Title: Towards Robust Pseudo-Label Learning in Semantic Segmentation: An Encoding Perspective
Venue: NeurIPS 2025
Accepted: yes
Keywords: Semantic segmentation
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

Abstract

Pseudo-label learning is widely used in semantic segmentation, particularly in label-scarce scenarios such as unsupervised domain adaptation (UDA) and semisupervised 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 .

1 Introduction

Semantic segmentation has seen significant improvements with recent advances in deep neural networks[55, 9, 17, 16]. However, a major challenge in semantic segmentation is the requirement of a large volume of fine-grained pixel-level labels, which can be time-consuming and labor-intensive to obtain [19]. Due to the readily available nature of image data, unsupervised domain adaptation (UDA) and semi-supervised learning (SSL) have been introduced in 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 a 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 selftraining 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 can be summarized as pseudo-label learning, where the network's predictions are used as supervision for unlabeled data.

Unlabeled image

Ground truth

Pseudo label 1

Pseudo label 2

Sheep

Cow

Horse

Person

(b) One-hot Encoding

(c) ECOC Encoding

Person

Horse

Sheep

Cow

class

code

1        2        3       4

N-class classifier

N=4

0.40

0.25

0.05

0.30

pixel feature

from class

sheep

softmax

pseudo label

pixel feature

from class

sheep

K binary classifiers

horn

long-tail  dense-fur  hoof       biped

N=4, K=5

Person

Horse

Sheep

Cow

class

code

0.55

0.95

0.45

0.2

sigmoid

0.75

threshold = 0.5

pseudo label

nearest

query

√

×

√     ×

×

Although achieving promising results, the inevitable errors in pseudo labels misled the training process. Typical approaches design filter-out mechanisms [93, 72] and only use high-confidence pseudo-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 to utilize weighting functions [36, 77] that assign weights based on confidence of pseudolabels. While potentially effective, this approach requires careful design and selection of appropriate hyperparameters, which inevitably compromise its applicability. Based on above discussions, we investigate existing works primarily concentrate on developing specific selection strategies for pseudolabels but rarely consider the impact of the encoding form assigned for classes. As shown in Fig.1 (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 (b)). We speculate that similar classes share common visual attributes, leading to confusing pseudo-labels and further misguiding the training process. How to utilize the shared attributes among confusing classes to design a suitable encoding form for pseudo-label learning is rarely explored.

To explore the encoding form tailored for pseudo-label learning, we explicitly disentangle the 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 error-correcting output codes (ECOC) [21] to assign a binary bit string (codeword) as 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 a 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 a 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 a tighter classification error bound under a sufficiently large minimum code distance.

In this paper, we propose ECOCSeg, a novel segmentation framework designed for pseudo-label learning. ECOCSeg leverages error-correcting output codes (ECOC) as the class representation and creates fine-grained 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) ECOCbased Encoding Form . To implement ECOC as an alternative to the typically argmax-based one-hot

(a) bit-wise pseudo label

prediction from teacher net

bit-wise

prediction

threshold = 0.5

(b) code-wise pseudo label

query the nearest codeword

codebook

class

A

B

C

D

codeword of class C

(c) hybrid pseudo label

query candidate classes

D

C

codebook

bit-wise

prediction

reliable bit mining

√

√

√

√

？

？

？

？

？

？

？

？

？

class

encoding in the segmentation paradigm, we explore two simple yet effective coding strategies, i.e., max-min distance encoding and text-based encoding , to consider robustness and the relationship between classes, respectively. (2) Bit-level Denoising Mechanism . To consider the noise in pseudo labels, we present two assigning forms: bit-wise pseudo label and code-wise pseudo label (Fig. 2 (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 as 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, we propose a 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 a 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, a bit-level denoising mechanism, and customized loss functions to enhance performance. (3) We theoretically analyze the performance of 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 to perform well in the target domain despite distribution differences. Semi-supervised learning (SSL) [12, 92, 87, 99, 76, 75] leverages a combination of a 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 a small number of annotated samples by leveraging prior knowledge and meta-learning techniques. UDA and SSL, in particular, share a similar objective of using unlabeled (target) data to improve the performance of models

trained with labeled (source) data only. In this work, we explore these two settings from a unified perspective of pseudo-label learning.

2.2 Pseudo-label Learning

Two popular paradigms are often employed when training a model with unlabeled data: self-trainingbased methods [105, 79, 34, 41, 46] and consistency regularization-based methods [72, 12, 3, 93]. In self-training, the model is trained on unlabeled samples using pseudo labels derived from a teacher network. Consistency regularization aims to ensure prediction stability across different perturbations. Both can be viewed as pseudo-label learning [103, 44, 66]. More recently, state-of-theart segmentation methods in UDA and SSL combine both technologies [85, 35, 54, 47, 74]. 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 an orthogonal direction to the above approaches.

3 Method

3.1 Preliminaries

For the general formulation of UDA and SSL in semantic segmentation, we are given n l labeled (source) samples D l = ( x l i , y l i ) n l i =1 , where x l i represents i -th image with y l i as the corresponding pixel-wise one-hot label covering N classes, and n u unlabeled (target) samples D l = { x u i } n u i =1 with the same label space. The supervised loss L s can be calculated on labeled data:

where ℓ ce denotes the cross-entropy loss. The segmentation model, F , can be defined as F = h ◦ g , where g : X → Z lifts each pixel of the input image in X to the feature space Z and h : Z → R N is a pixel-wise classifier to give a score for each class. The unsupervised loss L u can be formulated in a unified form of pseudo-label learning as:

where ˆ y u ij is pseudo label produced by teacher model ˆ F and A w / A s denotes weakly/stronglyaugmented strategies. We define q ( p ij ) as a quality estimate conditioned on confidence p ij for pseudo labels, which can be implemented with threshold filtering or a weighting function. The overall objective function is L = L s + λ L u .

3.2 Method Overview

An overview of our method ECOCSeg, a pseudo-label learning framework for semantic segmentation, is shown in Fig. 3. We propose an ECOC-based dense classification paradigm (Sec. 3.3), where error-correcting codes create a fine-grained output representation for each class. Then, we study the different forms of pseudo labels driven by ECOCSeg and propose a 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 z i ∈ R D is extracted from g and fed

Pseudo-labelLearning(Sec.3.1)

codebook

Code-wisePseudoLabel

Vegetation

Query

Candidate

Terrain

TeacherModel F

Classes

Road

Weakly-

Thresholding

ReliableBit Mining (Sec.3.4)

augmentedAw

by 0.5

Bit-wisePseudo Label!

Hybrid Pseudo Label}

Unlabeled

Image

Nearest Neighbor Query

Lbce (Eq. 8)

Strongly-

codebook(NxK)

augmentedAs

inference

StudentModel F

ECOC-basedDenseClassification(Sec.3.3)

CN

★Target Pixel

OptimizationCriterion(Sec.3.5)

into h for N -way classification:

In this paradigm, p ( n | z i ) ∈ [0 , 1] is the probability that pixel i being assigned to class n and h is a N -class classifier parameterized by W = [ w T 1 ; . . . ; w T N ] ∈ R N × D , in 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 a matrix of binary values with the size of N × K , where each class is represented by a specific codeword of length K . The N -class classifier is replaced by K binary classifiers, with p ( k | z i ) = sigmoid ( w T k z i ) to predict probability that the k -th bit of pixel i being assigned to digit 1 . The class is determined by nearest neighbor algorithm within the codebook where soft Hamming distance d SH is used as a metric:

where c n is the codeword of class n , consisting of c nk ∈ { 0 , 1 } , p i is predicted probability vector, consisting of p ( k | z i ) ∈ [0 , 1] , and ˆ n i 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 ∈ { 0 , 1 } N × K and ensure the validity. Please refer to Appendix B 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 { vegetation, terrain, road } when C = 3 . Therefore, the shared part within this set, i.e., P s ( c veg. , c ter. , c roa. ) can be guaranteed to be accurate, allowing us to consider these bits as reliable.

To provide an adaptive value of C for each pixel, we design an effective strategy to determine the candidate classes and mine the reliable bits at the same time (Alg. 1), where we define confidence q ( k | z i ) = max { p ( k | z i ) , 1 -p ( k | z i ) } for each bit and set a hyperparameter T as upper bound. Then, we obtain the hybrid pseudo label by fusing the bit-wise label ( c i bit ) and the reliable bits mined from the code-wise label ( c i code ) with mask M i :

A higher T aligns c i hyb. more closely with the bit-wise way, while a lower T aligns it closer with the code-wise way. The hybrid pseudolabel takes advantage of both forms and introduces less label noise, which provides a lownoise form of supervision for unlabeled images and improves the stability of pseudo-label learning in semantic segmentation.

3.5 Optimization Criterion

In ECOCSeg, the multiclass learning problem is decomposed to K binary classification problems, which can be addressed by a binary cross-entropy (BCE) loss:

where c i is the target codeword assigned for pixel i . 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 a 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. 8 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-aware loss that minimizes the cosine distance between logits and codewords:

where ˆ p i represents the logits predicted by K binary classifiers, and ˆ c i is the standardized version of the codeword c i , with ˆ c i k ∈ {-1 , 1 } .

Pixel-code contrast. Eq. 9 encourages intra-class similarity without considering inter-class separation. For two codewords c 1 and c 2 , we define the shared part between them as P s ( c 1 , c 2 ) and the distinctive part as P d ( c 1 , c 2 ) . The value of ˆ p i changes in P s ( c 1 , c 2 ) and P d ( c 1 , c 2 ) has the same impact on the Eq. 9, while the latter part is more significant since P s ( c 1 , c 2 ) does not distinguish between classes. Thus, a pixel-code contrastive learning strategy is introduced:

where ⟨ , ⟩ is cosine similarity, ˆ C -= { ˆ c n } N n =1 / ˆ c i and τ is the temperature to control the concentration level. Note that the target codeword ˆ c i is not necessarily included in { ˆ c n } N n =1 if we adopt the form of a bit-wise pseudo label. Furthermore, this loss term can be rewritten as:

which is only calculated on the P d (ˆ c i , ˆ c -) to distinguish between codewords. These two loss terms complement each other to enhance the representative capacity of the learning features. Then, the

Algorithm 1 Reliable bit mining strategy

1: Input: probability vector p i ∈ [0 , 1] K

2: Output: mask of the reliable part M i ∈ { 0 , 1 } K

3: Initialize: code matrix M , confidence threshold T , candidate set S c = {} , M i = { 1 } K

4: compute code distance for each class by Eq. 5;

5: sort the code distance and obtain sorted index I ;

6: compute confidence q i ;

7: for n = 1 to N do

8: add c I [ n ] to S c ;

9: compute the shared part P s ( S c ) ;

10: update M i with bit positions in P s ( S c ) ;

11: compute mean confidence q i m in P s ( S c ) ;

12: if q i m > T or M i = { 0 } K then

13: break ;

14: end if

15: end for

16: return M i

segmentation model is trained with combinatorial loss over all training pixel samples:

which can be utilized in both supervised loss L s and unsupervised loss L u in pseudo-label learning.

4 Theory

In this section, we present our main theoretical results on the performance and robustness of ECOCbased 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 pseudo-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 E ([ C ]) is nearly orthogonal, i.e., | E ([ C ]) T E ([ C ]) -nI | ≤ δ for some small δ > 0 , 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 δ .

Remark 1 . In practice, the codewords of ECOC are often designed to be approximately orthogonal. Due to the smoothness of the NTK, we can expect the performance of ECOC-based DNN to be close to that of one-hot encoding when the codewords are nearly orthogonal.

Theorem 4.2 (ECOC Robustness in Pseudo-Label Learning) . Suppose E ([ C ]) ∈ {-1 , +1 } C × n has code length n and minimum distance d , and the binary classifiers f 1 ( x ) , . . . , f n ( x ) satisfy the margin condition with parameters γ 1 , . . . , γ n . Assume that the pseudo-labels are treated as class labels that are corrupted by random noise with probability ϵ . If the minimum distance d satisfies:

where γ = min k γ k , ˆ γ = min j ˆ γ j , and κ = κ ( B,L,ϕ (0)) , then the classification error probability of the ECOC-based DNNs admits a tighter upper bound than that of one-hot encoding under the same noise level ϵ .

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 a 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 a larger minimum distance d to 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.

5 Experiment

5.1 Experimental Setup

Datasets. We evaluate our approach on two standard benchmarks for synthetic-to-real 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], a 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 an augmented set of 10,582 additional training images, and COCO [52], a challenging benchmark composed of 118k/5k training/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 GPU 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 × 10 -5 (encoder) and 6 × 10 -4 (decoder), weight decay of 0.01, and linear warm-up for the first 1.5K iterations. Images are rescaled and randomly cropped to 512 × 512 following DAFormer's augmentation, and the EMA coefficient for updating the teacher net is 0.999.

SSL Setting. We implement our method on ST++ [95], FixMatch [72], UniMatch [93] and adopt DeepLabv3+ [10] with a ResNet [29] backbone as our segmentation model. For Pascal, we use a crop size of 321 × 321 and 513 × 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 2 × RTX 3090 GPUs. More experiment settings are detailed in Appendix G.

ECOCSeg Parameters. ECOCSeg uses M text as the default codebook with codeword length K = 40 for Cityscapes and Pascal, and K = 60 for COCO. We set the loss weight λ 1 = 5 and λ 2 = 2 with the temperature τ = 0 . 5 . The confidence threshold T for reliable bit mining is set to 0.95. Specifically, we use the mean value of bit-wise confidence, i.e., 1 K ∑ K k =1 q ( k | z i ) , to estimate pixel-wise confidence, which is needed in Eq. 2.

5.2 ECOCSeg for UDA

We integrate ECOCSeg with three baselines and compare with state-of-the-art UDA approaches on GTAv → Cityscapes and SYNTHIA → Cityscapes benchmarks. For a 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 state-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 in 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 pseudo-labels provided by ECOCSeg.

In Appendix G, we evaluate on more powerful baselines, provide more quantitative results on the Cityscapes, COCO and additional real-world Scenarios. ECOCSeg demonstrates significant gains across multiple different datasets and network architectures, indicating the versatility of our method.

5.4 Diagnostic Experiment

Optimization Criterion. We evaluate the proposed optimization criterion under the fully supervised setting using DAFormer on Cityscapes in Table 3. The first line denotes the original argmax-based one-hot encoding supervised by cross-entropy loss. When implemented only with L bce , the accuracy for M text is lower than baseline due to sub-optimal learning by independent binary classification. Adding L pcd or L pcc 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 M mmd , the performance slightly degrades but still achieves competitive results.

Confidence Threshold T . We conduct a study comparing pseudo-label performance using code-wise and bit-wise forms in Table 4. The former performs better when combined with M text , while the latter achieves better results when combined with M mmd . 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 M mmd , 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 T = 0 . 5 , it is equivalent to code-wise form, while T = 1 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 T value can generate a robust hybrid label that combines the 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 between 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 classification, and the shared bits between code-wise labels of the two classes exhibit higher confidence, which can be viewed as reliable bits.

Image

Ground Truth

1 st Pseudo label

2 nd

Pseudo label

1 st Confidence map

1 st Confidence area

2 nd

Confidence map

2 nd

Confidence area

(a) Curve of bit count

(b) Visualization for reliable bit mining

Difference Count

Correction Count

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 a more robust and effective training process.

6 Conclusion

In this paper, we present ECOCSeg, a novel framework that introduces a new perspective that utilizes the error-correcting output codes as a fine-grained encoding form for each class and facilitates stable pseudo-label learning in semantic segmentation. By leveraging an ECOC-based encoding form, a bitlevel pseudo-label denoising mechanism, and customized optimization criteria, ECOCSeg effectively addresses the challenges associated with pseudo-label learning. The versatility of ECOCSeg allows it to be easily integrated with existing works, consistently demonstrating improvements across multiple unsupervised domain adaptation (UDA) and semi-supervised learning (SSL) benchmarks.

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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 ϕ is B-Lipschitz continuous, i.e., | ϕ ( x ) -ϕ ( y ) | ≤ B | x -y | for all x, y ∈ R .

Assumption A.2 (Bounded inputs) . The input data x satisfies || x || 2 ≤ 1 .

Assumption A.3 (NTK assumptions) . The Neural Tangent Kernel (NTK) converges to a deterministic kernel in the infinite width limit, and the NTK matrix K ( X,X ) is positive definite, where X is the 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 a deterministic 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 l ≤ L -1 and any δ > 0 ,

holds with probability at least 1 -δ when n is large enough, where the hidden layer width n l = α l n with constant α l > 0 for all 1 ≤ l ≤ L -1 .

Now we prove the theorems.

Proof of Theorem 4.1 . Let f ECOC and f one -hot denote the functions represented by the ECOCbased 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:

where ˜ Y denotes the one-hot encoded target, and the ECOC target is Y = E ([ C ]) ˜ Y . Then, the decoding process for the ECOC-based DNN is:

where e c ∈ R C is the c -th one-hot codeword and | x | A ≜ √ x T Ax is the Mahalanobis norm with positive definite matrix A . For the one-hot encoding DNN, the decoding process is:

When E ([ C ]) is orthogonal, i.e., E ([ C ]) T E ([ C ]) = nI , the Mahalanobis norm reduces to the scaled Euclidean norm:

In this case, the decoding processes for ECOC and one-hot encoding are equivalent up to a scaling factor, leading to the same classification results. When E ([ C ]) is nearly orthogonal, i.e., | E ([ C ]) T E ([ C ]) -nI | ≤ δ for some small δ > 0 , the Mahalanobis norm is a perturbed version of the scaled Euclidean norm. The difference in the decoding metrics leads to a difference in the classification performance. Specifically, let ˆ c ECOC and ˆ c one -hot be the predicted class labels from

the ECOC-based and one-hot encoding DNNs, respectively. Then,

̸

̸

let ∆ c = || e c -˜ Y ( K ( X,X ) + λI ) -1 K ( X,x ) || 2 . By definition of ˆ c one -hot , ∆ˆ c one -hot ≤ ∆ c for all c = ˆ c one -hot . Therefore,

̸

̸

̸

̸

When E ([ C ]) is orthogonal, i.e., δ = 0 , we have P (ˆ c ECOC = ˆ c one -hot ) = 0 . When E ([ C ]) is δ -nearly orthogonal, | ∆ c -∆ ˆ c one -hot | ≤ 2 √ n δ for all c . Thus,

̸

̸

̸

If δ = o ( 1 √ n ) , then 2 √ n δ → 0 as n → ∞ , while min c =ˆ c one -hot ∆ c -∆ ˆ c one -hot converges to a positive constant. Therefore, the indicator function becomes 0 for sufficiently large n , making P (ˆ c ECOC = ˆ c one -hot ) arbitrarily small. The ECOC-based DNN achieves performance equivalent to the one-hot encoding DNN up to an error term depending on δ .

̸

LemmaA.7 (Concentration of noisy functions) . Let f be a real-valued function on a probability space ( X , A , P ) such that E [ f 2 ] < ∞ . Let ˜ f be a noisy version of f such that E [( ˜ f ( x ) -f ( x )) 2 ] ≤ σ 2 for all x ∈ X . Then for any δ > 0 ,

Lemma A.8 (Binary classifier perturbation bound) . Under the margin condition and the random label noise model, for any δ > 0 , with probability at least 1 -δ , the error probability of each binary classifier f k ( x ) is bounded by

where ϵ k 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 γ k is margin.

Proof. We first review the conditions and notations in the lemma:

f k ( x ) represents the k -th binary classifier in ECOC, with input x and output in {-1 , +1 } .

y k ∈ {-1 , +1 } represents the true label of the k -th binary classification problem. ˜ y k ∈ {-1 , +1 } represents the noisy label.

̸

̸

̸

The function f k satisfies the margin condition, i.e., there exist constants µ 1 ,k , µ -1 ,k ∈ R and γ k ∈ (0 , 1) such that:

The label noise follows the random noise model, i.e., for any x , its true label y k is flipped to ˜ y k = -y k with probability ϵ k , independently.

The activation function σ of the network satisfies the B -Lipschitz condition, i.e., for any u, v ∈ R , we have:

Let f k ( x ) be the output of the k -th binary classifier in the ECOC-based DNN, satisfying the assumptions in the lemma. Our goal is to bound the error probability p k of the binary classifier f k under the noisy labels ˜ y k . First, we consider the case when the true label is y k = 1 . By the margin condition, we have:

Let ˜ f k ( x ) be the noisy version of f k ( x ) under the label noise model, i.e., ˜ f k ( x ) = f k ( x ) with probability 1 -ϵ k and ˜ f k ( x ) = -f k ( x ) with probability ϵ k . Then, we have:

By the Hidden Layer Output Bound (Lemma A.6) and the fact that n L = 1 , we have:

with probability at least 1 -δ for any δ > 0 . Therefore,

Combining the above inequalities, we get:

Now, applying the Concentration of Noisy Functions (Lemma A.7) with σ 2 = 4 ϵ k ( κ ( B,L,ϕ (0)) + δ ) 2 , we have:

Setting 2 √ 2 ϵ k ( κ ( B,L,ϕ (0)) + δ ) 2 log(2 /δ ) = µ 1 ,k and solving for δ , we obtain:

with probability at least 1 -δ . Similarly, for the case when the true label is y k = -1 , we can show that:

with probability at least 1 -δ . Combining the two cases, we obtain:

with probability at least 1 -2 δ . Then, with probability at least 1 -δ , we have

Proof of Theorem 4.2 . In Pseudo-Label Learning, suppose the class labels are corrupted by random noise with probability ϵ ∈ (0 , 1) , i.e., each true label y ∈ [ C ] is flipped to a uniformly random class ˜ y ∈ [ C ] \ y with probability ϵ . Under this noise model, the ECOC-based DNN has a label noise probability of ϵ k = ϵ · ( n + d ) / (2 n ) for each binary classifier f k .

̸

For the ECOC-based DNN , let ˆ y ∈ [ C ] be the predicted class label for an input x , and let ˆ E ( x ) ∈ {-1 , +1 } n be the corresponding predicted codeword, i.e., ˆ E ( x ) k = sign ( f k ( x )) for k ∈ [ n ] . Let y ∈ [ C ] be the true class label of x , and let E ([ y ]) ∈ {-1 , +1 } n be the corresponding true codeword. Under the given noise model, when the probability that y is flipped to a specific class ˜ y = y , the Hamming distance between E ([ y ]) and E ([˜ y ]) is at least d , by the definition of the minimum distance of the ECOC matrix. Therefore, for ˆ y to be misclassified as ˜ y , the predicted codeword ˆ E ( x ) needs to be closer to E ([˜ y ]) than to E ([ y ]) in Hamming distance, which means that ˆ E ( x ) must differ from E ([ y ]) in at least d/ 2 bits. By the union bound, the probability of this event is at most ( n d/ 2 ) p d/ 2 , where p is an upper bound on the error probability of each binary classifier. The total probability of misclassification is bounded by

̸

To bound the error probability of each binary classifier, we apply the simplified bound from Lemma A.8 with the label noise probability ϵ k = ϵ · ( n + d ) / (2 n ) and probability at least 1 -δ/n :

where γ = min { γ k } . Finally, the error probability of the ECOC-based classifier is bounded by:

̸

with probability at least 1 -δ and using the binomial coefficient bound ( n d ) ≤ ( en/d ) d .

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:

Assume each binary classifier f j ( x ) satisfies the margin condition similar as Lemma A.8. Let ϵ j be the label noise probability for the j -th binary classifier, we have ϵ j = ϵ . Then, with probability at least 1 -δ/C , the error probability of each binary classifier f j ( x ) under noisy labels is bounded by:

̸

Now, let E be the event that the multiclass classifier f ( x ) predicts the correct class label under noisy labels, i.e., ˆ y = arg max j ∈ [ C ] y j . For event E to hold, it suffices to have f j ( x ) > f k ( x ) for all k = j , where j = arg max j ∈ [ C ] y j is the true class label. Consider any class k = j . Under the true labels y , we have y j = 1 and y k = -1 . By the margin condition, with probability at least 1 -δ/C , we have f j ( x ) > f k ( x ) holds with probability at least 1 -δ/C if:

̸

̸

By the union bound, f j ( x ) > f k ( x ) holds for all k = j simultaneously with probability at least 1 -δ , implying that event E holds with probability at least 1 -δ .

̸

Based on Theorem 4.1 , one-hot can be viewed as using C binary classifiers. For correct prediction, the ground-truth score f j ( x ) must exceed all others f k ( x ) for k = j , we have the following proof sketch:

̸

Define the correct classification event: E = ⋂ k = j { f j ( x ) > f k ( x ) }

̸

The misclassification corresponds to the complement event: P ( E C ) = P ( ⋃ k = j { f k ( x ) > f j ( x ) } )

̸

Applying the union bound: P ( E C ) ≤ ∑ k = j P ( f k ( x ) > f j ( x ))

̸

Using the per-class binary upper bound p j , we obtain the overall one-hot upper bound: P one-hot (ˆ y = y ) ≤ ∑ C j =1 p j

Finally, the error probability of the multiclass classifier f ( x ) is bounded by:

̸

with probability at least 1 -δ , where ˆ γ = min { ˆ γ j } .

To derive the condition on the minimum distance d for the ECOC-based DNN to have a tighter error bound than the one-hot encoding DNN, we compare the two bounds (Equations 40 and 44):

Using the fact that d < n , and the monotonicity of lnx x , we have:

The equation suggests that when the noise level ( ϵ ) is higher, we can use a larger code distance ( d ) to obtain a tighter bound for ECOC-based classifer. The lower bound of d is determined by the ratio of the margins of the two classifiers ( 2 ˆ γ 2 γ 2 ).

Remark on Assumptions. The theoretical results presented above rely on two standard assumptions: (i) classifier independence and (ii) uniform random noise. Both assumptions are analytically tractable and justified in the context of our analysis.

Independence Assumption.

Theorem 4.1 analyzes ECOC decoding from a global perspective and does not require classifier independence.

Theorem 4.2 assumes bit-wise independence only to derive a worst-case error bound . In practice, classifier correlations tend to reduce joint error, so the assumption does not compromise the theorem's validity. Specifically,

̸

When classifiers are correlated, the expected joint error is lower than the product of marginal probabilities due to Jensen's inequality:

Therefore, modeling such dependencies would tighten the bound, and the assumption of independence yields a conservative estimate.

In practice, perfect independence is rarely satisfied. Even with orthogonal or class-agnostic codes (e.g., one-hot or M mmd), 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 pseudo-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 pseudolabel 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-based ECOC bound more conservative (see Independence Assumption ), since correlations typically reduce joint error. As a 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 two algorithms for codebook generation, as shown in Alg. 2 and Alg. 3, respectively.

Algorithm 2 Max-min distance encoding

Max-min distance encoding. A good error-correcting output code should satisfy row separation and column separation . For the former, the minimum Hamming distance between each pair of codewords d min _ r should be maximized, which can correct at least ⌊ d min _ r -1 2 ⌋ single bit errors. As for the latter, each bit classifier should be uncorrelated with the others. This can be ensured by maximizing d min _ c and N -d max _ c , which are calculated between columns of the code matrix. Although searching for an optimal encoding matrix is known as an NP-hard problem [20], we can obtain a sufficiently valuable encoding matrix, denoted as M mmd , through a random generation strategy due to the sparsity of the encoding space.

Due to the large size of the encoding space ( 2 K ) relative to the number of classes N , a randomly generated codebook typically ensures a sufficiently large minimum Hamming distance. Any pair of such random strings will be separated by a Hamming distance that is binomially distributed with mean K/ 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: (1) There are no identical codewords, which can be ensured by d min _ r > 0 . (2) There are no wholly identical or opposite classifiers, which can be ensured by d min _ c > 0 and d max _ c < N . In our case, we set iterations L = 100000 to generate a sufficiently robust codebook.

Algorithm 3 Text-based encoding

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 f text ∈ R N × C 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 M text . 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, we quantize the features into 0-1 encoding using the mean of the feature components as

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Text-basedencoding

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 a one-hot form, which is easily susceptible to the influence of label drift in the pseudo-label learning process. The M mmd aims to maximize the distance between classes, ensuring the robustness of the labels. Furthermore, M text 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 M mmd , it may generate more label noise for the code-wise form of pseudo-labels, leading to erroneous training in pseudo-label learning and limiting performance improvement. However, because of its sufficient robustness, bit-wise pseudo-labels can provide more stable performance gains for M mmd . In M text , this phenomenon is reversed because M text naturally perceives the relationships between classes, making its encoding form easy to learn, and thus code-wise pseudo-labels achieve higher performance, as shown in Table 4. Our hybrid pseudo-labels 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 M mmd and M text respectively, and evaluate performance on UDA setting with DAFormer [34] and SSL setting with UniMatch [93]. The results are shown in Table 5 and Table 6. We also We present a comprehensive comparison in Figure 6. Each code design has its own benefits:

M mmd ensures larger code distances and stronger error correction.

M text preserves semantic relationships between classes, which helps in learning easier-tooptimize binary classifiers.

Both M mmd and M text 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 M text as the default setting for ECOCSeg.

Note that our encoding strategies, focusing on class separability, visual similarity, and codeword length. These components are essential for building effective codebooks in ECOCSeg.

Class Separability. We propose two simple yet effective codebook generation strategies:

-M mmd : A class-agnostic strategy that maximizes the minimum pairwise Hamming distance among codewords.

-M text : 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 not strictly required-similar to how traditional one-hot encoding is class-agnostic by design. Specifically, M mmd does not rely on class semantics, while M text 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 E and G, including selection criteria and empirical results. Our findings indicate that moderately long codes offer a 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 benchmarks 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, T = 0 . 5 and T = 1 correspond to the pure code-wise and bit-wise forms respectively, while intermediate values yield more robust hybrid labels. This makes T a non-sensitive hyperparameter.

The choice of T is robust across datasets. We use a fixed setting of T = 0 . 95 in all experiments, achieving consistent performance gains.

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(a) DAFormer on GTAv→Cityscapes with UDA setting.

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(c) Unimatch on Pascal (1/4 partition) with SSL setting.

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(b) DAFormer on SYNTHIA→Cityscapes with UDA setting.

E Analysis of Encoding Length K

Generally, an adequate length of codewords (at least log N ) is required to ensure robust encoding. However, excessively long codewords can lead to redundancy and inefficient optimization. Table

7 studies the influence of encoding length K . ECOCSeg performs well even with a low encoding length of K = 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. To balance performance and computational 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.

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 is often among TopC 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 in Figure 7:

Across benchmarks, mAcc drops monotonically with lower-ranked predicted classes.

Aggregated mAcc over TopC classes quickly approaches 1, indicating correct class is usually included.

Since correct class's codeword contains only correct bits, the shared bits from TopC set are guaranteed to be accurate when correct class is included.

Therefore, our Reliable Bit Mining strategy leverages this phenomenon to robustly extract accurate bits, even in the presence of pixel-level noise.

(a) DAFormer on GTAv→Cityscapes with UDA setting

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(b) DAFormer on SYNTHIA→Cityscapes with UDA setting

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(c) Unimatch on Pascal (1/4 partition) with SSL setting.

(d)Top-C mAcc on different benchmarks.

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G More Experiments on SSL

In this section, we provide more experiment settings and results on SSL on more powerful baselines, challenging benchmarks and real-world scenarios. We emphasize that ECOCSeg is designed as a label representation improvement, independent of network architecture or training strategy. Therefore, it can be seamlessly integrated into a wide range of semi-supervised learning (SSL) frameworks as a plug-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 a SGD optimizer. The model is trained for 240, and 30 epochs under a poly learning rate scheduler. The training resolution is 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 3.2%, especially on most challenging 1/16 partition, verifying its robustness and generalization ability. We also show the results on COCO in Table 9, where ECOCSeg outperforms the baseline with gains ranging from 1.7% to 2.6%. We find ECOC is

efficient to handle a larger number of classes due to its binary decoupling property. Theoretically, a length of K = log 2 N is sufficient to represent classes, while excessively long encodings can lead to redundancy. Empirically, the optimal code length is roughly K = 10log 2 N [2]. Based on this empirical rule, we use K = 60 for COCO (81 classes) and conduct experiments with UniMatch, observing significant improvements.

Powerful Baselines. To demonstrate the compatibility of our method with modern architectures and training paradigms, we conduct additional experiments on 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, even when built upon strong semi-supervised learning baselines with large-scale pre-training.

Real-World Scenarios. To evaluate the generalizability of ECOCSeg beyond natural scene segmentation, 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 in Table 11.

Note that WHU-CD is a binary classification task, where ECOC encoding is not meaningful due to the absence of class diversity. In this case, the only difference introduced by ECOCSeg lies in the quality estimation strategy:

UniMatch uses threshold-based 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 on the ACDC dataset [5], a four-class cardiac MRI segmentation task. Results using UniMatch with a UNet [68] backbone are shown in Table 12.

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, as discussed above, the advantages of ECOCSeg are more pronounced in multi-class settings , where fine-grained class disentanglement and bit-level shared attributes play a larger role.

H Analysis of Quality Estimate

In pseudo-label learning, we need a quality estimate q ( p ij ) to control the optimization process for L u , where p ij is confidence and typically defined by maximum class probability. In DAFormer [34], it is defined by:

where [ · ] denotes the Iverson bracket, and this weight is applied to all pixels of the entire image simultaneously. In UniMatch [93], it is defined through a threshold filtering way:

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 1/4 labeled data with ResNet-101 on the Pascal dataset, as shown in Table 13. We set the same threshold τ ′ = 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

way, leading to no 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 a significant performance improvement. Based on the above discussions, we implement Eq. 47 for ECOCSeg and set the same threshold τ ′ as corresponding baseline methods to evaluate the performance.

I Influence of Parameters Setting

In this section, we study the hyper-parameter setting introduced in the optimization criterion for ECOCSeg, i.e., λ 1 , λ 2 , and τ . All experiments are built with DAFormer of a fully supervised learning setting on Cityscapes, and results are summarized in Table 14. We observe that ECOCSeg is robust to the two coefficients, λ 1 and λ 2 , and achieves the best performance at λ 1 = 5 , λ 2 = 2 . The setting of temperature τ has a 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 ECOCSegenhanced counterparts. The results are summarized in Table 15.

FLOPs: 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.

Memory and Training Time: The additional memory and training time primarily stem from two components:

A small ECOC codebook, represented as a binary matrix of size N × K .

The lightweight Reliable Bit Mining algorithm introduced during training.

These components incur modest overhead, which is acceptable considering the consistent performance improvements observed across various benchmarks.

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 a 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

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(b) ECOCSeg

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Confidence

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 two paradigms and evaluate on Pascal val. In Fig. 8, we present the reliability diagrams, which plot the expected pixel accuracy as a the function of confidence, and calculate the Expected Calibration Error (ECE) [28]:

where we divide the bins with an 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 is 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 our method with representative approaches that focus on 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, our 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 a complementary and scalable solution. We believe this direction opens up new opportunities for robust pseudo-label learning and could inspire further research in this area.

M Qualitative Results

In this section, we provide more qualitative results to compare ECOCSeg and corresponding baseline methods on different benchmarks. As shown in Fig. 9 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 a notable improvement in the performance of these classes, which further demonstrates the effectiveness of our method.

N Limitation and Impact Statement

While ECOCSeg demonstrates consistent improvements across a 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 mmd and M text ), sub-optimal

Image

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codeword configurations may still hinder performance in certain edge cases. Second, our theoretical analysis assumes bit-wise independence and uniform label noise, which may not fully capture the structured or 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/semisupervised semantic segmentation, a pivotal research area in the realm of computer vision, with no apparent negative societal implications known thus far.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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.\n\nSTRENGTHS AND WEAKNESSES:\n## **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\"\n\nQUESTIONS:\n- 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.\n\nLIMITATIONS:\nyes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe 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)\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\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.\n\nQUESTIONS:\nThe questions are listed above. The reviewer is interested to see how the authors may respond to the concerns.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\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.\n\nQUESTIONS:\n- 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?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis 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.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\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\n\nQUESTIONS:\n1. 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.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-06"}