SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Besides, due to the simplicity of ERDA, we are able to follow the setup of the baselines for training, which enables straightforward implementation and easy adaptation on various backbone models with little overhead.
Overall objective. Finally, with ERDA learning in Eq. (5), we maximize the same loss for both labeled and unlabeled points, segmentation task, and pseudo-label generation, where we allow the gradient to back-propagate through the (pseudo-)labels. The final loss is given as
$$
L = \frac {1}{N ^ {l}} \sum_ {\mathbf {x} \in \mathcal {X} ^ {l}} L _ {c e} (\mathbf {q}, y) + \alpha \frac {1}{N ^ {u}} \sum_ {\mathbf {x} \in \mathcal {X} ^ {u}} L _ {p} (\mathbf {q}, \mathbf {p}), \tag {6}
$$
where  $L_{p}(\mathbf{q},\mathbf{p}) = L_{ce}(\mathbf{q},\mathbf{p}) = H(\mathbf{q},\mathbf{p})$  is the typical cross-entropy loss used for point cloud segmentation,  $N^l$  and  $N^u$  are the numbers of labeled and unlabeled points, and  $\alpha$  is the loss weight.
We present the benefits of our proposed ERDA by experimenting with multiple large-scale datasets, including S3DIS [2], ScanNet [16], SensatUrban [33] and Pascal [19]. We also provide ablation studies for better investigation.
Table 2. The results are obtained on the S3DIS datasets Area 5. For all baseline methods, we follow their official instructions in evaluation. The **bold** denotes the best performance in each setting.
We choose RandLA-Net [34] and CloserLook3D [51] as our primary baselines following previous works. Additionally, while transformer models [17, 52] have revolutionized the field of computer vision as well as 3D point cloud segmentation [97, 42], none of the existing works have addressed the training of transformer for point cloud segmentation with weak supervision, even though these models are known to be data-hungry [17]. We thus further incorporate the PointTransformer (PT) [97] as our baseline to study the amount of supervision demanded for effective training of transformer.
For training, we follow the setup of the baselines and set the loss weight  $\alpha = 0.1$ . For a fair comparison, we follow previous works [94, 95, 32] and experiment with different settings, including the  $0.02\%$  (1pt),  $1\%$  and  $10\%$  settings, where the available labels are randomly sampled according to the ratio<sup>3</sup>. More details are given in the supplementary.
4.2 Performance Comparison
Results on S3DIS. S3DIS [2] is a large-scale point cloud segmentation dataset that covers 6 large indoor areas with 272 rooms and 13 semantic categories. As shown in Tab. 2, ERDA significantly improves over different baselines on all settings and almost all classes. In particular, for confusing classes such as column, window, door, and board, our method provides noticeable and consistent improvements in all weak supervision settings. We also note that PT suffers from severe over-fitting and feature collapsing under the supervision of extremely sparse labels of "1pt" setting; whereas it is alleviated with ERDA, though not achieving a satisfactory performance. Such observation agrees with the understanding that transformer is data-hungry [17].
<sup>3</sup>Some super-voxel-based approaches, such as OTOC [53], additionally leverage the super-voxel partition from the dataset annotations [32]. We thus treat them as a different setting and avoid direct comparison.
Figure 3. We show obvious improvement of our ERDA over baseline (RandLA-Net) on different scenes from S3DIS Area 5. In the office and hallway (top 2), ERDA produces more detailed and complete segmentation for windows and doors, and avoids over-expansion of the board and bookcase on the wall, thanks to the informative pseudo-labels. In more cluttered scenes (bottom 2), ERDA tends to make cleaner predictions by avoiding improper situations such as desk inside clutter and preserving important semantic classes such as columns.
settings	methods	mIoU
Fully	PointNet [56]	47.6
RandLA-Net [34]	70.0
KPConv [68]	70.6
HybridCR [47]	70.7
PT [97]	73.5
PointNeXt - XL [58]	74.9
RandLA-Net + ERDA	71.0
CloserLook3D + ERDA	73.7
PT + ERDA	76.3
1%	zhang et al. [94]	65.9
PSD [95]	68.0
HybridCR [47]	69.2
RandLA-Net + ERDA	69.4
CloserLook3D + ERDA	72.3
PT + ERDA	73.5
Table 3. Results on S3DIS 6-fold.
settings	methods	mIoU
Fully	PointCNN [48]	45.8
RandLA-Net [34]	64.5
KPCov [68]	68.4
HybridCR [47]	59.9
CloserLook3D + ERDA	70.4
20pts	MIL-Trans [87]	54.4
CloserLook3D + ERDA	57.0
0.1%	SQN [32]	56.9
RandLA-Net + ERDA	62.0
1%	zhang et al. [94]	51.1
PSD [95]	54.7
HybridCR [47]	56.8
RandLA-Net + ERDA	63.0
Table 4. Results on ScanNet test.
settings	methods	mIoU
Fully	PointNet [56]	23.7
PointNet++ [57]	32.9
RandLA-Net [34]	52.7
KPConv [68]	57.6
LCPFormer [36]	63.4
RandLA-Net + ERDA	64.7
0.1%	SQN [32]	54.0
RandLA-Net + ERDA	56.4
Table 5. Results on SensatUrban test.
methods	92	183	366	732	1464
FixMatch [64]	63.9	73.0	75.5	77.8	79.2
+ ERDA	73.5	74.9	78.0	78.5	80.1
Table 6. Results on Pascal dataset.
Impressively, ERDA yields competitive performance against most supervised methods. For instance, with only  $1\%$  of labels, it achieves performance better than its stand-alone baselines with full supervision. Such result indicates that the ERDA is more successful than expected in alleviating the lack of training signals, as also demonstrated qualitatively in Fig. 3.
Therefore, we further extend the proposed method to fully-supervised training, i.e., in setting "Fully" in Tab. 2. More specifically, we generate pseudo-labels for all points and regard the ERDA as an auxiliary loss for fully-supervised learning. Surprisingly, we observe non-trivial improvements (+3.7 for RandLA-Net and +3.4 for CloserLook3D) and achieve the state-of-the-art performance of 72.6 (+2.2) in mIoU with PT. We suggest that the improvements are due to the noise-aware learning from ERDA, which gradually reduces the noise during the model learning and demonstrates to be generally effective. Moreover, considering that the ground-truth labels could suffer from the problem of label noise [38, 90, 65], we also hypothesize that pseudo-labels from ERDA learning could stabilize fully-supervised learning and provide unexpected benefits.
We also conduct the 6-fold cross-validation, as reported in Tab. 3. We find our method achieves a leading performance among both weakly and fully-supervised methods, which further validates the effectiveness of our method.
Results on ScanNet. ScanNet [16] is an indoor point cloud dataset that covers 1513 training scenes and 100 test scenes with 20 classes. In addition to the common settings, e.g.,  $1\%$  labels, it also provides official data efficient settings, such as 20 points, where for each scene there are a pre-defined
ER	DA	mIoU	ent.
baseline	59.8	-
+ pseudo-labels	63.3	2.49
✓	65.1	2.26
+ ERDA	✓	66.1	2.44
✓	✓	67.2	2.40
(a) ERDA improves the results and reduces the entropy (ent.), individually and jointly.
LDA\λ	0	1	2
-	-	65.1	66.3
KL(p||q)	66.1	67.2	66.6
KL(q||p)	66.1	65.9	65.2
JS	65.2	65.4	65.1
MSE	66.0	66.2	66.1
(b) ER and DA provide better results when taking  $KL(\mathbf{p}||\mathbf{q})$  with  $\lambda = 1$
k	one-hot	soft	ERDA
64	63.1	62.8	64.5
500	63.0	62.3	64.1
1e3	63.3	63.5	65.5
1e4	63.0	62.9	65.6
dense	62.7	62.6	67.2
(c) ERDA consistently benefits the model with more pseudo-labels  $(k)$ .
Table 7. Ablations on ERDA. If not specified, the model is RandLA-Net trained with ERDA as well as dense pseudo-labels on S3DIS under the  $1\%$  setting and reports in mIoU. Default settings are marked in gray.
set of 20 points with the ground truth label. We evaluate on both settings and report the results in Tab. 4. We largely improve the performance under  $0.1\%$  and  $1\%$  labels. In 20pts setting, we also employ a convolutional baseline (CloserLook3D) for a fair comparison. With no modification on the model, we surpass MIL-transformer [87] that additionally augments the backbone with transformer modules and multi-scale inference. Besides, we apply ERDA to baseline under fully-supervised setting and achieve competitive performance. These results also validate the ability of ERDA in providing effective supervision signals.
Results on SensatUrban. SensatUrban [33] is an urban-scale outdoor point cloud dataset that covers the landscape from three UK cities. In Tab. 5, ERDA surpasses SQN [32] under the same  $0.1\%$  setting as well as its fully-supervised baseline, and also largely improves under full supervision. It suggests that our method can be robust to different types of datasets and effectively exploits the limited annotations as well as the unlabeled points.
Generalizing to 2D Pascal. As our ERDA does not make specific assumptions on the 3D data, we explore its potential in generalizing to similar 2D settings. Specifically, we study an important task of semi-supervised segmentation on image [72, 89, 8] and implement our method to the popular baseline, FixMatch [64], which combines the pseudo-labels with weak-to-strong consistency and is shown to benefit from stronger augmentation [89]. We use DeepLabv3+ [9] with ResNet-101 [30].
As in Tab. 6, we show that ERDA brings consistent improvement from low to high data regime, despite the existence of strong data augmentation and the very different data as well as setting<sup>4</sup>. It thus indicates the strong generalization of our method. We also see that the improvement is less significant than the 3D cases. It might be because 2D data are more structured (e.g., pixels on a 2D grid) and are thus less noisy than the 3D point cloud.
4.3 Ablations and Analysis
We mainly consider the  $1\%$  setting and ablates in Tab. 7 to better investigate ERDA and make a more thorough comparison with the current pseudo-label generation paradigm. For more studies on hyper-parameters, please refer to the supplementary.
Individual effectiveness of ER and DA. To validate our initial hypothesis, we study the individual effectiveness of  $L_{ER}$  and  $L_{DA}$  in Tab. 7a. While the pseudo-labels essentially improve the baseline performance, we remove its label selection and one-hot conversion when adding the ER or DA term. We find that using ER alone can already be superior to the common pseudo-labels and largely reduce the entropy of pseudo-labels (ent.) as expected, which verifies that the pseudo-labels are noisy, and reducing these noises could be beneficial. The improvement with the DA term alone is even more significant, indicating that a large discrepancy is indeed existing between the pseudo-labels and model prediction and is hindering the model training. Lastly, by combining the two terms, we obtain the ERDA that reaches the best performance but with the entropy of its pseudo-labels larger than ER only and smaller than DA only. It thus also verifies that the DA term could be biased to uniform distribution and that the ER term is necessary.
Different choices of ER and DA. Aside from the analysis in Sec. 3.2, we empirically compare the results under different choices of distance for  $L_{DA}$  and  $\lambda$  for  $L_{ER}$ . As in Tab. 7b, the outstanding result justifies the choice of  $KL(\mathbf{q}||\mathbf{p})$  with  $\lambda = 1$ . Additionally, all different choices and combina
<sup>4</sup>We note that the number in the first row in Tab. 6 denotes the number of labeled images, which is different from the setting of sparse labels in 3D point clouds.
tions of ER and DA terms improve over the common pseudo-labels (63.3), which also validates the general motivation for ERDA.
Ablating label selection. We explore in more detail how the model performance is influenced by the amount of exploitation on unlabeled points, as ERDA learning aims to enable full utilization of the unlabeled points. In particular, we consider three pseudo-labels types: common one-hot pseudo-labels, soft pseudo-labels (p), and soft pseudo-labels with ERDA learning. To reduce the number of pseudo-labels, we select sparse but high-confidence pseudo-labels following a common top- $k$  strategy [94, 53] with various values of  $k$  to study its influence. As in Tab. 7c, ERDA learning significantly improves the model performance under all cases, enables the model to consistently benefit from more pseudo-labels, and thus neglects the need for label selection such as top- $k$  strategy, as also revealed in Fig. 1. Besides, using soft pseudo-labels alone can not improve but generally hinders the model performance, as one-hot conversion may also reduce the noise in pseudo-labels, which is also not required with ERDA.
5 Limitation and Future Work
While we mostly focus on weak supervision in this paper, our method also brings improvements under fully-supervised setting. We would then like to further explore the effectiveness and relationship of  $L_{ER}$  and  $L_{DA}$  under full supervision as a future work. Besides, despite promising results, our method, like other weak supervision approaches, assumes complete coverage of semantic classes in the available labels, which may not always hold in real-world cases. Point cloud segmentation with missing or novel classes should be explored as an important future direction.
In this paper, we study the weakly-supervised 3D point cloud semantic segmentation, which imposes the challenge of highly sparse labels. Though pseudo-labels are widely used, label selection is commonly employed to overcome the noise, but it also prevents the full utilization of unlabeled data. By addressing this, we propose a new learning scheme on pseudo-labels, ERDA, that reduces the noise, aligns to the model prediction, and thus enables comprehensive exploitation of unlabeled data for effective training. Experimental results show that ERDA outperforms previous methods in various settings and datasets. Notably, it surpasses its fully-supervised baselines and can be further generalized to full supervision as well as 2D images.
Acknowledgement. This project is supported in part by ARC FL-170100117, and IC-190100031.
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A Supplementary: Introduction
In this supplementary material, we provide more details regarding implementation details in Appendix B, more analysis of ERDA in Appendix C, full experimental results in Appendix D, and studies on parameters in Appendix E.
B Supplementary: Implementation and Training Details
For the RandLA-Net [34] and CloserLook3D [51] baselines, we follow the instructions in their released code for training and evaluation, which are here (RandLA-Net) and here (CloserLook3D), respectively. Especially, in CloserLook3D[51], there are several local aggregation operations and we use the "Pseudo Grid" (KPConv-like) one, which provides a neat re-implementation of the popular KPConv [68] network (rigid version). For point transformer (PT) [97], we follow their paper and the instructions in the code base that claims to have the official code (here). For FixMatch [64], we use the publicly available implementation here.
Our code and pre-trained models will be released.
C Supplementary: Delving into ERDA with More Analysis
Following the discussion in Sec. 3, we study the impact of entropy regularization as well as different distance measurements from the perspective of gradient updates.
In particular, we study the gradient on the score of the  $i$ -th class i.e.,  $s_i$ , and denote it as  $g_i = \frac{\partial L_p}{\partial s_i}$ . Given that  $\frac{\partial p_j}{\partial s_i} = \mathbb{1}_{(i = j)}p_i - p_ip_j$ , we have  $g_i = p_i\sum_jp_j\left(\frac{\partial L_p}{\partial p_i} -\frac{\partial L_p}{\partial p_j}\right)$ . As shown in Tab. 8, we demonstrate the gradient update  $\Delta = -g_{i}$  under different situations.
In addition to the analysis in Sec. 3.2, we find that, when  $\mathbf{q}$  is certain, i.e.,  $\mathbf{q}$  approaching a one-hot vector, the update of our choice  $KL(\mathbf{p}||\mathbf{q})$  would approach the infinity. We note that this could be hardly encountered since  $\mathbf{q}$  is typically also the output of a softmax function. Instead, we would rather regard it as a benefit because it would generate effective supervision on those model predictions with high certainty, and the problem of gradient explosion could also be prevented by common operations such as gradient clipping.
In Fig. 4, we provide visualization for a more intuitive understanding on the impact of different formulations for  $L_{DA}$  as well as their combination with  $L_{ER}$ . Specifically, we consider a simplified case of binary classification and visualize their gradient updates when  $\lambda$  takes different values. We also visualize the gradient updates of  $L_{ER}$ . By comparing the gradient updates, we observe that only  $KL(\mathbf{p}||\mathbf{q})$  with  $\lambda = 1$  can achieve small updates when  $\mathbf{q}$  is close to uniform ( $q = \frac{1}{2}$  under the binary case), and that there is a close-0 plateau as indicated by the sparse contour lines.
Additionally, we also find that, when increasing the  $\lambda$ , all distances, except the  $KL(\mathbf{p}||\mathbf{q})$ , are modulated to be similar to the updates of having  $L_{ER}$  alone; whereas  $KL(\mathbf{p}||\mathbf{q})$  can still produce effective updates, which may indicate that  $KL(\mathbf{p}||\mathbf{q})$  is more robust to the  $\lambda$ .
D Supplementary: Full Results
We provide full results for the experiments reported in the main paper. For S3DIS [2], we provide the full results of S3DIS with 6-fold cross-validation in Tab. 10. For ScanNet [16] and SensatUrban [33], we evaluate on their online test servers, which are here and here, and provide the full results in Tab. 11 and Tab. 12, respectively.
LDA	KL(p||q)	KL(q||p)	JS(p,q)	MSE(p,q)
Lp	H(p,q)-(1-λ)H(p)	H(q,p)-H(q)+λH(p)	H(p+q)/2-(1/2-λ)H(p)-1/2H(q)	1/2∑i(pi-qi)^2+λH(p)
gi	pi ∑j pj(-log qi/qj+(1-λ) log pi/pj)	pi - qi - λpi ∑j pj log pi/pj	pi ∑j pj(-1/2 log pi+qi/pj+qi/(1/2-λ) log pi/pj)	pi(pi - qi) - pi ∑j pj(pj - qj) - λpi ∑j pj log pi/pj
Situations	Δ = -gi
pk→1	0	qi-1k=i	0	0
q1=⋯=qK	(λ-1)pip∑j pj log pi/pj	1/K - pi + λpi ∑j pj log pi/pj	pi ∑j ≠i ∑j pj(1/2 log Kpi+1/Pkj+1+(λ-1/2) log pi/pj)	-pi^2 + pi ∑j pj^2 + λpi ∑j pj log pi/pj
qi→1	+inf	1 - pi + λpi ∑j pj log pi/pj	pi ∑j ≠i ∑j pj(1/2 log pi+1/pj+(λ-1/2) log pi/pj)	-pi^2 + pi(1 - pi) + pi ∑j pj^2 + λpi ∑j pj log pi/pj
qk≠i→1	- inf	-pi + λpi ∑j pj log pi/pj	pi ∑j ≠i ∑j pj(1/2 log pi/pj+1/j=k+(λ-1/2) log pi/pj)	-pi^2 - pi p_k + pi ∑j pj^2 + λpi ∑j pj log pi/pj
Table 8. The formulation of  $L_{p}$  using different functions to formulate  $L_{DA}$ . We present the gradients  $g_{i} = \frac{\partial L_{p}}{\partial s_{i}}$ , and the corresponding update  $\Delta = -g_{i}$  under different situations. Analysis can be found in the Sec. 3.2 and Appendix C.
KL(p||q)	KL(q||p)	JS(p,q)	MSE(p,q)
(a)  $\lambda = 0$
(b)  $\lambda = 1$
(c)  $\lambda = 2$
(d) Gradient updates of  $L_{ER}$
Figure 4. Contour visualization of the gradient update with binary classes for better understanding. For a clearer view, we use red for positive updates and blue for negative updates, the darker indicates larger absolute values and the lighter indicates smaller absolute values.
m	mIoU
0.9	66.19
0.99	66.80
0.999	67.18
0.9999	66.22
(a) Momentum update.
projection	mIoU
-	65.90
linear	66.55
2-layer MLPs	67.18
3-layer MLPs	66.31
(b) Projection network.
α	mIoU
0.001	65.25
0.01	66.01
0.1	67.18
1	65.95
E Supplementary: Ablations and Parameter Study
We further study the hyper-parameters involved in the implementation of ERDA with the prototypical pseudo-label generation, including loss weight  $\alpha$ , momentum coefficient  $m$ , and the use of projection network. As shown in Tab. 9, the proposed method acquires decent performance (mIoUs are all  $>65$  and mostly  $>66$ ) in a wide range of different hyper-parameter settings, compared with its fully-supervised baseline (64.7 mIoU) and previous state-of-the-art performance (65.3 mIoU by HybridCR [47]).
Additionally, we suggest that the projection network could be effective in facilitating the ERDA learning, which can be learned to specialize in the pseudo-label generation task. This could also be related to the advances in contrastive learning. Many works [10, 11, 25] suggest that a further projection on feature representation can largely boost the performance because such projection decouples the learned features from the pretext task. We share a similar motivation in decoupling the features for ERDA learning on the pseudo-label generation task from the features for the segmentation task.
(c) Loss weight.
Table 9. Parameter study on ERDA. If not specified, the model is RandLA-Net with ERDA trained with loss weight  $\alpha = 0.1$ , momentum  $m = 0.999$ , and 2-layer MLPs as projection networks under  $1\%$  setting on S3DIS. Default settings are marked in gray.
settings	methods	mIoU	ceiling	floor	wall	beam	column	window	door	table	chair	sofa	bookcase	board	clutter
Fully	RandLA-Net + ERDA	71.0	94.0	96.1	83.7	59.2	48.3	62.7	73.6	65.6	78.6	71.5	66.8	65.4	57.9
CloserLook3D + ERDA	73.7	94.1	93.6	85.8	65.5	50.2	58.7	79.2	71.8	79.6	74.8	73.0	72.0	59.5
PT + ERDA	76.3	94.9	97.8	86.2	65.4	55.2	64.1	80.9	84.8	79.3	74.0	74.0	69.3	66.2
1%	RandLA-Net + ERDA	69.4	93.8	92.5	81.7	60.9	43.0	60.6	70.8	65.1	76.4	71.1	65.3	65.3	55.0
CloserLook3D + ERDA	72.3	94.2	97.5	84.1	62.9	46.2	59.2	73.0	71.5	77.0	73.6	71.0	67.7	61.2
PT + ERDA	73.5	94.9	97.7	85.3	66.7	53.2	60.9	80.8	69.2	78.4	73.3	67.7	65.9	62.1
Table 10. The full results of ERDA with different baselines on S3DIS 6-fold cross-validation.
settings	methods	mIoU	bathtub	bed	books.	cabinet	chair	counter	curtain	desk	door	floor	other	pic	fridge	shower	sink	sofa	table	toilet	wall	wdn
Fully	CloserLook3D + ERDA	70.4	75.9	76.2	77.0	68.2	84.3	48.1	81.3	62.1	61.4	94.7	52.7	19.9	57.1	88.0	75.9	79.9	64.7	89.2	84.2	66.6
20pts	CloserLook3D + ERDA	57.0	75.1	62.5	63.1	46.0	77.7	30.0	64.9	46.1	43.6	93.3	36.0	15.4	38.0	73.6	51.6	69.5	47.2	83.2	74.5	47.8
0.1%	RandLA-Net + ERDA	62.0	75.7	72.4	67.9	56.9	79.0	31.8	73.0	58.1	47.3	94.1	47.1	15.2	46.3	69.2	51.8	72.8	56.5	83.2	79.2	62.0
1%	RandLA-Net + ERDA	63.0	63.2	73.1	66.5	60.5	80.4	40.9	72.9	58.5	42.4	94.3	50.0	35.0	53.0	57.0	60.4	75.6	61.9	78.8	73.8	62.6
Table 11. The full results of ERDA with different baselines on ScanNet [16] test set, obtained from its online benchmark site by the time of submission.
settings	methods	mIoU	OA	Ground	Vegetation	Buildings	Walls	Bridge	Parking	Rail	Roads	Street Furniture	Cars	Footpath	Bikes	Water
Fully	RandLA-Net + ERDA	64.7	93.1	86.1	98.1	95.2	64.7	66.9	59.6	49.2	62.5	46.5	85.8	45.1	0.0	81.5
0.1%	RandLA-Net + ERDA	56.4	91.1	82.0	97.4	93.2	56.4	57.1	53.1	5.2	60.0	33.6	81.2	39.9	0.0	74.2
Table 12. The full results of ERDA with different baselines on SensatUrban [33] test set, obtained from its online benchmark site by the time of submission.