Towards Robust Pseudo-Label Learning in Semantic Segmentation: An Encoding Perspective
Authors: Wangkai Li
Rui Sun
Zhaoyang Li
Tianzhu Zhang
Venue: NeurIPS 2025 poster ()
Keywords: Semantic segmentation
Primary area: applications

Abstract: Pseudo-label learning is widely used in semantic segmentation, particularly in label-scarce scenarios such as unsupervised domain adaptation (UDA) and semi-supervised learning (SSL). Despite its success, this paradigm can generate erroneous pseudo-labels, which are further amplified during training due to utilization of one-hot encoding. To address this issue,  we propose ECOCSeg, a novel perspective for segmentation models that utilizes error-correcting output codes (ECOC) to create a fine-grained encoding for each class. ECOCSeg offers several advantages. First, an ECOC-based classifier is introduced, enabling model to disentangle classes into attributes and handle partial inaccurate bits, improving stability and generalization in pseudo-label learning. Second, a bit-level label denoising mechanism is developed to generate higher-quality pseudo-labels, providing adequate and robust supervision for unlabeled images. ECOCSeg can be easily integrated with existing methods and consistently demonstrates significant improvements on multiple UDA and SSL benchmarks across different segmentation architectures. Code is available at https://github.com/Woof6/ECOCSeg.

Towards Robust Pseudo-Label Learning in Semantic Segmentation: An Encoding Perspective
Wangkai Li", Rui Sun', Zhaoyang Li', Tianzhu Zhang University of Science and Technology of China
National Key Laboratory of Deep Space Exploration, Deep Space Exploration Laboratory (lwklwk, issunrui, lizhaoyang) @mail. ustc. edu. en, tzzhangdustc. edu.
Abstract
Pseudo-label learning is widely used in semantic segmentation, particularly in label-scarce scenarios such unsupervised domain adaptation (UDA) and semi- supervised learning (SSL). Despite its success, this paradigm can generate erro- neous pseudo-labels, which are further amplified during training due to utilization of one-hot encoding. To address this issue, we propose ECOCSeg, novel perspec- tive for segmentation models that utilizes error-correcting output codes (ECOC) to create fine-grained encoding for each class. ECOCSeg offers several advan- tages. First, an ECOC-based classifier is introduced, enabling model to disentangle classes into attributes and handle partial inaccurate bits, improving stability and generalization in pseudo-labes learning. Second, a bit-level label denoising mech- anism is developed to generate higher-quality pscudo-labels, providing adequate and robust supervision for unlabeled images. ECOCSeg can be easily integrated with existing methods and consistently demonstrates significant improvements on multiple UDA and SSL benchmarks across different segmentation architectures. Code is available at https:/ /gg thub........... www comm/oooff/EOCCSe
Introduction
Semantic segmentation has seen significant improvements with recent advances in deep neural networks[55, 9, 17, 16]. However, major challenge in semantic segmentation is the requirement of a large volume of fine-grate fine-grained pixel-level labels, which can tine-consuming and labor-intensive to obtain [19]. Due the readily available nature of image data, unsupervised domain adaptation (UDA) and semi-supervised learning (SSL) have been introduced semantic segmentation to handle the label-scarce scenarios. UDA involves learning from synthetic labeled data and transferring knowledge to real unlabeled target domains, while SSL utilizes a tiny portion of annotated data to generalize on unseen data. As result, UDA and SSL are gaining significant attention as promising approaches to reduce the reliance on extensive annotations in semantic segmentation.
In both UDA and SSL settings, models are trained using annotated and unlabeled data simultaneously. Existing mainstream methods introduce common paradigms, which can be grouped into the self- training pipeline and the consistency regularization framework. Specifically. self-training methods [79, 41] leverage a temporally smoothed exponential moving average (EMA) model as a teacher to generate stable pseudo labels for unlabeled data. On the other hand, the consistency regularization methods [72, 3] encourage the model to produce consistent predictions for the same sample across different perturbation views. These paradigms be summarized the network's ' predictions are used as supervision for unlabeled data.
neeudo-labe learning, where
"Correponndng author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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(a) Pseudo Label Learning
(b) One-hol Encoding
(c) ECOC Encoding
Figure 1: Comparison of two label encoding methods. (a) Examples of erroneous pseudo labels. (b) Existing methods perform pixel-level classification using argmax-based one-hot encoding. (c) The proposed ECOCSeg predicts the multi-bit binary encoding, which disentangles the classes into fine-grained attributes and enhances the stability of the training process in pseudo-label learning.
Although achieving promising results, the inevitable errors in pscudo labels misled the training process. Typical approaches design filter-out mechanisms [93, 72] and only use high-confidence pscudo-labels for training. However, this paradigm tends to make the model focus on learning from easy samples while neglecting difficult ones, resulting in a sub-optimal performance. Another alternative is utilize weighting functions [36, 77] that assign weights based on confidence of pseudo- labels. While potentially effective, this approach requires careful design and selection of appropriate hyperparameters, which inevitably compromise its applicability. Based on above discussions, investigate existing works primarily concentrate on developing specific selection strategies for pseudo- labels but rarely consider the impact of the encoding form assigned for classes. As shown in Fig. (a). the pixel features of the class sheep are being confused by the classifier as horse or cow, and an erroneous pseudo-label is typically encoded in a one-hot manner through the argmax operation (see Fig.1 I (b)). We speculate that similar classes share common visual attributes, leading to confusing pscudo-labels and further misguiding the training process. How utilize the shared attributes among confusing classes to design a suitable encoding form for pseudo-labe learning is rarely explored.
To explore the encoding form tailored for pseudo-label learning, classes into fine-grained attributes and consider each class a set of attributes. As shown in Fig. 1 (c), even with incorrect predictions in specific attributes, confusing classes still exhibit shared attribute characteristics. For instance, both sheep and cow have horn and hoof and are not biped. Despite potential misclassification, accurate prediction of these shared attributes can still provide valuable guidance for effectively training the network. Based on this observation, we resort to crror-correcting output codes (ECOC) [21] assign binary bit string (codeword) an encoding for each class, decomposing the N-class classification problem into K two-class subtasks. The collection of codewords corresponding to each class forms a codebook. This paradigm determines the class by predicting K-bit binary encoding and selecting the nearest neighbor query in the codebook. The encoding form created by suitable ECOC enjoys two properties: class discriminability, ensuring well-separated classes by sufficient Hamming distance between codewords, and attribute diversity, ensured by making each bit-position classifier uncorrelated. ECOC encoding endows the model with the ability to handle partial inaccurate bits and make classification decisions. With theoretical guarantee (Sec. 4), we show that ECOC can serve as an effective equivalent to one-hot encoding in fully supervised settings, and exhibits greater robustness in pseudo-label learning by achieving tighter classification error bound under a sufficiently large minimum code distance.
explicitly disentangle the
In this paper, we propose ECOCSeg, a novel segmentation framework designed for pseudo- learning. ECOCSeg leverages error-correctin output codes (ECOC) as the class representation and creates fine- tineggrined encoding forms to denoise pseudo-labels Compared to the widely adopted pseudo-label learning paradigm, which involves encoding form (typically one-hot), pseudo-label selection strategy (typically weighting), and optimization criteria (typically cross-entropy loss), ECOCSeg introduces innovations tailored to the challenges of pseudo-label learning. (1) ECOC- based Encoding Form. To implement ECOC as alternative the typically argmax-base based one-hot

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query oodoward
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predicion
reliable miinnng
oodeward dass
(n) bit-wise parao label
(b) code-wise psrudo label
(c) hyhrid psendo label
Figure 2: Demonstration of different forms of assigning pseudo labels introduced by ECOCSeg.
encoding in the segmentation paradigm, we explore two simple yet effective coding strategies, i.e., max-min distance encoding and text-based encoding, consider robustness and the relationship between classes, respectively. (2) Bit-level Denoising Mechanism. To consider the noise in pseudo labels, present two assigning forms: bit-wise pseudo label and code-wise pseudo label (Fig. (a) and (b)). The former provides softer supervision by quantifying the output into bit-level codes, while the latter queries the nearest codeword from the codebook pseudo labels, effectively rectifying inaccurate bits when the classification is accurate but potentially introducing additional noise when incorrect. To leverage the strengths of both forms, propose reliable bit mining algorithm to identify candidate classes and determine the shared bits among corresponding codewords as reliable bits, capturing the confidence part of code-wise labels. By combining them with bit-wise labels, we obtain more robust pseudo-labels in a hybrid way, improving pseudo-label learning stability. (3) Customized Optimization Criteria. Intuitively, we can directly use binary cross-entropy for training. However, it optimizes each binary classifier independently. lacking structured representation space constraints and leading to slower convergence. To address this issue, we introduce customized optimization criteria, namely pixel-code distance and pixel-code contrast. These criteria optimize our framework effectively, equipped with intra-class compactness and inter-class separation, further enhancing overall performance.
Our contributions can be summarized as follows: (1) We present new perspective to consider pseudo-label noise and propose designing a suitable encoding form for pseudo-label learning that utilizes shared attributes among confusing classes. (2) We formalize pseudo-label learning into three fundamental components for analysis: encoding form, pseudo-label selection strategy, and optimization criteria, and correspondingly develop an ECOC-based encoding form, bit-level denoising mechanism, and customized loss functions to enhance performance. (3) We theoretically analyze the performance ECOC and one-hot encoding in both fully supervised and pseudo-label learning settings, demonstrating that with suitable codebook design, ECOC has greater potential to tolerate label noise. (4) We implement ECOCSeg, which can be easily built upon existing pseudo-label learning frameworks and consistently improves performance on multiple UDA and SSL benchmarks.
2 Related Work
2.1 Label-scarce Semantic Segmentation
Although deep models have achieved remarkable success in various tasks [42, 29, 80, 23, 13, 48, 88, 86), they heavily rely on large amounts of labeled training data and struggle to generalize to data with shifted distributions. This is particularly evident in semantic segmentation, where alternative approaches have been introduced to avoid laborious pixel-wise annotation. Unsupervised domain adaptation (UDA) [27, 26, 81, 78, 15, 64, 32, 31, 14] aims to transfer knowledge from labeled source domains to unlabeled target domains, enabling models perform well in the target domain despite distribution differences. Semi- semi-superrised learning (SSL) [12, 92, 87, 99, 76, 75] leverages a combination of few manually annotated target samples with a large pool of unlabeled samples to enhance model performance. Weakly supervised learning [89, 37, 1, 6] addresses the challenge by utilizing less precise annotation signals, such as image-level labels or bounding boxes. Few-shot learning [22, 84, 53, 90, 50, 56, 51, 49] approaches tackle scenarios with small number of annotated samples by leveraging prior knowledge and meta-learning techniques. UDA and SSL, in particular, share similar objective of using unlabeled (target) data to improve the performance of models
3

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trained with labeled (source) data only. In this work, we explore these two settings from unified perspective of pseudo-label learning.
2.2 Pseudo-label Learning
Two popular paradigms are often employed when training model with unlabeled data: self-training- based methods [105, 79, 34, 41, 46] and consistency eggularizationbasee methods [72, 12, 3, 93]. In self-training, the model is trained on unlabeled samples using pseudo labels derived from teacher network. Consistency regularization aims to ensure prediction stability across different perturbations. Both can viewed as pseudo-label learning [103, 44, 66]. More recently, state-of-the- art segmentation methods in UDA and SSL combine both technologies [85, 35, 54, 47, 74J. Although making significant progress, incorrect pseudo-labels can mislead the model's training process. Typical approaches incorporate filtering mechanisms [72, 93] to train the model exclusively with highly confident pseudo-labels, while recent research focuses on identifying suitable weight functions to improve training stability [36, 77, 34]. Some works design new optimization criteria inspired by negative learning [66, 87] to improve learning from pseudo-labels. In this paper, we focus on the encoding form of the pseudo-label, which is orthogonal direction to the above approaches.
Method
3.1
Preliminaries
For the general formulation of UDA and SSL in semantic segmentation, (source) samples D, = (1), v/) where x! represents i-th image with vÊ as the corresponding pixel-wise one-hot label covering classes, and n, unlabeled (target) samples D; = { with the same label space. The supervised loss L can be calculated on labeled data:
given ny labeled
HW Σ (F(es))
(1)
TU
where fee denotes the cross-entropy loss. The segmentation model, F, can defined F g- where X'' + Z lifts each pixel of the input image in X' to the feature space Z and h 2 - R is a pixel-wise classifier to give score for each class. The unsupervised loss L can be formulated in unified form of pseudo-label learning as:
HXW Σ
(F
(2)
ny
0 or orgmaz (PAA"
(3)
where bi) is pseudo label produced by teacher model and AA" denotes weakly/strongly-
augmented strategies. We define ((:i)) as quality estimate conditioned confidence Pij for pseudo labels, which can be implemented with threshold filtering or a weighting function. The overall objective function is L - XL"
3.2 Method Overview
An overview of our method ECOCSeg, a pseudo-label learning framework for semantic segmentation, shown in Fig. 3. We propose an ECOC-basee dense classification paradigm (Sec. 3.3), where error-correcting codes create fine-grained output representation for each class. Then, we study the different forms of pseudo labels driven by ECOCSeg and propose reliable bit mining algorithm to refine pseudo labels in a bit-level way (Sec. 3.4). Finally, the optimization criteria are developed to train this framework for further enhanced performance (Sec. 3.5).
3.3 ECOC-based Dense Classification
Traditionally, semantic segmentation is formulated as a discriminative learning problem based on softmax projection. For each pixel example i, the embedding D is extracted from g and fed

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Pscudo-label Learning (See. 3.1)
sodebonk
Codenvit Preudo Laiel
Cadiilae Chess
Trarber Madel
Read
Weakly-
Thresholding
Reliable Bi Mining (Sec. 34)
inbabeted
Myfrii Pseudo Label
Naaest Neightor Query
Aur Coep
Strengt-
codcheok (N X
Inference
Face (Fq
Classffioation (Sec.
Fgee
Target Piud
Foeward Pass
Pacude-isbel Generation
Lam Direction
Optimization Criterion (Sec. 3.5)
Figure 3: Pipeline illustration of ECOCSeg. We introduce a new perspective for semantic segmen- tation (Sec. 3.3), propose reliable bit mining algorithm refine the pseudo label (Sec. 3.4), and develop customized optimization criteria (Sec. 3.5).
into h for N-way classification:
expl ceppww w
p(n|z))
(4)
Σ cxppw"" _
In this paradigm, p(n]z;) E [0, 1] is the probability that pixel i being assigned to class n and h is R.ND N-class classifier parameterized by W : [.N])RNNN
which bias term is omitted.
Our ECOCSeg reformulates the task from a view of dense classification based on error-correcting output codes. An error-correcting codebook is defined as matrix of binary values with the size of N x K, where each class is represented by specific codeword length K. The N-class classifier replaced by K binary classifiers, with p(k[z,) sigmoid( z;) predict probability that the k-th bit of pixel being assigned to digit 1. The class is determined by nearest neighbor algorithm within the codebook where soft Hamming distance dsh used metric:
dsu pp)
1 K
Σ
ll((kzz)) Caalli,
(5)
n¹ arg meggmin(dss (c., p')
(6)
where en is the codeword of class n, consisting of Cau E {0, 1). p¹ is predicted probability vector, consisting of pkk|z,) [0, 1], and ñ² is the class assigned for pixel i.
To enable the proposed paradigm, we construct the codebook using two algorithms: max-min distance encoding and text-based encoding. to generate the binary matrix M 10, Nx and ensure the validity. Please refer to Appendix for details on the implementation.
3.4 Reliable Bit Mining
Since ECOCSeg represents classes as multi-bit binary codes, it naturally leads to the introduction of two forms of pseudo-labels, as shown in Fig. 2. Both forms present varying levels of label noise in different scenarios. Notably, for the code-wise pseudo-label, the noise only comes from incorrect class decisions by Eq. 6, prompting us to explore more candidate classes to mine the reliable bits. As seen in Fig. 3, the ground truth for the target pixel is terrain, while the nearest codeword is vegetation, thus making the false classification. If we query the C-nearest neighbors, the correct class will fall into the candidate set like (vegelation, lerroin, road) when C = 3. Therefore, the shared part within this set, i.e., Ps (Creg.; Cter. Croa.) can be guaranteed to accurate, allowing us to consider these bits as reliable.
5

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To provide an adaptive value of C' for each pixel, we design an effective strategy determine the candidate classes and mine the reliable bits at the same time (Alg. 1), where we define con- fidence (kk|z,) = max (pke)((((]))))))) for each bit and set a hyperparameter I' as upper bound. Then, we obtain the hybrid pseudo label by fusing the bit-wise label (caat and the reli- able bits mined from the code-wise label (c with mask M
Algorithm 1 Reliable bit mining strategy
1: Input: probability vector p' E |o, 1
Output: mask of the reliable part M' (o. 1)
p(k| z,)]
3: Initialize: code matrix M, confidence threshold
T, candidate set S. = {). M' = {1}*
4: compute code distance for each class by Eq. 5;
5: sort the code distance and obtain sorted index T;
6: compute confidence q²:
to N do 8: add Czin| to Sa:
7: for
Chyo. MM' o Goode + (1 (1- M²) @ cbie
9: compute the shared part P. (Sc);
higher T aligns Gyyb. more closely with the
10: update M with bit positions (S.)::
11: compute mean confidence q in (S()::
bit-wise way, while lower 7 aligns closer
with the code-wise way. The hybrid pseudo-
12:
if Tim > T or M = (0) then
13:
break;
label takes advantage of both forms and intro-
14: end if
duces less label noise, which provides a low-
15:
end for
noise form of supervision for unlabeled images
16: return M
and improves the stability of pseudo-label learn-
ing semantic segmentation.
3.5 Optimization Criterion
In ECOCSeg, the multiclass learning problem is decomposed to K binary classification problems, which can be addressed by binary cross-entropy (BCE) loss:
Linee
1 K
Σ ccay log x.) + (1 ciu)) log(1 p(k(2,))),
(8)
where el is the target codeword assigned for pixel However, only adopting this training objective is insufficient for two reasons. First, Eq. 8 considers the classification of each bit independently, ignoring the relationships between bits and resulting in lack of intra-class compactness within features extracted by g. Second, this bit-level supervision fails to capture inter-class relationships, neglecting inter-class separation. Although Eq. ensures classifier robustness, it lacks structured representation space constraints. To address these issues, we introduce two extra training objectives: pixel-code distance and pixel-code contrast.
Pixel-code distance. To regularize representations and reduce intra-class variation, we introduce a compactness-awy aware loss that minimizes the cosine distance between logits and codewords:
Eped = cos(p'. 2²)
where ý³ represents the logits predicted by K binary classifiers, and é' is the standardized version of the codeword ex, with et E [-,
Pixel-code contrast. Eq. 9 encourages intra-class similarity without considering inter-class separa- tion. For two codewords e₁ and C2, define the shared part between them as (c 02) and the distinctive part as Pa(ci, 62). The value of p¹ changes in Ps(ci, 22) and Pa(ci, C2) has the same impact on the Eq. 9, while the latter part is more significant since (s C2) does not distinguish between classes. Thus, a pixel-code contrastive learning strategy is introduced:
exp exp (')'
Spce = - log exp ((8), (()//)/))+ E exp ((;)
(10)
where (.) is cosine similarity, C = NN and r is the temperature to control the concentration level. Note that the target codeword é is not necessarily included in (c, JN if we adopt the form of a bit-wise pseudo label. Furthermore, this loss term can be rewritten as:
Cyyce log(1
Σ A-Ee-
exp (1p', e- e²)/7)),
(11)
which is only calculated on the (a e-) to distinguish between codewords. These two loss terms complement each other to enhance the representative capacity of the learning features. Then, the

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segmentation model is trained with combinatorial loss over all training pixel samples:
Listat Liiee + X Lpod XzCroes
(12)
which can be utilized in both supervised loss L and unsupervised loss L in pseudo-label learning.
4 Theory
In this section, we present our main theoretical results on the performance and robustness of ECOC- based DNNs. We first introduce some key tools and concepts used in our analysis, including the Neural Tangent Kernel (NTK) [38] and its properties in the infinite width limit. Then we state our theorems, which characterize the behavior of ECOC compared to one-hot encoding in the fully supervised setting and the pscudo-label learning setting, respectively. The complete proofs with technical assumptions are deferred to the Appendix A.
Theorem 4.1 (ECOC Performance in Fully Supervised Setting). Suppose the ECOC encoding matrix B((C) is nearly orthogonal, i.e., |E([C))T E((C)) n/] S 5 for some small 5 > O, where n is the code length and I is the identity matrix. Then the ECOC-based DNN achieves performance equivalent to the one-hot encoding in the fully supervised setting, up to an error term depending on 6.
practice, the codewords ECOC are often designed to be approximately orthogonal. Due to the smoothness of the NTK, we can expect the performance of ECOC- DNN to be close to that of one-hot encoding when the codewords are nearly orthogonal.
Remark
Theorem 4.2 (ECOC Robustness in Pseudo-Label Learning). Suppose E((C1) (-1,+1)0x)
has code length n and minimum distance d, and the binary classifiers fi(x)...,, fn((x) satisfy the margin condition with parameters My.... T'n Assume that the pseudo-labels are treated as class labels that are corrupted by random noise with probability e. If the minimum distance d satisfie::
16ER?
(1++
20)) - -log(2C)) + +
d
(13)
72
2
7/2
where 7 = ming Tks 4 = min, 9j, and k= k(B, L, ((0)), then the classification error probability of the ECOC-based DNNs admits tighter upper bound than that of one-hot encoding under the same noise level e.
Remark 2. Theorem 4.2 provides a comparison between the robustness of ECOC and one-hot encoding under label noise in the context of pseudo-label learning. It shows that ECOC can achieve tighter error bound than one-hot encoding, provided that the minimum distance of the ECOC matrix is sufficiently large compared to the noise level. This result suggests that we can employ larger minimum distance cope with higher noise levels, demonstrating the robustness of the ECOC-based DNN against label noise. In our experiments, we also demonstrate that ECOC can achieve better model calibration (Appendix K), thus enhancing the reliability of pseudo-labels.
Experiment
5.1 Experimental Setup
Datasets. We evaluate our approach on two standard benchmarks for synthetic-to-red adaptation of street scenes in the UDA task. The synthetic datasets include GTAv [67] (24,966 images) and SYNTHIA [69] (9,400 images). Cityscapes [19], real-world urban dataset, serves as the target domain, with 2,975 training and 500 validation images. For the SSL setting, we use Cityscapes. PASCAL VOC 2012 [25], a generic object segmentation benchmark with 1,464 training and 1.449 validation images, along with augmented set of 10,582 additional training images, and COCO [52], a challenging benchmark composed of 1 118k/kk vrainiog/validation images with 81 classes.
UDA Setting. We evaluate ECOCSeg on three widely used frameworks, DACS [79] with ResNet101
[29] backbone, DAFormer [34], and MIC [35], with MIT-B5 [91] backbone. Experiments are
conducted on one RTX-3090 GPÚ for DACS and DAFormer, and two for MIC. The network is trained
for 40K iterations (batch size 2) using AdamW optimizer with learning rates of 6 x 10-5 (encoder) and 6 x 1 (decoder), weight decay of 0.01, and linear warm-up for the first 1.5K iterations. Images are rescaled and randomly cropped to 512 x 512 following DAFormer's augmentation, and the EMA coefficient for updating the teacher net is 0.999.
7

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Table 1: UDA performance on two synthetic-to-real benchmarks, where the IoU improved by ECOCSeg is marked as bold. For each benchmark, results are acquired based on CNN-based model [8] (C) and Transformer-base based model [91] (T). mloUs on SYN. are calculated over 16 classes.
Road
Sidewaul
Building
Woll
Fence
Pole
Torran
Roder
Bike
Method
Arch
miouU
GTAY
Chysepps
Val.)
PrDA [100]
87.8
56.0
79.7
46.1
448
45.6
53.5
53.5
55.6
45.2
82.1
70.7
39.2
88.8
45.5
30.4
1.0
48.9
56.4
57.5
CPSL, [45]
92.3
59.5
84.0
45.7
29.7
52.8
61.5
99.5
87.9
41.6
85.0
73.0
35.5
90.4
48.7
73.9
26.5
53.8
53.9
60.8
TransDA [1]]
ADFormer [30]
T
96.7
75
88.8
57.5
43.9
43.6
5344
59.8
90.2
45.6
92.1
70.8
43.0
91.0
78.9
79.3
68.7
52.7
65.0
69.2
CDAC [83]
T
97.1
78.7
91.8
59.6
57.1
99.1
66
72.2
91.8
53.1
94.5
79.4
51.6
94.6
84.9
87.8
78.7
64.9
67.6
75.3
DAC'S [d]
27.5
34.00
52.1
+ECOCSes
95.6
71.8
96.2
37.8
31.4
44.8
56.8
15.2
g4.5
DAFormer [84]
95.
R12
19.4
53.3
451
40.6
55.8
59.4
10.0
47.0
92.5
72.2
44.7
02.3
74.
78.
65.1
83.9
61.8
68.5
+ECOCSeg
96.7
75.6
89.4
51.4
70.5 2..
"MICT3T
91.4
W0.1
91.3"
61.2"
363
55.1"
66.0
71.33
31.4"
94.33
75.88
36.1
94.66
8574
90.3
80.4
611.
66.3
+ECOCSeg
97.9
81.4
91.9
62.1
54.3
64.2
67.4
76.1
92.9
54.4
94..2
82,1
53.0
95.2
89.6
90.8
82.3
61.9
69.4
76.9.1.
Clssscapes Val.)
ProtAA [100]
87.8
45.7
84.6
57.1
0.6
44.0
54.6
$7.0
38.1
$4.4
74.2
24.3
88.2
51.1
40.5
45.6
55.5
CPSL [45]
87.2
43.9
85.5
33.6
0.3
47.7
57.4
37.2
87.8
88.5
79.0
32.0
90.6
49.4
50.8
59.8
57.9
TransDA [1]]
90.4
86.4
59.3
ADFermer [30]
91.8
53.6
57.0
40.5
4688
54.9
59.4
92.6
72.5
45.7
61.6
504
62.1
CDAC [83]
T
93.1
68.5
89.8
51.2
8.9
50.4
65.5
65.3
84.7
94.4
81.2
$7.0
90.5
56.9
66.8
66.4
68.7
DACS [79]
R06
25.1
K19
21.3
24
37.2
22.1
24.0
83.1
90.8
67.6
38.3
82.9
38.9
28.5
47.6
48.3
#ECOCSeg
88.0
17.6
17.3
41.7
47.4
50.2
87.8
72.6
52.13.8..
LXtiormer [34]
55.1
11.3
633
300
35.0
34.6
96.0
89.8
7322
48.2
"122""
332"
339 61.5
60.9
+ECOCSes
90.6
50.3
89.1
41.8
11.3
89.5
56.8
58.3
86.9
91.9
76.2
44.2
88.4
61.3
57.8 58.3
633
"IICTSST
8666
5015
193
473
59.4
06.7
63.4
SXT
94.6
31.0
38.9
96.
619
67.
613
67.3
+ECOCSeg
94.3
68.8
89.0
42.3
13.6
60.5
68.8
57.5
90.4
94.4
80.1
54,5
90.7
68.7
64.0
67.1
69.0-1.7
SSL Setting, We implement our method on ST++ [95], FixMatch [72], UniMatch [93] and adopt DeepLabv3+ [10] with a ResNet [29] backbone our segmentation model. For Pascal, we use crop size of 321 x 321 and 513 x 513, a batch size of 8, and a learning rate of 0.001 with an SGD optimizer. The model is trained for 80 epochs using a poly learning rate scheduler on 2x RTX 3090 GPUs. More experiment settings are detailed Appendix G.
ECOCSeg Parameters. ECOCSeg uses Mtert as the default codebook with codeword length
K = 40 for Cityscapes and Pascal, and K = 60 for COCO. We set the loss weight X = 5 and A2 = 2 with the temperature = 0.5. The confidence threshold T for reliable bit mining is set to the mean value of bit- confidence, i.e., K Σk (kk]2,)) estimate pixel-wise confidence, which is needed in Eq. 2.
0.95. Specifically,
5.2 ECOCSeg for UDA
We integrate ECOCSeg with three baselines and compare with state-of-the-art UDA approaches on Giyv-sCityscppes and SYNTHIA-~Citscant benchmarks. For fair comparison, we train the model with same hyperparameters as the baseline methods. We report results based on whole inference on DACS, DAFormer and slide inference on MIC without other test time augmentation strategies. As shown in Table 1, ECOCSeg achieves 2.4% and 2.9% gains on the two benchmarks built with DACS and 2.2% and 2.4% gains built with the strong baseline DAFormer. Compared to the previous theee-of-the-art method MIC, ECOCSeg also achieves consistent improvements for most classes, resulting in 1.0% and 1.7% gains.
Furthermore, significant gains are primarily observed in confusing classes (e.g., (road, sidewalk) ) (truck, bus, train)). which typically encounter unstable adaptation in pseudo-label learning based on one-hot encoding. This observation is also reflected in qualitative results (Appendix M). While previous methods struggle to distinguish confusing classes, ECOCSeg significantly improves their accuracy, primarily attributed to the supervision provided by higher-quality pseudo-labels
5.3 ECOCSeg for SSL
We evaluate the performance using 1/16, 1/8, and 1/4 labeled data with ResNet-50 and ResNet-101 backbones with three different SSL frameworks. As shown Table 2, ECOCSeg consistently outperforms the baselines under different partition protocols, training resolutions, and backbone architectures, with gains ranging from 1.1% to 3.7%. This confirms that these pseudo-label learning methods can benefit from the robust pscudo-labels provided by ECOCSeg.
8

---

In Appendix G, we evaluate on more powerful baselines, provide more quantitative results on the Cityscupes, COCO and additional real-world Scenarios. ECOCSeg demonstrates significant gains across multiple different datasets and network architectures, indicating the versatility of our method.
Table 2: SSL performance on Pascal. The 321 and 513 denote the training resolution.
Table 3: Ablation study optimization criterion, built with DAFormer under the fully supervised learning setting on Cityscapes.
Method
Rox.
1/16
50
1/8
1/4
1/16
ResNe; 101
1M
1/4
Encoding
Lee
Lhce
Eped
Lpec
maool
Sap-only
X21
67.3
70.5
70.4
72.8
[4C]
321
72.4
74.0
72.4
74.6
76.3
one hoi
17.0
"66.3"
ST-4 [55]
921
72.6
74.4
75.4
24.5
76.3
76.6
+ECOCSeg
321
76.1
76.5
77.9
78.0
Mext
UniMarch [95]
921
75.8
76.1
76.5
77.0
77.2
77.8
-ECOCSeg
321
76.4
77.5
77.6
78.1
78.6
78.9
78.1
Sup-only
513
62.4
6822
72.3
67.5
71.1
74.2
187]
513
72.0
75.1
76.2
24.4
77.6
78.7
Table 4: Ablation study on confidence threshold
PS-MT [54]
513
72.8
75.7
76.4
75.5
78.2
78.7
DAW
515
77.6
77.4
79.6
T. built with DAFormer under the UDA setting
RankMatch [S]]
513
77.8
75.3
79.2
50.0
on GTAv -TyyssCiyscapps..
Fixmatch [22]
513
70.6
75.9
75.1
74.3
76.3
76.9
-ECOCSeg
513
74.3
75.5
76.3
76.0
77.8
78.2
Encoding
baselane
cods
bit
0.9
0.95
0.99
onacle
UniMaich [93]
513"
76.9
16.5
N6.1
18.1
'1922
M Mommd
68.3
69.0
69.6
69.4
69.9
70.2
17.7
.ECOCSeg
513
77.1
78.3
78.5
79.2
79.8
90.3
MeEEE
68.3
69.7
69.4
70.0
70.5
5.4 Diagnostic Experiment
Optimization Criterion. We evaluate the proposed optimization criterion under the fully supervised setting using DAFormer Cityscapes in Table 3. The first line denotes the original argmax- -baee one-hot encoding supervised by cross-entropy loss. When implemented only with Lbee, the accuracy for Mteas is lower than baseline due sub-optimal learning by independent binary classification. Adding Leed or Lee individually brings gains with 1.6% and 1.5%. Combining all the losses yields the best performance, surpassing the one-hot paradigm by a higher margin of 0.5%. When implemented with Mmmmd the performance slightly degrades but still achieves competitive results.
Confidence Threshold T. We conduct study comparing pseudo-label performance using code-wise and bise forms in Table 4. The former performs better when combined with Meent. while the latter achieves better results when combined with Mmmdd This is because the code-wise form introduces more noise with larger code distance (please refer to Appendix C for more analysis). The hybrid form combines the advantages of both forms to achieve consistent improvements. It is worth noting that despite the lower oracle performance (fully supervised setting) with Mmmmd it achieves competitive domain adaptation capability, benefiting from robust pseudo-label learning. Furthermore, the confidence threshold T controls the mixing ratio in hybrid labels as discussed in Sec. 3.4: when 0.5, it is equivalent to code-wise form, while T is equivalent to bit-wise form. To further investigate the impact of T, we quantify the count of differing bits between the code-wise labels and bit-wise labels (Difference Count), and the count of bits corrected by the reliable bit mining algorithm (Correction Count) in Fig. 4 (a). Across different values of T, as the training process progresses, the differences between the two pseudo-label forms decrease, and the count of corrected bits increases. An appropriate selection of I" value can generate robust hybrid label that combines the ad advantages of both forms, thereby reducing pseudo-label noise.
Analysis of Reliable Bit Mining. Fig. 4 (b) shows an example of the reliable bit mining algorithm during training. The model first queries the nearest class and calculates the confidence map. Due to the confusion be-
tween sidewalk and road classes in the marked area, the confidence of this area falls below the threshold T. When querying the second class, the model obtains accurate classifica- tion, and the shared bits between code-wise labels of the two classes exhibit higher con- fidence, which can be viewed as reliable bits. As classification errors tend to occur in low confidence regions, the bit-wise pseudo-label provides softer supervision with lower noise compared to the code-wise form. This hybrid approach combines the advantages of both forms, allowing for more robust and effective training process.
90 Curve ba count
(b) Vansalatiin for raaale bit mining
Figure 4: (a) Bit count curves under different T. (b) Visualization of 2-nearest codewords and confidence map: dotted boxes indicate confusing areas.

---

Conclusion
In this paper, we present ECOCSeg, novel framework that introduces a new perspective that utilizes the error-correcting output codes fine-grained encoding form for each class and facilitates stable pseudo-label learning in semantic segmentation. By leveraging an ECOC- encoding form, a bit- level pseudo-label denoising mechanism, and customized optimization criteria, ECOCSeg effectively addresses the challenges associated with pseudo-label learning. The versatility of ECOCSeg allows be easily integrated with existing works, consistently demonstrating improvements across multiple unsupervised domain adaptation (UDA) and semi-supervised learning (SSL.) benchmarks.
Acknowledgements
This work was partially supported by the National Key R&D Program of China (Grant No. 2024YFB3909902,, and the Youth Innovation Promotion Association of the Chinese Academy of Sciences (CAS).
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A Proofs of the Theoretical Results
In this appendix, we provide the complete proofs of the theorems presented in the main text. We first state the assumptions and lemmas used in our analysis, and then present the detailed proofs. Assumption A.1 (Lipschitz continuity). The activation function Ø B-Lipschitz continuous, i.e., [ō(x) d()) v B|x y for all y E R.
Assumption A.2 (Bounded inputs). The input data satísfies ||0||| S 1.
Assumption A.3 (NTK assumptions). The Neural Tangent Kernel (NTK) converges to deterministic is positive definite, where X is the
kernel in the infinite width limit, and the NTK matrix training data matrix.
Assumption A.4 (Initialization). The weights and biases of the DNN are initialized according to a standard Gaussian distribution with appropriate scaling.
Lemma A.5 (NTK convergence, [38]. Under Assumptions A.1-A.4, the NTK of a DNN converges in probability to deterministie kernel K as the width of the hidden layers goes to infinity.
Lemma A.6 (Hidden Layer Output Bound, (96]). Let Assumptions A-1-A.4 hold. Then, for any
hidden layer I & L and any > O,
1 VTi
B+ (100)(01 111- 1-B
1 (1
B (60)
B¹
(14)
1-
holds with probability least 1 when is large enough, where the hidden layer width ny ogt with constant og > for all 1 < 1.
Now we prove the theorems.
Proof of Theorem 4.1. Let fECOc and Sone-hot denote the functions represented by the ECOC- based DNN and the one-hot encoding DNN, respectively. By Lemma A.5, in the infinite width limit, the outputs of these DNNs can be expressed using the Neural Tangent Kernel (NTK) as:
(x) = x(X,)))K((X) x) A/) B(C)) + X
(15)
fone-hot (z)
(16)
where Y denotes the one-hot encoded target, and the ECOC target is Y E(CC)ý. Then, the decoding process for the ECOC-based DNN is:
D(fEcoc(z)) = arg min
[[CC))
c
(17)
arg min
lle. (K((X, (X,=
cE(C]
where e, E I is the c-th one-hot codeword and |x|A
Vo Vx"AAx Ax is the Mahalanobis norm with positive definite matrix A. For the one-hot encoding DNN, the decoding process is:
D (Jone-bat (x)) arg min rE(C] ee (K((X, + XX)
(18)
When E(CC) is orthogonal, i.e., E((C)) E(C)) nT, the Mahalanobis norm reduces to the scaled Euclidean norm:
| E(C)) V
(19)
In this case, the decoding processes for ECOC and one-hot encoding are equivalent up to a scal- ing factor, leading to the same classification results. When E(CC)) nearly orthogonal, i.e., [F([CT)" E((C)) n/| < 8 for some small 5 > 0, the Mahalanobis norm is a perturbed ver- sion of the scaled Fuclidean norm. The difference the decoding metrics leads difference the classification performance. Specifically, let êgCoc and hote-hot be the predicted class labels from

---

the ECOC-based and one-hot encoding DNNs, respectively. Then,
P'ćECOC + hot) = (p33e= + hote-bot - ( 1
hoone-hot - -VKK1X..)0--M000KK33:04401001110
P(le - "UU1,X,.)HH,,,,,,,K:::X)0)000000
cap hos
|eionn-hat - -YXXXX...0+-..-00XXXXXX000000010
Σ P(vnilec
CypCane hoo
VilleRowe hot -XIX(XXXX)++))=XXXX,,,, +
1leCone-hot E - - -ht
Rone hoo
_00
2
+
- vn
(20)
let A. = - V(K(X, X) + K(X By definition of come-hot, hot, Adone hot S A, for all # Cone-hot- Therefore,
2
P'êECoc # cone- hot)
Σ
P(A.
Adonn hot - 8)
(21)
cxcone-hot
When E((C)) is orthogonal, i.e., ô = 0, have P(CEcoo * Eone-hot) hot) 0. When E([C]) is ô-nearly orthogonal, D. Acone S 2 for all Thus,
P(ćECoc + cone- hot) S (C 1)
Vn 82mim hot A. - cone-hot
If 10=00 then 3/ 0 as n - 0o, while min bot A Dinic hot converges to
positive constant. Therefore, the indicator function becomes O for sufficiently large n, making P(EECo * hos) arbitrarily small. The ECOC-based DNN achieves performance equivalent to the one-hot encoding DNN up an error term depending on 6.
Lemma A.7 (Concentration of noisy functions). Let be real-valued function probabiliit space (X, A. P) such that [f < cc. Let be noisy version of f such that ([]((())((())))) o² for all x E X. Then for any d > 0,
P sup (f()))((((())))) [[f(x)]] o 2logg(()/)) S 8. DEX
(22)
Lemma A.8 (Binary classifier perturbation bound). Under the margin condition and the random
label noise model, for any 8 > O, with probability at least - 8, the error probability of each binary classifier fx(x)) is bounded by
(- (BE L. (0)) (-
22
P& S 2exp
(23)
8/2)2
where Eg. is the label noise probability for the k-th bit, B is the Lipschitz constant of the activation function, L is the depth of the network, and is margin.
Proof. We first review the conditions and notations in the lemma:
fa(2) represents the k-th binary classifier in ECOC, with input æ and output in {-1, +1}.
Uk E +1) represents the true label of the k-th binary classification problem. Øt
[-1,+1} represents the noisy label.
25

---

The function fkr satisfies the margin condition, i.e., there exist constants p1,k P- E I and Y (0, 1) such that:
(f)(())) yk 1] 2 MI 2 (x)((())) y/ = -1] - 1-1,K S O, 7 min -M-1I))
(24)
(25)
(26)
The label noise follows the random noise model, i... for any æ, its true label yk flipped to = -/x with probability eg. independently.
The activation function a of the network satisfies the B-Lipschitz condition, i.e., for any u, v E R, we have:
(a(u) - o())] S Blu-10 v/.
(27)
Let (z) be the output of the k-th binary classifier in the ECOC-baset DNN, satisfying the assump- tions in the lemma. Our goal is to bound the error probability Ps of the binary classifier fx under the noisy labels ÿk- First, we consider the case when the true label is yk 1. By the margin condition, we have:
[zfx(z) yv = 1] 2 M1,k-
(28)
Let fx) be the noisy version of (x) under the label noise model, i... fa(x) = fx( with probability - cR and (x) = - fx (x) with probability <g. Then, we have:
[[(f<(z)= fx(1))) ys 1] ((f(() Mi = 1].
(29)
By the Hidden Layer Output Bound (Lemma A.6) and the fact that ag = 1, we have:
[f(())] B |0(0]]
B² + B + (0) 5
1 1-B B
(30)
RR ((0) +
with probability at least
8 for any > Therefore,
(z) yk S (x(B,L,(00) +6)
(31)
Combining the above inequalities, we get:
[[(f(())- fx(2))² yh 1| S
+ +8
(32)
Now, applying the Concentration of Noisy Functions (Lemma A.7) with 0² 4cce(1s(B,, I, L,0)) 5)², we have:
P { S P1,
2e (
yk = 1) <
(33)
Setting B, L, (x, 6))
M1,6 and solving for 6, we obtain:
1 8en B, L, (0)) + 8)
PP (f(()) 50 yk = 1) < 2exp
(34)
2 (ex(n((, L, (0) + 8)2
s 2xp
with probability at least 1 8. Similarly, for the case when the true label is yr: 1, we can show that:
IP (fu(#) 2 0 yk 1) < 2 exp
22 (- 8EN (E,( (0)) + 8)2
(35)
with probability at least 8. Combining the two cases, we obtain:
Pk = (fu(x) 50 ys = P(y 1) + P (fa(x) 2 yk -1) Plye = -1)
2eex (-
2
(36)
(B, (()) + 8)3
26

---

with probability at least - 26. Then, with probability at least - 8, we have
7
Pk s 2exp
(37)
88x +/2))
Proof of Theorem 4.2. In Pseudo-Label Learning, suppose the class labels are corrupted by random noise with probability E (0, 1), i.e., each true label y [C] flipped uniformly random class
ÿ E [C] \ y with probability e. Under this noise model, the ECOC-based DNN has label noise probability of c = c- (n + (2) for each binary classifier fi-
For the ECOC-based DNN, let V E [C] be the predicted class label for an input x, and let E(x) E [-1,+11" be the corresponding predicted codeword. i.c., E(r)+ )+ = sign(f for k E [n] Let y E [C] be the true class label of æ, and let ((bl) {-1,+1}" be the corresponding true codeword. Under the given noise model, when the probability that is flipped to specific class ÿ + y, the Hamming distance between E(yl) and ( is at least d, by the definition of the minimum distance of the ECOC matrix. Therefore, for ÿ to be misclassified as ÿ. the predicted codeword (xx) needs to be closer to ((]) than to F((v)) in Hamming distance, which means that E(x) must differ from E(yl) in least d/2 bits. By the union bound, the probability of this event is at most (4/2) where is upper bound the error probability of each binary classifier. The total probability of misclassification is bounded by
PECOC (Ū + v)
pd12.
(38)
d/2)
To bound the error probability of each binary classifier, we apply the simplified bound from Lemma A.8 with the label noise probability C% (n d2) and probability at least 1 5/n:
ny²
p s
2exp
(39)
4(n + d)e(x(B, L, (0) + 6/2n)3
where 7 min(7 Finally, the error probability of the ECOC-based classifier is bounded by:
PEcoc(Ū # y) -
n2
d/2
d/2
(40)
I (2en/ (d 2//22///2
with probability at least 8 and using the binomial coefficient bound (7) S (en/d)4.
For the one-hot-based DNN, the multiclass classifier f(x) predicts the class label of x by taking the argmax of the predicted probabilities:
0 = arg max (x)). JE[C]
(41)
Assume each binary classifier (xx) satisfies the margin condition similar Lemma A.8. Let ej be the label noise probability for the j-th binary classifier, we have = e. Then, with probability at least 1 8/C, the error probability of each binary classifier fz) under noisy labels is bounded by:
(- (- I, (0)) 8/20y²
53
Pj < 2 exxp
(42)
Now, let E be the event that the multiclass classifier f(x predicts the correct class label under noisy labels, i.e., arg maXjejc] Mjj For event E hold, it suffices to have fz(x) fx(x) for all k: o where = arg ma Vj is the true class label. Consider any class k * j. Under the true labels we have y/ = and ye = -1 1. By the margin condition, with probability at least - 5/C, we have [x) (a) holds with probability at least 1 5/C if:
P111 33 > Pk,-1 + 5/k
(43)
By the union bound, fz()) > (x) holds for all A simultaneously with probability at least 1 - 8, implying that event holds with probability at least 8.
Based on Theorem 4.1, one-hot can be viewed as using C binary classifiers. For correct prediction, the ground-trute score (z( must exceed others fx((x) for k + j. we have the following proof sketch:
27

---

1. Define the conrect classification event: E = Akz)(f5(2) fx(x))
2. The misclassification corresponds to the complement
event:
P(EC) =
IP (Un=)(fn(E)> > f)()))
3. Applying the union bound: P(E ( fz())
4. Using the per-class binary upper bound Pj. we obtain the overall one-hot upper bound:
IP ho ( v) Pj
Finally, the error probability of the multiclass classifier ((x) is bounded by:
P Pone-hot (ÿ + y) = I(EE)
C
Σ
Pj
(44)
j=1
4.2 Bc(x(( I,, ((0)) + 6/2012
S 20 exp
with probability at least - 6, where ý min(fs}-
To derive the condition on the minimum distance d for the ECOC-based DNN to have tighter enror bound than the one-hot encoding DNN, we compare the two bounds (Equations 40 and 44):
2en d
ndy²
42
)
exp
2C exp
8(n d)c(k(B, L, (0)) + 8/2m)3
88((((B, L, ((0)) + 8/2C)3
2en
$
ndd?
422
d
exp
8(n + d)c(ks 5/2n)2
2xexp
8c(K + 8/2C)2
2en
$
ndh22
72
d
exp
8(n + d)cn?
20 exp
8CK2
2en
$
ndy2
42
exp
8(n + d)eR?
expxx
8EK2
2en
ndy2
922
log
log (2C)
8(n + d)ek?
8EK2
nd72
72
d
2en
log
log (2C')
8(n + d)en²
SEK
2
d
8(n + d)ek²
4en
52
log
log (2C) +
ny?
SEN2
(45)
Using the fact that d < n, and the monotonicity of lor we have:
16ER? 72
(1 (1+ log2)m log (2C)
222
(46)
The equation suggests that when the noise level (e) is higher, can larger code distance (d) to obtain a tighter bound for ECOC- ECOC-based classifer. The lower bound of determined by the ratio of the margins of the two classifiers (2
Remark on Assumptions. The theoretical results presented above rely on two standard assumptions: (i) classifier independence and (ii) uniform random noise. Both assumptions analytically tractable and justified in the context of our analysis.
(1) Independence Assumption.
28

---

Theorem 4.1 analyzes ECOC decoding from a global perspective and does not require classifier independence.
Theorem 4.2 assumes wis- independence only to derive a worst-case error bound. In practice, classifier correlations tend to reduce joint error, the assumption does not compromise the theorem's 's validity. Specifically,
d/2
2en
Fecoc +) -
pd/2
d
When classifiers are correlated, the expected joint error is lower than the product of marginal probabilities due to Jensen's inequality:
E| (Ep)
Therefore, modeling such dependencies would tighten the bound, and the assumption of independence yields conservative estimate.
In practice, perfect independence is rarely satisfied. Even with orthogonal or class-agnostic codes (e.g., one-hot or Mmma), optimization often introduces correlations. Explicitly modeling these dependencies is non-trivial and beyond our scope. Thus, the independence assumption offers a tractable and analyzable abstraction.
(2) Uniform Noise Assumption.
We adopt uniform random noise as a clean baseline, following standard theoretical practice. While real-world pscudo-label noise may exhibit correlations and structured patterns, this assumption does not undermine our results:
At the class level, such structure affects both one-hot and ECOC similarly, as both operate at the pixel level. Our primary goal is to replace one-hot encoding with ECOC within pseudo- label learning frameworks, and thus the relative comparison remains valid. Furthermore, our Reliable Bit Mining mechanism partially mitigates such structure by exploiting semantic relationships across classes.
At the bit level, correlations make the independence-bause based ECOC bound more conservative (see Independence Assumption), since correlations typically reduce joint error. As result, practical performance often surpasses the worst-case bound derived under independence.
B Implementation of Encoding Strategy
In this section, we give implementation details of algorithms for codebook generation, as shown in Alg. 2 and Alg. 3, respectively.
Algorithm 2 Max-min distance encoding
Input: classes number N, codeword length K, iterations Output: binary matrix of codebook Mmma {0, 1
1: D Deum =
2: for
to L do 3: Generate random binary matrix m E {0.1)
4: Compute dimin_r r, dimnnnes dmaar_e.
5: if dminn r = or dminn."" or dmaz_c N then
6: continue
7:
end if
8:
dram = dmii_r + dmin_e + dmaz_c
9:
if doum > Doum then
10: Deum daum, Momd = m
11: end if
12:
end for
13:
return M M.mdd
29

---

Max-min distance encoding. A good crror-correctngg output code should satisfy row separation and column separation. For the former, the minimum Hamming distance between each pair of codewords dmin_r should be maximized, which can correct at least | single bit errors. As for the latter, each bit classifier should be uncorrelated with the others. This can be ensured by maximizing dminge and N - dmaa_es which are calculated between columns of the code matrix. Although searching for an optimal encoding matrix is known an NP-hard problem [20], we can obtain a sufficiently valuable encoding matrix, denoted as Mmmds through a random generation strategy due to the sparsity of the encoding space.
Due to the large size of the encoding space (2*) relative to the number of classes N, a randomly generated codebook typically ensures sufficiently large minimum Hamming distance. Any pair of such random strings will be separated by a Hamming distance that binomially distributed with mean K/2. 2. We can search for the appropriate codebook through multiple iterations to satisfy the optimal row separation and column separation. At the same time, we should ensure the validity of the codebook from two perspectives: (I) There are no identical codewords, which can be ensured by dmiinr > O. (2) There are no wholly identical or opposite classifiers, which can be ensured by dmiine 0 and dmaz=c N. In our case, set iterations L 100000 to generate sufficiently robust codebook.
Algorithm 3 Text-based encoding
Input: classes names {class), J. codeword length K, Output: binary matrix of codebook Meext E {0, 1j
1: "[class)" word2vec, Stent RR
2: Scale by the 1.2 norm Stert = Stext/ [l
3: Calculate channel-wise variance a E R
4: Sort freat in descending order based on o
5: k=1
6: for J ERR frent E NR do
7: Calculate the mean m of f
8: for n = 1 to do
9:
if fn mean then
10:
Miest [n,, k] =
11:
else
12:
Miest [n, k] =
13:
end if
14:
end for
if Mreet is valid then
16:
k = k: ++
k > K then
break end if 20: end if
18:
21:
end for
22:
return Mrent
Text-based encoding. According to the above criteria, we can design encoding matrices that exhibit desirable properties and sufficient robustness. However, the resulting codewords are class-agnostic, and the corresponding binary classification problem may be difficult to optimize. Other than manually designing encodings based on class attributes, we adopt a concise and automated method based on text embedding to generate codewords for the classes. Specifically, N class names are mapped to the feature space ftezt E IR NxC through word2vec [60]. Then, we compress extracted continuous features and quantize them into binary encodings of length K to obtain the code matrix, denoted as Mtezt- This encoding strategy considers the relationships and structural information among classes, facilitating more efficient encoding learning.
To consider the relationships and structural information among classes, we resort to word2vec [60] to extract class-related features. Then, we select the most discriminant feature components based on variance magnitude to compress the feature dimensionality to the length of the codeword. Furthermore, quantize the features into 0-1 encoding using the mean of the feature components as
30

---

One-hot encoding
Max-min distance encoding
Text-hased encoding
Figure 5: The similarity matrix of different encoding forms for 19 classes in Cityscapes, where the minimum code distance in Mond is and Mext is 8. Note that we standardize the binary value (0, 1) to {-1,1} to calculate similarity for ECOC encoding.
a threshold. During this process, we also need to ensure the validity of the codebook, as discussed above.
C Analysis of Coding Strategy
We first visualize the similarity matrix of different encoding forms in Fig. 5. The classes are typically encoded in one-hot form, which is easily susceptible to the influence of label drift in the pseudo-label learning process. The Mamdd aims to maximize the distance between classes, ensuring the robustness of the labels. Furthermore, Mtent takes into account the relationships and structures between different classes, ensuring that similar classes have similar encodings. This property makes the resulting binary classification problems easier to optimize.
Due to the larger code distance in Moomd. it may generate more label noise for the code-wise form of pseudo-labels, leading erroneous training pseudo-label learning and limiting performance improvement. However, because of its sufficient robustness, bit-wise pseudo-labels can provide more stable performance gains for Mandd In MIZst, this phenomenon reversed because Miari naturally perceives the relationships between classes, making its encoding form easy to learn, and thus code-var wise pseudo-labels achieve higher performance, shown in Table 4. Our hybrid pseudo-labed effectively combine the advantages of both forms, achieving the best performance gains.
To further study the different selections for coding strategy, we conduct experiments built with denoted as Mymd and Miest respectively, and evaluate performance on UDA setting with DAFormer [34] and SSL setting with UniMatch [93]. The results are shown Table 5 and Table 6. We also We present a comprehensive comparison in Figure 6. Each code design has its own benefits:
Myan ensures larger code distances and stronger error correction.
Miext preserves semantic relationships between classes, which helps in learning easier-to- optimize binary classifiers.
Both Myodd and Miart show consistent competitive performance, meaning that the pseudo-label learning process can benefit from ECOC encoding and proposed hybrid pseudo-labels. In our experiments, we implement Mtart as the default setting for ECOCSeg.
Table 5: Results on Cityscapes of UDA setting built with DAFormer [34].
Source dataset
baseline
M Momd
Meest
GTAv
68.3
70.2
70.5
SYNTHIA
60.9
63.1
63.3
Note that our encoding strategies, focusing on class separability, visual similarity, and codeword length. These components are essential for building effective codebooks in ECOCSeg.
31

---

Table Results on Pascal SSL setting bulit with UniMatch [93].
Partition protocol
baseline
Momd
Meent
1/16
76.5
78.
78.1
1/4
77.2
78.8
78.9
Class Separability. We propose two simple yet effective codebook generation strategies:
Mmmd: A class-agnosti strategy that maximizes the minimum pairwise Hamming distance among codewords.
MMezt: A text-guided strategy that ensures code diversity via balanced 0/1 quantization of pretrained language embeddings.
Both strategies guarantee sufficient inter-codeword Hamming distance, which is crucial for the error-correction capability of ECOC. As visualized in Figure 5, the constructed codebooks provide meaningful inter-class separation in the Hamming space.
Visual Similarity. Incorporating visual similarity into the codebook is optional and strictly gqqured-similat to how traditional one-hot encoding is class gagsstag by design. Specifically, Mmmd does not rely on class semanties, while Miest implicitly captures semantic and visual similarity via language priors from pretrained text embeddings. These strategies are compatible and effective under various settings, as demonstrated in Figure 6.
Codeword Length. We analyze the impact of codeword length K in Appendices and G, including selection criteria and empirical results. Our findings indicate that moderately long codes offer favorable trade-off between robustness and computational efficiency.
D Analysis of Threshold T
We analyze the influence of T in Table 4, and further present sensitivity results on different bench- marks in Figure 6. Based on these analyses, we conclude:
Both code-wise and bit-wise pseudo-labels independently improve the performance due to the explicit attribute-level decoupling enabled by ECOC.
In the Reliable Bit Mining,
0.5 and T correspond to the pure code-wise and bit-wise forms respectively, while intermediate values yield more robust hybrid labels. This makes T' non-sensitive hyperparameter.
The choice of T is robust across datasets. We fixed setting of T 0.95 in all experiments, achieving consistent performance gains.
13.0
Ours
Ours
Ours
63.5
10.
-100
59.5
02.0
78.0
68.0
Mard
Newr
Mur
Mar
77.5
Benditre
18.5
00.0
60.
0331
0.92
3.61cwl
0.51c..)
64) DA Former GTAY -Ciysccggs with wetting (b) D.F.Frrmrr SWWTIIIA--CCissaaaa.e with UDA sotting, (d Unimattc on Pascal (114 partition) with SSL wttlig.
Figure 6: Sensitivity analysis of across different benchmarks.
E
Analysis of Encoding Length K
Generally, an adequate length of codewords (at least log N) required to ensure robust encoding. However, excessively long codewords can lead to redundancy and inefficient optimization. Table
32

---

7 studies the influence of encoding length K. ECOCSeg performs well even with a low encoding length of 10. which is lower than the number of classes N 19. The performance improves continuously as the encoding length increases within the range of less than 40. However, when K 40, the performance shows negligible improvement. costs, we select K = 40 for both Cityscapes (19 classes) and Pascal (21 classes). In Appendix G, we also show that ECOCSeg can handle a larger number of classes efficiently.
balance performance and computational
Table Ablation study on K, built with DAFormer under the fully supervised learning setting on Cityscapes.
K
10
20
30
40
50
60
mloU
77.1
77.5
78.0
78.1
78.1
78.2
F Analysis of Shared Bits
The assumption used in Reliable Bit Mining (sec. 3.4) that "shared bits are more reliable" stems from observation that "correct class often among Top-C' nearest neighbors' in the codeword space. This is a widely observed property, as confusing classes often lie close to each other in the feature or code space due to small discriminative margins.
This is empirically confirmed Figure 7:
Across benchmarks, mAce drops monotonically with lower-ranked predicted classes,
Aggregated mAce over Top-C classes quickly approaches 1, indicating correct class is usually included.
Since correct class's codeword contains only correct bits, the shared bits from Top-C set guaranteed to be accurate when correct class is included.
Therefore, our Reliable Bit Mining strategy leverages this phenomenon to robustly extract accurate bits, even the presence of pixel-level noise.
Figure 7: (a.b,c) Histogram of mAce corresponding to the C-th nearest codeword. (d) Accumulated mAce of the Top-C classes different benchmarks.
G More Experiments on SSL
In this section, we provide more experiment settings and results on SSL more powerful baselines, challenging benchmarks and real-world scenarios. We emphasize that ECOCSeg is designed as label representation improvement, independent of network architecture training strategy. Therefore, it can be seamlessly integrated into a wide range semi-supervised learning (SSL) frameworks as plug-and-ple and-play module.
Challenging Benchmarks. Follow the basic setting of UniMatch [93], the initial learning rate is set as 0.005 and 0.004 for Cityscapes and COCO respectively, with SGD optimizer. The model is trained for 240, and 30 epochs under a poly learning rate scheduler. The training resolution set as 801, and 513 for these two datasets. We adopt the Xception-65 [18] as backbone when trained on COCO. In Table 8, we implement the experiments on Cityscapes. ECOCSeg consistently outperforms baselines with gains ranging from 1.0% to 3. 3.2%, especially on most challenging 1/16 partition, verifying its robustness and generalization ability. We also show the results on COCO in Table where ECOCSeg outperforms the bascline with gains ranging from 1.7% 7% to 2.6%. We find ECOC is
33

---

efficient to handle larger number of classes due to its binary decoupling property. Theoretically, length of K log, N is sufficient to represent classes, while excessively long encodings can lead to redundancy. Empirically, the optimal code length is roughly K = 10 N [2]. Based on this empirical rule, we use K' 60 for COCO classes) and conduct experiments with UniMatch, observing significant improvements.
Table 8: SSL segmentation performance on Cityscapes. resolution.
The 321 and 513 denote the training
ResNet-50
ResNet- 101
Method
1/16
1/8
1/4
1/2
1/16
1/8
1/4
1/2
Sup-only
63.3
70.2
73.1
76.6
66.3
72.8
75.0
78.0
U [87]
70.6
73.0
76.3
77.2
74.9
76.5
78.5
79.1
AugSeg [102]
73.7
76.4
78.7
79.3
75.2
77.8
79.5
80.4
DAW [77]
75.2
77.5
79.1
79.5
76.6
78.4
79.8
80.6
RankMatch [58]
75.4
77.7
79.2
79.5
77.1
78.6
80.0
80.7
Fixmatch [72]
72.6
75.7
76.8
78.2
74.2
76.2
77.2
78.4
+ECOCSeg
75.8
78.1
78.5
79.3
77.3
78.4
78.9
79.4
UniMatch [93]
75.0
76.8
77.5
78.6
76.6
77.9
79.2
79.5
+ECOCSeg
77.1
78.2
78.9
79.6
78.2
79.3
80.5
80.7
Table 9: SSL segmentation performance COCO.
Method
1/512
1/256
1/128
1/64
1/32
Sup-only
22.9
28.0
33.6
37.8
42.2
PseudoSeg [106]
29.8
37.1
39.1
41.8
43.6
Seg [104]
29.9
37.5
40.1
43.7
46.1
AllSpark [82]
34.1
41.6
45.4
49.5
50.9
UniMatch [93]
31.9
38.9
44.4
48.2
49.8
+ECOCSeg
34.5
41.8
46.2
49.9
51.6
Powerful Baselines. To demonstrate the compatibility of our method with modern architectures and
training paradigms, we conduct additional experiments UniMatch V2 [94] using the Pascal VOC high-quality set, with a DINOv2-S [63] encoder. The results are summarized in Table 10. These results confirm that ECOCSeg consistently improves performance, when built upon strong semi-supervised learning baselines with large-scale pre-training.
Table 10: SSL segmentation performance on Pascal VOC (high-quality set),
Setting
1/16 (92)
1/8
(183)
1/4
(366)
(732)
Full (1464)
AugSeg [102] (RN-101)
71.1
75.5
78.8
80.3
81.4
ComMMatch [73] (RN-101)
76.4
78.5
79.4
80.6
81.8
BeyondPixels [33] (RN-101)
77.3
78.6
79.8
80.8
81.7
UniMatch V2 [94] (DINOv2-S)
79.0
85.5
85.9
86.7
87.8
+ +ECOCSeg
81.1
86.6
87.1
87.8
88.9
Real- Sorld Scenarios. To evaluate the generalizability of ECOCSeg beyond natural scene segmen- tation, we conduct experiments on two real-world, label-scarce domains: remote sensing and medical imaging.
Remote Sensing: We integrate ECOCSeg into UniMatch [93] (PSPNet [101]) for binary change detection on the WHU-CD dataset [39]. To thoroughly evaluate the effectiveness of ECOCSeg, we split the WHU-CD dataset into three subsets following previous methods [93]: a training set containing 5,947 images,a verification setwith 743 images,and a test set comprising 744 images. The results are shown Table 11.
Note that WHU-CD is a binary classification task, where ECOC encoding is not meaningful due to the absence of class diversity. this case, the only difference introduced by ECOCSeg lies in the quality estimation strategy:
34

---

Table 11: Binary change detection results on WHU-CD (PSPNet).
Method
5%
10%
20%
40%
Sup-only
48.3
60.7
69.7
69.5
S4GAN [61]
18.3
62.2
70.8
76.4
SemiCDNet [65]
51.7
62.0
66.7
75.9
SemiCD [4]
65.8
68.1
74.8
77.2
UniMatch [93]
77.5
78.9
82.9
84.4
ECOCSeg
78.0
79.6
83.5
84.6
UniMatch uses threshold-basee filtering;
ECOCSeg adopts a global confidence-based quality score (see Appendix H).
We find that this modification leads to a modest performance gain.
Medical Imaging: We also evaluate ECOCSeg the ACDC dataset [5], four-class cardiac MRI segmentation task. Results using UniMatch with UNet [68] backbone are shown in Table 12.
Table 12: Multi-class segmentation results on ACDC (UNet).
Method
Case
Cases
Cases
Sup-only
28.5
41.5
62.5
UA-MT [97]
61.0
81.5
CPS [12]
60.3
83.3
CNN&Trans [57]
65.6
86.4
UniMatch [93]
85.4
88.9
89.9
+ ECOCSeg
86.7
90.1
90.5
Unlike WHU-CD, ACDC benefits more substantially from ECOCSeg due to the presence of multiple correlated classes. This enables our bit-level label refinement mechanism to take effect, improving segmentation quality.
These experiments demonstrate that ECOCSeg is applicable across diverse real-world domains. However, discussed above, the advantages of ECOCSeg settings, where fine-grained class disentanglement and bit-level shared attributes play a larger role.
pronounced in multi-class
H Analysis of Quality Estimate
In pscudo-label learning, we need a quality estimate ((Pt)) to control the optimization process for L" where Ptj is confidence and typically defined by maximum class probability. In DAFormer [34], it is defined by:
HxW ES [p;j > r']
(47)
HxW
where [-] denotes the Iverson bracket, and this weight is applied to all pixels of the entire image simultaneously. In UniMatch [93], defined through a threshold filtering way:
((v)) [p.j 7%.
(48)
meaning that only high-confidence pixel samples are used for training. To study the differences between the two estimate methods, we implement ablation experiments based on UniMatch, using labeled data with ResNet-101 on the Pascal dataset, as shown in Table 13. We set the same threshold r' = 0.95 to ensure similar proportions of loss introduced by pseudo-labels. For Eq. 48, due to the selection of high-confidence samples only, the robustness of the pseudo label generated by ECOCSeg is meaningless, and the introduced reliable bit mining mechanism does not work in this
35

---

way, leading to advantage compared to the one-hot encoding approach. For Eq. 47, the training process is modulated by gradually increasing weights, and all samples are taken into consideration. In this way, the one-hot encoding approach faces a performance decline due to the introduction of a large number of erroneous labels, while ECOCSeg can handle this label noise and benefit from the sufficient training of all samples, resulting in significant performance improvement. Based on the above discussions, we implement Eq. 47 for ECOCSeg and set the same threshold r' as corresponding baseline methods to evaluate the performance.
Table 13: The performances based on different quality estimates Pascal of SSL setting.
Method
Eq. 47
Eq. 48
UniMatch
76.7
77.2
+ECOCSeg
78.9
77.0
Table 14: Analysis of hyper-parameter in optimization criterion, built with DAFormer under the fully supervised learning setting.
X1 mIoU
0.5
2
10
20
50
77.9
78.1
78.1
78.1
78.0
77.8
X2
0.1
0.5
2
5
20
mloU
77.8
77.9
78.1
78.1
78.0
77.6
0.1
0.2
0.5
1
5
mloU
77.5
77.7
78.1
78.0
77.6
77.2
I Influence of Parameters Setting
In this section, we study the apger--rramtter setting introduced the optimization criterion for ECOCSeg. i.e., Åι, Az, and r. All experiments built with DAFormer of fully supervised learning setting on Cityscapes, and results are summarized in Table 14. We observe that ECOCSeg is robust the two coefficients, A and X2, and achieves the best performance λ₁ 5, A2 2. The setting of temperature J has more significant impact, and we set it to 0.5 for stable performance.
J ECOCSeg Efficiency Analysis
We provide a detailed comparison of training cost between baseline methods and their ECOCSeg- enhanced counterparts. The results are summarized in Table 15.
Table 15: Training cost comparison between baseline methods and ECOCSeg versions.
Method
FLOPs (G)
GPU Memory (MB)
Training Time (h)
DAFormer [34]
116.64
9,807
13.7
ECOCSeg
116.72
12,817
16.2
UniMatch [93]
96.16
19,542x2
16.8
+ ECOCSeg
96.24
24,314x2
21.5
ECOCSeg only modifies the final classification head, changing the output dimension from N (number of classes) to K (code length). This introduces a negligible increase in FLOPS. Therefore, the inference cost remains nearly unchanged.
FLOPs:
Memory and Training Time: The additional memory and training time primarily stem from two components:
A small ECOC codebook, represented binary matrix of size N K.
. The lightweight Reliable Bit Mining algorithm introduced during training.
These components incur modest overhead, which acceptable considering the consistent performance improvements observed across various benchmarks.
36

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Importantly, our method operates purely in the label representation space and is orthogonal to network architectures or training strategies. As a result, ECOCSeg can be seamlessly integrated into wide range of pseudo-label learning frameworks as a plug-and-play module. This is further validated through experiments across both unsupervised domain adaptation (UDA) and semi-supervised learning (SSL.) settings, demonstrating its broad applicability and efficiency.
K
Confidence Calibration
(a) One-hot encoding
(b) ECOCSeg
1.0
1.0
Accuracy
Accuracy
Gap
Gap
0.8
0.8
Accuracy
0.6
0.6
0.4
0.4
0.2
0.2
ECE:0.02434
CCE:0.00648
0.0
0.0
0.2
0.8
0.2
0.4
0.8
10
Confidence
Figure 8: Reliability diagrams for DeepLabv3+ [10] based on one-hot encoding (a) and ECOCSeg (b) on Pascal val.
In this section, we further study the model calibration of ECOCSeg and compare it with the one-hot encoding form. We implement DeepLabv3+ [10] based on these paradigms and evaluate Pascal val. In Fig. 8, we present the reliability diagrams, which plot the expected pixel accuracy as the function of confidence, and calculate the Expected Calibration Error (ECE) [28]:
M
Bml n
ECE
Σ
(cc(Bm) - con (Bm))
(49)
where divide the bins with interval of 0.1. Note that the reliability diagram is obtained through the bit-wise way in ECOCSeg, meaning that every pixel will provide K samples in total. As observed, ECOCSeg demonstrates smaller gaps between the expected accuracy and confidence, indicating superior calibration of predictions. While the one-hot encoding form typically notorious for inflating the probability of the predicted class [70] and suffers higher calibration error accordingly, ECOCSeg exhibits better reliability and interpretability through fine-grained bit-level label representation.
L Comparison with Previous Methods
We compare method with representative approaches that focus on fine- fine-grained modeling and pseudo-label refinement, as summarized in Table 16. While fine-grained representation learning is a common and intuitive strategy, it is not the central contribution of our work. Instead, method introduces a novel perspective by addressing pseudo-label noise through the lens of the label encoding space, rather than the feature space.
ECOCSeg is orthogonal to existing methods that operate primarily at the representation level. By leveraging error-correcting output codes and explicitly modeling inter-class separability through binary attributes, we provide complementary and scalable solution. We believe this direction opens up new opportunities for robust pscudo-label learning and could inspire further research in this area.
37

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Table 16: Comparison with previous methods
Task
Motivation
Implementation Alternating op- 1) cluster sub-classes
Key Difference
[]]
Weakly-
Discriminative
Sub-class discov-
supervised
regions incomplete pseudo-labels
yield
timization:
ery the feature level
per class; 2) train sub-class classifier Online prototype update for con- trastive learning
2 [40]
Domain adaptive
Prior works focus on intra-class alignment without explicitly mod- cling inter-class structure
Structure mod- eling via class prototypes
[3] [100]
Domain adaptive
Improve pseudo-
Prototype-based denoising
Feature-space method
labels via feature clustering
[4] [71]
Domain adaptive
manual Avoid
Symmetric distilla-
Threshold-free feature-level
thresholds
tion & consensus
[5] [98]
Domain adaptive
Fuse onlinc-offline
multi- Unified
Fusion feature space
pscudo-labels
branch fusion Anchor-based soft alignment
6 [62]
Active Domain adaptive
Using small amount of labeled target data to guide adaptation Treat prediction er- ror as a Iearnable correction term
Feature-space
alignment
[ [59]
Semi-supervised
Introduce a correc- tion network that learns refine pre- dictions with resid- ual errors.
Prediction refine- ment via residual correction
8 [24]
Semi-supervised
Reduce confirma- tion bias
Improve pseudo- labels by peeking at future model states
Modification of the teacher model
Ours
Domain adaptive/Semi- supervised
SConfusing classes share
1) Use ECOC- based classifica- tion decouple
1) Bit-level de- noising via ECOC; 2) Label encod- ing perspective, orthogonal to prior feature-level methods
attributes we exploit this to re- duce pscudo-label noise
classes into shared binary attributes;
2) Design Reliable Bit Mining and hy- brid pseudo-labels to denoise
M Qualitative Results
In this section, we provide more qualitative results to compare ECOCSeg and corresponding baseline methods on different benchmarks. As shown Fig. and Fig. 10, the baseline methods face challenges in distinguishing between confusing classes such as sidewalk and road, pole and building, bus and truck, cow and horse, and so on. These classes are challenging to learn in pseudo-label learning due to the influence of label drift. When built with ECOCSeg, there is notable improvement in the performance of these classes, which further demonstrates the effectiveness our method.
N Limitation and Impact Statement
While ECOCSeg demonstrates consistent improvements across wide range of benchmarks, several limitations remain. First, the effectiveness of the ECOC encoding depends on the quality of the codebook design. Although we propose two practical strategies (M and Mtezt). sub-optimal
38

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Image
GT
MIC
MIC+ECOCSeg
Figure 9: More qualitative comparison built with MIC [35] on UDA benchmark of GTAv CityyCisseee.... The significant improvements marked with dotted boxes.
codeword configurations may still hinder performance in certain edge cases. Second, our thcoretical analysis assumes bit-wise independence and uniform label noise, which may not fully capture the structured correlated noise patterns commonly observed in real-world scenarios. These assumptions, while analytically tractable, may limit the theoretical guarantees when applied to more complex distributions.
Within this paper, we present an approach for pseudo-label learning, especially domain adaptive/semii supervised semantic segmentation, a pivotal research area in the realm of computer vision, with no apparent negative societal implications known thus far.
39

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Image
GT
UniMatch
UniMatch-EECOCSeg
background
Acro plane
Bicycle
Bird
Boat
Bottle
Bus
Car
Cut
Chair
Cow
Dining tuble
Dug
Horse
plant
Sheep
Figure 10: More qualitative comparison built with UniMatch [93] on SSL benchmark Pascal, The significant improvements are marked with dotted boxes.
40


Reviews:
[{"review_id": "DKWBwYHTRz", "reviewer": "Reviewer_Tj3N", "summary": "This paper introduces error-correcting output codes (ECOC), a framework for learning robust pseudo-labels in semantic segmentation under label-scarce scenarios. The core idea is to improve error tolerance by replacing conventional one-hot encoding with multi-bit binary encodings. The paper provides both theoretical and empirical validation demonstrating the robustness of multi-bit binary encodings compared to one-hot encodings.\n\nThe main contributions can be summarized as:\n1. Proposes a novel view of pseudo-label learning by designing an encoding scheme.\n2. Formalizes pseudo-label learning into three components: encoding form, bit-level denoising mechanism, and a customized loss function.\n3. Provides theoretical analysis showing that ECOC can tolerate label noise more effectively than one-hot encoding when the codebook is properly constructed.\n4. Implements ECOCSeg as a plug-and-play module that integrates with existing UDA and SSL methods, showing consistent performance gains across various benchmarks and architectures.", "questions": "1. Computation of Confidence Score $q^i_m$ and $P_s$\n\nIn Algorithm 1, it is not clearly explained how the confidence score $q^i_m$, the shared part $P_s$, and the mask $\\mathcal{M}^i$ are computed and updated in practice. Specifically, for the first iteration, how does the process work?\n\n2. Analysis of Hybrid Pseudo-Label Strategy\n\nWhile mixing the generated bit codes with those from the nearest codeword is intuitively appealing, the rationale behind using the mean confidence score to identify reliable bits is unclear. Why not directly select the common bits among the top-C nearest neighbors in the codebook? A comparison or analysis between these two strategies would strengthen the justification for the proposed method. Additionally, is there a specific reason for selecting the confidence threshold values T, such as 0.5, 0.8, 0.9, 0.95, 0.99, or 1.0? It would be helpful to explain the sharp performance changes observed in the range between 0.9 and 1.0, and whether this sensitivity has theoretical or empirical backing\n\n3. Selection of Comparison Method\n\nECOCSeg appears compatible with various pseudo-labeling frameworks. Is there a specific reason for choosing DACS, DAFormer, FixMatch, and UniMatch, rather than other methods such as CDAC, CPSL, RankMatch, or DAW, which have been reported to achieve stronger baseline performance?\n\n4. Codebook Design Using Image Features\n\nThe current codebook construction uses random generation or text-based semantic embeddings (e.g., Word2Vec), which may not reflect the full visual context. Have the authors considered generating the codebook using image-based priors, such as features from pre-trained vision models (e.g., DINO, CLIP), followed by dimensionality reduction (e.g., PCA) to obtain visually aligned codebooks?  \n\n5. Choice of Binary Encoding over Other Schemes\n\nThe paper adopts binary encoding as the default representation, but it is unclear why this scheme was chosen over other alternatives. What is the rationale for preferring binary codes rather than quantized, continuous, or other structured embeddings? A brief discussion or empirical comparison would help clarify why binary encoding is particularly suitable for the pseudo-label learning setting in this work.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. The use of multi-bit binary encoding instead of one-hot encoding is conceptually simple. It provides a natural way to introduce redundancy and attribute sharing among classes, which is highly relevant for noisy label settings like pseudo-label learning.\n\n2. The theoretical analysis is accessible and supports the motivation behind using multi-bit encoding for noise robustness.\n\nWeaknesses\n1. The core idea of disentangling class attributes appears conceptually similar to prior work in areas such as concept learning, where the classifier matrix functions as a codebook and the label assignment relies on similarity measures such as cosine distance. While the proposed use of binary encoding is interesting, the paper would benefit from a clearer comparison with alternative encoding schemes, such as using K-independent classifiers that predict continuous or quantized vectors instead of binary bits.\n\n2. The paper provides a theoretical justification for the effectiveness of multi-bit label encoding in improving robustness to label noise. \n Despite the insight, it can be somewhat intuitive, or even expected, that extending a one-hot vector to a longer encoding offers benefits in noisy settings. To strengthen the contribution, further theoretical justification would be valuable for other important design choices, such as the selection of the number of classifiers K, the construction of hybrid pseudo-labels and the codebook, and the design of the loss function.\n\n3. The paper contains several typographical issues (e.g., lines 26, 81, 189, and Algorithm 2 line 5) that may occasionally make it harder to follow the core ideas. Additionally, the figure captions and explanations (e.g., Figure 3) could be more detailed to help readers better understand the proposed method and its results. More careful proofreading and consistency checks, particularly in notation and references (e.g., line 28, where Ref. [60] is incorrectly stated to utilize a teacher model), would improve the clarity and polish of the paper", "was_revised": true, "final_justification": "The authors have addressed my main concerns through a clear and convincing rebuttal. Based on their response, I have decided to raise my score to Borderline Accept.", "rebuttal": "Thanks for taking the time to share your comments in the review assessment, as well as for acknowledging the  **simple concept**, **accessible theoretical analysis** and **well-supported motivation**. Below, we address each concern in detail.\n\n---\n\n**Q1:** Comparison with Other Encoding Schemes / Why Binary Encoding?\n\n**A1:**  \nWe appreciate the reviewer’s insightful observation. While there is conceptual overlap between our binary encoding and structured representation learning (e.g., concept learning), our formulation is specifically motivated by the **pseudo-label learning paradigm**, which is fundamentally classification-oriented. Using continuous codewords would transform the problem into multi-dimensional regression, which introduces several drawbacks in the context of pseudo-label learning:\n1. Learning Difficulty: For each individual bit, binary classification is generally easier to optimize than regression over continuous targets. This is especially critical in low-data or noisy-label settings such as UDA and SSL.\n2. Mismatch with Pseudo-labeling: Pseudo-label learning methods are inherently designed for classification tasks. Applying them to regression targets (e.g., continuous codes) violates the underlying assumption of discrete label prediction.\n3. Bit-level Interpretability and Denoising: In binary encoding, each bit can be interpreted as a shared visual or semantic attribute. This allows us to isolate and refine reliable supervision at the bit level via our Reliable Bit Mining strategy. Such fine-grained denoising is not directly applicable in continuous encoding, where the semantics of each dimension are not well-defined or disentangled.\n\nTo validate this empirically, we implement a version of ECOCSeg using continuous-valued codewords (*C*) and compare it against our binary encoding on two UDA benchmarks. As shown below, the performance degrades significantly:\n|Dataset|Baseline|*C*|ECOCSeg|\n|-|-|-|-|\n|GTA.→ CS.|68.3|62.3|70.5|\n|SYN.→ CS.|60.9|53.8|63.3|\n\nThese results confirm that binary encoding not only aligns better with the pseudo-labeling framework but also leads to superior empirical robustness.\n\n---\n\n**Q2:**  Theoretical Justification \n\n**A2:**  We thank the reviewer for this valuable point.\n\nOur theoretical analysis (Theorems 4.1 and 4.2) is intended as a **supporting justification** for the **feasibility and robustness** of using ECOC in pseudo-label learning. Specifically, it shows that ECOC encoding is more tolerant to label noise than one-hot encoding under reasonable assumptions (e.g., sufficient code distance).\n\nThat said, our work is **primarily application-oriented**. The overall design of ECOCSeg—including the code length, hybrid pseudo-label strategy, and codebook construction—is guided by practical needs in real-world UDA and SSL settings. These components are **systematically validated through extensive experiments** (see Tables 4–7 and Figures 6–7), which we believe offer strong empirical support.\n\nWe will clarify in the revised manuscript that our **theoretical results are meant to complement** empirical findings—not to serve as formal guarantees for each design choice.\n\n---\n\n**Q3:** Typos, Captions, and References.\n\n**A3:** We thank the reviewer for pointing this out. We will carefully fix all typographical errors (e.g., Lines 26, 81, 189, Algorithm 2) and revise the figure captions to provide clearer and more informative descriptions.\n\nRegarding Line 28: DACS is indeed a classic self-training-based method, and while it does not explicitly frame itself as a teacher-student model, its implementation relies on an EMA-updated model to generate pseudo-labels, which effectively plays the role of a teacher. We will revise the description to accurately reflect this and cite a more appropriate reference if needed to clarify the context.\n\n---\n\n**Q4:** Computation In Algorithm 1\n\n**A4:** We clarify that the iterations in Algorithm 1 refer to the process of class querying for each pixel, not the training iterations of the model. Specifically, for each unlabeled pixel, we perform the following steps:\n1. We iterate over all $N$ classes, ranked by their codeword distance to the predicted bit vector.\n2. The first iteration initializes the candidate class set $S_c$ with the top-1 nearest class.\n3. The shared bit positions $P_s{(S_c)}$ are then computed as the set of bit indices where all classes in $S_c$ agree (i.e., bits that are identical across the selected codewords).\n4. The confidence score $q^i_m$ is calculated as the mean of the predicted bit-wise confidence values over the shared bits $P_s$.\n5. If $q^i_m<T$ (the confidence threshold), we expand $S_c$ by including the next closest class and recompute the shared bits and confidence. This process continues until either $q^i_m>T$ or the shared bit set becomes empty.\n6. The resulting reliable mask $M_i$ is a binary mask indicating which bits are in the shared set $P_s$ and used as reliable bits for that pixel.\n\nFigure 4(b) shows an simple example.\nWe will revise Algorithm 1 to make this procedure clearer and include a concrete step-by-step example to illustrate how the confidence grows as more classes are queried.\n\n---\n\n**Q5:**   Analysis of Hybrid Pseudo-Label Strategy\n\n**A5:**\n- **Selection of top-$C$ classes**:\n   In our hybrid pseudo-label strategy, for each unlabeled pixel, we directly select the common bits among the top-$C$ most similar classes based on Hamming distance to the predicted bit vector. These shared bits define the partial supervision signal. Importantly, the mean confidence score is not used to select classes, but is instead used in the Reliable Bit Mining algorithm to guide the choice of $C$—i.e., to determine how many top classes should be included such that the shared bits remain sufficiently confident. We provide a detailed analysis of this process in Figure 4. \n- **Sharp performance changes near confidence threshold 1.0**:\n   As shown in Figure 6, we observe a sharp performance drop when the confidence threshold approaches 1.0. This is due to a well-known phenomenon: **modern neural networks are typically overconfident and poorly calibrated**, as discussed in [1].  Therefore, we empirically select a relatively high but not extreme threshold (e.g., 0.9), which balances reliability and coverage. As shown in Table 4, and further analyzed in Appendix D, our method is robust to a wide range of confidence thresholds between 0.5 and 1.0, consistently improving performance.\n\n[1] On calibration of modern neural networks.  ICML2017\n\n---\n\n**Q6:** Comparison Method\n\n**A6:**  We selected DACS, DAFormer, FixMatch, and UniMatch due to the following reasons:\n- They are representative and widely-recognized benchmarks in UDA and SSL.\n- All selected methods offer open-source implementations, enabling consistent and controlled integration of our ECOCSeg module.\n- These methods adopt modular architectures, making them suitable for plug-and-play evaluation of new components like ours.\n\nRegarding other methods such as CPSL and CDAC in UDA:\n- Their report performance does not surpass our strongest baseline (MIC), which we already include.\n- We intentionally select three baselines of increasing strength (DACS → DAFormer → MIC) to verify our method's generality across different backbones.\n\nFor methods like RankMatch and DAW in SSL:\n- These methods introduce specialized supervision signals for pseudo-labels, often designed specifically for one-hot class predictions (e.g., class-wise consistency regularization or weighting functions).\n- Their frameworks are tightly coupled with their pseudo-labeling strategies, making it non-trivial to integrate our bit-level supervision.\n- Most importantly, our method still outperforms their reported results, even without such targeted designs.\n\nTo further support the generality of ECOCSeg, we implemented it on CDAC using its official codebase. As shown below, ECOCSeg still provides noticeable improvements:\n|Method|Road|Sidewalk|Building|Wall|Fence|Pole|Light|Sign|Veg|Terrain|Sky|Person|Rider|Car|Truck|Bus|Train|Motor|Bike|mIoU|\n|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|\n|CDAC*|96.0|73.5|88.4|57.2|50.2|53.9|58.5|62.8|88.8|52.5|90.5|70.5|49.4|92.8|81.4|79.2|59.5|53.3|61.5|69.5|\n|+ECOCSeg|96.9|76.5|90.1|59.4|44.7|56.5|55.1|62.6|89.3|49.3|89.1|74.2|50.4|93.1|81.1|84.9|78.2|59.8|61.2|71.2|\n\nThis result confirms that even for methods not originally selected due to coupling or complexity, ECOCSeg is still compatible and beneficial. We will clarify these rationale and include the additional CDAC result in the revised version.\n\n---\n\n**Q7:**   Codebook Using Image Features\n\n**A7:**  \nWe thank the reviewer for the constructive suggestion.\nFollowing your advice, we replace the Word2Vec (w2v) in Algorithm 3 with CLIP and conduct additional experiments in both UDA and SSL settings. The results are shown below:\n\nUDA with DAFormer:\n|Dataset|Base|$M_{mmd}$|$M_{w2v}$|$M_{clip}$|\n|-|-|-|-|-|\n|GTA.|68.3|70.2|70.5|70.3|\n|SYN.|60.9|63.1|63.3|63.4|\n\nSSL  with UniMatch:\n|Partition|Base|$M\\_{mmd}$|$M\\_{w2v}$|$M\\_{clip}$|\n|-|-|-|-|-|\n|1/16|76.5|78.1|78.1|78.3|\n|1/4|77.2|78.8|78.9|79.1|\n\nThese results show that while CLIP provides a slight improvement, the gains are not significant compared to w2v. We attribute this to the robustness of our overall framework, where the ECOC-based encoding and Reliable Bit Mining mechanism are both effective without strong prior knowledge from pretrained models. \n\nMoreover, introducing CLIP embeddings brings in additional data-driven priors, which may complicate fair comparisons in low-label regimes like UDA and SSL. To keep the comparison fair and controlled, we chose to use w2v as a lightweight and open semantic prior, which still achieves strong performance.\n\nWe will include these new results and analysis in the final version.\n\n---\n\nWe hope our response can resolve your concern. Please do not hesitate to let us know if you have further questions :)"}, {"review_id": "dUfDXzSckP", "reviewer": "Reviewer_3QXA", "summary": "This paper proposes ECOCSeg, which is a new pseudo-labeling framework for domain adaptive semantic segmentation. Instead of using one-hot labels, it encodes each class into a binary codeword and turns the multi-class task into multiple binary classification tasks. This helps reduce the impact of noisy pseudo labels.", "questions": "- The paper's claims would be significantly strengthened by quantifying the variance in results. Could the authors provide results from a few repeated runs (e.g., 3-5 trials) for at least one key experiment to report the mean and standard deviation? This would provide strong evidence that the observed gains are not due to random chance.\n- The choice of codeword length K seems heuristic (e.g., K=60 for 81 classes on COCO). How does the authors' approach to choosing K and designing the codebook scale to datasets with a much larger number of classes, such as ImageNet with 1000 classes? Does the linear increase in binary classifiers (and thus computational cost) with K become a bottleneck?", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n- The paper is well-organized and easy to follow, with clear figures, pseudocode, and explanations for each component.\n- The framework is general and modular, easily plugged into existing UDA or SSL pipelines without modifying model architecture.\n- The method is technically sound, with clear motivation and stroong envidence results.\n\nWeakness\n- Relies heavily on codebook design. If the ECOC codewords are poorly chosen, performance may degrade.\n- Though effective, improvements over SOTA are *incremental*. (Lack of reported statistical significance)\n- While the core idea is solid, the method largely builds on a well-established concept (ECOC) without fundamentally innovating it. The contribution lies more in adapting and engineering an old idea into a practical tool for modern semantic segmentation than in proposing a novel learning paradigm.", "was_revised": true, "final_justification": "I thank the authors for their detailed and thoughtful rebuttal, which has effectively addressed my primary concerns. Specifically, their new experiments with multiple runs provide the necessary statistical validation for their claims, and their discussion clarified the novelty of adapting the ECOC framework for this specific task. I am maintaining my score of Borderline Accept.", "rebuttal": "Thanks for taking the time to share your comments in the review assessment, as well as for acknowledging the  **well-organized structure**, **general and modular framework**, **technically sound method**, **clear motivation** and **strong evidence results**.\n\nBelow, we address each concern in detail.\n\n---\n\n**Q1:**    Codebook Design Sensitivity\n\n**A1:**   \n\nThank you for raising this important point. We agree that codebook quality is a key factor for ECOC-based methods. \n\nTo mitigate this sensitivity, our framework is designed with two complementary codebook strategies, supported by both theoretical properties and empirical robustness:\n\n1. **Two Codebook Strategies with Complementary Design Principles** \n\n  - $M\\_{\\text{mmd}}$: Ensures large inter-class Hamming distance, maximizing error-correction capacity.\n- $M\\_{\\text{text}}$: Leverages semantic relationships via pre-trained word embeddings to create more learnable and semantically consistent codewords.\n\n2. **Robustness  to Codebook Choice** \n\n    Thanks to the inherent noise-tolerant property of ECOC and our Reliable Bit Mining mechanism, ECOCSeg is robust to suboptimal codebooks. Even when some bits are noisy or non-discriminative, our method learns selectively from reliable bits, ensuring stable performance.\n\n\n3. **Empirical Validation** \n\n    As shown in Tables 5, 6 and Figure 6, both codebooks consistently yield improvements across UDA and SSL settings, demonstrating robustness to codebook variations. We also provide an ablative study in Appendix C showing how each strategy contributes differently under different supervision settings.\n\n\n\n---\n\n**Q2:**    Lack of Reported Statistical Significance\n\n**A2:**    We appreciate the reviewer’s suggestion regarding statistical significance.\n\nWe appreciate this suggestion and agree that demonstrating statistical significance is essential. We have now conducted 5 repeated runs on two representative tasks (UDA and SSL) and report the mean and standard deviation:\n\n\n**1. UDA: GTA5 → Cityscapes (DAFormer + ECOCSeg)**\n\n| Run  | Road | Sidewalk | Building | Wall | Fence | Pole | Light | Sign | Vegetation | Terrain | Sky  | Person | Rider | Car  | Truck | Bus  | Train | Motor | Bike | mIoU (%) |\n| ---- | ---- | -------- | -------- | ---- | ----- | ---- | ----- | ---- | ---------- | ------- | ---- | ------ | ----- | ---- | ----- | ---- | ----- | ----- | ---- | -------- |\n| 1    | 96.7 | 75.6     | 89.4     | 54.0 | 51.4  | 55.1 | 59.4  | 61.9 | 90.1       | 46.6    | 90.0 | 71.5   | 42.4  | 92.8 | 79.7  | 85.4 | 79.1  | 60.0  | 58.2 | 70.5 |\n| 2    | 96.7 | 74.1     | 90.0     | 49.8 | 48.8  | 55.0 | 59.6  | 65.4 | 89.4       | 53.3    | 88.6 | 74.0   | 46.9  | 93.2 | 78.1  | 79.4 | 70.1  | 60.3  | 62.5 | 70.3 |\n| 3    | 96.7 | 77.5     | 90.3     | 49.0 | 50.8  | 56.2 | 59.4  | 67.4 | 90.5       | 51.8    | 89.6 | 72.1   | 51.1  | 92.4 | 72.1  | 76.6 | 69.5  | 53.0  | 62.5 | 69.9|\n| 4    | 96.3 | 74.0     | 90.0     | 55.9 | 48.4  | 55.4 | 54.7  | 66.2 | 89.5       | 50.1    | 90.3 | 72.9   | 49.0  | 92.9 | 78.7  | 83.1 | 73.5  | 59.1  | 60.5 | 70.6 |\n| 5    | 96.4 | 76.1     | 89.5     | 53.1 | 50.1  | 56.1 | 58.9  | 66.1 | 90.4       | 45.1    | 90.8 | 74.3   | 49.4  | 93.2 | 77.7  | 82.7 | 71.8  | 53.1  | 61.6 | 70.3 |\n\nCompared to the baseline DAFormer (68.3), we achieve a $+2.0$ mIoU gain with low variance (0.24 std), confirming the improvement is statistically consistent.\n\n**2. SSL: Pascal 1/4 Partion (UniMatch + ECOCSeg)**\n\n| Run          | 1    | 2    | 3    | 4    | 5    | Mean ± Std  |\n| ------------ | ---- | ---- | ---- | ---- | ---- | --------------- |\n| mIoU (%) | 78.9 | 78.9 | 79.1 | 79.0 | 78.6 | 78.9 ± 0.17 |\n\nAgain, our method shows stable improvements over the UniMatch baseline (77.2), with $+1.7$ mIoU gain and low standard deviation (0.17 std).\n\nThese results confirm that our gains are statistically consistent and robust. We will include these results in the revised version of the paper.\n\n---\n\n**Q3:**    Limited Novelty – ECOC is a Known Concept\n\n**A3:**    \n\nWe understand the concern and would like to clarify that while ECOC itself is a classical technique, our work contributes **a novel perspective and practical framework** tailored for **pseudo-label learning in dense prediction tasks**, which poses unique challenges not previously addressed by ECOC literature.\n\nSpecifically, our contributions go beyond a direct application of ECOC, and include several **task-oriented innovations**:\n\n- **Hybrid Pseudo-Labeling**: We propose a new paradigm that combines bit-wise soft supervision and code-wise hard supervision, enabling partial but reliable supervision, especially beneficial in noisy contexts like UDA/SSL.\n- **Bit-Level Denoising via Reliable Bit Mining**: Unlike traditional ECOC, we introduce a mechanism to selectively retain trusted bits from top-k nearest classes, adapting to pixel-wise uncertainty — a key innovation for semantic segmentation.\n- **Task-Specific Optimization Objectives**: We design new loss functions (pixel-code distance and pixel-code contrast) to enforce intra-class compactness and inter-class separation in code space, which is absent in classical ECOC applications.\n- **Theoretical Justification of ECOC for Noisy Pseudo-Labels**: We provide a formal analysis showing that ECOC offers tighter classification error bounds than one-hot encoding under label noise, supported by Neural Tangent Kernel (NTK)-based generalization theory. Our theorems establish conditions under which ECOC is provably more robust, offering a theoretical foundation for its use in pseudo-label learning.\n- **Modularity and Generality**: ECOCSeg is plug-and-play and compatible with a wide range of architectures and learning paradigms, making it practical and impactful.\n\nImportantly, the proposal of ECOCSeg is **not an arbitrary or isolated tweak**, but a **task-specific** strategy that is **analytically motivated by the inherent challenges of pseudo-label learning in pixel-level segmentation**. \nWe believe that simplicity in implementation does not imply lack of novelty. On the contrary, we view the ability to **integrate a classical idea into a modern context effectively and practically** as an important and underexplored direction in representation learning.\n\n\n---\n\n\n**Q4:**    Codeword Length K and Scalability\n\n**A4:**    \n\nThank you for this insightful question. We agree that the choice of codeword length K is important for both robustness and scalability.\nWe provide a detailed analysis in Appendix E and G, and summarize our theoretical insights, empirical findings, and practical guidelines below.\n\n**1. Theoretical & Empirical Motivation**\n\n- A minimum of $K ≥ \\log_{2}{N}$ is required to uniquely represent $N$ classes.\n\n- Prior literature on ECOC [1] suggests a \ncode length of $K = 10 \\times \\log_{2}{N}$ as a practical guideline for ensuring sufficient Hamming distance and error-correction.\n\nIn our case:\n\n- For Cityscapes ($N = 19$) and Pascal ($N = 21$), this yields $K ≈ 40–45$\n- For COCO ($N = 81$), we use $K = 60$, aligning with this principle\n\n**2. Ablation Study on $K$**\n\nWe conduct an extensive study on Cityscapes under the fully supervised setting with DAFormer. Results are shown in Appendix E, Table 7:\n\n- Performance improves as $K$ increases, due to increased error tolerance.\n- However, the gain saturates beyond $K = 40$, and overly long codes introduce slight redundancy.\n- This validates $K = 30–50$ as a sweet spot, balancing robustness and efficiency.\n\n**3. Practical Recommendation**\n\n- We adopt $K = 40$ as a default setting for all experiments on Cityscapes and Pascal.\n- For larger class spaces (e.g., COCO), we follow $K = 10 \\times \\log_{2}{N}$ for scalability and effectiveness.\n\n\n**4. Scalability to Large-Class Datasets** \n\nWe also address the scalability of ECOCSeg when applied to datasets with hundreds or thousands of classes, such as ImageNet ($N = 1000$):\n\n- $K$ grows logarithmically, not linearly.\n\n  Using the $K = 10 \\times \\log_2 N$ rule, we would use $K \\approx 100$ for ImageNet — still much smaller than N.\n\n- Binary classifiers are lightweight and parallelizable.\n\n   Each of the $K$ binary heads is a single-output sigmoid classifier, which can be trained in parallel. Compared to a 1000-way softmax, this design is computationally efficient per-head.\n\n- FLOPs and memory overhead grow modestly.\n\n   As discussed in Appendix J, the increase in FLOPs and memory is negligible, and ECOCSeg remains efficient.\n\n\n[1] Reducing multiclass to binary: A unifying approach for margin classifiers. JMLR2000\n\n---\n\nWe hope our response can resolve your concern. Please do not hesitate to let us know if you have further questions :)"}, {"review_id": "h8Tb6JqzPc", "reviewer": "Reviewer_4otC", "summary": "The paper introduces ECOCSeg for pseudo-label learning in semantic segmentation, particularly for unsupervised domain adaptation (UDA) and semi-supervised learning (SSL). The main contribution lies in reformulating the encoding strategy for pseudo-labels by leveraging Error-Correcting Output Codes (ECOC) instead of traditional one-hot encoding. This approach addresses the issue of erroneous pseudo-labels, which can mislead training in label-scarce scenarios. ECOCSeg decomposes the multi-class segmentation problem into multiple binary classification subtasks, using a fine-grained encoding that captures shared attributes among classes to enhance robustness against label noise. The effectiveness proposed method is validated on standard UDA and SSL benchmarks (e.g., GTAv→Cityscapes, SYNTHIA→Cityscapes, Pascal VOC, COCO)", "questions": "The questions are listed above. The reviewer is interested to see how the authors may respond to the concerns.", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength:\nThe paper is well-written and the motivation is clear. The proposed method ECOC-based pseudo-labels considering multi-attributes within the same class looks interesting. The claims are supported by theoretical analysis and the corresponding experiments.\n\nWeakness:\n1. There is a missing analysis. Since the paper particularly studies how to improve pseudo-labels during training, there is a missing section where the authors are supposed to compare their proposal with prior methods that study the same aspect, ideally showing the differences and their optimality with experimental supports. For instance, ProDA [1] proposes to improve pseudo-labels by prototyipical denoising, while DiGA [2] proposes a threshold-free pseudo-labelling mechanism. MFA [3] adopts an online-offline label fusion technique to improve pseudo-label quality. The paper claims will be more convincing with these comparisons.\n\n2. Limited analysis of codebook design: while max-min distance and text-based encoding are proposed, the paper does not deeply explore other ECOC codebook construction strategies (e.g., random codes, Hadamard codes) or their impact on performance. The choice of codeword length (K=40 for Cityscapes/Pascal, K=60 for COCO) seems arbitrary, with little justification. For example, as they put in line 53, they ''assign a binary bit string (codeword) as an encoding\", how to choose these codewords? By manual definition or it follows a certain automatic mechanism? If it is manual, what if it comes to semantic segmentation datasets with hundreds of classes?\n\n3. Hyperparameter sensitivity: The reliable bit mining algorithm relies on a confidence threshold T = 0.95, but the paper lacks a sensitivity analysis to show how performance varies with different T values or other hyperparameters (e.g., lambda_1, lambda_2, tau).\n\n4. Computational concerns: The proposed method decomposes an N-class problem into K binary classifiers, which may increase computational complexity, particularly when it comes to datasets with many classes (e.g., COCO with 81 classes). Does the computational overhead increase with the numbers N and K?\n\n5. Further comparison with related works:\n\n     i. Mendel et al. (2020) [46]: \"Semi-supervised segmentation based on error-correcting supervision\" (ECCV 2020) also uses ECOC for semi-supervised segmentation, focusing on error-correcting supervision to handle noisy labels. While ECOCSeg extends this idea with a reliable bit mining algorithm and customized loss functions (pixel-code distance and contrast), the core concept of using ECOC for segmentation is related. The paper does not sufficiently differentiate ECOCSeg from it, particularly in terms among shared attributes (e.g., horn, hoof) that can be leveraged for robust pseudo-label learning. The paper should include a detailed comparison with Mendel et al. to clarify how ECOCSeg’s bit-level denoising and optimization criteria offer distinct advantages. \n\n    ii. Paper [4] also suggests that using multiple attributes within one class can help improve the adaptation ability of a segmentor. Is this conceptually similar to what the authors proposed? \n\nReferences:\n[1] Zhang, P., Zhang, B., Zhang, T., Chen, D., Wang, Y., & Wen, F. (2021). Prototypical pseudo label denoising and target structure learning for domain adaptive semantic segmentation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 12414-12424).\n\n[2] SHEN, Fengyi, et al. DiGA: Distil to generalize and then adapt for domain adaptive semantic segmentation. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2023. S. 15866-15877.\n\n[3] Zhang, K., Sun, Y., Wang, R., Li, H., & Hu, X. (2021). Multiple fusion adaptation: A strong framework for unsupervised semantic segmentation adaptation. arXiv preprint arXiv:2112.00295.\n\n[4] NING, Munan, et al. Multi-anchor active domain adaptation for semantic segmentation. In: Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021. S. 9112-9122.", "was_revised": true, "final_justification": "My concerns are resolved by the author's rebuttal. I would like to raise my ratings and recommend an acceptance of the paper. Meanwhile, the authors should make sure that the missing comparison and analysis on different pseudo-labeling methods should be included in the camera-ready version to improve the completeness of this paper.", "rebuttal": "Thanks for taking the time to share your comments in the review assessment, as well as for acknowledging the  **well-written paper**, **clear  motivation**, **interesting idea**,  **well-supported claims**.\n\nBelow, we address each concern in detail.\n\n---\n**Q1:** Comparison with pseudo-label refinement methods\n\n**A1:** \n\nThank you for the suggestion. As partially discussed in **Appendix L**, we now explicitly compare representative pseudo-label refinement methods with ours in the table below.\n\nMost existing works primarily focus on **feature-space refinement**, such as filtering noisy samples or fusing multi-view predictions. In contrast, **our approach views pseudo-label learning from the angle of label representation**, offering an **orthogonal and complementary strategy**.\n\n| Method    | Task | Motivation | Key Idea | Difference |\n|-----------|------|------------|----------|------------|\n| ProDA     | UDA  | Improve pseudo-labels via feature clustering | Prototype-based denoising | Feature-space method |\n| DiGA      | UDA  | Avoid manual thresholds | Symmetric distillation & consensus | Threshold-free, feature-level |\n| MFA       | UDA  | Fuse online-offline pseudo-labels | Unified multi-branch fusion | Fusion in feature space |\n| Ours      | UDA/SSL | Exploit shared attributes among confusing classes | ECOC-based label encoding + bit-level denoising | Encoding-space perspective (new angle) |\n\nUnlike prior methods, our method improves pseudo-label **robustness** by decoupling classes into fine-grained binary attributes and performing **bit-level denoising**. This perspective is rarely explored and can potentially be combined with the above methods.\n\n\n---\n**Q2:** Codebook design\n\n**A2:** \n\nWe appreciate the reviewer’s interest in the design of the ECOC codebook. Our framework addresses this issue from three complementary perspectives:\n\n**1. Codebook Design**\n\nour framework is designed with two complementary codebook strategies, supported by both theoretical properties and empirical robustness:\n\n- Two Codebook Strategies with Complementary Design Principles \n\n  - $M\\_{\\text{mmd}}$: Ensures large inter-class Hamming distance, maximizing error-correction capacity.\n  - $M\\_{\\text{text}}$: Leverages semantic relationships via pre-trained word embeddings to create more learnable and semantically consistent codewords.\n\n- Robustness  to Codebook Choice\n\n    Thanks to the inherent noise-tolerant property of ECOC and our Reliable Bit Mining mechanism, ECOCSeg is robust to suboptimal codebooks. Even when some bits are noisy or non-discriminative, our method learns selectively from reliable bits, ensuring stable performance.\n\n- Empirical Validation\n\n    As shown in Tables 5, 6 and Figure 6, both codebooks consistently yield improvements across UDA and SSL settings, demonstrating robustness to codebook variations. We also provide an ablative study in Appendix C showing how each strategy contributes differently under different supervision settings.\n\nTo clarify further, we also considered two widely used ECOC strategies:\n- Random codes offer flexibility in codeword length and class count, but often lack structure. Without filtering, they may generate redundant or poorly-separated codes, leading to inconsistent performance.\n- Hadamard codes provide orthogonal codewords with strong theoretical error correction properties. However, they are only defined for certain code lengths (e.g., 8, 16, 32, ...), and thus cannot flexibly adapt to arbitrary class counts (e.g., 19 classes in Cityscapes). This introduces unnecessary code length, and increases training complexity.\n\n**2. Choice of $K$**\n\nWe provide a detailed theoretical and empirical analysis in Appendix E and G, summarized as follows:\n- Theoretical & Empirical Motivation\n  - A minimum of $K ≥ \\log_{2}{N}$ is required to uniquely represent $N$ classes.\n  - Prior literature on ECOC [1] suggests a \ncode length of $K = 10 \\times \\log_{2}{N}$ as a practical guideline for ensuring sufficient Hamming distance and error-correction.\n\n  In our case, we follow $K = 10 \\times \\log_{2}{N}$ for scalability and effectiveness.:\n   - For Cityscapes ($N = 19$) and Pascal ($N = 21$), this yields $K ≈ 40–45$\n   - For COCO ($N = 81$), we use $K = 60$, aligning with this principle\n\n-  Ablation Study on $K$\n\n    We conduct an extensive study in Appendix E, Table 7:\n   - Performance improves as $K$ increases, due to increased error tolerance.\n   - However, the gain saturates beyond $K = 40$, and overly long codes introduce slight redundancy.\n   - This validates $K = 30–50$ as a sweet spot, balancing robustness and efficiency.\n\n**3. Manual Definition and Class Semantics**\n\nOur method is fully automatic and does not require manual class-wise design of codewords. Considering semantic or visual relationships is optional, not required:\n- In $M_{\\text{mmd}}$, we adopt a class-agnostic strategy that maximizes codeword separability without relying on class semantics.\n- In $M_{\\text{text}}$, semantic similarity is implicitly captured from text embeddings, which can reflect visual relationships as well.\n\nAs analyzed in Appendix C, both strategies function effectively within our framework. Importantly, like one-hot encoding, it is not necessary for each codeword to carry a specific meaning—the codewords only need to be separable in label space. This design allows flexibility and general applicability across datasets.\n\n---\n**Q3**: Sensitivity Analysis\n\n**A3:**\nWe thank the reviewer for the suggestion. We would like to emphasize that we have already provided detailed sensitivity analyses in the main paper and appendices.\n\n**Threshold $T$**\n\nWe analyze the influence of $T$ in Section 5.4 and Table 4, and further extend the results across datasets in Appendix D. Our findings show:\n1. Both code-wise and bit-wise pseudo-labels independently contribute to performance improvements, enabled by the attribute-level decoupling introduced by ECOC.\n2. In Reliable Bit Mining, $T=0.5$ and $T=1$ correspond to pure code-wise and bit-wise forms, respectively. Intermediate values (e.g., $T=0.95$) produce more robust hybrid labels, making $T$ a non-sensitive hyperparameter.\n3. The effect of $T$ is consistent across datasets. We adopt a fixed setting of $T=0.95$ in all experiments and observe stable gains.\n\n**Loss Weights $\\lambda_1$, $\\lambda_2$ and Temperature $\\tau$**\n\nAs analyzed in Appendix I (Table 14):\n- $\\lambda_1$ and $\\lambda_2$ weigh auxiliary loss terms that enhance feature structure. These only need to ensure comparable gradient scales across losses. We find they are insensitive over a wide range and easy to tune.\n- $\\tau$, which controls the softness of predicted probabilities, influences pseudo-label confidence. We fix $\\tau = 0.5$ in all experiments and observe stable, high performance.\n\nThese analyses confirm that our method is robust to all key hyperparameters ($T$, $\\lambda_1$, $\\lambda_2$, and $\\tau$), and does not require extensive tuning to perform effectively.\n\n[1] Reducing multiclass to binary: A unifying approach for margin classifiers. JMLR2000\n\n---\n**Q4:** Computational Overhead for Large $N$ and $K$\n\n**A4:**\nWe acknowledge the reviewer’s concern regarding scalability. As shown in Appendix J, we provide a detailed efficiency analysis (table 15).\n- The FLOPs increase is negligible, as only the segmentation head is modified—replacing a single $N$-way classifier with $K$ binary classifiers.\n- The increase in GPU memory and training time is due to:\n  1. The $K$-bit prediction, which replaces the original output.\n  2. A small ECOC codebook, represented as a binary matrix of size $N \\times K$  \n  3. The Reliable Bit Mining algorithm, which involves simple operations (e.g., confidence ranking and bit masking) and is lightweight relative to the overall training cost.\n\nImportantly, inference-time overhead is minimal, since Reliable Bit Mining is only used during training, and the binary classifiers are highly parallelizable. Moreover, for large-class datasets like COCO (N = 81), our design uses $K = 60 < N$, meaning that the number of classifiers is actually reduced compared to standard N-way classification.\n\nOverall, ECOCSeg introduces only minor computational overhead while delivering significant performance gains, making it a practical and scalable solution even for large-scale semantic segmentation tasks.\n\n---\n**Q5:** Further comparison with related works:\n\n**A5:**   We appreciate the reviewer for pointing out the connection to [a] and [b].  We have already discussed partial works in Appendix L, and now restate and clarify the key differences here for completeness.  While all three methods aim to improve learning under limited supervision, our approach differs significantly in both motivation and methodology.\n- [a] introduces a correction network to refine pseudo-labels based on confidence, aiming to reduce overfitting in semi-supervised segmentation.\n- [b] focuses on feature-space alignment by using a small amount of labeled target data to guide adaptation via anchor-based soft alignment.\n- In contrast, our method takes a novel label-space perspective, leveraging ECOC-based class encoding to model shared attributes between confusing classes. We further propose Reliable Bit Mining and hybrid pseudo-labels to perform fine-grained, bit-level denoising—an orthogonal strategy not explored in [a] or [b].\n\nOur method introduces a structured, fine-grained label encoding that enables attribute-level correction, offering an orthogonal perspective to the confidence-based and feature-alignment strategies in [a] and [b]. By addressing pseudo-label noise at the encoding level, it captures inter-class relationships—such as shared visual attributes—often overlooked by prior work. This complementary view enhances robustness and can be integrated with existing methods for further gains.\n\n---\nWe hope our response can resolve your concern. Please do not hesitate to let us know if you have further questions :)"}, {"review_id": "CULyboLFE6", "reviewer": "Reviewer_Wcbt", "summary": "The paper introduces a novel approach for filtering pseudo-labels in Unsupervised Domain Adaptation (UDA) and Semi-Supervised Learning (SSL) for semantic segmentation tasks. The method leverages error-correcting output codes (ECOC) as an innovative encoding strategy for semantic classes while simultaneously providing more reliable pseudo-labels for self-training processes. The approach demonstrates improvements over state-of-the-art UDA and SSL methods across multiple benchmarks.", "questions": "- Can you provide class-wise analysis explaining why certain classes (e.g., rider, motorcycle) experience IoU degradation while others (e.g., sidewalk) show substantial improvement, and how does this relate to your codebook design ?\n\nI am inclined toward a borderline accept given the paper's interesting and novel contributions that could significantly impact researchers working in self-training and knowledge distillation for instance, particularly those seeking improved pseudo-label filtering methods. However, I assign a confidence level of 2, as my limited expertise in Error-Correcting Output Codes (ECOC) prevents me from reliably evaluating certain design choices in the pseudo-label construction. I will consider other reviewers' feedback before reaching a final decision.", "limitations": "yes.", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "## **Strengths**\n\n**Clear Presentation:** The paper is well-written with good explanations of ECOC application in semantic segmentation contexts and its effectiveness in mitigating pseudo-label noise between confusing classes.\n\n**Novel Approach:** The innovative reframing of pseudo-label problems using ECOC represents a significant contribution that will likely interest the broader research community.\n\n**Consistent Improvements:** The method enhances self-training performance across various UDA and SSL approaches on multiple benchmarks, demonstrating broad applicability.\n\n**Comprehensive Validation:** Both main paper and supplementary ablation studies thoroughly examine each loss component's impact while justifying all design decisions made throughout the methodology.\n\n## **Weaknesses**\n\n**Limited Class-wise Analysis:** The paper lacks detailed class-specific analysis explaining why ECOC fails to improve certain classes' IoU scores and how this relates to codebook design. For example, in GTA→Cityscapes adaptation, DACS+ECOCSeg shows significant IoU decline for rider (35.8→23.5) and motorcycle (27.3→15.2) classes, while sidewalk dramatically improves (39.7→71.8). Understanding these disparities would provide valuable insights into the method's limitations and potential improvements.\n\n## **Clarification Points**\n\n**Typos:**\n- L26 contains repetitive sentence: \"Existing mainstream methods introduce common paradigms\".\n- L81 contains repetitive word : \"improving\"", "was_revised": true, "final_justification": "I thank the authors for their detailed response and the comprehensive class-wise analysis and its connection to the codebook design. This explanation has satisfactorily addressed my initial concerns, therefore I increase my score to accept.", "rebuttal": "Thanks for taking the time to share your comments in the review assessment, as well as for acknowledging the  **Clear Presentation**, **Novel Approach**, **Consistent Improvements** and **Comprehensive Validation**.\n\nBelow, we address each concern in detail.\n\n------\n\n**Q1:** Class-wise IoU Variance and Codebook Design\n\n**A1:**\n\nWe appreciate the reviewer’s insightful question regarding the observed per-class IoU variations, especially the degradation in classes such as rider and motorcycle, and the notable improvements in classes like sidewalk. We provide a multi-faceted analysis below:\n\n\n\n**1. Attribute Decoupling and Class-Specific Difficulty**\n\nECOCSeg introduces a bit-wise classification paradigm that decouples classes into attributes. This is particularly beneficial for visually confusing classes (e.g., road vs. sidewalk, car vs. bus). However, for **fine-grained or underrepresented classes** (e.g., rider, motorcycle), this decoupling introduces new challenges:\n\n- These classes are often underrepresented in the source domain and have sparse or low-confidence pseudo-labels.\n- Their bit-wise predictions tend to have lower confidence, which negatively affects ECOC decoding and final prediction accuracy.\n\n\n\n**2. Reliable Bit Mining and Class Imbalance**\n\nOur Reliable Bit Mining module selects only high-confidence bits during training. For rare classes with **low-confidence predictions across most bits**, fewer bits may be selected, leading to weaker supervision and potential underfitting. This phenomenon is **orthogonal to the codebook design**, and primarily stems from **data imbalance** and **pseudo-label sparsity**.\n\nWe note that this issue is particularly **pronounced under the DACS framework**, which **does not include rare-class sampling or class-balancing strategies**. As a result, the quality and quantity of pseudo-labels for rare classes (e.g., rider, motorcycle) are inherently unstable, even before applying ECOCSeg. Our method may **amplify this effect slightly** due to its reliance on bit-level confidence, but it is not the root cause.\n\n\n\n**3. Codebook Design Is Not the Root Cause**\n\nWe emphasize that the observed per-class IoU variations are **not caused by our specific codebook design**, as clarified in Appendix C. By default, we use random dense binary codes, which are **class-agnostic**, in line with the spirit of traditional one-hot encoding. Importantly, our **theoretical analysis** shows that under ideal learning conditions, **ECOC is functionally equivalent to one-hot encoding**, ensuring that the code structure itself does not inherently bias performance toward or against specific classes.\n\nTo further validate this, we conduct experiments using **multiple random codebooks** (denoted as different $M_{\\text{mmd}}$ matrices). As shown below, **mIoU remains stable** across codebooks, and class-wise variations fall within expected stochastic ranges:\n\n| $M_{\\text{mmd}}$ | Road | Sidewalk | Building | Wall | Fence | Pole | Light | Sign | Vegetation | Terrain | Sky  | Person | Rider | Car  | Truck | Bus  | Train | Motor | Bike | **mIoU** |\n| ---------------- | ---- | -------- | -------- | ---- | ----- | ---- | ----- | ---- | ---------- | ------- | ---- | ------ | ----- | ---- | ----- | ---- | ----- | ----- | ---- | -------- |\n| **Base**         | 95.7 | 70.2     | 89.4     | 53.5 | 48.1  | 49.6 | 55.8  | 59.4 | 89.9       | 47.9    | 92.5 | 72.2   | 44.7  | 92.3 | 74.5  | 78.2 | 65.1  | 55.9  | 61.8 | **68.3** |\n| 1                | 95.9 | 72.0     | 89.4     | 58.1 | 51.5  | 56.2 | 58.2  | 64.1 | 90.1       | 52.5    | 89.0 | 73.2   | 50.1  | 92.0 | 73.0  | 79.8 | 66.3  | 58.0  | 64.5 | **70.2** |\n| 2                | 96.7 | 77.4     | 89.3     | 58.5 | 51.9  | 54.9 | 59.1  | 65.1 | 90.0       | 52.9    | 89.0 | 70.3   | 51.0  | 91.7 | 71.1  | 75.2 | 61.2  | 60.1  | 65.7 | **70.0** |\n| 3                | 96.4 | 77.3     | 88.4     | 55.4 | 45.8  | 54.8 | 58.6  | 64.8 | 90.3       | 53.3    | 90.0 | 74.2   | 48.8  | 92.0 | 74.9  | 78.4 | 65.9  | 58.6  | 64.9 | **70.1** |\n\nThese results confirm that **ECOCSeg is robust to different codebook instantiations**, and the **codeword assignment is not responsible** for class-specific performance drops.\n\n\n\n**4. Optional Use of Semantics-Aware Codebooks** \n\nIn Appendix C, we further explore semantics-aware encoding using pretrained text embeddings (denoted as $M_{\\text{text}}$) to reflect inter-class similarity. However, this is **not required for the method to work**, and serves only as an optional enhancement to facilitate smoother optimization.\nAnalogous to one-hot vectors, our default ECOC design is **semantically agnostic by construction**, ensuring fair and unbiased treatment of all classes.\n\n------\n\n**Q2:** Typos.\n\n**A2:** We thank the reviewer for pointing this out. We will carefully fix all typographical errors in the revised version.\n\n------\n\nWe hope our response can resolve your concern. Please do not hesitate to let us know if you have further questions :)"}]

Author rebuttal:

Meta-review: Summary:
- This paper introduces ECOCSeg. It improves pseudo-label learning in semantic segmentation by using error-correcting output codes (ECOC) instead of one-hot labels. It introduces an ECOC-based classifier for better generalization and a bit-level denoising mechanism for cleaner pseudo-labels. The paper achieves significant gains on UDA and SSL benchmarks.

Strength:
- Using multi-bit binary encoding instead of one-hot encoding introduces redundancy and attribute sharing among classes, making it well-suited for handling noisy labels in pseudo-label learning.
- The paper is well-written, and the motivation is clear.

Weakness:
- Improvements over SOTA seem incremental
- Relies heavily on codebook design

Initially, reviewers are all on the fence. While they appreciate the interesting ideas of using error-correcting output codes for attribute-level supervision. They have concerns about the reliance on codebook design and the improvement over the state-of-the-art. The authors' rebuttal effectively addresses most of these major concerns, including comparisons between binary and continuous codes, demonstrating robustness to threshold choices, codebook design, and comparisons with prior work (ProDA, DiGA, MFA, FST), as well as the addition of per-class performance. All reviewers are satifisfied with the rebuttal and raise their scores to borderline accept. The AC checks the reviews and discussions and agrees with the concensus among the reviewers.
Decision: Accept (poster)