Hub for Outliers, Spokes for Inliers: Uniform Latent Space Construction for Dual-Mismatched Semi-Supervised Learning

Li Yuan; Yaxin Hou; Jiawei Tang; Yongbiao Gao; Yuheng Jia

cs.LGOct 6, 2026

Hub for Outliers, Spokes for Inliers: Uniform Latent Space Construction for Dual-Mismatched Semi-Supervised Learning

Authors: Li Yuan, Yaxin Hou, Jiawei Tang, Yongbiao Gao, Yuheng Jia

Organizations: School of Computer Science and Engineering, Southeast University, Nanjing, China

Abstract

Semi-supervised learning typically assumes that labeled and unlabeled data share an identical class distribution and label space. However, this setting is often violated: unlabeled data may be imbalanced and contain unknown class samples, causing mismatches in both class distribution and label space. Such dual mismatch leads to majority classes dominating the latent space and unknown class samples being overconfidently misclassified, degrading feature discriminability and pseudo-label quality. To address this, we propose a hub-spoke latent geometry, where known classes are uniformly distributed around a central hub and each class forms compact clusters around its prototype, while the hub provides an anchor for a low-evidence region specifically designed for high-uncertainty unknown class samples. Integrated with an evidence-based classifier, this geometry ultimately enhances feature discriminability and uncertainty separation by mitigating majority-class domination through structured feature organization and guiding high-uncertainty unknown class samples toward the hub. Extensive experiments show that our method outperforms state-of-the-art methods, with a maximum improvement of 3.25% across various settings.

Figures & tables

Figure 1: A comparison of the class distributions in semi-supervised learning (SSL), open-set semi-supervised learning (OSSL), long-tailed semi-supervised learning (LTSSL), and the dual-mismatched semi-supervised learning (DMSSL) scenarios. DMSSL considers a more realistic scenario where the labeled data is balanced, while the unlabeled data is imbalanced and contains samples from both known and unknown classes.

Panel of Figure 2 — Figure 2: (a) presents the proposed hub-spoke geometry; (b) presents the t-SNE visualizations of CIFAR-10 ( Krizhevsky et al., 2009 ) test set for Meta-Expert ( Hou and Jia, 2025 ) and our proposed method, respectively; (c) shows a comparison of the pseudo-label accuracy on CIFAR-10 among IOMatch ( Li et al., 2023 ) , CaliMatch ( Bae et al., 2025 ) , and our method across three settings, with 4 (lb4), 10 (lb10), and 25 (lb25) labeled samples per class, respectively; (d) presents the uncertainty distributions on CIFAR-10 for the cases without guiding and with guiding high - uncertainty unknown class samples toward the central hub in the hub-spoke geometry, respectively.

Figure 3: A comparison of the mean deviation distance between the overall class prototype and the labeled class prototype.

Dataset		CIFAR-10		CIFAR-100		SVHN		Food-101		ImageNet-100
Known / Unknown		10 / 10		100 / 50		10 / 10		101 / 50		100 / 50
Labels per class		10	25	10	25	10	25	10	25	10	25
SL	CE	78.69± 5.10	80.21± 4.85	51.01± 0.73	55.74± 0.57	88.93± 1.19	89.18± 1.05	39.79± 0.48	42.56± 0.38	44.63± 0.27	46.61± 1.16
SL	LA	85.45± 2.64	86.08± 2.47	56.20± 0.48	59.67± 0.45	92.31± 1.01	92.63± 1.19	45.48± 0.37	47.44± 0.20	49.61± 0.25	51.37± 0.86
SSL	FixMatch	69.57± 5.03	76.86± 4.69	39.40± 1.31	51.23± 1.29	89.71± 2.60	90.82± 1.02	15.95± 0.55	23.23± 0.25	27.44± 0.81	34.95± 0.76
	FreeMatch	64.45± 6.47	75.72± 5.27	32.56± 1.62	47.52± 1.21	89.10± 2.30	89.83± 2.54	19.64± 0.34	27.65± 0.20	27.39± 0.45	36.31± 0.97

Table 1: Classification accuracy (%) on the test data of CIFAR-10, CIFAR-100, SVHN, Food-101, and ImageNet-100 with varying known/unknown classes and labeled set sizes. We report the mean with standard deviation over three runs with different random seeds.

Panel of Figure 4 — Figure 4: Ablation studies on HGC module for minority class accuracy and UCIM module for pseudo-label accuracy.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 5 — Figure 5: (a) and (b) respectively compare classification accuracy on the CIFAR-10 test data for $k\in\{0\%,10\%,20\%\}$ and $v\in\{0.05,0.1,0.2\}$ across the three settings. We clearly see that $k=10\%$ and $k=20\%$ yield comparable results, and performance remains stable across different values of $v$ .

$\lambda$	lb4	lb10	lb25
0.05	52.74	69.18	77.43
0.10	56.89	70.96	78.05
0.20	55.34	68.43	78.24

Appendix

Table 3: Classification accuracy (%) with different

\lambda

values on CIFAR-10. The results show that

\lambda=0.1

achieves the best or near-best performance across all settings.

Panel of Figure 6 — Figure 6: (a) reports classification accuracy on CIFAR-100 under different numbers of unknown classes (50, 40, 30, 20, 10) across the three lb settings; (b) compares our method with K-means clustering on the identified unknown class samples on CIFAR-10.

Module				CIFAR-10			CIFAR-100
LIL	LOL	LIG	LOG	lb4	lb10	lb25	lb4	lb10	lb25
✓				50.61	67.75	76.52	29.18	43.12	52.47
	✓			43.35	67.71	76.63	28.77	42.44	52.98
✓	✓			50.80	68.05	76.95	30.24	43.25	53.49
✓	✓	✓		52.16	67.29	76.68	29.81	42.25	52.55
✓	✓		✓	49.33	67.26	76.34	28.65	43.20	53.20

Appendix

Table 5: Classification accuracy (%) with and without the

\mathcal{L}_{il}

(LIL),

\mathcal{L}_{ol}

(LOL),

\mathcal{L}_{ig}

(LIG), and

\mathcal{L}_{og}

(LOG) losses of the proposed method across three settings, with 4, 10, and 25 labeled samples per class. All ablation studies are conducted with the class-adaptive re-weighting (CAW) module integrated as the foundation. The datasets are CIFAR-10 and CIFAR-100, which comprise a balanced labeled dataset (imbalance ratio

\gamma_{l}=1

) of only known classes and an imbalanced unlabeled dataset (imbalance ratio

\gamma_{u}=100

) of both known and unknown classes.

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Semi-Supervised Learning Unlabeled Data

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Semi-supervised learning faces significant challenges in realistic scenarios where labeled data is scarce and unlabeled data follows unknown, arbitrary distributions. We formalize this critical yet under-explored paradigm as Universal Semi-supervised Learning (UniSSL). Existing methods typically leverage unlabeled data via pseudo-labeling. However, they often rely on the idealized assumption of a uniform unlabeled data distribution or require sufficient labeled data to estimate it. In the UniSSL setting, such dependencies lead to numerous erroneous pseudo-labels, thereby triggering representation confusion. Fortunately, we observe that inter-sample relations captured by representations are more reliable than pseudo-labels. Leveraging this insight, we shift our focus to representation-level structural inference to bypass distribution estimation. Accordingly, we propose Simplex Anchored Graph-state Equipartition (SAGE), which captures high-order inter-sample dependencies to establish structural consensus for guiding representation learning. Meanwhile, to mitigate representation confusion, we employ vectors that satisfy a simplex equiangular tight frame to serve as a coordinate frame for guiding inter-class representation separation. Finally, we introduce a weighting strategy based on distribution-agnostic metrics to prioritize reliable pseudo-labels and an auxiliary branch to isolate potentially erroneous pseudo-labels. Evaluations on five standard benchmarks show that SAGE consistently outperforms state-of-the-art methods, with an average accuracy gain of

\textbf{8.52%}

Abstract

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