USE: Uncertainty Structure Estimation for Robust Semi-Supervised Learning

Tsao-Lun Chen; Chien-Liang Liu; Tzu-Ming Harry Hsu; Tai-Hsien Wu; Chi-Cheng Fu; Han-Yi E. Chou; Shun-Feng Su

cs.LGFeb 28, 2026

USE: Uncertainty Structure Estimation for Robust Semi-Supervised Learning

Authors: Tsao-Lun Chen, Chien-Liang Liu, Tzu-Ming Harry Hsu, Tai-Hsien Wu, Chi-Cheng Fu, Han-Yi E. Chou, Shun-Feng Su

Organizations: National Taiwan University of Science and Technology, Taipei, Taiwan · National Taiwan University, Taipei, Taiwan · Chang Gung University, Taoyuan, Taiwan · Massachusetts Institute of Technology, Cambridge, MA, USA ·

Abstract

In this study, a novel idea, Uncertainty Structure Estimation (USE), a lightweight, algorithm-agnostic procedure that emphasizes the often-overlooked role of unlabeled data quality is introduced for Semi-supervised learning (SSL). SSL has achieved impressive progress, but its reliability in deployment is limited by the quality of the unlabeled pool. In practice, unlabeled data are almost always contaminated by out-of-distribution (OOD) samples, where both near-OOD and far-OOD can negatively affect performance in different ways. We argue that the bottleneck does not lie in algorithmic design, but rather in the absence of principled mechanisms to assess and curate the quality of unlabeled data. The proposed USE trains a proxy model on the labeled set to compute entropy scores for unlabeled samples, and then derives a threshold, via statistical comparison against a reference distribution, that separates informative (structured) from uninformative (structureless) samples. This enables assessment as a preprocessing step, removing uninformative or harmful unlabeled data before SSL training begins. Through extensive experiments on imaging (CIFAR-100) and NLP (Yelp Review) data, it is evident that USE consistently improves accuracy and robustness under varying levels of OOD contamination. Thus, it can be concluded that the proposed approach reframes unlabeled data quality control as a structural assessment problem, and considers it as a necessary component for reliable and efficient SSL in realistic mixed-distribution environments.

Figures & tables

Figure 1: This figure displays the entropy density distribution computed using a proxy model trained on 200 labeled samples from the CIFAR-100 dataset. The blue curve represents in-distribution (ID) samples (CIFAR-100), concentrated in the low-entropy region; the orange curve represents near-OOD samples (Tiny ImageNet), exhibiting an approximately uniform distribution; and the green curve represents far-OOD samples (SVHN), concentrated in the high-entropy region.

Figure 2: Illustration of the USE threshold. The threshold

u^{\ast}

corresponds to the first descending downward crossing of the entropy density, separating informative low-entropy samples from uninformative high-entropy ones. The intersection with the reference curve density

F_{0}^{\prime}(u)

can be interpreted as the point of maximum structural discrepancy.

Figure 3: Overview of the USE pipeline. A proxy model trained on labeled data computes entropy scores for the unlabeled pool. By comparing the empirical entropy distribution with a structureless reference curve, a threshold $u^{\ast}$ is determined to separate structured from structureless samples, ensuring that downstream SSL is trained only on data with meaningful structure.

		CIFAR-100 (200 labeled)		CIFAR-100 (1000 labeled)		Yelp (250 labeled)
Supervised		0.6469		0.8010		0.5992
OOD types		Tiny ImageNet	SVHN	Tiny ImageNet	SVHN	IMDB	AGNews
Pseudo Label	Base	0.6644	0.6763	0.8047	0.8122	0.5968	0.5978
Pseudo Label	+ USE	0.6741	0.6778	0.8120	0.8168	0.5971	0.5971
FixMatch	Base	0.6570	0.6780	0.8270	0.8380	0.6187	0.6162
FixMatch	+ USE	0.6696	0.6693	0.8446	0.8504	0.6201	0.6233

Table 1: Mean top-1 accuracy over OOD contamination ratios (

r=\frac{D_{\text{OOD}}}{D_{\text{ID}}+D_{\text{OOD}}}

) across datasets.

Figure 4: Performance comparison of SSL methods on CIFAR-100 with 200 labeled samples. For each method, the six bars show the top-1 accuracy difference (USE – baseline) under contamination ratios

r\in\{0.0,0.2,0.4,0.5,0.6,0.8\}

, with Tiny ImageNet (near-OOD) and SVHN (far-OOD) used as contamination sources. Green bars indicate that USE outperforms the baseline, while red bars indicate the opposite.

Figure 5: Performance comparison of SSL methods on CIFAR-100 with 1000 labeled samples. For each method, the six bars show the top-1 accuracy difference (USE - baseline) under contamination ratios

r\in\{0.0,0.2,0.4,0.5,0.6,0.8\}

, with Tiny ImageNet (near-OOD) and SVHN (far-OOD) used as contamination sources. Green bars indicate that USE outperforms the baseline, while red bars indicate the opposite.

Setting	Rslope	GM	BAD	WAD	$P_{AD\geq 0}$
C100/200/Far	↑	↑	↑	↑	↓
C100/200/Near	↑	↑	↓	↑	→
C100/1k/Far	↓	↑	↑	↓	↓
C100/1k/Near	↓	↑	↑	↑	↓
Yelp/250/Near	↑	↑	↑	↓	↑
Yelp/250/Far	↑	↓	↓	↑	↓

Table 2: Robustness comparison (USE vs. w/o). ↑ better, ↓ worse, → neutral.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Method	r=0.0	r=0.2	r=0.4	r=0.5	r=0.6	r=0.8	Avg.	Rslope	GM	BAD	WAD	$P_{AD\geq 0}$
Supervised	0.6469
near-OOD (Tiny ImageNet)
Pseudo Label	0.6757	0.6776	0.6604	0.6591	0.6571	0.6565	0.6644	-0.0301	0.0490	0.0095	-0.0860	0.2000
Pseudo Label + USE	0.6741	0.6739	0.6734	0.6750	0.6742	0.6738	0.6741	0.0001	0.0022	0.0160	-0.0080	0.2000
FixMatch	0.6752	0.6522	0.6691	0.6692	0.6357	0.6403	0.6570	-0.0393	0.0853	0.0845	-0.3350	0.6000
FixMatch + USE	0.6657	0.6887	0.6783	0.6576	0.6741	0.6533	0.6696	-0.0222	0.0645	0.1650	-0.2070	0.4000

Appendix

Table 3: CIFAR-100 with 200 labeled samples.

Method	r=0.0	r=0.2	r=0.4	r=0.5	r=0.6	r=0.8	Avg.	Rslope	GM	BAD	WAD	$P_{AD\geq 0}$
Supervised	0.6469
near-OOD (Tiny ImageNet)
Pseudo Label	0.8027	0.8111	0.8050	0.8032	0.8029	0.8031	0.8047	-0.0040	0.0135	0.0420	-0.0305	0.4000
Pseudo Label + USE	0.8187	0.8225	0.8127	0.8092	0.8062	0.8026	0.8120	-0.0244	0.0359	0.0190	-0.0490	0.2000
FixMatch	0.7940	0.8485	0.8428	0.8360	0.8289	0.8119	0.8270	0.0101	0.0963	0.2725	-0.0850	0.2000
FixMatch + USE	0.8536	0.8526	0.8464	0.8454	0.8435	0.8259	0.8446	-0.0314	0.0395	-0.0050	-0.0880	0.0000

Appendix

Table 4: CIFAR-100 with 1000 labeled samples.

Method	r=0.0	r=0.2	r=0.4	r=0.6	r=0.8	Avg.	Rslope	GM	BAD	WAD	$P_{AD\geq 0}$
Supervised	0.5992
near-OOD (IMDB)
Pseudo Label	0.5995	0.5985	0.5946	0.5966	0.5950	0.5975	-0.0055	0.0086	0.0100	-0.0195	0.2500
Pseudo Label + USE	0.5978	0.6015	0.5944	0.5935	0.5983	0.5971	-0.0035	0.0126	0.0240	-0.0355	0.5000
FixMatch	0.6230	0.6208	0.6176	0.6176	0.6146	0.6187	-0.0100	0.0127	0.0000	-0.0160	0.2500
FixMatch + USE	0.6228	0.6198	0.6202	0.6174	0.6204	0.6201	-0.0036	0.0061	0.0150	-0.0150	0.5000

Appendix

Table 5: Yelp Review with 250 labeled samples.

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Beyond Distribution Estimation: Simplex Anchored Structural Inference Towards Universal Semi-Supervised Learning

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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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