.8 | 53.3 | 32.1 |\n\n---\n\n## Q4:\nCould you clarify how Mamba is integrated into your architecture (e.g., at voxel level or raw sequence)? Additionally, how does your use of Mamba compare in motivation and performance to recent long-range modeling methods such as PointTransformer v3? A conceptual and empirical contrast would help clarify the choice.\n\n## A4:\nWe appreciate your inquiry and would like to provide a detailed explanation:\n\nTo effectively model long-range dependencies, we deploy Mamba within the feature space generated by the segmentation model's encoder. This feature space offers significant advantages: reduced spatial sizes, higher dimensionality, and semantically enriched representations. By serializing these features and processing them through the Mamba architecture, we achieve alignment between corresponding features from different sequential orderings. This approach **facilitates the encoder's acquisition of structural priors, thereby enhancing segmentation performance in the target domain.**\n\nRegarding your suggestion about **Point Transformer v3 (PTv3), which implements attention mechanisms within locally grouped point cloud sequences**, our analysis reveals that the standard PTv3 implementation possesses a receptive field limited to 1024, which proves insufficient for our application. As demonstrated in line 71 of our manuscript, the minimum requisite receptive field exceeds 1300 (potentially considerably more, contingent upon mixing strategies or scanning methodologies). However, Mamba exhibits an unbounded receptive field, rendering it particularly suitable for modeling long-range dependencies essential to our task domain.  As presented in Table R4, our theoretical assertions are substantiated by quantitative experimental results.\nConcurrently, the Pamba study [1] illustrates in Figure 1 that Mamba's effective receptive field substantially surpasses that of PTv3.\n\nFurthermore, Pamba [1] establishes that \"SSM can process the whole 100,000+ points expeditiously without subdivision and model uncompressed long-range dependencies,\" asserting that \"SSM is more suitable than transformer for extracting long-term dependencies.\" This aligns precisely with our requirements, as each scan in our outdoor LiDAR dataset comprises over 100,000 points. While we experimented with PTv3 (P=2048), the quadratic computational complexity inherent to transformer architectures rendered the processing speed prohibitively inefficient for practical implementation.\n\n[1] Pamba: Enhancing Global Interaction in Point Clouds via State Space Model. AAAI2025\n\n**Table R4: Comparison between Different Long-range Modeling Methods.**\n|Method |mIoU (%)|\n|-| -|\n| PTv3（P=1024）| 45.6|\n| Mamba| **46.2** |"}]

Author rebuttal:

Meta-review: This paper introduces BeyondMix, a novel framework for unsupervised domain adaptation (UDA) in LiDAR semantic segmentation. BeyondMix leverages State Space Models (specifically Mamba) to model long-range dependencies in point cloud data, utilizing space-filling curves for sequential ordering. The method explicitly formalizes and exploits three structural priors—permutation invariance, local consistency, and geometric consistency—that have been underexploited in existing approaches. Extensive experiments on established benchmarks (SynLiDAR → SemanticKITTI and SemanticPOSS) demonstrate significant improvements over previous state-of-the-art methods.

**Strengths**:
- Clearly identifies key limitations of existing mix-based UDA methods and proposes an innovative solution.
- Explicitly models multiple complementary structural priors and integrates them within a unified framework.
- Employs Mamba for effective long-range context modeling, overcoming receptive field constraints.

**Weaknesses**:

- The additional computational complexity and overhead introduced by feature serializations and Mamba integration are only briefly acknowledged.
- Limited experimental analysis of generalization settings beyond synthetic-to-real adaptation (although partially addressed in the rebuttal).

**Rebuttal**:

The authors presented quantitative analysis of training/inference efficiency, showing comparable computational costs at inference with only modest training overhead. Generalization was substantiated through additional experiments on real-to-real and cross-sensor adaptation, with strong results. Architectural choices (Mamba vs. PointTransformer v3) were discussed both conceptually and empirically, reinforcing the design decisions.

**Suggestions for Improvement**:
- Expand empirical evaluation to encompass additional adaptation scenarios and modalities for broader impact.
- Further document computational/resource overhead and clarify efficiency trade-offs.
- Provide more interpretability on structural priors’ class-wise effects and deeper comparative studies against alternative architectures.
Decision: Accept (poster)