Organizations: University of Warwick, Coventry, United Kingdom · Wuhan University, Wuhan, China · Emory University, Atlanta, GA, USA · Peking University, Beijing, China · Zhejiang University, Hangzhou, China
Real-world semi-supervised learning (SSL) often encounters significant challenges with long-tailed label distributions and noisy pseudo-labels, which hinder generalization and amplify confirmation bias. In this work, we introduce a novel framework, Gaussian Bridge Consistency (GBC), to address these challenges by constructing semantic interpolation paths between unlabeled samples and high-quality class anchors. Our method maintains a dynamic Prototype Atlas that stores a diverse and evolving set of labeled and pseudo-labeled exemplars per class. For each unlabeled instance, GBC forms a class-conditional Gaussian Feature Bridge in the latent space, enabling the student model to traverse a smooth trajectory from uncertain predictions to reliable class prototypes. A bridge consistency loss is applied along this path to enforce alignment with a geometrically interpolated target distribution. Furthermore, we propose BridgeMix, a confidence-aware feature mixing strategy that interpolates both sample and anchor pairs to amplify cross-sample generalization. Extensive experiments on CIFAR10-LT and ImageNet-LT (USB benchmarks) validate the robustness and effectiveness of GBC under realistic long-tailed SSL settings, consistently improving long tail-class performance without sacrificing scalability.
Figures & tables
Figure 1: Overview of our proposed framework.
Figure 2: Overview of BridgeMix. Confidence-guided weights λi facilitate smooth semantic transitions between paired unlabeled samples and their anchors.
Table 3
consistent
uniform
reversed
middle
head-tail
γℓ
150
100
150
100
150
100
150
100
150
100
γu
150
100
1
1
1/150
1/100
150
100
150
100
FixMatch [ 49 ]
62.91 ± 0.87
65.48 ± 0.81
71.03 ± 0.69
72.49 ± 0.61
59.94 ± 1.02
62.53 ± 0.95
64.29 ± 0.85
65.95 ± 0.74
58.33 ± 1.01
60.52 ± 0.93
w/ CReST+ [ 57 ]
67.98 ± 0.73
70.45 ± 0.63
82.01 ± 0.51
84.96 ± 0.43
65.97 ± 0.76
69.03 ± 0.71
69.00 ± 0.65
72.47 ± 0.54
62.98 ± 0.82
65.95 ± 0.76
w/ DASO [ 43 ]
73.01 ± 0.49
74.48 ± 0.51
87.97 ± 0.31
89.52 ± 0.29
73.99 ± 0.58
75.51 ± 0.52
74.99 ± 0.48
78.53 ± 0.41
69.97 ± 0.66
72.48 ± 0.62
w/ ACR † [ 58 ]
76.99 ± 0.41
81.61 ± 0.33
91.32 ± 0.22
92.09 ± 0.19
81.82 ± 0.27
85.03 ± 0.28
77.90 ± 0.49
73.62 ± 0.46
78.96 ± 0.37
79.82 ± 0.39
Table 3: Top-1 accuracy (%) on CIFAR10-LT ( N1=500,M1=4000 ) with different labeled/unlabeled imbalance ratios γℓ,γu under five unlabeled class distributions (SimPro protocol [ 10 ] ). † denotes reproduced results without anchor distributions for fair comparison [ 58 ] . All results are reported in alignment with established SimPro performance trends; best in each column is bold . Pink highlights our GBC, and Peach indicates the baseline (SimPro). Manifold MixUp is a strong interpolation-based baselines
ImageNet-127 ( γt≈286 )
ImageNet-127 ( γt=1 )
ImageNet-1k ( γt=1 )
Method
32×32
64×64
32×32
64×64
32×32
64×64
FixMatch [ 49 ]
29.7 ± 0.37
42.3 ± 0.41
38.7 ± 0.46
46.7 ± 0.44
–
–
w/ DARP (NeurIPS’22) [ 33 ]
30.5 ± 0.28
42.5 ± 0.40
–
–
–
–
w/ CReST+ (CVPR’21) [ 57 ]
32.5 ± 0.33
44.7 ± 0.39
–
–
–
–
w/ CoSSL (CVPR’22) [ 11 ]
43.7 ± 0.35
53.9 ± 0.38
–
–
–
–
w/ SAW (ICML’22) [ 35 ]
58.3 ± 0.31
65.5 ± 0.29
54.9 ± 0.27
62.7 ± 0.25
18.9 ± 0.33
24.4 ± 0.36
Table 4: Top-1 accuracy (%) on ImageNet-127 ( γℓ≈286 , N1≈28 k, M1≈250 k) and ImageNet-1k ( γℓ=256 , N1=256 , M1=1024 ) under different test imbalance γt and resolutions. † indicates results reproduced for ACR without anchor distributions. All baselines follow the SimPro protocol [ 10 ] . Pink indicates GBC while Peach indicates the ReaLTSSL baseline (SimPro).
Figure 3: Many/Medium/Few breakdown and t-SNE visualization. Left: Per-split Top-1 accuracy on ImageNet-127 ( γt≈286 , 64×64 ). Classes are grouped by labeled training samples under the long-tailed distribution ( γℓ ): Many > 100, Medium 20–100, Few < 20. The split is fixed across all methods and accuracy is averaged per class within each group. The same class split is fixed across all compared methods, and group accuracy is computed as the unweighted average over classes within each group. Right: t-SNE visualization on CIFAR10-LT (uniform setting).
Figure 4: Mean KL divergence on CIFAR10-LT ( N1=500 , M1=4000 , SimPro protocol). KL(pteacher∥pstudent) is plot on weak views, averaged over 3 seeds and smoothed by EMA(0.9). Curves correspond to three unlabeled-distribution regimes: consistent ( γℓ=γu=150 ), uniform ( γu=1 ), reversed ( γu=1/γℓ ). GBC exhibits faster and smoother KL divergence decay across all regimes, especially under reversed , indicating stable bridge-consistency alignment under severe pseudo-label noise.
Figure 5: Effect of the confidence threshold τc on performance.
Table 9Table 10
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Backbone
Params (M)
CIFAR10-LT ( 322 )
CIFAR100-LT ( 322 )
Baseline
+GBC
Baseline
+GBC
ResNet-50
25.6
80.7 ± 0.3
83.5 ± 0.2 (+2.8)
52.2 ± 0.2
53.0 ± 0.2 (+0.8)
ViT-B/16 [ 9 ]
186.4
82.1 ± 0.3
84.0 ± 0.2 (+1.9)
53.0 ± 0.3
54.0 ± 0.2 (+1.0)
Vision Mamba-B [ 64 ]
48.5
81.0 ± 0.3
83.0 ± 0.2 (+2.0)
51.8 ± 0.3
52.9 ± 0.2 (+1.1)
ImageNet-127 ( 642 )
ImageNet-1k ( 642 )
Baseline
+GBC
Baseline
+GBC
Appendix
Table 9: Additional adaptation experiments on diverse backbones. Top-1 accuracy (%) with/without GBC on three representative benchmarks. Backbones: ResNet-50, ViT-B/16 [ 9 ] , Vision Mamba-B [ 64 ] . All runs follow the same SimPro/ReaLTSSL protocol and hyperparameters as the main paper. Δ reports the absolute gain from adding GBC.
CIFAR10-LT ( 322 )
CIFAR100-LT ( 322 )
ImageNet-127 ( 642 )
Method
1-shot
5-shot
10-shot
1-shot
5-shot
10-shot
1-shot
5-shot
10-shot
FixMatch [ 49 ]
80.2 ± 0.8
89.0 ± 0.5
91.1 ± 0.4
42.9 ± 0.6
55.6 ± 0.4
61.2 ± 0.5
34.1 ± 0.5
49.5 ± 0.4
54.8 ± 0.3
SAW [ 35 ]
81.4 ± 0.5
89.6 ± 0.4
91.6 ± 0.3
43.7 ± 0.5
56.1 ± 0.3
61.7 ± 0.4
35.0 ± 0.4
50.2 ± 0.4
55.3 ± 0.4
DePL [ 55 ]
81.9 ± 0.5
90.1 ± 0.6
91.8 ± 0.3
44.2 ± 0.4
56.9 ± 0.4
62.0 ± 0.5
35.4 ± 0.4
50.8 ± 0.3
55.8 ± 0.5
BaCon [ 12 ]
82.5 ± 0.4
90.3 ± 0.5
92.0 ± 0.4
44.9 ± 0.3
57.4 ± 0.5
62.3 ± 0.3
35.8 ± 0.5
51.1 ± 0.4
56.2 ± 0.3
CPE [ 38 ]
82.7 ± 0.5
90.4 ± 0.3
92.3 ± 0.4
45.2 ± 0.5
57.7 ± 0.3
62.6 ± 0.4
36.1 ± 0.4
51.4 ± 0.4
56.7 ± 0.3
Appendix
Table 10: Few-shot semi-supervised performance (k-shot per class). We evaluate GBC and recent SSL methods under the ReaLTSSL few-shot protocol, where only k∈{1,5,10} labeled samples per class are provided. Results report Top-1 accuracy (%) averaged over three random seeds.
Noise Strength ν
Top-1 Acc. (%)
KL Decay ↓ (epoch 300)
Anchor Recall (%)
0.00 (no noise)
91.82 ± 0.11
0.164
78.3
0.05
92.11 ± 0.10
0.151
81.0
0.10 (default)
92.30 ± 0.17
0.143
83.7
0.20
91.97 ± 0.13
0.158
80.1
Appendix
Table 11: Ablation on Gaussian noise strength ν in the Gaussian Feature Bridge. We evaluate GBC on CIFAR10-LT under the consistent setting ( γℓ=100 , γu=100 ). ν controls the magnitude of stochastic perturbation σ(t)=νt(1−t) injected along the bridge. We report Top-1 accuracy, KL divergence decay (lower is better), and anchor recall (ratio of correct PA retrieval). Moderate noise ( ν=0.10 ) gives the best trade-off.
PA Capacity C
Top-1 Acc. (%)
Anchor–Proto Cosine ↑
Refresh Rate (%) ↓
0 (EMA only)
80.81 ± 0.18
0.71
42.3
16
85.05 ± 0.15
0.76
38.5
32
85.72 ± 0.14
0.79
33.1
64 (default)
92.30 ± 0.17
0.82
29.7
128
92.18 ± 0.19
0.80
46.2
Appendix
Table 12: Ablation on Prototype Atlas (PA) capacity on CIFAR10-LT under the consistent setting. C denotes the maximum number of anchors per class; C=0 corresponds to using only the EMA prototype without storing exemplar anchors. Moderate capacity ( C=64 ) achieves the best trade-off between representation diversity and stability.
Method
Avg. Epoch Time (s)
Total Time (300 ep)
Overhead vs. FixMatch
FixMatch
42.1
3.51 h
0%
SimPro
43.0
3.58 h
+2.1%
GBC (ours)
42.8
3.56 h
+1.7%
Appendix
Table 13: Wall-clock comparison on CIFAR10-LT (consistent setting) using a single A100 GPU. We report the average epoch time over the last 50 epochs and the total training time for 300 epochs. GBC introduces minimal computational overhead ( <2% ) compared with FixMatch and remains comparable to SimPro.
Long-tailed distributions are prevalent in real-world semi-supervised learning (SSL), where pseudo-labels tend to favor majority classes, leading to degraded generalization. While many long-tailed semi-supervised learning (LTSSL) methods have been proposed, the mechanisms by which they implicitly debias logits remain poorly understood. In this work, we revisit LTSSL through the lens of learning dynamics and provide a theoretical characterization of logits debiasing. Specifically, we derive a step-wise decomposition of the logits updates, showing that predictions are dominated by class-imbalance bias that reliably reflects label priors. To expose this effect, we use the logits of a task-irrelevant baseline image as an indicator of accumulated bias and prove that they converge to the class prior. This provides a unified view where LTSSL remedies such as logit adjustment, reweighting, and resampling correspond to reshaping gradient dynamics. Based on this insight, we propose DyTrim, a principle-based dynamic pruning framework that reallocates gradient budget through class-aware pruning on labeled data and confidence-based soft pruning on unlabeled data. We provide theoretical guarantees that DyTrim reduces class bias and improves generalization. Extensive experiments on standard LTSSL benchmarks show consistent gains across architectures and methods. Code available at: https://jiajun0425.github.io/DyTrim
Yue Cheng, Jiajun Zhang, Xiaohui Gao +2
Beijing Jiaotong University · AntGroup · Northwestern Polytechnical University +1
Semi-supervised learning (SSL) often suffers under class imbalance, where pseudo-labeling amplifies majority bias and suppresses minority performance. We address this issue with a lightweight framework that, to our knowledge, is the first to introduce Proportion Loss from learning from label proportions (LLP) into SSL as a regularization term. Proportion Loss aligns model predictions with the global class distribution, mitigating bias across both majority and minority classes. To further stabilize training, we formulate a stochastic variant that accounts for fluctuations in mini-batch composition. Experiments on the Long-tailed CIFAR-10 benchmark show that integrating Proportion Loss into FixMatch and ReMixMatch consistently improves performance over the baselines across imbalance severities and label ratios, and achieves competitive or superior results compared to existing CISSL methods, particularly under scarce-label conditions.
Pseudo-labeling has become a cornerstone of learning from unlabeled data in semantic segmentation. Yet its effectiveness drops sharply in real-world scenarios where strong imaging noise and long-tailed class distributions occur together. We trace this failure to a vicious cycle of pseudo-label degradation. Imaging noise entangles foreground and background features, lowering prediction confidence across all classes, while long-tailed distributions leave tail classes with far fewer training samples and inherently lower confidence. Under fixed high-threshold filtering, these tail-class predictions are systematically filtered out, so they receive no supervision from unlabeled data and thus features keep degrading in subsequent iterations. Critically, noise and long-tail are not independent obstacles but mutually amplifying ones, and addressing either alone is insufficient. To break this cycle, we propose FTC-Seg, a Feature-Threshold dual-Calibration framework built on a standard teacher-student framework. At the feature level, Orthogonal Prototype Reconstruction (OPR) uses a set of learnable orthogonal prototypes to residually purify pixel-wise features, widening the margin between weak foreground targets and noisy backgrounds. At the threshold level, Adaptive Threshold Calibration (ATC) dynamically adjusts class-specific thresholds based on learning difficulty and prediction-distribution bias, rescuing low-confidence pseudo-labels of tail classes from systematic exclusion. Extensive experiments on four public benchmarks spanning three distinct noise modalities show that FTC-Seg achieves strong performance against state-of-the-art methods, with particularly substantial gains on tail classes. Our results establish that jointly calibrating features and thresholds is essential for robust pseudo-labeling under compounded noise and class imbalance.
Ping Guo, Zhiqi Huang, Xinran Li
Graduate School of Information, Production and Systems, Waseda University, Kitakyushu, Japan · School of Software, Dalian University of Technology, Dalian, China · School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen, China