Dataset Distillation of 3D Point Clouds via Distribution Matching
Authors: Jae-Young Yim
Dongwook Kim
Jae-Young Sim
Venue: NeurIPS 2025 poster ()
Keywords: Dataset Distillation
Dataset Condensation
Primary area: applications

Abstract: Large-scale datasets are usually required to train deep neural networks; however, they increase computational complexity, hindering practical applications. Recently, dataset distillation for images and texts has attracted considerable attention, as it reduces the original dataset to a small synthetic one to alleviate the computational burden of training while preserving essential task-relevant information. However, dataset distillation for 3D point clouds remains largely unexplored, as point clouds exhibit fundamentally different characteristics from those of images, making this task more challenging. In this paper, we propose a distribution-matching-based distillation framework for 3D point clouds that jointly optimizes the geometric structures and orientations of synthetic 3D objects. To address the semantic misalignment caused by the unordered nature of point clouds, we introduce a Semantically Aligned Distribution Matching (SADM) loss, which is computed on the sorted features within each channel. Moreover, to handle rotational variations, we jointly learn optimal rotation angles while updating the synthetic dataset to better align with the original feature distribution. Extensive experiments on widely used benchmark datasets demonstrate that the proposed method consistently outperforms existing dataset distillation approaches, achieving higher accuracy and strong cross-architecture generalization.

Dataset Distillation of 3D Point Clouds via Distribution Matching
Young Yim', Dongwook Kim and Yau-Young Sim' Ulsan National Institute of Science and Technology (yimjaeo, donguk071, jysim) @unist.... ac kr
Equal contribution
Corresponding author
Abstract
Large-scale datasets are usually required to train deep neural networks; however, they increase computational complexity, hindering practical applications. Recently, dataset distillation for images and texts has attracted considerable attention, as it reduces the original dataset to a small synthetic one to alleviate the computational burden of training while preserving essential task-relevant information. However, dataset distillation for 3D point clouds remains largely unexplored, as point clouds exhibit fundamentally different characteristics from those of images, making this task more challenging. In this paper, propose distribution-matchinn matching-based distillation framework for 3D point clouds that jointly optimizes the geomet- ric structures and orientations of synthetic 3D objects. To address the semantic misalignment caused by the unordered nature of point clouds, we introduce a Semantically Aligned Distribution Matching (SADM) loss, which is computed on the sorted features within each channel. Moreover, to handle rotational variations, we jointly learn optimal rotation angles while updating the synthetic dataset better align with the original feature distribution. Extensive experiments on widely used benchmark datasets demonstrate that the proposed method consistently out- performs existing dataset distillation approaches, achieving higher accuracy and strong cross- arssttcrchee generalization.
Introduction
With the increasing demand for large-scale training datasets, the high cost of retraining models from scratch has become a major challenge, motivating research on dataset distillation [22]. The objective of dataset distillation is to produce significantly smaller synthetic dataset from large original dataset, that preserves the essential task-relevant information contained in the original dataset. Hence the models trained on the reduced synthetic dataset are encouraged to achieve comparable performance to those trained on the original dataset. Existing dataset distillation methods [3] 6 g can be broadly classified into gradient matching. trajectory matching. and distribution matching approaches. The gradient matching and trajectory matching methods aim to ensure that the synthetic dataset produces similar optimization dynamics to the original dataset. To this end, the gradient matching method 300 minimizes the difference between the gradients computed on the synthetic and original datasets. However, it potentially overlooks long- term dependencies in the training process. Rather than comparing individual gradients, the trajectory matching methods 3 6 [ encourage the models trained on the synthetic dataset follow similar optimization trajectories to those trained the original dataset. Note that these methods train the networks while optimizing the synthetic dataset, and significantly increase the computational complexity. To alleviate the computational burden in dataset distillation, the distribution matching techniques 29 31 8 27 have been introduced. The networks are randomly initialized and used
II 30 29 18
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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without training to extract features, after which the feature distributions of the original and synthetic datasets are compared.
While dataset distillation has been extensively studied for structured data such as images 33 3
29
and texts [0] 12 131, its application 3D point clouds remains almost unexplored. PCC
[2 simply
applied an existing distillation method for images [30] to the 3D point clouds without considering in- herent characteristies of 3D point clouds, however still suffers from high computational complexity. Unlike the structured data, 3D point clouds consist of unordered and irregularly distributed points in 3D space. Therefore, semantically similar regions across different 3D models are often associated with inconsistent orders (i.e., point indices), which makes direct feature comparison incorrect, thereby worsening the performance distribution-mall cettiioo--aaccin--bbbae -ased dataset distillation. We refer this issue as semantic misalignment. Moreover, the datasets of 3D point clouds also suffers from rotational variation. 3D point clouds are often captured or synthesized under arbitrary poses due to the absence of canonical orientations. Such rotational differences cause objects of the same class to produce different features, significantly increasing intra-class variability. As a result, it becomes difficult to construct representative synthetic dataset that faithfully follows the feature distribution of the original dataset.
In this paper, we propose an optimization framework combining Semantically Aligned Distribution Matching (SADM) and orientation optimization for dataset distillation of 3D point clouds. A major challenge in this setting is achieving effective feature alignment despite the unordered nature of point clouds and their arbitrary orientations. The SADM loss addresses the issue of misaligned semantic structures by sorting the point-wise feature values within each channel before computing the distance between two feature distributions. parallel, we employ learnable rotation parameters to address the orientation variation by estimating the optimal poses of 3D models while generating the synthetic dataset. By simultaneously enforcing semantic consistency and orientation aligmment, the proposed method achieves superior performance of dataset distillation compared with the existing methods, as demonstrated by extensive experiments on standard 3D point cloud classification benchmarks.
The key contributions of this paper are summarized as follows:
To the best of our knowledge, we are the first to propose distribution matching based dataset distillation method of 3D point clouds, that jointly optimizes the shapes and orienta- tions of synthetic dataset.
We devised the SADM loss, computed on the sorted features within each channel, to preserve semantic alignment between the compared 3D objects.
We validated the proposed method through extensive experiments on the four benchmark datasets widely used for 3D) point clouds classification, and showed the superiority of the proposed method over the existing dataset distillation techniques.
2 Related Works
2.1 3D Point Data Analysis
3D point clouds are generally unordered exhibiting irregular characteristics, that makes it difficult to apply the convolution operations in deep neural networks commonly used for images. To process such data, early studies 226 33 converted point clouds into structured representations, such as multi-view images or voxel grids, enabling the use of standard convolutional neural networks (CNN) architectures. However, these conversions introduce quantization errors and increase memory overhead. PointNet [13] addressed this limitation by directly learning the features from unordered points, which serves as the backbone in our dataset distillation framework. Subsequent methods, such as PointNet++ [16), PointConv [24], and DGCNN (3). extended PointNet by capturing local geometric relationships through hierarchical architecture. Additionally, attempts have been also made to apply the transformer [2]] to 3D point clouds processing, where Point Transformer (22 utilizes the attention mechanism to capture the long-range dependencies. We adopt these architectures as evaluation networks to assess the cross-architecut generalization capability of our distilled datasets.

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Multiplictiion
Sorting Function
PointNict Feature Extractor
Real Daiase!
L
PointNet
Festure
0
Extracior
Synthetic
Semuntically Aligned Distribution Masching
Figure 1: The overall framework the proposed dataset distillation method for 3D point clouds.
2.2 Coreset Selection
Coreset selection is technique designed to select representative samples from a given dataset, while maintaining the model's performance even with the sampled data. The random selection method [T7] randomly chooses subset of data samples from the whole dataset. It is simple but suffers from the robustness due to the lack of informative criteria for sampling. The K-center method [99] selects data samples iteratively that maximize the minimum distance to the set of already selected ones, taking into account the data distribution. The Herding method [ iteratively takes data points that minimize the discrepancy between the mean embeddings of the selected subset and the entire dataset in the feature space. The coreset selection operates within the space of existing samples, and hence lacks the flexibility to synthesize informative patterns. This limitation naturally leads to the emergence dataset distillation, which generates synthetic datasets capturing task-specific patterns beyond the original samples.
2.3 Dataset Distillation
Dataset distillation [22] methods can be largely categorized into the gradient matching 330, trajectory matching 3 6 & III. and distribution matching [29 31
18 27 approaches. The gradient match- ing, first introduced by DC (30), minimizes the difference between the gradients computed from the original and synthetic datasets, respectively, guiding the synthetic dataset to follow the training direction of the original dataset. The trajectory matching methods [ 6
8 I1,, initially proposed by MTT 3 encourage the models trained the synthetic dataset follow the optimization trajectories similar to those trained on the original dataset rather than comparing individual gradients. ATT (I1) automatically adjusts the length of the training trajectories between synthetic and original datasets, enabling more effective and precise matching. The distribution matching, introduced by DM [29). focuses on minimizing the distance between the feature distributions of the original and synthetic datasets. DataDAM (18) enhances the distribution matching by aligning the feature maps using attention mechanism, achieving unbiased feature representation with low computational overhead. Furthermore, M3D [27] employs the Gaussian kernel function in the distribution matching loss, enabling the aligmment across higher-order statistical characteristics of the feature distributions. Re- cently, gradient matching- matching-based point clouds distillation method (28) has been introduced, however simply applied the existing image-based method without considering the unique characteristics of 3D point clouds.
3 Methodology
We propose a novel dataset distillation method for 3D point clouds that first addresses the key challenges semantic misalignment and rotational variation. perform SADM that effectively aligns the features of semantically consistent structures across different 3D models. To handle the rotational variation, we also estimate optimal orientations while generating the synthetic dataset. Figure shows shows the overall framework of the proposed method.

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3.1 Preliminaries
Problem Definition. The objective of dataset distillation is to compress the task-relevant information in the original dataset T = {t,, {t,)]=) and generate a much smaller synthetic dataset S {s: |||
where |8| < [7), such that model trained on S achieves close performance that trained on T. Given 3D point cloud sample following a real data distribution with the corresponding class label
I, the optimal synthetic dataset S" can be obtained via
S' = arg min P (I) - ())
where L. denotes task-specific loss function, such the cross-entropy loss, and or and Φs represent the models to estimate the class label which are trained on T and S, respectively.
Distribution Matching. The distribution matching (DM) strategy focuses aligning the feature distributions derived from the original and synthetic datasets, respectively, via
S arg min (T)(T), ((S)),
s
where ø is the feature extractor and D denotes a distance function. We employ a randomly initialized, untrained network, which has been demonstrated to sufficiently capture the structural information for distribution alignment 22 Also, the Maximum Mean Discrepancy (MMD) loss LMMD is often
used as D, given by
CMDD(T S)
(T, S), K(T, + K(S,)) - (T
(3)
where K(;-)) is kernel function. We used the Gaussian kernel in this work
|lø(t) - <(s)
K(T
(4)
T
2o
RET SES
3.2 Semantically Aligned Distribution Matching
Whereas the pixels of image exhibit well struc- tured spatial relationships with one another and consistently indexed across different images, the points in 3D point clouds are unordered with different indices across different models. Therefore, the conventional distribution match- ing methods cannot be directly applied to 3D point clouds, since the features of semantically similar structures are not aligned between two compared models. Motivated by the importance of preserving semantic correspondence, we in- vestigate the relationship between the feature values and semantic significance in 3D point clouds. We first extracted point-wise features us- ing a randomly initialized network Φ, and sorted
Figure 2: Visualization of the points corresponding to the largest (top), 200th largest (middle), and 500th largest (bottom) features in each channel.
the feature values for each of 1024 channels according to their size. Figure 2 visualizes the points corresponding to the largest (top), 200th largest (middle), and 500th largest (hottom) features, respec- tively. We observe that, consistently capture semantically meaningful regions, such as edges and corners, across different classes. In contrast, the points yielding low-ranked features are distributed around less informative regions. This suggests that the features reflect the relative importance of points in characterizing the structures of 3D objects, and the points with similar orders of sorted features tend capture semantically related regions across different 3D models.
without model training, the points associated with the largest features
In order to preserve the semantic correspondence across different 3D models, propose Semanti- cally Aligned Distribution Matching (SADM) loss. Specifically, given a 3D point cloud object we extract the features using via
f11
f2,1
fcr
f1,2
f2.2
fcz
x(p)
f.
fol.
f F
(5)
fi,
f2.N
fc.

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where N denotes the number of points in P. C' is the number of feature channels, and f, ff fi.v) represents the feature vector of the i-th channel where fi, the feature value of the j-th point. We then perform channel-wise sorting to the extracted features of Si ' in the descending order of their values, and obtain the sorted feature vector f; = fu.1 fr.,, fi.N such that fin 2 fist1- Then we have the set of the sorted feature vectors
x(p) F.. fg... ....,,,....... fr......ffc.. F.E.V.
(6)
Note that t in the original dataset T and s in the synthetic dataset 8 exhibit different orders of points in general, and therefore the features in o(t) and ((s) are inconsistently aligned with each other worsening the desired behavior of comparison in (3). On the contrary, the sorted features @(t) and ((s) exhibit consistent ordering of features in each channel reflecting their relative semantic importance, and thus facilitates reliable feature comparison across different 3D objects. To measure the discrepancy between the sorted features, we redefine the Gaussian kernel as
(T.,)) T
1
Σ LET BES
[Iā(t) x(s) 2x
exp
S
Then we devise the loss La from LMMD
33) given by
LT K(T +
(5,8)-2K(7) - (T.
(8)
We additionally employ La to boost the role of the most significant feature in each channel, defined as
Ca Kmp (T, T) + ( S) 2 I (T,S),
where (: denotes the Gaussian kernel computed with only the largest feature in each channel. The SADM loss is then formulated weighted sum of the losses, given by
CSADM(T (T, AI ST + A2
(10)
where Å1 A2 are the weighting parameters. By using LSADM instead of LVMD. we facilitate reli- able matching of feature distributions considering semantic structures of 3D point clouds, thereby improving the performance dataset distillation.
3.3 Estimation of Optimal Rotations
3D objects usually exhibit different orientations from each other. Therefore, while generating optimal 3D objects in the synthetic dataset in terms of their geometric shapes, we also estimate their optimal rotations best representing various orientations of 3D objects in the original dataset. In practice, we introduce three rotation angles, 0z. fy. and 0z. corresponding to rotations around the ær, }-, and z-axes, respectively. These angles are treated as learnable parameters, allowing the orientation of each synthetic 3D object in S be adaptively adjusted during dataset distillation. Therefore, instead of minimizing LSADM S) in (10), we minimize LSADM (T, Ro (S)), where RRo denotes the rotation operator according to the rotation parameters = =0z, 0g 0z). The overall objective is formally defined as
(S",0") = arg min LSADM (T, Ro(S)) (5.0)
(11)
Note that we optimize the synthetic 31) objects as well as their rotation parameters simultaneously. during the dataset distillation process. Specifically, at each iteration, we randomly initialize the network parameters and construct the synthetic dataset S by randomly selecting samples from the original dataset. We then form (S) by rotating the objects in S according to the angles 0_. 0y. and 82, initially set to zero. For each class, a mini-batch is sampled from T, with a batch size of 8 per class. The corresponding synthetic mini-batch is sampled from Re(S), with the batch size determined by the number of point cloud objects per class (PPC). The joint optimization process iteratively updates both the geometric structure of the synthetic dataset and their rotation parameters by minimizing LSADM(? (T. Ro(S)) This ensures that the synthetic dataset preserves the geometric characteristics of the original dataset while aligning their orientations more effectively. The benefit of this joint optimization is justified in the following proposition.
5

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Table I: Comparison of quantitative performance. DC, DM, and the proposed method were initialized with random selection [17] for fair comparison. 'Whole' refers to the classification accuracy obtained by training the network on the entire original dataset without any distillation. 'Ratio' represents the percentage of the size of the distilled dataset compared to that of the original dataset. The best and the second best scores are highlighted in bold and underlined, respectively.
Datasets
Mode 65
ModdNNe400 25
ShapeNet
SeamOhjerNN
Xi
PPC
10
10
10
3
10
Ratio (%)
0.25
0.15
0:45
0.15
0:45
1.5
Whole
87,84
Random
35.5+4.7
75.2+1.7
853++11
346+18
60.0+133
74.1+0.4
34.0+3.0
54.8-1.5
631++.0
13.9+14
304+1.3
14.8-1.1
Herding
40:1 15.2
28.0 11.3
86.100
12.
68.5 11.0
28.8 10.4
19.5 12.3
59.8 10..
66.9 10.5
15.7 11.7
22.2 11.4
15.2 L.7
K-eenter
40.1 =5.2
774
83221.4
$4.4220
63.0 #2.7
05.3 #1.1
49.5 +2.8
5144
47.8 +11.7
15.7 #1.7
19.8 40.8
24.0 =1.0
DM
31.9513
774+16
8.1+08
32,3+4.8
62,0+1.9
75.2+0.5
27.8+1.
56.1=12
64.3+0.7
14.9+20
23.3+11.5
35.4=14
DC
43.935.5
75002.4
86.13111
52.011.7
66.6.11.
75.6.10.5
49,8:13
80.1:144
64.6.0077
186:1.
24.3:125
35.3-1.2
Ours
44.7 16.1
$4.4 11.
87.8 11.0
558 11.
72,1 108
80,1
50.2 11.4
63.7 10.7
68.4 10.5
17.4 11.5
3.6 11.
43,9 119
Table 2: Comparison of cross-architecture generalization performance evaluated on PointNet++ [16] DGCNN (23], PointConv [24], and PT (32), respectively.
Datasets
ModelNeti0 M
MudelNeit0 [6
ShapeNet 1]
StunObjeccNN
20
Method
DM
DC
Ours
DM
DC
Ours
DM
DC
Ours
DM
DC
Ours
PointNeta
35.028.3
515=78
82.9-14
14.1227
469eG0
68.5=0.5
20.3+1.7
3433-34
532+1.5
11.6=222
22.0=3.9
DGCNN
$6.645.3
626+22
79.0-22
348+33
523-22
66.9-11
138+22
380+27
528-166
137424
12:5=13
19.0-1.5
PointCony
334+62
20.0+005
5666-49
200+577
370+39
51.3-6,2
17.4+30
340+48
47.++2.
152+1.7
142++18
168--15
PT
485166
518116
776616
26.715.0
475.27
616.1.1
342155
426125
555105
17.
14910.
219.2.
Proposition 1. Jointly optimizing the synthetic dataset S and the rotation parameters 0 guarantees lower or equal loss to that of optimizing S alone.
min (SADM(T, Ro(S)) < min CSADM(T, (8.0)
(12)
where Ro denotes the rotation operator according to O.
Proof Sketch. The proof is provided in Appendix A. Jointly optimizing S and I enlarges the feasible set, as the original optimization over S alone is special case of the joint optimization with fixed (0.,, 0y 02) (0,0,0) 0).
4 Experimental Results
4.1 Experimental Setup
The proposed method was evaluated on the ModelNet10 25
ModelNet40 25], ShapeNet 4 and ScanObjectNN (20] datasets. The ModelNet10, ModelNet40, and ShapeNet are synthetic datasets generated from CAD models, containing 10, 40, and 55 classes, respectively. The ScanObjectNN consists of real-world scanned objects from 15 classes. Following previous methods [30 22), we measure the classification accuracy trained on the distilled synthetic dataset. We ensure the fairness by training the network 10 times and report the mean and standard deviation of accuracy. We evaluate the performance across different PPC values of 1, 3, and 10. Fach point cloud object contains 1 1,024 points, which is a common standard used in the 3D point clouds classification tasks [15] 16]. The dataset distillation process for the synthetic dataset was optimized for 1,500 iterations, where the performance was evaluated at every 250 iterations by training the PointNet on the synthetic dataset and testing it on the original test dataset.
4.2 Performance Comparison
4.2.1
Dataset Distillation
We compare the performance of the proposed method with that of 1) the three most representative
coreset selection methods: random selection [77, Herding 2 and K-Center [19] 2) two existing
image dataset distillation methods of DC 30 and DM 29 Table [ compares the quantitative
performance of the proposed method with that of the existing methods. DM and DC were initialized
with random selection. The synthetic datasets were optimized using PointNet [15), and classification

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Table 3: Comparison of cross-dataset gen- eralization performance at the PPC value of 3, where the models are trained on a subset of ModelNet40 and evaluated on a subset of ShapeNet, and vice versa.
Table 4: Performance comparison across different initialization strategies. The accuracies for PPC val-
ues of I, 3. and 10 are averaged. MN10: Model- Ner10. MN40: ModelNet4O. SN: ShapeNet. SONN: ScanObjectNN.
Setting
DC
DM
PCC
Ours
Init
Method
MN10
MN40
SN
SONN
SN + MN40
54.43
49.66
57.43
61.54
DC
18.77
6.05
5.24
12.73
MN40 - SN
53.75
47.35
49.42
54.40
Noise
DM
26.53
12.04
12.09
13.55
Ours
70.69
65.25
58.44
29.03
DC
68.32
64.71
58.15
26.07
Table 5: Comparison of training times (in hours) required for dataset distillation at the PPC value of 3.
Random
DM
65.17
56,50
49.39
24.57
Ours
72.48
69.31
60.76
31.01
DC
69.57
61.85
42.88
21.65
K-center
DM
63.04
49.93
44.82
21.59
Method
MN10
MN40
SN
SONN
Ours
72.72
68.20
60.70
28.25
DC
71.50
66.79
59.23
26.98
DC DM
1.52
5.43
7.57
2.19
Herding
DM
64.76
59.16
52.61
27.58
0.04
0.11
0.15
0.05
Ours
72.93
69.67
62.25
31.08
Ours
0.08
0.26
0.35
0.11
f DC 30 with Herding initialization corresponds to PCC
PX
performance was evaluated PointNet demonstrate their validity. Among the coreset selection methods, Herding achieves the best overall performance. When PPC is set to I, Herding and K-Center yield identical results since K-Center selects the first data point using the same algorithm Herding. As PPC increases, Herding consistently outperforms other coreset selection methods, showing its effectiveness. However, because coreset selection methods rely solely on sample selection without further optimization, they struggle to capture complex feature distributions. The features used in DM are extracted from the layer before the classifier, and they discard substantial information through the global max pooling process of PointNet. This information loss weakens the effectiveness of the distribution matching, preventing DM from accurately capturing the feature distribution of the original dataset. DC, on the other hand, aims to match the gradients of the network. However, PointNet is significantly larger than typical networks to precisely align the gradients. As result, it consistently underperforms compared to the proposed method. The proposed method outperforms both coreset selection and existing distillation techniques. When the PPC is small, accurately capturing the original distribution is challenging, leading less noticeable improvement. As the PPC increases, the proposed method more effectively matches the feature distributions significantly improving the performance.
magee-base distillation tasks, making it difficult for DC
4.2.2 AresttArchetecture Generalization
We also present the cross-architecture generalization performance in Table 2 where the synthetic dataset is optimized using PointNet [15] and evaluated on different backbone networks including PointNet++ 16). DGCNN 23), PointConv 24,, and PT (32,, respectively. Unlike PointNet, the architectures used for generalization performance comparison follow hierarchical structure similar to CNN-based networks in image processing, exhibiting significantly different characteristies from those of PointNet. This difference makes it essential for the distilled dataset to retain rich and transferable features that generalize well toward different architectures. Due to significant information loss caused by the pooling operation, DM primarily captures the features specific the PointNet, failing to preserve the original feature distribution. Consequently, the synthetic dataset lacks diverse structural details, resulting poor generalization performance, particularly on hierarchical models. DC, while performing better than DM, also suffers from key limitations. It matches the gradients obtained from trained PointNet, the synthetic dataset becomes overfitted that specific architecture and fails to generalize toward other networks. Consequently, the generalization ability of DC degrades when applied to other architectures. In contrary, the proposed method addresses these limitations by directly matching the feature distributions extracted from randomly initialized network. By comparing feature maps containing richer and less architetture-biased information, the synthetic dataset captures the features relevant to the PointNet while following the original data distribution more closely. Wherease DC suffers from the overfitting and DM loses critical information, the proposed method yields higher adaptability showing strong generalization performance across various backbone networks.
7

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Table 6: Performance comparison between DM and the proposed method at the PPC value of 3, where the proposed method was trained during the same time as DM.
Table 7: Ablation study of the proposed semantic alignment (SA) method. Experiments were per- formed at the PPC value of 3.
Method
MN10
MN40
SN
SONN
Method
MN10
MN40
SN
SONN
Random
75.17
59.96
54.84
20.42
DM
77.58
62.04
56.14 14
23.33
w/o SA
75.01
59.96
53.91
20.20
Ours
83.64
70.56
63.34
33.06
w/ SA
84.42
72.08
63.74
31.84
4.2.3
Cross-Datased Generalization
To further evaluate the generalization capability of the distilled datasets across different domains, provide an experimental result of cross-dataset experiment in Table 3 Specifically, we constructed the subsets of ShapeNet and ModelNet40, respectively, by selecting the 16 object classes shared between them. Then we performed the experiments in which the dataset was distilled on the subset of ShapeNet and tested on ModelNet40 (SN + MN40), and vice versa (MN40 - SN). As shown in Table 3 the proposed method consistently achieves the best performance in both settings of the cross-dataset evaluation, indicating that our distilled datasets effectively capture geometric patterns that are useful regardless of the datasets.
4.2.4 Initialization Strategies
Table 4 presents the classification performance of DC [30]. DM
29 and PCC 28 under different
initialization strategies, including uniform noise, random selection 17 Herding [2] D1 and K-
Center [9] Note that the results for PCC are obtained using our implementation, where PCC is equivalent to performing DC with Herding initialization. When initialized with noise, DC fails to effectively optimize the synthetic dataset because the network has far more parameters than typical networks used for image dataset distillation, making it difficult to align the gradients. Therefore, the original dataset cannot properly guide the training process, leading to poor convergence. In contrast, the structured initializations such as random selection, Herding, or K-Center improve the performance, where the Herding performs the best by selecting the most representative samples. Unlike DC, DM directly matches feature representations rather than relying gradients, making it less sensitive to initialization strategies. However, due to information loss, DM consistently underperforms DC, even when structured initializations used. In contrast, the proposed method achieves favorable performance even when initialized from uniform noise. Furthermore, significantly outperforms other approaches under heuristic initialization strategies, such random selection. These results demonstrate that the proposed method is robust across diverse initialization schemes and effectively addresses the instability issues inherent in existing dataset distillation methods.
4.2.5 Training Time
Table/]comppare the training times between the proposed method and the existing methods. DM 29 achieves the fastest training time it uses only small subset of the overall features, however often ignores many useful features leading to performance degradation. In contrast, DC (30) incurs a significantly higher computational cost as it aligns the gradients across the parameters. Notably, for the largest dataset of ShapeNet 44. DC requires over 7 hours for training 50 times slower that DM that completes the training in just minutes (0.15 15 hours). Since the proposed method is based on the distribution matching approach, its training time is marginally increased compared to DM, yet achieves significant improvement in dataset distillation performance. To further justify the computational overhead, we conducted an experiment where DM was trained with its default setting, whereas the proposed method was trained during the same training time DM. As shown in Table 6 even under the same training time condition, our method consistently outperforms DM.
4.2.6 Qualitative Comparison Synthetic Datasets
Figure compares the resulting synthetic datasets distilled by using the proposed method and the existing methods, respectively. The first row shows the original datasets and the second row shows initialized point cloud objects. DC 30 fails deviate significantly from the initialized objects and
causes noise. Similarly, DM [29 also maintains the original shape of the initialized objects while
8

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Airplane
Bathrub
Bed
Car
Guitar
Keyboard
Lamp
Monitor
Figure 3: Comparison of synthetic datasets distilled from the ModelNet40 225 dataset. Point clouds were colorized according to the y-coordinates. From top to bottom, the orginal dataset (first), initialized point cloud models (second), and the distilled synthetic datasets by using DC [30] (third), DM (29] (fourth), and the proposed method (fifth).
shifting certain points only, that hinders to capture meaningful structural changes. In contrast, as shown the bottom row, the proposed method successfully preserves the overall semantic structures of 3D objects in each class, while selectively learning essential features. For example, in the airplane class, we observe significant changes in the edges and corners, that are critical for class discrimination, especially around the wings. Also, in the guitar class, the proposed method jointly optimizes the shape and orientation of the synthesized 3D objects.
4.3
Ablation Study
4.3.1
Effeet of SADM Loss
Table presents an ablation study on the impact of the proposed SADM loss on classification performance using PointNet [15]. Without preserving semantic aligmment, the unordered nature of point clouds restricts effective feature matching, resulting performance nearly identical to that of random selection [17]. This indicates that the model has not been properly optimized. In contrast, when semantic alignment applied, accuracy improves across all datasets, the aligned features provide a consistent and structured representation that facilitates more effective feature matching during optimization. These results confirm that preserving inherent semantic alignment via feature sorting enables the network to exploit well-aligned corresponding features, significantly enhancing classification performance.
4.3.2 Effeet of Optimal Rotation Estimation
the ablation study evaluate the impact of joint optimization of synthetic dataset and rotation angles. We categorized the test datsets into the aligned, mixed, and rotated groups to analyze the effectiveness of the proposed rotation estimation. The aligned group consists of the datasets where the objects maintain consistent orientations, including ModelNet10 and ShapeNet [4. The mixed group includes ModelNet40 25 where only certain classes exhibit rotation variations. The rotated group is ScanObjectNN 20 where the objects exhibit arbitrary rotations across all classes. The baseline (first row) shows the performance without optimization which identical to that the random selection. In the second row, we present the results where only the orientation of the synthetic data optimized using the proposed SADM loss, without updating the synthetic dataset. This leads to performance improvements across all the groups compared to random selection. The improvement

---

Table 8: Ablation study of the proposed optimal rotation estimation. Experiments were performed at the PPC value of 3.
Table 9: Performance comparison of different point sort- ing schemes at the PPC value 3. For fair comparison, the rotation parameter optimization not applied.
S
0
Aligned
Mixed
Rotated
Method
MN10
MN40
SN
SONN
65.01
59.96
20,42
Unsorted
75.21
59.96
53.91
20.20
66.22
62.17
24.89
Axis-Aligned
76.44
60.85
53.97
21.80
73.96
71.51
29.72
Z-order [14]
76.55
61.47
55.17
21.76
/
7
74.35
72.08
31.84
SADM 83.17
67.52
60.71
27.66
becomes more significant as the classes with rotation variation become more dominant. Optimizing the synthetic dataset further boosts the performance, with the best results achieved when both the synthetic data and rotation angles are optimized simultaneously. In particular, the accuracy on the rotated dataset improves significantly, demonstrating that the proposed joint optimization enables the model to be resilient to rotation variations.
4.3.3 Effect of Point Sorting
We compared the performance of the proposed SADM against two representative point sorting schemes. The axis-aligned sorting method simply orders the points in the ascending order of their z-coordinates, without considering any structural or semantic relationships. The Z-order sorting method [4] assigns an index to each point based on its 3D coordinates simultaneously, ensuring that points close in space receive nearby indices. As shown in Table | only marginal improvements over the baseline that does not use point sorting. Moreover, they fail to provide consistent semantic alignment across different samples. In contrast, the proposed SADM significantly outperforms these methods by achieving semantically consistent matching, thereby enhancing the effectiveness of dataset distillation for 3D point clouds.
the existing sorting methods yield
4.4 Limitation
While the proposed SADM loss enhances the semantic consistency by sorting the features, it does not completely align semantically meaningful regions across different point cloud objects. Estimating optimal rotations also increases the complexity, particularly when the datasets are already well-aligned to the canonical axes.
5 Conclusion
We proposed a semantically aligned and diientation-awae dataset distillation framework for 3D point clouds. To address the inconsistency in point ordering between compared 3D objects, devised Semantically Aligned Distribution Matching (SADM) loss that compares sorted features within each channel. Additionally, we introduced learnable rotation angle parameters estimate the optimal orientation of synthetic objects. The geometric structures and orientations of the synthetic objects are jointly optimized during dataset distillation. Experimental results four widely used benchmark Madasetss-ModeNNelll (25), ModelNet40 (25). ShapeNet [4) and ScanObjectNN [20] 2e)-dnmonttraae that the proposed method outperforms existing distillation approaches while maintaining strong cross-architecture generalization. Furthermore, the effectiveness of each component is validated through extensive ablation studies.
Acknowledgement
This work was supported in part by the National Research Foundation of Korea (NRF) Grant funded by Korea Govermment [Ministry of Science and ICT (MSIT)) under Grant RS-2004-00392533 in part by the Institute of Information and Communications Technology Planning and Evaluation (IITP) Grant funded by Korea Government (MSIT) (Leading Generative Human Resources Development) under Grant UTTP-2025-R- 20P-2022-RRS-2224403366607 00022024-00360022; in part by the Artificial Intelligence Gradate School Program, Ulsan National Institute of Science of Technology, under Grant 25--2000011003355 and in part by the Artificial Intelligence Innovation Hub under Grant RS 2222002-1122222
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Appendix
A Proof of Proposition
Proposition 1. Jointly optimizing the synthetic dataset S and the rotation parameters 0 = (92, fg. 0z)
guarantees a lower or equal loss to that of optimizing S alone.
min , RR(S)) - min LSAUM( (8.0)
(13)
where Rg denotes the rotation operator according O.
Proof. Let us consider two optimization objectives. The first the baseline optimization, which optimizes only the synthetic dataset without applying any rotation
L == min SSADM (T, S)
(14)
The second the proposed joint optimization over both the synthetic dataset S and the rotation parameters 0 (fz, By. 0z), given
L min LSADM (T, Ro(S)). {S.0)
(15)
Consider a special case of the proposed joint optimization framework where no rotation applied, i... the rotation parameters are fixed to 0 (0, O, 0). In such a case, Rg(S) S. and the baseline optimization can be regarded as a special case of the proposed joint optimization. This implies that the feasible set of the baseline optimization is subset of that of the joint optimization such that
{S 0) 0 (0, 0)) S {(S, 0)).
(16)
The joint optimization is performed over larger feasible set than that of the baseline optimization, and therefore its optimal solution must not higher than that of the baseline. Therefore,
S L.
(17)
B Expeimental Details
Datasets. Table 10 summarizes the number of training and testing samples for ModelNet10 (25). ModelNet40 251 ShapeNet 41, and ScanObjectNN 20].
ModelNet10 consists of 10 categories of aligned 3D CAD models. There is rotational variation.
ModelNet40 includes 40 categories from the same source ModelNet10, with partially misaligned instances introducing moderate rotational variation.
ShapeNet contains 55 categories of manually aligned 3D models without rotational varia- tion.
ScanObjectNN consists of 15 categories from real-world RGB-D scans with background clutter, occlusion, and sensor noise. Objects are unaligned, and rotation variation is inherent. We use the rotation, and scaling.
RS split, which includes perturbed background, translation jitter,
Table 10: Train/test statistics for ModelNet10, ModelNet40, ShapeNet and ScanObjectNN,
ModelNet10
ModelNet40
ShapeNet
ScanObjectNN
of training samples
3991
9843
35708
11416
# of test samples of classes
908
2468
10261
2882
10
40
55
15
# of points for each sample
1024
1024
1024
1024
Network Architecture. We evaluate our method on five representative posnt-based architectures:
PointNet [15), PointNet++ [16), DGCNN (23), PointConv (24, and Point Transformer [32].
20

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PointNet is a widely used neural network designed for processing 3D point clouds. We use PointNet as the backbone dataset distillation model. While the original PointNet includes two transformation modules for aligning input and features, we only use the input transformation module. The rest of the architecture follows the standard PointNet design.
PointNet++ is used for cross-architecture evaluation. To reduce computational cost and accelerate training, we decrease the width of all MLP layers by half, while keeping the overall structure unchanged. We use
abstraction modules with multi-scale grouping and one with single-scale grouping to extract point features, followed by two linear layers and final classifier for prediction.
DGCNN employs dynamic graph construction and EdgeConv layers to capture local ge- ometric relationships by recomputing a k-NN graph (k = 20) at each layer in the feature space. We use the default architecture, which consists of four EdgeConv layers followed by two linear layers and a final classifier.
PointConv extends convolution to point clouds by accounting for non-uniform point densi- ties during feature learning. The architecture consists of three density- awarre set abstraction layers, followed by two linear layers and a final classifier.
Point Transformer applies self- self-attention mechanisms point clouds capture both local and global dependencies. We use the default configuration with four transformer blocks, followed by linear layers and final classifier.
Implementation Details. We optimized the synthetic dataset S using stochastic gradient descent (SGD) with a learning rate 0.01, a momentum 0.5, a weight decay of 0, and a batch size of per class sampled from the original dataset T, while the batch size of the synthetic dataset was set equal to the number of synthetic samples per class (PPC). The synthetic dataset optimization was performed for 1,500 iterations, and the corresponding configuration is summarized in Table ITa To preserve fine- mne-grained geometric details, the SADM loss was computed using the feature maps before the max pooling layer. Additionally, secondary loss term was applied to the top-1 sorted feature values in each channel to emphasize semantically dominant regions. The loss weights a1 and X2 were determined based PPC, and set to 0.002, 0.006, and 0.02 for λ1, and 0.001, 0.003, and 0.01 for A when PPC was 1, 3, and 10, respectively.
The rotation parameters 0 (O.., Oy. 0z) were jointly optimized with the synthetic dataset using SGD with a momentum 0.5 and weight decay of O. The learning rates were set to 0.5 for 0, and 0z. and 5.0 for yy. reflecting that the samples in datasets are vertically aligned. A step decay scheduler was used with a step size of 100 and a decay factor of 0.5. This setup is detailed in Table [Tb]
For evaluation, we trained all backbone networks including PointNet, PointNet++, DGCNN, Point- Cony, and Point Transformer using SGD with a learning rate of 0.01, a momentum of 0.9, and weight decay of 0.0005. A step decay scheduler was applied with step size of 250 and a decay factor of 0.1. Each model was trained for 500 epochs with batch size of 8. These test-time settings are listed in Table [[c
All experiments were conducted single NVIDIA GeForce RTX 3090 GPU.
Table Hyperparameter settings used for (a) optimizing the synthetic dataset, (b) optimizing the rotation parameters, and (c) evaluation network.
Hyperparameters
PPC1
PPC3
PPC10
Hyperparameters
Hyperparameters
Optimizer
SGD
SGD
SGD
Optimizer
SGD
Optimizer
SGD
Momentum
0.5
0.5
Momentum
0.5
Momentum
Weight Decay
0.0
Weight Decay
0.0
Weight Decay
0.0005
Learning Rate
0.01
0.01
0.01
Learning (0x)
0.5
Leaming Rate
Iteration
Leamning Rate (6,)
5.0
Epochs
500
Learning Rate (8
0.5
Batch Size
A
0.002
0.006
0.02
0.001
0.003
0.01
Scheduler
StepLR
Scheduler
StepLR
Step Size
Step Size
Batch Size (7)
Gamma
0.5
Gamma
0.1
(a)
(b)
(c)
21

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Figure 4:
Visualization of synthetic samples of ModelNet40 [25 at PPC 1, obtained by using the random selection (top), DataDAM (middle)) and MTT 3 (bottom).
Baselines, All baseline methods were implemented on 3D point clouds using PointNet as the feature extractor, following their original designs. All methods were trained for 1,500 iterations using batch size of 8 per class from the original dataset T, and the training configurations are summarized in Table 12 Details for each method are as follows
We followed the original framework and performed gradient matching. The number of inner and outer loop steps were set to 1/1/10 and 1/5/3 for PPC values of 1, 3, and 10, respectively
DC [30]:
DM [29]: Following the original setup, we used the feature vector obtained before the final classifier to compute the matching loss between the original and synthetic datasets.
MTT 3 We followed the original framework for trajectory matching, with modifications only in the hyperparameter settings.
DataDAM [8]
We followed the original framework for feature matching, making only minor adjustments to hyperparameters.
Table 12: Hyperparameter settings of the basclines.
DC
DM
MTT
DataDAM
Mode
PointNet
PointNet
PointNet
PointNet
Learning Rate
0.0001
0.0001
0.0001
Batch Size (T)
8
8
8
Iteration
1500
1500
1500
1500
Inner Loop
1/1/10
Outer Loop
1 1/5/3
C Comparison with Additional Baselines
Table presents the additional comparison results of the classification accuracy with DataDAM [88 and MTT 33 For DataDAM and MTT, used possible learning rate prevent divergence on the synthetic datasets. The performance of both DataDAM and MTT is almost similar to that of random selection [17), shown in the second and third rows in Figure 4 where points remain nearly unchanged from their random initialization in the first row.
D Additional Ablation Studies
To further support the effectiveness of the proposed rotation optimization method, we compared widely used rotation augmentation that applies random rotations to the training data to address the
22

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Table 13: Classification accuracy of the proposed method compared with DataDAM 18 and MTT initialized with randomly selected samples.
Datasets
ModelNet10
ModelNet40
ShapeNet
ScanObjeetNN
PPC
1
10
3
10
3
10
MTT
28.95
76.73
85.19
34.42
59.81
73.88
33,90
52.92
62.73
13.94
20.28
34.07
DataDAM
40.51
76.60
86.56
34.54
60.37
74.94
35.70
54.56
63.64
16.29
20.51
35.45
Ours
44.70
84.96
87.79
55.80
72.08
80.07
50.20
63.74
68.35
17.29
31.84
43,91
rotation variation of 3D point clouds. While this strategy is effective when dealing with datasets showing severe rotational variations, such as ScanObjectNN, it does not achieve good performance on datasets where the 3D objects are fully partially aligned, such ModelNet10, ShapeNet, and ModelNet40, As shown in Table [4, the proposed learnable rotation estimation method consistently improves the performance across all datasets, however, the random rotation augmentation introduces unnecessary variation in already aligned datasets, degrading the performance. This highlights the benefit of explicitly modeling the orientation via optimization over the naive augmentation.
Table 14: Performance comparison between the proposed rotation optimization and the random rotation augmentation (Aug.). All experiments conducted PPC 3.
Prop.
Aug.
Aligned
Mixed
Rotated
65.01
59.96
20.42
7
58.92
52.56
31.42
7
74.35
72.08
31.84
E
Additional Qualitative Results
Figure shows randomly sampled 3D models from ModelNer40. Figures 6 7 and visualize the synthesized models at PPC 1 obtained by using DC, DM, and the proposed method, respectively. While DC and DM maintain the geometric shapes of the original data with only slight movement of some points, the proposed method generates noise-free samples with high visual quality across all classes.
Figure compares the optimization process for DM and the proposed method. DM fails to converge even after multiple training iterations, however the proposed method progressively refines the point cloud models into more structured shapes.
Figure 10 shows the results of the proposed method on ModelNet40 at different PPC values: 1, 3, and 10. As PPC increases, the distilled synthetic datasets exhibit more diverse shapes and orientations. In particular, as shown in the last row, the human class appears diverse poses. Additional qualitative results of the proposed method the ShapeNet and ScanObjectNN datasets can be found in Figures and 12 respectively.
23

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Figure Randomly sampled 3D) models of all classes from ModelNet40 25
Figure 6: The synthetic dataset distilled from Mede by using DC at PPC 1.
24

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Figure 7: The synthetic dataset distilled from ModelNer40 by using DM PPC 1.
Figure 8: The synthetic dataset distilled from ModelNet40 by using the proposed method at PPC 1.
25

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(a)
Itraavo
(b)
Figure 9: Optimization process in the ModelNet40 at PPC initialized from uniform noise, distilled
by using (a) DM [29] and (b) the proposed method.
(a) PPC1
(b) PPC3
(c) PPC10
Figure 10: The synthetic dataset distilled from ModelNet40 by using the proposed method at three PPC values of 1, 3, and 10, respectively.
26

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Figure 11: The synthetic dataset distilled from ShapeNet by using the proposed method at PPC 1.
Figure 12: The synthetic dataset distilled from ScanObjectNN by using the proposed method at PPC
27


Reviews:
[{"review_id": "3UCw4bcWfq", "reviewer": "Reviewer_66sg", "summary": "This paper presents a distribution matching-based dataset distillation framework for 3D point clouds that introduces two key components: (1) a Semantically Aligned Distribution Matching (SADM) module to address misaligned semantic structures, where semantically similar regions across different 3D models are often associated with inconsistent point orders; (2) learnable rotation parameters (three rotation angles around the x, y, and z axes)  to estimate optimal orientations for synthetic data generation, which account for intra-class variability caused by different acquisition poses due to the absence of canonical orientation. SADM solves the optimization problem of aligning the feature distributions derived from the original and synthetic datasets by minimizing the SADM loss between features extracted by a randomly initialized, untrained network.  The authors conducted extensive experiments on four benchmark datasets to evaluate their framework, showing that the proposed method outperforms existing distillation approaches while maintaining strong cross-architecture generalization. Additionally, an ablation study was conducted to assess the effectiveness of the simultaneous optimization of both the geometric structure (semantic distribution matching) and the orientation of objects in the distilled dataset.", "questions": "- Did the authors consider using the Kullback-Leibler divergence instead of the Gaussian kernel to measure the discrepancy between the sorted features?\n- Regarding the guitar class (lines 306–307), why do the authors claim that the proposed method jointly optimizes the shape and orientation of the synthesized 3D objects? In my opinion, the qualitative results for this class are not very convincing.\n\nAs reported under weaknesses,\n- Lines 162-169: What does the feature channel in ϕ(p) (p) represent?\n- Lines 185-192: How are the rotation angles learned?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths \n- Quality and Originality. The authors’ claims regarding the effectiveness of their dataset distillation method in addressing key limitations of existing approaches, namely, semantic misalignment and rotational variations, are well supported by the experimental results. The joint optimization of the data distillation process, which minimizes the SADM loss and incorporates learnable rotation angles, is a novel contribution to 3D point cloud dataset distillation.\n- Significance. This framework has the potential to impact the research in 3D computer vision since 3D point clouds are widely used in autonomous cars, in environmental monitoring (forest, costal erosion), and in industrial applications. \n\nWeaknesses\n- Clarity. Although the paper is generally well-structured and well-written, the following parts are not clear to me:\n  - Lines 162-169: What does the feature channel in ϕ(p) (p) represent?\n  - Lines 185-192: How are the rotation angles learned?", "was_revised": true, "final_justification": "The authors have addressed my concerns, so I'd like to raise my score to 5.", "rebuttal": "We thank the reviewer to recognize the originality and significance of our paper. We respond to the reviewer's comments as follows.\n\n**Q1: Feature channel**\n\nFor the $j$-th point ${\\\\bf p}\\_j \\in  \\\\mathbb{R}^{3}$ in a 3D point cloud object, a feature vector of $C$ features, \n$\\\\phi({\\\\bf p}\\_j) = \\\\{ f\\_{1,j}, f\\_{2,j}, \\\\cdots, f\\_{C,j} \\\\} \\\\in \\\\mathbb{R}^{C}$, is obtained by applying a randomly initialized feature extractor $\\\\phi$. Hence we have $C$ channels of features extracted from a 3D point cloud object ${\\\\bf p} \\\\in \\\\mathbb{R}^{3 \\\\times N}$ with $N$ points as\n$$\n\t\\\\phi({\\bf p}) = \n\t\\begin{bmatrix}\n\t\tf\\_{1,1} & f\\_{2,1} & \\\\cdots & f\\_{C,1} \\\\\\\\\n\t\tf\\_{1,2} & f\\_{2,2} & \\\\cdots & f\\_{C,2} \\\\\\\\\n\t\t\\vdots & \\vdots & \\\\ddots & \\\\vdots \\\\\\\\\n\t\tf\\_{1,N} & f\\_{2,N} & \\\\cdots & f\\_{C,N}\n\t\\end{bmatrix}\n\t= \\\\left[{\\\\bf f}\\_1, {\\\\bf f}\\_2, \\\\dots, {\\\\bf f}\\_C\\\\right],\n$$\nwhere the $i$-th column ${\\\\bf f}\\_i = \\\\{f\\_{i,1}, f\\_{i,2}, \\\\ldots, f\\_{i,N} \\\\} \\\\in \\\\mathbb{R}^{N}$ means the vector of the $i$-th feature channel of $N$ points among $C$ channels. We will clarify this in the camera-ready.\n\n**Q2: Learning of rotation angles**\n\nDuring dataset distillation, the rotation angles $\\\\boldsymbol{\\\\theta}=(\\\\theta\\_{x}, \\\\theta\\_{y}, \\\\theta\\_{z})$ are treated as learnable parameters which are jointly optimized with the synthetic dataset. At each iteration, the synthetic dataset $\\\\boldsymbol{\\\\mathcal{S}}$ is rotated by $\\\\mathcal{R}\\_{\\\\boldsymbol{\\\\theta}}(\\\\cdot)$ to produce $\\\\hat{\\\\boldsymbol{\\\\mathcal{S}}}=\\\\mathcal{R}\\_{\\\\boldsymbol{\\\\theta}}(\\\\boldsymbol{\\\\mathcal{S}})$. The SADM loss $\\\\mathcal{L}\\_{\\\\text{SADM}}(\\\\boldsymbol{\\\\mathcal{T}}, \\\\hat{\\\\boldsymbol{\\\\mathcal{S}}})$ is then computed with $\\\\hat{\\\\boldsymbol{\\\\mathcal{S}}}$ and the real dataset $\\\\boldsymbol{\\\\mathcal{T}}$. To minimize the loss, the gradients are back-propagated not only to $\\\\boldsymbol{\\\\mathcal{S}}$ but to $\\\\boldsymbol{\\\\theta}$ simultaneously, updating both the point coordinates of $\\\\boldsymbol{\\\\mathcal{S}}$ and the rotation angles $\\\\boldsymbol{\\\\theta}$. This joint optimization objective is fomulated as\n$$\n\\\\operatorname*{argmin}\\_{\\\\boldsymbol{\\\\mathcal{S}}, \\\\boldsymbol{\\\\theta}} \\\\mathcal{L}\\_{\\\\text{SADM}}(\\\\boldsymbol{\\\\mathcal{T}},  \\\\hat{\\\\boldsymbol{\\\\mathcal{S}}}) \\\\quad \\\\text{where} \\\\quad  \\\\hat{\\\\boldsymbol{\\\\mathcal{S}}}=\\\\mathcal{R}\\_{\\\\boldsymbol{\\\\theta}}(\\\\boldsymbol{\\\\mathcal{S}}).\n$$\nThis will be clarified in the camera-ready.\n\n**Q3: Comparison of KL divergence and MMD with Gaussian kernel**\n\nBoth of Kullback-Leibler divergence (KLD) and Maximum Mean Discrepancy (MMD) are used to measure the distance between two distributions, but MMD is more proper in our framework since KLD is a parametric method requiring accurate probability density estimation. According to the reviewer’s suggestion, we have experimented with two experiments of Kullback-Leibler divergence (KLD) as alternatives to the MMD loss with a Gaussian kernel for measuring the discrepancy between the features. First, we followed the same setting as proposed method by measuring the discrepancy between the sorted features using KLD, after representing the feature distribution to the probability distribution using the softmax operation. We refer to this variant as Feature-KLD. Second, we adopted a knowledge distillation setup where the logits of the network, after being converted to probabilities, were used to compute the KLD loss between the original and synthetic datasets. This is denoted as Logits-KLD. As shown in the below table, the Feature-KLD approach yields significantly lower performance because the probability density estimation might be unreliable on high-dimensional and sparse feature space of 3D point clouds. Likewise, in Logits-KLD, the performance still results in low performance, because logits are highly compressed and lack the rich semantic information present in earlier feature maps. In addition, we also tested other kernel functions, including the linear and Laplacian kernels that show still less performance than the Gaussian kernel.\n\n|Methods| ModelNet10 | ModelNet40 | ShapeNet | ScanObjectNN | \n|------------|:------------:|:------------:|:------------:|:------------:|\nFeature-KLD  | 35.6 | 33.0 | 33.9 | 13.3 |\nLogits-KLD   | 28.3 | 35.0 | 32.9 | 13.7 |\nLaplace      | 34.1 | 54.2 | 50.1 | 17.2 |\nLinear       | 44.0 | 34.0 | 40.3 | 14.1 |\nGaussian     |**44.7** | **55.8** | **50.2** | **17.4** |\n\n\n**Q4: Qualitative results for the guitar class**\n\nThe proposed method changes an initial sample to better represent the global distribution of the class. As shown in Figure 3, the proposed method largely changed the shape and orientation of the initial guitar sample (2nd row) into the last row, that reflects more diverse shapes and is more aligned with the dominant orientation of the diverse instances in the guitar class (1st row). In contrary, the existing methods generate almost same synthesized samples (3rd and 4th rows) to the initial sample, that fail to capture diverse shapes and representative orientation. Consequently, the proposed method optimizes more representative shape and orientation than the existing methods. To quantitatively evaluate the benefit of the proposed method, we compared the L2 distance between the class-wise averaged orientation of the samples in the original dataset and the orientation of the resulting synthetic samples obtained by DC[29], DM[28], and the propoised method, respectively. As shown below, our method achieves significantly better orientation alignment than existing methods across all datasets. Similar results have been also observed in Figures 2$\\\\sim$5 in the Supplementary material. We will discuss the effect and benefit of the proposed method over the existing ones in more detail.\n|Methods| ModelNet10 | ModelNet40 | ShapeNet | ScanObjectNN |\n|------------|:------------:|:------------:|:----------:|:--------------:|\n|DC| 0.977 | 0.959 | 0.896 | 0.844 |\n|DM| 0.977 | 0.960 | 0.894 | 0.845 |\n|Ours | **0.961** | **0.812** | **0.755** | **0.724** |"}, {"review_id": "XDFB79uuZk", "reviewer": "Reviewer_ZBoM", "summary": "To address the issue of semantic misalignment in point clouds caused by their unordered nature, this paper introduces a Semantically Aligned Distribution Matching (SADM) loss function. It proposes a novel framework for 3D point cloud dataset distillation based on distribution matching, which simultaneously optimizes the geometric structure and orientation of the synthetic 3D objects.", "questions": "See Weakness for details.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n(1) Semantic Alignment via Feature Sorting: The method achieves semantic alignment by sorting the point feature values within each channel before computing the distance between two feature distributions.\n\n(2) Robustness to Rotational Variance: To mitigate the issue of rotational variance, the framework jointly learns an optimal rotation angle during the update of the synthetic dataset, enabling a better alignment with the original feature distribution.\n\nWeaknesses:\n\n(1) Although the SADM loss enhances semantic consistency by sorting feature values, it cannot perfectly align semantically meaningful regions between different point cloud objects. This implies that in some cases, the semantic alignment may still be insufficiently accurate, thereby compromising the quality of the distilled dataset.\n\n(2)  While the proposed method holds some advantages in training time over certain existing methods, its computational cost can still be high, especially for large-scale datasets or more complex 3D models. Furthermore, the joint optimization of the synthetic dataset and rotation parameters adds to the computational burden. Experimental data shows that its processing time is at least double that of the baseline Distribution Matching (DM) method.\n\n(3) The SADM loss is designed to operate on sorted features within each channel to maintain semantic alignment. However, while the proposed method is effective for 3D point cloud dataset distillation, its core idea remains within the well-established distribution matching paradigm. The contribution is arguably an incremental improvement over existing distribution matching methods, and the work lacks a more fundamental insight or a novel approach to the distribution matching problem itself.", "was_revised": true, "final_justification": "Thanks to the author's feedback, most of my confusion has been resolved. Therefore, I have decided to raise the ranking of this paper.", "rebuttal": "We thank the reviewer for highlighting the strengths of our proposed semantically and rotationally aligned matching algorithm. We respond to the reviewer's comments as follows.\n\n**Q1: Limitations of SADM loss**\n\nWe agree with the reviewer that the proposed SADM loss may not perfectly match semantically corresponding regions across diverse point cloud objects. However, our goal is not to achieve perfect matching but to improve the dataset distillation performance by matching the feature distributions more reliably. As shown in Table 5 in the supplementary material (below), our SADM-based feature sorting achieves significantly better performance compared with the unsorted setting and the other sorting strategies.\n\n|Methods| ModelNet10 | ModelNet40 | ShapeNet | ScanObjectNN |\n|------------|:------------:|:------------:|:----------:|:--------------:|\n| Unsorted | 75.21 | 59.96 | 53.91 | 20.20 |\n| Axis-Aligned | 76.44 | 60.85 | 53.97 | 21.80 |\n| Z-order | 76.55 | 61.47 | 55.17 | 21.76 |\n| SADM | **83.17** | **67.52** | **60.71** | **27.66** |\n\n\n**Q2: Computational overhead**\n\nOur method introduces additional computational overhead compared to the baseline DM, primarily due to the joint optimization of the synthetic point clouds and the rotation parameters. However, in this paper, we first introduced a new problem: 3D point cloud dataset distillation via distribution matching, and demonstrated the proposed method achieves significantly higher performance of dataset distillation compared with existing methods. To further justify the computational overhead, we conducted an experiment where DM was trained with its default setting, whereas the proposed method was trained during the same training time to DM. As shown below, even under the same training time, our method still significantly outperforms DM. We will discuss the computational overhead of the proposed method.\n\n|PointNet| ModelNet10 | ModelNet40 | ShapeNet | ScanObjectNN | \n|------------|:------------:|:------------:|:------------:|:------------:|\n| DM | 77.6 | 62.0 | 56.1 | 23.3|\n| Ours(Fixed) | **83.6** | **70.6** | **63.3** | **31.1** |\n\n|PointNet++| ModelNet10 | ModelNet40 | ShapeNet | ScanObjectNN | \n|------------|:------------:|:------------:|:------------:|:------------:|\n| DM | 51.5 | 46.9 | 34.3 | 11.6|\n| Ours(Fixed) | **81.9** | **67.9** | **51.1** | **18.2** |\n\n\n**Q3: Contribution**\n\nDistribution matching (DM) is a widely used approach in numerous studies on dataset distillation. For example, various methods of image dataset distillation also have been developed based on DM, such as DataDAM [17] and M3D [26], and their contributions are improving the performance of DM with attention-based feature alignment or high-order distribution statistics. Moreover, as shown in Table 1 in the main paper and Table 4 in the supplimentary material, directly applying the dataset distillation methods for 2D images to the 3D point clouds, e.g., DM, DC, MTT, DataDAM, does not provide sufficient performance due to severely different characteristics between two domains. Considering the above, we are the first to explore the novel research area of dataset distillation for 3D point clouds via DM. Our contribution does not lie in the DM itself, but rather in proposing an efficient and reliable framework that jointly optimizes both the synthetic dataset and the rotational angles. By leveraging the unique properties of 3D point clouds, this framework is carefully designed to achieve substantially better performance than existing approaches."}, {"review_id": "KboA9owG5B", "reviewer": "Reviewer_H221", "summary": "This paper proposes a distribution matching-based dataset distillation method for 3D point clouds. Most existing dataset distillation methods are designed for images, and the only existing method for point clouds overlooks the unordered and rotation-invariant nature of point clouds. To address these limitations, the paper:\n+ Proposes Semantically Aligned Distribution Matching (SADM) method sorts the point features before performing distribution matching, resulting in preserved semantic structure. \n+ Directly optimizes for orientation to align the synthetic dataset and the original dataset more effectively.\nExperiment results show that the proposed method outperforms baseline dataset distillation methods.", "questions": "1. Please refine the related work section to connect the related works to the proposed method.\n2. Please clarify the inconsistency between Table 5 and Table 6.\n3. Can you provide cross-dataset performance if possible?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "$\\\\textbf{Strengths}$\n+ This paper explored how to leverage the unique properties of point clouds to perform dataset distillation.\n+ More sorting methods addressing the unordered nature of point clouds are tested, and results are given in Table 5 of appendix.\n+ Experiment results show the proposed method improves over baselines.\n\n$\\\\textbf{Major Weaknesses}$\n+ All related works, including those on 3D point data analysis, coreset selection, and data distillation, are merely listed without in-depth discussion. The authors fail to analyze how these works are connected to the proposed method, rendering the related work section both overly lengthy and disconnected from the rest of the paper.\n+ Concern about ablation study. In Table 5, the result of w/SA + MN40 is 72.08, which is consistent with the S+$\\\\theta$+Mixed (Mixed = MN40, see line 327) setting of Table 6, showing that **in Table 5, $\\\\theta$ orientation optimization is also used**. However, the w/oSA + MN40 result in Table 5 is 59.96, while the $\\theta$ + Mixed result in Table 6 (row 2) is 62.17. This inconsistency should be clarified.\n+ Figure 3 shows that the proposed method will cause relative large change of shape of point clouds, and loss of details / over-smoothing is also observed. Will the proposed cause degraded generalizability across datasets because of these behaviors? This should be explored.\n\n$\\\\textbf{Minor Weaknesses}$\n+ In line 168, should be 'descending order of their values' instead of 'descending order of their sizes'.\n+ In line 179, should be 'largest' instead of 'most largest'.\n+ The results in Table 5 of the appendix are important and should be placed in the main text.\n+ Table 5 and Table 6 are highly redundant and can be considered to be merged to together.\n+ Proposition 1 is quite obvious and does not need a large space in the main text.", "was_revised": true, "final_justification": "The authors have addressed my concerns on the evaluation protocol and potential harm to cross-dataset generalization capability of the proposed method.\n\nAlthough the related work part of this paper is not well organized, failing to give a good background to the readers, given that data distillation of point cloud data is less researched and the proposed method have relative good performance, I will suggest a borderline accept to this paper.", "rebuttal": "We thank the reviewer to acknowledge our effort to leverage the unique properties of point clouds to perform dataset distillation. We respond to the reviewer's comments as follows.\n\n**Q1: Related work refinement**\n\nWe appreciate the reviewer for the feedback on the Related Works section. Section 2.1 introduces point cloud analysis methods to clarify which architectures are used in our framework. Specifically, PointNet serves as the backbone architecture in our dataset distillation pipeline, while the other architectures are used as evaluation networks in our cross-architecture generalization experiments (Table 2). Section 2.2 discusses coreset selection methods, which were widely used before the emergence of dataset distillation. These methods share the same objective of reducing training data size while preserving model performance, but they achieve this by selecting real samples rather than generating synthetic ones. Since they operate solely within the space of existing samples, they lack the flexibility to represent rare or task-specific patterns. We compare against these methods in Table 1 to highlight the advantages of distillation-based approaches. Section 2.3 covers recent dataset distillation techniques, including gradient matching, trajectory matching, and distribution matching. These methods are parallel to ours in their goal of synthesizing informative datasets, but they are primarily designed for image data. Applying them to 3D point clouds is non-trivial due to challenges such as the unordered nature of point cloud data and its sensitivity to rotational variance. While PCC~[27] is the only existing method designed for 3D point clouds, it directly adopts an image-based gradient matching strategy without addressing these domain-specific challenges. Our method addressed these limitations by incorporating 3D-specific mechanisms that enable dataset distillation to effectively operate on point cloud data. We will revise the Related Work section in the camera-ready version to better reflect these critical connections between prior limitations and the design of our proposed method.\n\n**Q2: Clarification on the experimental settings in Tables 5 and 6**\n\nLet us clarify the experimental settings in Table 5 and Table 6. Whereas Table 5 presents an ablation study to evaluate the effectiveness of Semantic Alignment (SA) in our SADM loss, Table 6 analyzes the impact of synthetic dataset optimization and orientation optimization, with SA consistently applied in all cases. Specifically, we clarify the difference in terms of the optimization objectives. The optimization objective for 'w/ SA (proposed)' in Table 5 is formulated as\n$$\n\t\\\\operatorname*{argmin}\\_{\\\\boldsymbol{\\\\mathcal{S}}, \\\\boldsymbol{\\\\theta}} \\\\mathcal{L}\\_{\\\\text{SADM}}(\\\\boldsymbol{\\\\mathcal{T}},  \\\\hat{\\\\boldsymbol{\\\\mathcal{S}}}) \\\\quad \\\\text{where} \\\\quad  \\\\hat{\\\\boldsymbol{\\\\mathcal{S}}}=\\\\mathcal{R}\\_{\\\\boldsymbol{\\\\theta}}(\\\\boldsymbol{\\\\mathcal{S}}), \\\\tag{a}\n$$\nand that for `w/o SA' in Table 5 is\n$$\n\\\\operatorname*{argmin}\\_{\\\\boldsymbol{\\\\mathcal{S}}, \\\\boldsymbol{\\\\theta}} \\\\mathcal{L}\\_{\\\\text{MMD}}(\\\\boldsymbol{\\\\mathcal{T}},  \\\\hat{\\\\boldsymbol{\\\\mathcal{S}}}) \\\\quad \\\\text{where} \\\\quad  \\\\hat{\\\\boldsymbol{\\\\mathcal{S}}}=\\\\mathcal{R}\\_{\\\\boldsymbol{\\\\theta}}(\\\\boldsymbol{\\\\mathcal{S}}),\n$$\nwhere the SADM loss is replaced with the standard MMD loss.\nOn the other hand, the optimization objective with '${\\\\boldsymbol{\\\\mathcal{S}}}$' in Table 6 is \n$$\n\\\\operatorname*{argmin}\\_{\\\\boldsymbol{\\\\mathcal{S}}} \\\\mathcal{L}\\_{\\\\text{SADM}}(\\\\boldsymbol{\\\\mathcal{T}},  \\\\hat{\\\\boldsymbol{\\\\mathcal{S}}}),\n$$\nand that with '${\\\\boldsymbol{\\\\theta}}$' is \n$$\n\\\\operatorname*{argmin}\\_{\\\\boldsymbol{\\\\theta}} \\\\mathcal{L}\\_{\\\\text{SADM}}(\\\\boldsymbol{\\\\mathcal{T}},  \\\\hat{\\\\boldsymbol{\\\\mathcal{S}}}). \n$$\nThe optimization objective with both '${\\\\boldsymbol{\\\\mathcal{S}}}$' and '${\\\\boldsymbol{\\\\theta}}$' in Table 6 is the same to Equation (a).\n\n**Q3: Generalizability and cross-dataset performance**\n\nFigure 3 presents the qualitative results at PPC = 1, where only one synthetic sample represents the entire distribution of a certain class. In such an extreme case, it is natural to generate a smoothed shape (more generalized) to represent diverse shapes of samples in the class. However, as shown in Figure 7 in the supplementary material, our method gradually recovers more fine-grained details as PPC increases. \n\nWe also evaluated the generalizability performance of the proposed method. In Table 2, we reported the cross-architecture generalization performance of the proposed method at PPC=3, where PointNet is used for dataset distillation and the resulting synthetic samples are evaluated on different backbone networks. Our method achieves the best performance across all architectures, demonstrating strong generalizability despite using the smoothed shapes of synthetic dataset. To further support our claim, we additionally conducted cross-architecture evaluation on ModelNet10 with a more challenging setting of PPC=1. The below table shows that the proposed method consistently outperforms both DC [29] and DM [28], and even surpasses the random selection, confirming that the distilled synthetic shapes retain critical semantic features with strong generalizability.\n\n| Method | Random | DC | DM | SADM |\n|--|:--:|:--:|:--:|:--:|\n| PointNet++ | 22.43 | 15.31 | 12.14 | **25.93** |\n| DGCNN | 43.71 | 16.69 | 10.57 | **50.43** |\n| PointConv | 17.70 | 14.22 | 10.76 | **20.52** |\n| PT | 42.74 | 26.73 | 22.40 | **49.03** |\n\n**Minor Weaknesses**\n\nWe sincerely thank the reviewer for careful reading and constructive suggestions. We will revise the camera-ready version according to the reviewer’s comments, except for the merging of Tables 5 and 6, as they focus on different ablation studies, as explained above."}, {"review_id": "bmI79YO5DQ", "reviewer": "Reviewer_WfS3", "summary": "The paper presents a dataset distillation method that explores distribution matching for distillation of 3D point clouds. The method jointly optimizes the geometric structures and the orientations of the synthetic 3D objects. It introduces a Semantically Aligned Distribution Matching loss that sorts point features to address the semantic misalignment caused by unordered points, In addition, it learn the optimal rotation angles to better align with the original feature distribution to address the rotation variation. Experiments show promising results.", "questions": "1. The comparison involves a single point cloud dataset distillation method only, and the method just applies one existing image dataset distillation method that uses gradient matching. The experiments should include comparisons with other image dataset distillation methods like trajectory matching and distribution matching that apply to point cloud dataset distillation. \n\n2. What does the row 'whole' mean in Table 1? What is the meaning of the row 'Ratio' in Table 1? The text mentions comparison with PPC [27] in Table 1 but I don't see the comparison there. \n\n3. Why does DC perform better than DM for synthetic data but worse than DM for real data consistently? Why does the proposed method improves less on the natural point clouds?", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strength\n1. The work addresses a relatively new problem of dataset distillation of point clouds.\n2. The work presents a method that address the unordered point features and rotation issue with promising performance.\n\nWeakness\n1. The significance of the proposed method is not clear. The motivation of the work is to suppress datasets without sacrificing useful information. On the other hand, the second point is not well discussed and reflected in the experiment part. \n2. The experimentation is not convincing. The comparison involves a single point cloud dataset distillation method only, and the method just applies one existing image dataset distillation method that uses gradient matching. However, there are many other image dataset distillation methods that use trajectory matching, distribution matching, etc. The experiments should include comparisons with other image dataset distillation methods that apply to point cloud dataset distillation.\n3. The experiments are not clear. Take Table 1 as an example. What does the row 'whole' mean? Is it the performance using the original dataset? If so, the performance of the proposed distillation method drops sharply especially for the natural data, instead of without sacrificing much useful information. In addition, the meaning of the row 'Ratio' is not explained clearly either. Further, the text mentions comparison with PPC [27] in Table 1 but I don't see the comparison there. \n4. The unclarity applies to other experimental results as well. For example, DC performs better than DM for synthetic data but worse than DM for real data consistently, why? In addition, why does the proposed method improves less on the natural point clouds?", "was_revised": true, "final_justification": "The rebuttal have addressed most of my concerns. Nevertheless, I still think some claims are too strong and not well supported by experiments.", "rebuttal": "We thank the reviewer for recognizing the novelty of our work in addressing the relatively new problem of dataset distillation for point clouds. We respond to the reviewer's comments as follows.   \n\n**Q1: Significance of the proposed method**\n\nTable 1 provides the comparison of quantitative performance at the same PPC (point clouds per class). 'Whole' refers to the classification accuracy obtained by training the network on the entire original dataset without any distillation. It serves as an upper bound for evaluating the performance drop introduced by using reduced (distilled) datasets. 'Ratio(\\%)' represents the percentage of the distilled dataset size compared to that of the entire original dataset. The experimental results demonstrate that the proposed method significantly improves the performance compared with the existing methodologies, that means our distilled dataset preserves more useful information than the other methods. Furthermore, Table 2 reports the cross-architecture generalization results, in which our proposed method consistently outperforms existing approaches by substantial margins, reinforcing the claim that it effectively retains useful information. We will discuss and reflect this in more detail in the experiments section.\n\n\n**Q2: Comparison with other image dataset distillation methods**\n\nThe dataset distillation for 3D point clouds remains a largely unexplored research area, with PCC [27] being the only existing method introduced thus far. With respect to the comparison against image-based dataset distillation methods, we would like to highlight that our paper already presents comprehensive experimental results. Section 4.2 and Table 1 in the main paper provided the comparative results with DC [29] of gradient matching and DM [28] of distribution matching. In addition, Table 4 in the supplementary material also provided comparative experimental results with MTT [3] of trajectory matching and DataDAM [17] of another distribution matching-based method. We present these results again in the table below. Notably, all experimental findings demonstrate that the proposed method significantly outperforms both representative image dataset distillation methods across various datasets and PPC settings.\n\n\n\n|Datasets || ModelNet10 |||| ModelNet40 |||| ShapeNet |||| ScanObjectNN ||\n|--|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|\n|PPC     | 1  | 3   | 10   || 1   | 3   | 10   || 1   | 3   | 10   || 1   | 3   | 10   |\n|DM      |31.9| 77.6| 86.1 || 32.3| 62.0| 75.2 || 27.8| 56.1| 64.3 || 14.9| 23.3| 35.6 |\n|DC      |43.9| 75.0| 86.1 || 52.0| 66.6| 75.6 || 49.8| 60.1| 64.6 || **18.6**| 24.3| 35.3 |\n|MTT     |29.0| 76.7| 85.2 || 34.4| 59.8| 73.9 || 33.9| 52.9| 62.7 || 13.9| 20.3| 34.1 |\n|DataDAM |40.5| 76.6| 86.6 || 34.5| 60.4| 75.0 || 35.7| 54.6| 63.6 || 16.3| 20.5| 34.5 |\n|Ours    |**44.7**| **85.0**| **87.8** || **55.8**| **72.1**| **80.1** || **50.2**| **63.7**| **68.4** || 17.3| **31.8**| **43.9** |\n\n\n\n**Q3: Clarification of Table 1**\n\nWe thank the reviewer for carefull reading. 'Whole' refers to the classification accuracy obtained by training the network on the entire original dataset without any distillation. It serves as an upper bound for evaluating the performance drop introduced by using reduced (distilled) datasets. 'Ratio (\\%)' represents the percentage of the distilled dataset size compared to that of the entire original dataset. We apologize for the unclear explanation regarding the comparison with PCC [27]. The comparison with PCC is included in Table 3 (not Table 1). As annotated in Table 3, PCC is equivalent to DC initialized with Herding (DC$^\\dagger$). We see that our method consistently outperforms PCC regardless of different initialization strategies even with random initialization. We will revise the related sentances to clarify this.\n\n**Q4: Performance comparison between DC, DM, and Ours**\n\nAs illustrated in Figures 3 and 4 in the supplementary material, DC tends to generate less noisy shapes compared to DM, and hence achieves relatively better generalization performance than DM on noise-free synthetic datasets such as ModelNet10, ModelNet40, and ShapeNet. On the other hand, ScanObjectNN consists of real-world scans that include background clutter, occlusion, and sensor noise. DM effectively captures the data distributions of such real dataset faithfully, leading to improved generalization performance compared to DC, as shown in Table 2. \n\n\nOn the other hand, dataset distillation methods tend to yield relatively lower performance on natural datasets, such as ScanObjectNN, due to the challenges of capturing complex and noisy data distributions, particularly at low PPCs. This doesn't apply only to our method, but to other methods in general.However, as shown in Table 1, the proposed method significantly outperforms the compared methods at higher PPCs of 3 and 10 on ScanObjectNN."}]

Author rebuttal:

Meta-review: This paper proposes a dataset distillation framework for 3D point clouds based on distribution matching. It introduces a Semantically Aligned Distribution Matching (SADM) module to resolve misaligned semantic structures across different models. Additionally, it incorporates learnable rotation parameters to handle intra-class variability arising from different acquisition poses. The reviewers unanimously gave positive feedback. The paper makes a novel contribution by jointly optimizing dataset distillation with semantic alignment and learnable rotations, effectively addressing key limitations of existing methods. 

Recommendation: Accept. The AC valued this paper and suggested cross-dataset evaluation and suggested additional experiments confirming the method’s superiority.
Decision: Accept (poster)