Distribution Guidance Network for Weakly Supervised Point Cloud Semantic Segmentation
Authors: Zhiyi Pan
Wei Gao
Shan Liu
Ge Li
Venue: NeurIPS 2024 poster (2024)
Keywords: distribution guidance
weak supervision
point cloud
semantic segmentation
Primary area: machine_vision

Abstract: Despite alleviating the dependence on dense annotations inherent to fully supervised methods, weakly supervised point cloud semantic segmentation suffers from inadequate supervision signals. In response to this challenge, we introduce a novel perspective that imparts auxiliary constraints by regulating the feature space under weak supervision. Our initial investigation identifies which distributions accurately characterize the feature space, subsequently leveraging this priori to guide the alignment of the weakly supervised embeddings. Specifically, we analyze the superiority of the mixture of von Mises-Fisher distributions (moVMF) among several common distribution candidates. Accordingly, we develop a Distribution Guidance Network (DGNet), which comprises a weakly supervised learning branch and a distribution alignment branch. Leveraging reliable clustering initialization derived from the weakly supervised learning branch, the distribution alignment branch alternately updates the parameters of the moVMF and the network, ensuring alignment with the moVMF-defined latent space. Extensive experiments validate the rationality and effectiveness of our distribution choice and network design. Consequently, DGNet achieves state-of-the-art performance under multiple datasets and various weakly supervised settings.

Distribution Guidance Network for Weakly Supervised Point Cloud Semantic Segmentation
Zhiyi Pan
Wei Gao
SECE, Peking University Peng Cheng Laboratory panzhiyi@stu, pku. edu.
SECE, Peking University gaowei262@pku. edu. en
Shan Liu
Ge Li'
Media Laboratory, Tencent Sean@@tencent.. com
SECE, Peking University gelißece pku. edu.
Abstract
Despite alleviating the dependence dense annotations inherent to fully super- vised methods, weakly supervised point cloud semantic segmentation suffers from inadequate supervision signals. In response to this challenge, introduce novel perspective that imparts auxiliary constraints by regulating the feature space under weak supervision. Our initial investigation identifies which distributions accurately characterize the feature space, subsequently leveraging this priori to guide the align- ment of the weakly supervised embeddings. Specifically, analyze the superiority of the mixture of von Mises-Fisher distributions (moVMF) among several common distribution candidates. Accordingly, develop Distribution Guidance Network (DGNet), which comprises a weakly supervised learning branch and a distribution alignment branch. Leveraging reliable clustering initialization derived from the weakly supervised learning branch, the distribution alignment branch alternately updates the parameters of the VoV and the network, ensuring alignment with the mo WMF--effine latent space. Extensive experiments validate the rationality and effectiveness of our distribution choice and network design. Consequently. DGNet achieves ttate-of-the art performance under multiple datasets and various weakly supervised settings.
Introduction
As fundamental task in 3D scene understanding, point cloud semantic segmentation [42 32 29 is
widely entrenched in 3D applications, such as 3D reconstruction [15 33 autonomous driving 20), and embodied intelligence [4] [50] Despite significant accomplishments in tackling the disorder and disorganization, point cloud semantic segmentation remains imntation-intensive,, hindering its expansion in big datasets and large models. For this reason, the academic community explores achieving point cloud semantic segmentation in weakly supervised manner. However, due the lack of supervision signals, learning point cloud segmentation sparse annotations is nontrivial.
In recent years, considerable effort has been made pursue additional constraints in weak supervision. As shown in Fig. [ representative work can be broadly categorized into several paradigms: 1) Contrastive Learning Perturbation Consistency imposes contrastive loss consistency constraint between network embeddings of original and perturbed point clouds, respectively. 2) Self-training progressively enhances segmentation quality by treating reliable predictions as pseudo-labels, with
"Ge Li is the corresponding author.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Previous Stage Embeddinng
3D
<
Perfurbaton
20
00
Point Cloud
Backbone
Embedding
Sparto Label
Point Cloud
Bookbonc
Embedding
Pscudo Label
(a) Contrastive Learning/ Porturbation Consistency
(b) Self-traiining
Siiilority Map
Custering
Nommllzaiion
Fimbedding
Sparse
Embecding
Similarity Metric
(Ours)
Figure I: Visual comparisons of mainstream weakly supervised point cloud semantic segmentation paradigms and our DGNet. The solid and dashed lines represent the network forward process and the loss function, respectively.
given sparse annotations as initial labels. 3) Similarity Metric transfers supervision signals from annotated points to unlabeled regions via leveraging the low-level features or the embedding similarity. Nevertheless, most constraints stem from heuristic assumptions and ignore the inherent distribution of network embedding, resulting in ambiguous interpretations of point-level predictions. In contrast to existing paradigms, in this paper, we re-examine two fundamental issues: How to characterize the semantic segmentation feature space for weak supervision and how to intensify this intrinsic distribution under weakly supervised learning?
For the first issue about oughtness, we expect to provide mathematically describable distribution for weakly supervised features. Consequently, we attempt to precisely describe the feature space in terms of two dimensions: distance metric and distribution modeling. In distance metric, we compare the Euclidean norm and cosine similarity between representations, and in distribution modeling, the category prototype model and the mixture model are considered. Among our candidate combinations, the mixture of von Mises-Fisher distributions (moVMF) with cosine similarity is finalized, due to its
powerful fitting capability to segment head and insensitivity to the Curse of Dimensionality believe that superior weakly supervised feature space should adhere to this distribution.
4.] We
For the second issue about practice, we dynamically align the embedding distribution in the hid- den space to mo VMF during weakly supervised learning. Accordingly, we propose a Distribution Guidance Network (DGNet), comprising weakly supervised learning branch and distribution alignment branch. Specifically, the weakly supervised learning branch learns semantic embeddings under sparse annotations, while the distribution alignment branch constrains the distribution of the network embeddings. Via Nested Expectation- Maximmm Algorithm, the semantic features are dynamically refined. Therefore, restricting and fitting is mutually reinforcing, iterative optimization process. To curtail the pattern of feature distribution, we derive the vMF loss based on the maxi- mum likelihood estimation and the discriminative loss inspired by metric learning [22]. For joint optimization, consistency loss is imposed between the segmentation predictions and the posterior probabilities. During the inference phase, only the weakly supervised learning branch is activated to maintain inference consistency with fully supervised learning.
We validate DGNet on three prevailing point cloud datasets, i.e., S3DIS [. ScanNetV2 [I], and SemanticKITTI []. After the constraints of feature distribution, DGNet provides significant performance improvements over multiple baselines. Across various label rates, our method achieves state-of-the-art weakly supervised semantic segmentation performance. Extensive ablation studies also confirm the effectiveness of each loss term we proposed. addition, posterior probabilities under the mo VMF provide plausible interpretation for predictions unlabeled points.

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2
Related Work
Weakly Supervised Point Cloud Semantic Segmentation. Weakly supervised point cloud seman- tic segmentation methods aim to provide reliable additional supervision with sparse annotations. Four paradigms have been successively proposed in recent years, ie., perturbation consistency, contrastive learning, self-training, and similarity metric. Perturbation consistency methods are based on the assumption of perturbation invariance of network features, imposing diverse perturbations (such affine transforms with point jitter [59] [54], downsampling [56), masking [85] etc.) to construct pairs of point clouds. Several methods [31 34 introduce contrastive learning in weak supervision to encourage the discriminability of hidden layer features. Additionally, pre-training methods [55] I7 with contrastive learning similarly demonstrate the ability to bias induction in the face of downstream semantic segmentation tasks with sparse annotations. Self-training methods generate reliable dynamic pseudo-labels based previous stage predictions for subsequent training stages. Via CAMs [62] MPRM [51] and J2D3D [25] dynamically generate point-wise pseudo-labels from subcloud- annotations and image-level annotations, respectively. Recently, REAL 24 integrate SAM 23 to self-training. Similarity metric methods measure the similarity between labeled and unlabeled points propagate supervision information, in which the similarity is elaborated low-level fea- tures [49 [2]. network embedding [36 18 40) or category prototypes [58, 46]. Most similar to our method is the similarity metric strategy. However, the distinction is that DGNet focuses on describing network embeddings holistically, rather than constructing pair relationships between features.
Feature Distribution Constraints. The constraints of feature distribution are always presented in the form of feature clustering. DeepClustering [6). which integrates clustering and unsupervised feature learning. utilizes the clustering results pssulo-laaels to extract visual features dynamically. Following this groundbreaking work, a series of subsequent studies 7 2 30 apply feature clustering in unsupervised learning obtain discriminative visual features for pretraining. For point cloud semantic segmentation, PointDC [10] delineates semantic objects by aligning the features on the same super-voxel in unsupervised manner. Feng el al. [12) imposes clustering-
representation learning to enhance the discrimination of embeddings under full supervision. In contrast, our DGNet oriented towards weakly supervised semantic segmentation by restricting the feature distribution.
Mixture of von Mises-Fisher Distributions. The VMF 3 describes the embeddings of multiple categories the unit hypersphere in feature space, where the parameters are jointly optimized with the clustering results by Expectation- Maxiiinm algorithm S 4 Some work attempts to combine neural networks with the VoV in the deep learning as a direct application of clustering, introducing a vMF loss to align the distribution of face features. Segsort (21), on the other hand, utilizes the prior of the moV over-segment images. DINO- VMF [13 achieve a more stable pre-trained method by precisely describing DINO S as a MoV In this work, discuss the superiority of mo VMF in characterizing semantic embeddings and trust. it as priori to guide weakly supervised learning.
For example, [16] view face verification
3 Methodology
3.1 Preliminaries
Task Definition.
Without loss of generality, a point cloud for weakly supervised learning is denoted as (X,, Y), (X,, Ø)} = {(x1, "1.,.... (Xm, .,,), Xm+1, where X, and X., are the point sets with and without annotations, respectively. Y is the corresponding annotations on X,, in which V: E C and C is the set of category indices. n and m are the point numbers of the point cloud and labeled set, respectively. Fed into the segment head, the network embedding f, is projected into the category probability vector p;. The partial cross-entropy loss is employed in conventional weakly supervised semantic segmentation:
1
SpCE
Log(p,")
(I)
where p represents the probability of y--th category in p..
3

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Cosine similarity can be viewed as the inner product of von Mises-Fisher Distribution (vMF), The vMF has demonstrated strong data fitting and gener- alization capabilities in the fields of supf-super learning [ classification [44) variational inference [47], and online continual learning [38 This distribution describes the distribution of normalized embedding v, norm(f.) on the unit hypersphere, with the probability density function:
( u, k) = Ca(xs) exp(Ruu Tv:),
(2)
where u represents the mean vector of vMF and z is a concentration parameter that controls the probability concentration around μ.. Ca(K) is the normalization constant.
Mixture vMF (moVMF). Similar to other mixture models, mo VM treats vMF as a sub- distribution to describe the overall distribution of multiple categories. Over the entire set of categories C, the probability density function of moVMF is formulated as:
P)) Σ aaf((vilue = CxCaa())) vv))
cEC
CEC
where = {Cke Key Ualc E C) is the parameters of VOME ag denotes the proportion of the von Mises-Fisher distribution for the e-th category and Σ a. 1.
3.2 Feature Space Description
We intend to provide additional supervision signals for weakly supervised learning by portraying and enhancing its inherent distribution. Specifically, We explore it in two dimensions, i.e., the distance metric and the distribution modeling:
Distance metric. Distance metric influences the similarity relationship between features. We consider the two most commonly used distance measures in clustering, i.e., Euclidean norm and cosine similarity. For given vectors u and v, the Euclidean norm defined as ||u - vll2 and the cosine similarity is defined as normalized and v.
u
Tullal vila"
Distribution modeling. Distribution modeling determines the clustering results of features. A straightforward model the Category Prototype (45). In this model, clusters are assigned by com- paring the distance between the features and each category prototype. In addition, we incorporate mixture models into the comparison. Depending on the distance measure, we categorize into the Gaussian Mixture Model (GMM) with Euclidean norm and the mixture of von Mises-Fisher distributions (moVMF) with cosine similarity, respectively.
Describing the feature space of neural network remains an open problem. Various factors influence the feature space, including network architecture, training data, parameter configurations, and the optimization (loss) function. Given this intractability, deriving universally optimal mathematical de- scription is impractical. Therefore, we discuss the merits and demerits of these candidate distributions from the following perspectives:
Segment head. To facilitate the analysis. we simplify the structure of the segment head as SegHead(f)) = argmax (softmax }), where is the semantic feature extracted by the decoder and w is the parameter of the output layer. Consider a group of feature vectors {kf]k l 2 0 & f + 0}. For any two feature vectors f and kyf within this group, the segmentation predictions are identical, i.e., SegHead(k, f) argmax argmax(softman (softmax (k, wf )) argmax (softmax (kg wf )) = SegHead f)f). If the general case of using activation function is taken into account, it does not change the result after argmax since the activation function is usually monotonically nondecreasing. Therefore, the segment head is a radial classifier with a more pronounced classification performance on the angles, so cosine similarity describes the feature space better than the Euclidean norm.
Curse of dimensionality, Another advantage of cosine similarity can be explained in terms of the Curse of Dimensionality. Most high-dimensional features are far from each other, causing the Euclidean distance to become ineffective distinguishing differences between feature vectors. Cosine similarity, on the other hand, is more effective in distinguishing differences between features by measuring the angle between the vectors. Besides, the Fuclidean norm sensitive to scale while cosine similarity is not affected by the length of the vectors.

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Distribution Alignment
PAL
E stop
PALAA
step Soft-moVMF
Normalized Embedding
Lois
LRON
100
Embedding
Prediction tion
Sparse
Segment Weakly Supervised Learning
Lice
Segment Backbone
Embedding Unlabeled Point
Semantic Embedding
Category Probability
Unit Hypersphere
Embedding
Labeled Point
Posterior Probability
Feature Space
Figure 2: Structure of Distribution Guidance Network.
Fitting ability. Despite its computational simplicity, the Category Prototype Model clusters the features by comparing the distance between features and category prototypes. This means that the Category Prototype Model ignores the distribution within categories and the variability between categories. contrast, the Mixture Model possesses intra-category fitting and inter-category perception capabilities.
Based on the above analysis and experimental validation in Sec. 4.3 we characterize the feature space MoVMF and propose the Distribution Guidance Network enhance this distribution.
3.3 Distribution Guidance Network
To enhance the intrinsic distributions discussed in Section Network (DGNet). The structure of DGNet is shown in Fig. which comprises the weakly supervised learning branch and the distribution alignment branch.
3.2 we propose a Distribution Guidance
3.3.1 Weakly Supervised Learning Branch
Sparse annotations pose two challenges for the point cloud semantic segmentation. The first is underfitting the entire dataset, as the supervision signals are insufficient for complex structured point clouds. To address underfitting, we introduce additional signals by reinforcing the inherent distribution of the feature space. The second challenge is overfitting within the labeled set X,, as the model capacity is than adequate fit the labeled points. To mitigate overfitting, we replace the conventional partial cross-entropy loss Eq. with the truncated cross-entropy loss (60] the weakly supervised learning branch, which defined as:
L.CE = m Σ min (Iog(p."), (,og())))log(()))
where 3 E [0, 1] represents the threshold for truncating the cross-entropy loss. With LICE, the gradient of the cross-entropy loss is curtailed when the predicted class probability for annotated point exceeds 3. Over-optimization for that point is halted, thereby preventing overfitting.
The weakly supervised learning branch also provides robust initialization for the distribution align- ment branch by utilizing the average feature vector of the labeled points. According to the Central Limit Theorem [27]. the difference between the initialization vector from the weakly supervised
5

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learning branch and the theoretical optimal average vector conforms to Gaussian distribution with mean of O. The initialized mean vector DGNet has high probability of appearing in the vicinity of the optimal solution, which facilitates the clustering algorithm in achieving rapid and stable convergence.
3.3.2 Distribution Alignment Branch
The feature space descriptor moVFF, investigated in Sec. 3.2 is employed to regulate the feature space under weakly supervised learning. Initially, the network embeddings are normalized and projected onto the unit hyperspherical surface of the feature space, i.e., V; norm(f,). Following this, the optimization objective function defined utilizing maximum likelihood estimation
max P(VIZ,0) 2,
= min 6.2.0
Σ [log(a.)) + ku k
(5)
where の, 1/ [v.). normalized network embeddings, the corresponding clustering results and the parameters of mo VMF, respectively. To avoid the long-tai problem and simplify computations, the concentration parameter R is fixed as a constant in our implementation. Since the clustering initialization is category- the clustering results 2, C are with category labels. While the primary optimization goal is the learning of network parameters Ø, we dynamically resolve and + to furnish a more precise feature space description. Consequently, we develop Nested Expectation- Maxiimum Algorithm manage the challenge associated with the three optimization variables delineated in Eq. S
z 2 (z, and O {ae, U denote the learnable network parameters, the
E Step (Optimize @ and 2): Regarding network embeddings input conditions, we integrate the soft-mo VMF EM algorithm [3] into the network to alternately optimize θ and 2. To enhance the stability and computational efficiency of the algorithm, points from the weakly supervised branch to initialize u. The posterior probability set Q = {q}} serves the soft assignment for the clustering results 2, where qi is defined
utilize the average features of labeled
Ote exp(sut v:)
q: = P(c +) Eiec On exp(xu, v.)
(6)
Compared to other algorithms in 33. the soft-moVMF algorithm updates θ by weighting all features according their posterior probabilities, considering inter-cluster similarities, thereby achieving more accurate parameter updates. The posterior probability qi [0, 1| is employed not only as a weighting factor for updates but also in the calculation the loss function for joint optimization. Furthermore, Q provides probabilistic explanation for the predictions during the inference phase.
The complexity of the soft-vo VMF is O(tn(()) where is the iteration number, n is the point number of the point cloud, and |C| is the number of semantic categories. Since I,, n., and |C] all set to constant values during network training, the extra computation introduced by the distribution alignment branch is trivial.
M Step (Optimize Φ): With the converged parameters è and Z fixed, we optimize ó by the backpropagation process. Consistent with the philosophy of the Soft-moVMF, we incorporate the posterior probability Q into Eq. 5) and reformulate it into the loss function as follows:
n
LVM ΣΣ q log(a.) + xu [v.
i=1 cEC
Additionally, acknowledging the significance of distinct decision boundaries within the mixture model, incorporate discriminative loss derived from metrie learning (22) which is defined as:
LDIS = |C[[| - 1) C1
01
Usy
(8)
The interpretation of Bayesian posterior probabilities for predictions based on the moVMF is an attractive property of DGNet. Fig. visualizes the posterior probabilities for some categories. Taking the floor as an example, according to the Bayesian theorem, those points with relatively high posterior probabilities are more likely to be floor, which explains the prediction results.
A complete reasoning process can be found in the Appendix.

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Probabilistic
Explanation
DGNet
Floor
Chair
Table
Point Cloud
Prediction
Posterior Probability
Figure 3: DGNet provides segmentation predictions from the weakly supervised learning branch and explains it probabilistically by posterior probabilities from distribution alignment branch.
3.3.3 Loss Function
In addition to the previously mentioned initialization, we introduce a consistency loss to fortify the exchange of information between the two branches. This consistency loss is imposed the class probability map from the weakly supervised learning branch and the posterior probability q from the distribution alignment branch, in the form of cross-entropy:
LOON 1 Σ q. log(
(9)
If regard the posterior probability q pseudo-labels. the consistency loss is proved to diminish prediction uncertainty and alleviate distribution discrepancies [48).
Without laborious adjustments to the weight: the overall loss function is defined as follows:
L = L,cr + LvMP + LDI + CcON.
(10)
4 Experimental Analysis
4.1 Experiment Settings
Datasets. S3DIS [ encompasses six indoor areas, constituting total of 271 rooms with 13 cate- gories. Area 5 within S3DIS serves as the validation set, while the remaining areas allocated for network training. ScanNerV2 [11 offers a substantial collection of 1,513 scanned scenes originating from 707 indoor environments with 21 indoor categories. Adhering to the official ScanNetV2 par- tition, we utilize 1,201 scenes for training and 312 scenes for validation. SemanticKITTI [5] with 19 classes is also considered. Point cloud sequences 00 10 used in training, with sequence 08 as the validation set. To simulate sparse annotations, we randomly discard the dense annotations proportionally.
Implementation details. ResGCN-28 in DeepGCN 29 and PointNeXt-1 43 are reimplemented the segment backbones with OpenPoints library 43 We discard the last activation layer of the decoder to extract orientation-com orientation-completed feature space. We maintain a memory bank [53] to store class prototypes across the entire dataset. In cases where class annotations the class prototypes from the memory bank are employed as supplementary initialization. We employ the LaDS [39] to maintain higher rate of training supervision after point cloud sampling. For truncated cross-entropy loss, 3 0.8. The concentration constant = 10 and the iteration number activated in the first 50 epochs stabilize the feature learning. In our implementation, the DGNet is trained with one NVIDIA V100 GPU on S3DIS, eight NVIDIA TESLA T4 GPUs on ScanNetV2, and one NVIDIA V100 GPU on SemanticKITTI. In the inference stage, only the weakly supervised learning branch is activated to produce predictions.
absent from the scene,
1= 10. The distribution alignment branch
4.2 Comparative Analysis
Results on S3DIS. We detail the segmentation performance at 0.1% and 0.01 % label rates on S3DIS Area 5. DGNet boosts performance for each baseline, which is evenly distributed across categories.
The experiments demonstrate that DGNet not sensitive loss term weights.

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Table 1: Quantitative comparisons on S3DIS Area 5 under various weakly supervised settings. The bold denotes the best performance.
Sctting
Method
mloU
ceiling
flocr
wall
beam
column
window
Goor
chair
table
bookcase
sofa
board
clutter
NointNot
41
41.1
88.8
97.3
69.88
9.1
3.9
46.3
10.8
59.0
52.6
5.9
40.3
26.4
33.2
SQN
18
63.7
92.8
96.9
81.8
0.0
25.9
50.5
65.9
79.5
85.3
55.7
72.5
65.8
55.9
(Pally)
100%
HybridCR
ERDA
31
65.8
93.6
98.1
82.3
28.9
24.4
59.5
79.6
87.9
67.1
73.0
66.8
58.7
55.7
DCcpCCN
29
60.0
90.8
97.5
76.7
24.9
51.4
52.7
76.7
83.0
61.1
62.2
58.5
44,6
NeX
3
69.2
94.7
98.5
82.9
0.0
24.2
59.9
74,3
83.0
91.4
76.3
75.5
78.6
60.4
PointTransV
41
70.4
94.0
98.5
N6.3
0.0
38.0
63.4
74.3
89.1
82.4
74.3
80.2
76.0
59.3
SQN
15
64.1
91.7
95.6
78.7
24.2
55,9
63.1
70.5
83.1
60.7
67.8
56.
50.6
95.5
PointMatch
63.4
0.1%
AAD
10
67.2
93.7
98.0
81.5
0.0
19.4
59,5
72.0
80.9
86.5
788.
73.0
72.
56.1
DeppCNN
43.9
93.4
97.6
68.3
0.0
19.6
59.6
4.9
47.4
35.2
$9.5
30.2
2.2""
52.2"
NGN
58.4
91.2
97.3
76.5
0.0
22.7
47.2
42.8
73 2
85.0
62.0
59.7
58.
44,2
PointNeXi [1
97.8
79.5
27.3
53.6
98.4
28.9
90.7
74.1
0.03%
PSD (5)
48.2
87,9
96.0
62.1
20.6
49.3
40.9
55.
61.9
43.9
50.7
27.3
31.1
0.03%
HybrilCR 11
$1.5
K5.
91.9
65.9
0.0
18.0
$1.4
34.2
63.8
78,3
$2.4
59.6
29.9
39.0
0.03%
DX1 1
59.6
91.7
95.8
76.4
0.O
21.2
58.3
29.6
72.6
83.3
64.2
69.6
63.4
48.6
0,028
MILTmmn
50
5144
86.6
93.2
75.0
29.3
45.3
62.3
56.5
33.7
32.2
0029
ERDA
87.3
96.3
65.1
36.4
6020
MulPro
5b
47.5
90.1
96.3
71.8
0.0
6.7
46.7
39,2
67.2
67.4
21.8
29.2
33.0
38.0
0.00%
SQN 18
45.3
89.2
93.5
71,3
0.0
1,1
34.7
41.0
$1.9
66.9
25,7
55.4
12.8
39.6
0.01%
CPCM 35
59.3
0.01%
AADNet
92.5
20.9
0.01%
DeepGCN 29
35.9
76.7
97.1
65.2
0.0
0.4
57.6
58.0
49.1
8.5
26.2
0.01%
DGNNet
52.8
92.0
97.9
75.2
0.0
23.4
22.7
33.4
74.1
83.6
29.8
62.0
47.1
45.1
0.01%
PointNeXi 03
$8.4
89,1
96.5
75.7
0.1
22.6
56.3
44.5
74.2
81.3
$4.2
62.8
52.5
47.0
9.01%
DGNNN
62.4
93,3
98.1
M0.1
23.3
47.9
53.1
79.4
87.2
60.0
70.6
65.2
53.1
The lower the label rate, the more distinct the en- hancement brought by DGNet, which suggests that the guidance feature distribution is more valu- able with extremely sparse annotations. Specifically, DGNet achieves more than 97% performance of fully- supervision with only 0.1% % points labeled. The 0.02% label rate denotes a sparse labeling form of "one-thing- one-click". DGNet outperforms these methods without introducing super-voxel information. In addition, Fig. visualizes a qualitative comparison. DGNet provides a holistic enhancement to the baseline. Although photos on the wall are misclassified, DGNet captures consistent objects more accurately than the baseline.
Table Quantitative comparisons on
ScanNet.
Setting
Method
mIoU (%)
PointNet 41
33.9
100% (Fully)
HybirdCR 31
59.9
PointNeXt
43
71.2
Zhang et al.
[58
51.1
PSD
55
54.7
HybirdCR 31
56.8
DCL 57
59.6
1%
GaIA 28
65.2
EDRA 48
63.0
AADNet
339
66.8
Results on ScanNetV2. Compared to S3DIS, ScanNetV2 involves diverse categories and versatile scenes. Therefore, following the super-voxel setting in OTOC (36), we report the segmentation performances with 20 labeled points per scene and 1% points labeled. The cross-entropy loss term generates relatively suffi- cient supervised information to train the network due to introducing pseudo-labeling, resulting in a less pro- nounced DGNet improvement than S3DIS. However, DGNet still slightly superior to the latest SOTA meth- ods.
DGNet (PointNeXt))
67.4
Hou er al.
55.5
OTOC
36
59.4
MILTrans
56
54.4
DAT
54
55,2
20pts
PointMatch
52
62.4
EDRA
48
57.0
AADNet
33
62.5
DGNet (PointNeXt)
62.9
Table 3: Quantitative comparisons on Se-
ManticKITTI.
Results on SemanticKITTI DGNet performs ex- cellently on indoor datasets and demonstrates strong weakly supervised learning efficiency on outdoor Se- manticKITTI. For fair comparison, we replace the DGNet backbone with RandLA-Net [9). DGNet out- performs SQN [8] with 1.0% and 2. 1% mloU on 0.1% and 0.01 % label rates, respectively, demonstrating the necessity of supervision feature space.
Setting
Method
mloU (%)
RPSC 26
50.9
0.1%
SQN 18
50.8
DGNet (RandLA-Neel
51.8
CPCM
35
34.7
0.01%
SQN 18
39.1
DGNet (RandI.A-Nel)
41.2
8

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Point Cloud
Ground Truth
PointNeXt
DGNet (PointNext)
Figure 4: Visual comparisons between baseline and our DGNet on S3DIS Area at 0.01% label rate.
Table Comparisons on feature distribution description selection in distribution alignment branch.
Distance Metric
Distribution
Distribution Modeling
mIoU (%)
Euclidean Norm
Cosine Similarity
45
59.9
Category Prototype
HPN 37
60.3
GMM
61.3
Mixture Models
moVMF
62.4
4.3
Ablations and Analysis
All ablation studies are performed on S3DIS with PointNeXt-I as baseline.
Distribution comparison. We impose comparison experiment in the distribution alignment branch of DGNet for distribution selection. The relevant experimental results are reported Tab. 4 For category prototype models, discard the vMF loss L<MF and consistency loss Lcon due to the lack of corresponding forms. For the mixture model with Euclidean Norm (GMM), we replace the maximum likelihood estimation in GMM form with the LyME in DGNet. In terms of distance metrics, cosine similarity trumps Euclidean norm. In terms of distribution modeling, mixture models have a significant performance advantage over the category prototype models. Integrating these aspects, the stronger fitting ability of moVMF leads to more accurate and effective supervised signals for weakly supervised learning in DGNet.
Ablation study for loss terms. Tab. 5 demonstrates the validity each loss term in DGNet. Compared with partial cross-entropy loss, the truncated cross-entropy loss improves segmentation performance due to its avoidance of overfitting. Performance improvements are obtained by imposing LvMP with soft assignment form, LDIS and LCON individually, and optimal performance achieved by using these loss terms simultaneously. In contrast to the soft assignment, the hard assignment does not take into account the inter-cluster similarity and is mismatched with the soft-mo VMF algorithm. Therefore, LvMF with hard assignment form in hard-moV VMF algorithm and KNN-mo VMF algorithm undermines the segmentation efficiency.
Ablation study for Nested EM Algorithm. We ablate the proposed Nested Expectation Maxiiamm
Algorithm in two respects. First, optimize certain parameters mo mo VMF and fix other parameters with initialized values. The first, second, third, and last rows in Tab. reveal that individually optimizing parts of the parameters impairs the segmentation performance. Secondly, the parameters of moVMF are updated. Compared with kNN-mo VM (fourth raw) and hard-mo VMF (fifth raw) in 33 the soft assignment strategy delivers 2.6% and 2.2% mloU improvements, respec- tively. This shows that the optimization of mo VM parameters benefits from the soft assignment strategy.
ablate how
Hyperparameter selection. In Tab. we search the parameter space for suitable k, 4, and 3. We observe that (a) the segmentation performance shows an increasing and then decreasing trend the

---

Table 5: Ablation study for loss terms.
Table 6: Ablation studies for Nested
Sppectation-Maximae Algorithm.
LCE
LYMF
LpS
COON
mloU (%)
CpCB
LIR
hard
soft
E step
mloU (%)
58.4
None
61.0
59.1
soft-mo VMF
60.9
58.9
soft-mo VMF
60.0
60.4
hard-moVMF
59.8
59.8
KNN-mo VMF
60.2
61.1
62.4
soft-mo VMF
62.4
concentration constant x increases. Our analysis suggests that too small x leads to a dispersion of features within the class, which can be easily confused with other classes, And too large forces overconcentration of features within the class and overfits the network. (b) As the iteration number t increases, the segmentation performance gradually rises and then stabilizes. We believe that the soft-mo MMF algorithm gradually converges as t increases, and increasing t after convergence will no longer bring further gains to the network. (c) As the truncated threshold 3 decreases, the segmentation performance shows a tendency to first increase and then decrease. The conventional cross-entropy loss function is the truncated cross-entropy loss function with 3 1. When decreases, the overfitting on sparse annotations is alleviated, but when | is too small, it weakens the supervised signal on sparse labeling leading to performance degradation.
Table 7: Hyperparameter selection for (a) concentration constant K, (b) iteration number and (c) truncated threshold B.
(a)
(b)
(c)
mIoU (%)
t
mloU (%)
8
mIoU (%)
0.1
57.7
0
61.0
0.7
61.9
1
60.3
5
61.5
0.8
62.4
10
62.4
10
62.4
0.9
62.2
20
59.5
15
62.3
1
61.7
5
Limitations and Future Work
Despite the promising performance achieved by DGNet, exploring the distribution of embeddings is preliminary. Feng el al. [12) proposes more sophisticated distribution to restrict feature learning with full supervision. However, such refinement restrictions will lead to overfitting under sparse annotations. Therefore, how to prevent wcakly-supervised learning overfitting with enhanced feature description a promising research topic.
Conclusion
In this paper, we propose novel perspective by regulating the feature space for weakly supervised point cloud semantic segmentation and develop a distribution guidance network verify the supe- riority of this perspective. Based on the investigation of the distribution of semantic embeddings, we choose VM describe the intrinsic distribution. In DGNet, we alleviate the underfitting across the entire dataset and overfitting within the labeled points. Extensive experimental results demonstrate that DGNet rivals or even surpasses recent SOTA methods on S3DIS, ScanNerV2, and SeTanticKITTI. Moreover, DGNet demonstrates the interpretability of network predictions and scalability various label rates. We expect our work to inspire the point cloud community to strengthen the inherent properties of weakly supervised learning.
10

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Acknowledgements
This work was supported by Shenzhen Science and Technology Program under Grant KQTD201 101112487711143338
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Appendix A
Derivation of Optimization Objective Function
According to maximum likelihood estimation, the optimization objective function defined as:
P(VI2.0) +) 2,2,
II P(vi|22,0.. θ2,)
min 6.2,e
min 6.2,0
Σ
u2;))
(11)
min 9.2,9
Σ Ca Ca(x,, up v:))
Σ log(Ca((i.)) log(as.) Rs. u. 2.2.0
min
To avoid the long-tail problem and simplify computations, set constant value for x on each class Therefore, the objective optimization function Eq. I1 can be further simplified as:
max P(V|2,0) 2.2.6
= min 6.2,9
log(az.) + kuy va)
(12)
Algorithm I: soft-mo Algorithm
Input: Normalized Embeddings V = [v. 1,2, ... ,n., Initial Clustering Centers H. = (helc C}
Output: Soft Assignments Q, Clustering Results Z, Parameters of mo VMF θ
j Initialize in è */ for category index of C do
Cee Ue
2 h.
end
repeat
1 The Expectation step of EM */ for point index i 1 do
for category index e of C
f(velss u.) Ca(ks exp(rcu, v.) end
Compute posterior probability q: */ for category index of C do
P(clvi, +) og exp(au [.v] v:)
Eiec (xpparrsp v,]
end end
Maximization step for category index e of C do
21 ((c|vi, !) 21 0(
u.
end
until Convergence
return P(CVV 0). argmax Q),
(ac, uolc E C)
Appendix B
The soft-mo VMF Algorithm
Initialization. Due to the sparsity of the annotations, some classes in the scene may lack any labeled points, thereby hindering proper initialization. Consequently, maintain memory bank (53 to store class prototypes across the entire dataset. Specifically, the mean embedding directions on labeled points are set the initial vectors for categories with labeled points in the point cloud scene.
14

---

For the missing categories of this scene, we retrieve the category prototypes p from the memory bank as supplementary initialization. Consequently, the initial vector h, is formulated as:
Vu V vill CE Y 1 1
h
(13)
Pe
c Y
Pseudo Code. As presented in Algorithm|] 1 incorporate prior knowledge about the semantics during the optimization process based on Soft-moVMF [3]. The weights a = 1/ICI are initialized uniformly. Subsequently, based the cosine similarity between features each point and mean directions of each category, the prior probability f and the posterior probability qu are estimated. Finally, determine the clustering result 2; for each point by argmax(q:). After updating the mean directions u and weights a, the process is repeated until the clustering results converge.
Appendix C More Experimental Results
Impact label rates. To demonstrate the capability of DGNet extreme label rates, we compare the segmentation performance on sparse annotations over larger range of rates. Tab, reports the mloU performance of the DGNet and baseline 10%, 1%, %. 0.01 %, and 0.001 label rates. It can be observed that at 100,000 times less sparse annotations, the baseline fails to learn accurate semantic embedding from it. At the same time, our DGNet still maintains acceptable segmentation performance since it can be conducted unsupervised.
Method
10%
1%
0.1%
0.01% %
0.001 %
PointNeXt
69.3
68.3
67.0
60.8
44.7
DGNet (PointNeXI)
69.5
68.8
67.8
62.4
51.5
Table 8: Performance comparison on various label rates.
we verified the sensitivity of DGNet (PointNeXt) to different labeled points at the same label rate. We repeated the experiment five times for each label setting, keeping the network and label rate unchanged and changing only the labeled points' locations. In Tab. 9
Varying labeled points. Following SQN 18
we observe slight performance fluctuation within reasonable range.
Setting
Trail#1
Trail#2
Trail#3
Trail#4
Trail#5
Mean
STD
0.1%
67.8
66.9
66.7
67.6
67.3
67.3
0.42
0.01%
62.0
62.4
61.4
61.7
62.0
61.9
0.33
Table 9: Sensitivity analysis of DGNet on S3DIS Area 5.
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NeurIPS Paper Checklist
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Justification:
The complete derivation of Eq. 5 given in Appendix.
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Reviews:
[{"review_id": "4Ihi9PkYAN", "reviewer": "Reviewer_bWaK", "summary": "This paper outlines a study focusing on distance metric and distribution modeling, highlighting the effectiveness of combining mixture of von Mises-Fisher distributions (moVMF) with cosine similarity. A Distribution Guidance Network (DGNet) is introduced, featuring two main branches: weakly supervised learning and distribution alignment. The network utilizes reliable clustering initialization from the weakly supervised branch to iteratively update moVMF parameters and network parameters, ensuring alignment with moVMF-defined feature spaces.", "questions": "Please answer the questions in Weaknesses.", "limitations": "The authors have thoroughly discussed the limitations of DGNet, and there are no potential negative societal impacts associated with their work.", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "Originality: DGNet is a distribution guidance network that combines a weakly supervised learning branch and a distribution alignment branch. The weakly supervised learning branch makes use of reliable cluster initialization for learning. This means that the network is able to perform preliminary learning and classification of data through clustering methods without detailed labeling. This approach helps to reduce the dependence on large amounts of labeled data and improves the robustness and scalability of the model. The distribution alignment branch alternately updates the parameters of the moVMF (von Mises-Fisher distribution) and the parameters of the network to ensure that the network parameters are aligned with the feature space defined by the moVMF. This method helps to guide the network to learn the structure and characteristics of data distribution, so as to improve the generalization ability and adaptability of the model.\n\nQuality: DGNet explains the prediction probability from the perspective of Bayes' theorem and provides the confidence of each prediction, which proves the rationality of DGNet selection distribution and network design. In addition, extensive experiments confirm the soundness and efficacy of the chosen distribution and network design.", "weaknesses": "1. The section of 4.2 and 4.3 can be written in more detail. In particular, the explanation of changes in model performance in ablation experiments should be added. Specifically, a thorough explanation of the changes in model performance observed during ablation experiments should be incorporated. Ablation experiments involve systematically removing components or features from the model to analyze their impact on performance. By detailing how each modification affects the overall performance metrics, readers gain insights into the critical elements contributing to the model's effectiveness.\n2. In Abstract, there is no a clear problem to address from existing methods of weakly supervised learning for 3D point clouds. Similarly, in Introduction, it’s also not clear about the motivation of this work and existing problems of this topic.\n3. There is no main contributions about this work in Introduction.\n4. How to balance weights of each loss function in Equation (9)? \n5. There is no any qualitative comparison between this work with others.\n6. Some quantitative results from this work are also incremental improvements compared to others within one percentage point.\n7. Compared with previous work, the performance improvement of DGNet model may not be substantial enough to justify its superiority over existing methods, especially on the ScanNet and SemanticKITTI datasets.\n8. In the section of 4.3, why does the performance of the model degrade when optimizing some parameters? What is the impact of parameter optimization on resource consumption?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Response to Reviewer bWaK\nWe appreciate your valuable comments and suggestions. We will respond to each of your concerns and hopefully eliminate them.\n\n* **R1 (About detailed explanation):**\n\n  Due to page constraints, we analyze and interpret the main and important experimental results in the manuscript. We will provide a detailed elaboration of the analysis of the experimental results in Sec. 4.2 and 4.3 during the reviewer-author discussion period, due to the character limit in the rebuttal period.\n\n* **R2 (About writing):**\n\n  In our writing experience, there are generally three main types of writing in academic articles:\n  * The article proposes a new task, which requires a description of the significance of the new task and the difficulties in solving it.\n  * The article provides specific improvements to the existing methodology, which needs to describe the problems faced by the methodology.\n  * The article develops a new paradigm to address the current challenges, which entails summarizing the previous paradigms and elaborating on the advantages of the proposed new paradigm.\n\n  We believe that DGNet is more per the third writing logic. Therefore, we focus on the challenges of weakly supervised point cloud semantic segmentation in the Abstract. In the second paragraph of the Introduction, we summarize current methods into three paradigms and draw out their common problem, for which we propose a new paradigm.\n\n* **R3 (About contribution summary):**\n\n  According to our understanding, NeurIPS 2024 does not have a mandatory requirement to summarize contributions. Some highly cited papers also do not summarize major contributions, such as ResNet, Attention is All You Need, Non-local Neural Networks, ViT, *etc*.\n\n* **R4 (About balance weights):**\n\n  As mentioned in line 221 of the text, instead of adjusting the weight of each loss term, DGNet significantly improves the network's performance by simply adding them together, reflecting the robust performance improvement from each loss term. Recognizing that careful tuning of the weights may lead to superior segmentation performance, we fix the $\\mathcal{L}\\_\\text{tCE}$ and balance the weights of other loss terms by magnitude, the results of which are shown in Tab. 1 of *Rebuttal.pdf*. The balanced loss function is $\\mathcal{L}\\_\\text{tCE}+\\mathcal{L}\\_\\text{vMF}+0.1\\mathcal{L}\\_\\text{DIS}+0.1\\mathcal{L}\\_\\text{CON}$, but essentially equal in performance to the loss function used in the manuscript.\n\n* **R5 (About qualitative comparison):**\n\n  Our work follows the visualization experimental setup of state-of-the-art methods (such as ERDA, CPCM, PointMatch, *etc*) in the field of weakly supervised point cloud semantic segmentation, focusing on visual comparisons between the baseline and the proposed method.\n\n* **R6 & R7 (About performance improvement):** \n\n  For a detailed explanation of performance, including why DGNet has less boost in some cases, please refer to the specific response in R1.\n\n  We would like to emphasize that DGNet is not an incremental work, *i.e.*, it is not an adaptation or refinement of an existing weakly supervised learning paradigm, but rather a new weakly supervised learning paradigm constructed from the perspective of describing the distribution of feature space. Therefore, the purpose of the comparison experiments is to demonstrate that this novel weakly supervised learning paradigm is feasible and has the potential to outperform other weakly supervised learning paradigms. We recognize that there is still room for performance improvement in some datasets, but we believe the current comprehensive performance benefits across multiple datasets and multiple sparse labeling settings are sufficient to demonstrate the potential of this new paradigm. We look forward to the subsequent ongoing efforts of the Point Cloud community to fully exploit the weakly supervised performance of this paradigm.\n\n* **R8 (About performance degradation and resource consumption):** \n\n  * **Explanation for performance degradation** We find two places that could be considered performance degradation in Sec. 4.3. The first place is the introduction of $\\mathcal{L}\\_\\text{vMF}$ with hard assignment form. In contrast to the soft assignment, the hard assignment does not take into account the inter-cluster similarity and is mismatched with the soft-moVMF algorithm. So DGNet uses $\\mathcal{L}\\_\\text{vMF}$ with soft assignment form. The second place is to optimize $\\alpha$ and $\\mathbf{u}$ individually because the fixed parameters affect the accurate update of the optimizable parameters. Therefore, DGNet simultaneously optimizes $\\alpha$ and $\\mathbf{u}$.\n  * **Explanation for resource consumption** In the inference phase, there is no additional memory consumption compared to the baseline since DGNet only activates the weakly supervised learning branch for inference. In the training phase, the resource consumption mainly comes from the Memory Bank and Soft-moVMF algorithm. Compared to the baseline, DGNet only increases 25.8M during the training phase, and this resource consumption increase is not significant compared to the baseline network itself.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "rFmlZKrKR3", "reviewer": "Reviewer_KHTz", "summary": "This paper addresses the problem of weakly supervised point cloud semantic segmentation. The authors propose imparting supplementary supervision signals by regulating the feature space under weak supervision. The initial investigation identifies which distributions accurately characterize the feature space in fully supervised learning, subsequently leveraging this prior knowledge to guide the alignment of weakly supervised embeddings. The authors first investigate different feature space characterizations and find that a mixture of von Mises-Fisher (moVMF) distributions with cosine similarity best describes the fully supervised embedding space. Based on this finding, DGNet is proposed with two branches: a weakly supervised learning branch and a distribution alignment branch. Leveraging reliable clustering initialization derived from the weakly supervised learning branch, the distribution alignment branch alternately updates the parameters of the moVMF and the network, ensuring alignment with the moVMF-defined feature space. Experimental results demonstrate that DGNet achieves state-of-the-art performance on multiple datasets.", "questions": "See weakness", "limitations": "A main limitation is the computational complexity of the training.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.\tThe proposed framework presents a novel and intriguing approach, distinguishing itself from consistency training, self-training, and similarity metric methods.\n\n2.\tThe authors perform a comprehensive study to identify the most appropriate model for characterizing the feature space in fully supervised learning.\n\n\n3.\tDGNet is designed with two complementary branches: one dedicated to weakly supervised learning and another focused on distribution alignment. This dual-branch structure facilitates the effective integration of the distribution prior into the learning process.\n\n4.\tDGNet demonstrates its efficacy by achieving superior results across multiple datasets and various weakly supervised settings.", "weaknesses": "1. Computational Complexity: The paper omits a crucial discussion on the computational complexity of the distribution alignment branch, particularly regarding the EM-like algorithm. This is important, given that EM-based clustering methods traditionally tend to be computationally intensive.\n\n2. Ablation Study: The current ablation study would benefit from exploring a broader range of loss term combinations. For instance, examining the performance of the complete loss function without $L_{DIS}$ or without $L_{CON}$ would provide more comprehensive insights into the contribution of each component.\n\n3. Discussion and Analysis of moVMF: The paper lacks a deep analysis or discussion explaining why the mixture of von Mises-Fisher (moVMF) distribution outperforms other distributions. Additionally, it fails to provide formal guarantees on convergence or optimality. A more thorough discussion or justification for the choice of moVMF over alternative distributions would be better.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Response to Reviewer KHTz\n\nWe express our sincere gratitude for your valuable comments. In response to your concerns, we carefully structure our response as follows:\n\n* **R1 (About computational complexity):** \n\n  The main computational complexity of the distribution alignment branch comes from the soft-voVMF algorithm. According to the pseudocode in the Supplementary Material, the complexity of the soft-voVMF is $O(tn|\\mathbb{C}|)$, where $t$ is the iteration number, $n$ is the point number of the point cloud, and $|\\mathbb{C}|$ is the number of semantic categories. Since $t$, $n$, and $|\\mathbb{C}|$ are all set to constant values during network training, the extra computation introduced by the distribution alignment branch is trivial. A detailed explanation of why the algorithm converges quickly at a constant $t$ is given in R3.\n\n* **R2 (About ablation study):**\n\n  Table 6 of the manuscript illustrates the ablation experiments with the loss term added individually. Based on your valuable suggestion, we show the ablation study for removing the loss terms individually in the *rebuttal.pdf*. As can be seen, each loss term contributes to the final result. Removing or modifying loss terms results in sub-optimal performance, where vMF loss has the most significant effect.\n\n* **R3 (About discussion and analysis of moVMF):**\n\n  * **Why moVMF?**\n\n    How to describe the feature space of a neural network is an open problem. Since the feature space is affected by a variety of factors such as network structure, training data, parameter settings, optimization (loss) function, *etc.*, it is unrealistic to mathematically derive an optimal and general description. Nevertheless, we construct different distributions from two dimensions and try to explain the merits and demerits of these candidate distributions in describing the feature space.\n\n    * From the distribution modeling perspective, we compare the Category Prototype Model with the Mixture Model. Despite its computational simplicity, the Category Prototype Model describes the features only by comparing the distance of features to the category prototypes. This means that the Category Prototype Model ignores the distribution within categories and the variability between categories. In contrast, the Mixture Model has a larger parameter optimization space and a relatively stronger fitting ability.\n\n    * For the distance metric, we compare the Euclidean norm and cosine similarity. We attempt to analyze these two distances with the segment head structure in the Supplementary Material. To facilitate the analysis, we simplify the structure of the segment head and define it as $\\text{SegHead}(\\mathbf{F})=\\text{argmax}(\\text{softmax}(\\mathbf{WF}^\\top))$, where $\\mathbf{F}$ is the semantic feature extracted by the decoder and $\\mathbf{W}$ is the parameter of the output layer. Consider a group of feature vectors {$k\\mathbf{F} |k\\geq 0 \\And \\mathbf{F} \\neq \\mathbf{0}$}. For any two feature vectors $k_1\\mathbf{F}$ and $k_2\\mathbf{F}$ within this group, the segmentation predictions are identical, $$\\text{SegHead}(k_1\\mathbf{F})=\\text{argmax}(\\text{softmax}(k_1\\mathbf{WF}^\\top))=\\mathop{\\text{argmax}}\\limits_{i} \\frac{e^{k_1 \\mathbf{W}_{i,:} \\mathbf{F}\\_{i,:}^\\top } }{\\sum_j e^{k_1 \\mathbf{W}\\_{j,:}\\mathbf{F}\\_{j,:}^\\top}} = \\text{argmax}(\\text{softmax}(\\mathbf{WF}^\\top))=\\text{argmax}(\\text{softmax}(k_2\\mathbf{WF}^\\top))=\\text{SegHead}(k_2\\mathbf{F}).$$ If the general case of using an activation function is taken into account, it does not change the result after argmax since the activation function is usually monotonically nondecreasing. Therefore, **the segment head is a radial classifier** that has a more pronounced classification performance on the angles, so that cosine similarity describes the feature space better than the Euclidean norm.\n\n    In summary, the mixture of von Mises-Fisher distribution with both cosine similarity and mixture model is optimal among the candidate distributions, and the experimental comparisons in Tab 1 validate our analysis.\n\n  * **Convergence proof.**\n\n    The soft-moVMF belongs to the EM algorithm. In 1983, Jeff Wu proved the convergence properties of the EM algorithm in [1]. He proved that the EM algorithm can make the log-likelihood function of the observed data converge to a stable value under certain conditions. \n\n    However, this stable value is not necessarily optimal, which is related to the initialization of the EM algorithm. Therefore, we prove that the difference between the initialization $\\mathbf{h_c}$ from the weakly supervised learning branch and the theoretical optimal mean vector $\\mathbf{u^*\\_c}$ conforms to a Gaussian distribution with a mean value of 0. According to maximum likelihood estimation, $\\mathbf{u}^*\\_c=\\frac{1}{n_c}\\mathop{\\sum}\\limits_{y\\_i = c} (\\mathbf{F}\\_i)$, where $n_c$ denotes the point number belonging to c-th category and $y_i$ denotes the i-th label of full annotations. The initialization $\\mathbf{h_c}$ from the weakly supervised learning branch can be defined as $\\mathbf{h_c}=\\frac{1}{m_c}\\mathop{\\sum}\\limits_{y'_i = c} (\\mathbf{F}_i)$, where $m_c$ is the labeled point number belonging to c-th category in sparse annotations and $y'_i$ is the i-th label of sparse annotations. Sparse labeling can be considered as the result of sampling over the full labeling, *i.e.*, $y'=s(y)$. Assume that the sample is independently redistributed and obeys a certain distribution $\\mathcal{D}(\\mu,\\sigma^2)$. According to the Central Limit Theorem, the following convergent distribution can be obtained: $$(\\mathbf{u}^*\\_c-\\mathbf{h}\\_c) \\sim \\mathcal{N}(0, \\frac{\\sigma^2}{m_c}).$$ This means that the initialized mean vector in DGNet has a high probability of appearing in the vicinity of the optimal solution. Therefore, the soft-moVMF converges quickly at a constant iteration number $t$.\n\n [1] Wu, CF Jeff. \"On the convergence properties of the EM algorithm.\" The Annals of statistics (1983): 95-103.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "h2aBhv96gc", "reviewer": "Reviewer_ruvS", "summary": "A weakly-supervised approach has been studied to relieve the annotation burden for point cloud semantic segmentation. Unlike conventional works that mainly use priors (such as similarity or augmentation-based regularization) to overcome the lack of information in weak labels, this paper introduces a novel approach directly aligning the features on the latent space of a neural network. Specifically, the proposed method employs a mixture of von Mises-Fisher distribution to model the feature distribution. This brings meaningful gains on multiple distinct architectures across various benchmarks.", "questions": "See the weaknesses.", "limitations": "Yes.", "rating": 7, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The feature distribution is a core problem but has not yet been deeply addressed, at least in the field of weakly supervised point cloud semantic segmentation.\n2. The methodology and presentation for it are pretty good.\n3. The performance is impressive.", "weaknesses": "I think this paper has no major flaws in methodological aspects.\nTherefore, I would like to ask some questions for further discussion.\n\n1. Table 1 shows that a mixture of vMF distributions represents the distribution of normalized features better than the other choices. But why? Can you discuss the \"oughtness\" in more detail, at least at the level of the hypothesis? For example, why is using a mixture of vMFs better than that of Gaussians? \n\n2. Intuitively, using a hypersphere can represent each feature as an angle, resulting in a more concise distribution. However, if the number of categories increases, this kind of approach may not effectively use the latent space, as all the points on a line map to one single point on the hypersphere (due to normalization). I wonder if the proposed method faces difficulty when handling the dataset including more categories.\n\n3. It will be interesting if the authors check the feature distribution of the neural network trained by fully-supervised learning. Do the features still follow the mixture of vMFs well or not? Can the proposed method even enhance the performance in a fully-supervised setting?\n\n4. Related works.\nAs far as I know, MPRM does not use 2D images (Line 82). And it would be better if the authors could cite recent papers in CVPR 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Response to Reviewer ruvS\n\nWe sincerely appreciate your insightful feedback and positive evaluation. In response to your valuable comments, we structure our response as follows:\n\n* **R1 (About oughtness and moVMF):**\n\n  Next, we discuss \"oughtness\" and the superiority of the mixture of vMFs (moVMF).\n\n  * **Discussion about \"oughtness\"**.\n\n    In DGNet, the \"oughtness\" is a constraint on the feature space distribution under weakly supervised learning. The goal of weakly supervised learning is to enable the network to achieve comparable performance under sparse annotations as under full annotations. To achieve this, the features under weakly supervised learning should be as identical as possible to those under fully supervised learning. Due to the great discrepancy in the quality of the annotations between weakly supervised learning and fully supervised learning, obtaining the same features is difficult. Therefore, in this paper, we relax this restriction and expect to realize **the alignment of fully supervised learning and weakly supervised learning in the feature space of the neural network**. The \"oughtness\" means that the feature space distribution under weakly supervised learning should be identical to the feature space distribution under fully supervised learning.\n\n  *  **The superiority of moVMF**.\n\n      Above we discuss the \"oughtness\" of weakly supervised learning, but how to describe the feature space distribution under fully supervised learning to provide a prior for weakly supervised learning has not been addressed. Unfortunately, how to describe the feature space of a neural network is an open problem. However, it is undeniable that von Mises-Fisher has demonstrated strong data fitting and generalization capabilities in the fields of self-supervised learning [1,2], classification [3], variational inference [4], online continual learning [5], and so on.  For our explanation of the superiority of moVMF, please refer to the *R3 (About discussion and analysis of moVMF)* in the response to the Reviewer KHTz.\n\n* **R2 (About representation ability):**\n\n    Firstly, normalized features only as an input to the distribution alignment branch to provide additional supervised signals to DGNet, while the weakly supervised learning branch uses unnormalized features, and thus for the theoretical upper bound of the representation, DGNet does not differ from the baseline. Second, for the D-dimensional semantic feature $\\mathbf{F}$, the normalized feature $\\text{norm}(\\mathbf{F})$ in the distribution alignment branch is a feature distributed on a D-1 dimensional hypersphere. Given that D is typically large (set to 256 in our implementation), the loss due to projection is almost negligible. Furthermore, we know from previous analyses that the segment head is a radial classifier, so the normalized features do not affect the segmentation results either.\n\n* **R3 (About performance on full supervision):**\n\n    The experiment in Table 1 is a validation of the neural network feature distribution under full supervision. The experimental results illustrate that the feature space distribution under full supervision fits more closely to the mixture of von Mises-Fisher distribution than the other distributions. Following your suggestion, we impose our DGNet to full supervision. With PointNeXt-L as the baseline, DGNet slightly improves mIoU from 69.2% (baseline) to **69.5%** on S3DIS, which means that distribution guidance is similarly effective for full supervision.\n\n* **R4 (About typos and reference):**\n\n    Thanks for your meticulous reading! The sentence in Line 82 should be \" Via CAMs, MPRM and J2D3D dynamically generate point-wise pseudo-labels from subcloud-level annotations and image-level annotations, respectively. \" We will correct this typo in the next version. We also note that some encouraging work has emerged from CVPR 2024, but these articles were not available before submission. We will cite them in the next version.\n\n[1] Chen, Xinlei, and Kaiming He. \"Exploring simple siamese representation learning.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2021.\n\n[2] Hariprasath Govindarajan, Per Sidén, Jacob Roll, Fredrik Lindsten. \"DINO as a von Mises-Fisher mixture model.\" ICLR 2023.\n\n[3] Scott, Tyler R., Andrew C. Gallagher, and Michael C. Mozer. \"von mises-fisher loss: An exploration of embedding geometries for supervised learning.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021.\n\n[4] Taghia, Jalil, Zhanyu Ma, and Arne Leijon. \"Bayesian estimation of the von-Mises Fisher mixture model with variational inference.\" IEEE transactions on pattern analysis and machine intelligence 36.9 (2014): 1701-1715.\n\n[5] Michel, Nicolas, et al. \"Learning Representations on the Unit Sphere: Investigating Angular Gaussian and Von Mises-Fisher Distributions for Online Continual Learning.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 38. No. 13. 2024.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "hJJRBJ9KLx", "reviewer": "Reviewer_fVFW", "summary": "In this work, the authors use a selected feature space distribution as supplementary supervision signals, combining with cosine similarity as the distance metric, and implement a dual-branch weakly supervised point cloud semantic segmentation network. Experiments show that using feature space distribution as supervision information can improve the performance of existing point cloud semantic segmentation networks.", "questions": "Please respond to my comments written above.", "limitations": "Evaluation on outdoor datasets is insufficient.", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "This work proposes to use moVMF distribution to regulate the feature space for weakly supervised point cloud semantic segmentation. Experimental results show that this approach can improve the performances of backbone networks.", "weaknesses": "As the feature space distribution is selected in a fully supervised manner, it is questionable whether it is suitable for weakly supervised scenarios where labeled samples are extremely sparse. Directly comparing different distributions in the distribution alignment branch of DGNet is more convincing.\n\nEq. 1 in supplementary material, the last term should be log(a_zi) + k_zi * u^T_zi * vi, instead of log(a_zi) * k_zi * u^T_zi * vi.\n\nIn Eq. 9, why use the same weight for each loss term? Considering that these losses are defined from very different perspectives, their values can be of different orders of magnitude.\n\nThere are some minor flaws in the writing: some tables and figures are not referenced in the text, and some figures are not numbered in the order referenced.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Response to Reviewer fVFW\n\nWe sincerely appreciate your volunteered time. We will respond to your concerns and hopefully eliminate them.\n\n* **R1 (About comparing distributions):**\n\n  As you mentioned, we compare the fitting ability of several candidate distributions in describing the feature space from a fully supervised learning perspective in Section 3.2 of the manuscript. Based on your valuable suggestions, we impose a comparison experiment in the distribution alignment branch of DGNet for several distributions to enhance the credibility of the article. The relevant experimental results are reported in Table 3 of *rebuttal.pdf*. \n\n  We make the following modifications to embed the other three distributions individually into the distribution alignment branch of DGNet. (1) The Category Prototype models cluster features by distance magnitude, so we could not design a loss derived from maximum likelihood estimation like $\\mathcal{L}\\_\\text{vMF}$ and the total loss used for Category Prototype models is $\\mathcal{L}\\_\\text{tCE}+\\mathcal{L}\\_\\text{DIS}+\\mathcal{L}\\_\\text{CON}$. Correspondingly, there is no EM algorithm for optimizing the parameters in the distribution alignment branch. (2) For the Gaussian Mixture Model, we modify the Gaussian Mixture Model loss [1] used for images into the distribution alignment branch of DGNet.\n\n  The experimental results show that the segmentation performance of different distributions under weak supervision is consistent with the feature space fitting ability under full supervision. The stronger feature space fitting ability of moVMF under full supervision leads to more accurate and effective supervised signals for weakly supervised learning with the distribution alignment branch in DGNet.\n\n* **R2 (About typos and minor flaws):**\n\n  Thanks for the meticulous reading! The typos and minor flaws you mentioned will be rectified in the next release.\n\n* **R3 (About balance weights):**\n\n  As mentioned in line 221 of the text, instead of adjusting the weight of each loss term, DGNet significantly improves the network's performance by simply adding them together, reflecting the robust performance improvement from each loss term. Recognizing that careful tuning of the weights may lead to superior segmentation performance, we fix the $\\mathcal{L}\\_\\text{tCE}$ and balance the weights of other loss terms by magnitude, the results of which are shown in Tab. 1 of *Rebuttal.pdf*. The balanced loss function is $\\mathcal{L}\\_\\text{tCE}+\\mathcal{L}\\_\\text{vMF}+0.1\\mathcal{L}\\_\\text{DIS}+0.1\\mathcal{L}\\_\\text{CON}$, but essentially equal in performance to the loss function used in the manuscript.\n\n* **R4 (About outdoor datasets):**\n\n  Only a few works provide segment performance on outdoor datasets in weakly supervised point-cloud semantic segmentation.  With the same baseline method RandLa-Net, DGNet improves 1.0% and 2.1% mIoU over SQN on SemanticKITTI at 0.1% label rate and 0.01% label rate, respectively. Considering the inherent density inhomogeneity of outdoor scenes, the excellent performance with such sparse annotations validates the effectiveness of DGNet with the outdoor dataset.\n\n  To enrich the evaluation of the outdoor dataset, we compare the segmentation performance of the baseline method RandLA-Net and DGNet on the *Semantic8* subset of Semantic3D. At 0.01% label rate, DGNet achieves **59.4%** mIoU compared to 55.8% of the baseline.\n\n[1] Wu, Linshan, et al. \"Sparsely annotated semantic segmentation with adaptive gaussian mixtures.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
# Summary of Author Rebuttal

We respectfully appreciate the constructive comments and valuable suggestions given by each reviewer. We are confident that each reviewer has given sufficient time to scrutinize our work. To respond to the issues raised and to dispel some misconceptions, we analyze and explain each comment. All the effects we made in the rebuttal period can be summarized in three aspects:

* **Explanation of distribution choice.** We re-emphasize the superiority of the chosen mixture of the von Mises-Fisher distribution (moVMF) from several perspectives, including the distribution modeling, the structure of the segment head, and the feature-fitting ability. We also expect that this work will stimulate further exploration in the point cloud community concerning the feature space description.

* **Supplementation of experiments.** Based on the suggestions, our main supplementary experiments include (1) a weight-balancing experiment for loss terms, (2) an ablation experiment for removing loss terms, and (3) a comparison experiment for different distribution priors in the distribution alignment branch. Due to the character limitations of the dialog box, we place the results of the three experiments in *rebuttal.pdf*.

* **More interpretation for DGNet.** We explain the writing logic of the article, the complexity of the algorithm, the convergence of the algorithm, the representation ability of the features, and so on. These explanations provide a more consolidated theoretical support for DGNet.

We expect that these responses during the rebuttal period will address the main concerns raised by reviewers, and we also look forward to further polishing this work with the experts during the reviewer-author discussion period.

Meta-review: This paper receives bipolar ratings of 1 accept, 1 borderline accept, and 2 borderline reject. Most reviewers agree the core problem of investigating feature distribution raised by the paper is important and interesting, and the authors did sufficient experiments on the benchmark datasets. However, there are few concerns raised regarding the oughtness of the selected moVMF distributions, incremental improvements against existing methods, and lack of evaluation on large-scale outdoor datasets. Some reviewers' concerns are addressed by the rebuttal but not all of them.

After carefully reading the paper, reviews, and the rebuttal discussion, AC finds that the paper is well-written, logically sound with adequate evaluation. Therefore, AC thinks the paper is ready and suitable for publication in NeurIPS. The authors are encouraged to add more justification on the oughtness of moVMF, given cosine similarity simply outperforms euclidean distance in high dimensional space and moVMF is the only distribution candidate in the design space. We congratulate the authors on the acceptance of their paper!
Decision: Accept (poster)