USE: Uncertainty Structure Estimation for Robust Semi-Supervised Learning

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%}.

Standard semi-supervised learning (SSL) typically relies on labelled and unlabelled data sharing a common marginal distribution. This assumption is often violated by biased spatial sampling mechanism, when labels are collected under spatially biased or preferential site selection. We treat this marginal mismatch, spatial autocorrelation, and spatial non-stationarity as three distinct mechanisms, varied independently via a labelled-sampling concentration parameter, a spatial length scale, and a non-stationarity strength parameter, and ask how mismatch degrades SSL, whether the cluster and manifold assumptions survive it, and how the resulting failure can be diagnosed. Using a controlled synthetic framework alongside PovertyMap-WILDS, California housing, socio-economic and US air quality monitoring datasets, we systematically vary the degree of mismatch while accounting for spatial autocorrelation and non-stationarity. Through a series of analyses including a segmented-regression changepoint, we show that in the synthetic generator, SSL performance does not degrade gradually but instead exhibits a threshold-like breakdown between approximately 0.71 and 0.77 once distribution mismatch becomes sufficiently severe. We further demonstrate that spatial non-stationarity contributes to performance loss independently of marginal mismatch and that models become increasingly overconfident outside the regions where labels are available. To support practical deployment, we evaluate several distribution-divergence measures as indicators of reliability and introduce a kernel-weighted local divergence metric that provides a more stable estimate of spatial mismatch than a naïve localised approach. These findings provide empirical evidence and diagnostic tools for better documenting the risk of incorporating unlabelled spatial data into semi-supervised learning workflows.

Pseudo-label-based semi-supervised learning has achieved strong performance due to its simplicity and scalability. However, it is typically developed under a closed-world assumption that unlabeled data are drawn from the same distribution as labeled data. In practical deployment, unlabeled data are often collected from open environments and may contain OOD samples. Under such contamination, OOD samples may still receive high-confidence predictions and be incorporated into training as if they were valid target examples. This creates an important evaluation problem: clean in-distribution test accuracy may appear stable even when the internal learning dynamics of SSL have already deteriorated. To address this issue, we study hidden collapse in pseudo-label-based SSL under open-world unlabeled contamination from a diagnostic evaluation perspective. We present C-Score, a compact framework that evaluates training behavior in three complementary spaces: prediction, feature representation, and optimization. C-Score includes PLE and CCI for unlabeled prediction behavior, Sem-Drift for deviation from labeled semantic anchors, and Grad-Align for the compatibility between labeled and unlabeled optimization. Experiments on CIFAR-10 and CIFAR-100 with multiple OOD sources, varying contamination ratios, and four pseudo-label-based SSL algorithms show that C-Score metrics reveal hidden degradation that clean accuracy alone fails to detect: under SVHN contamination, CCI rises over 280% while best-accuracy remains within 3% of the uncontaminated baseline; near-OOD sources (CIFAR-100, STL-10) cause up to 14.9% accuracy collapse (FlexMatch, r=0.5). The results suggest that clean accuracy alone is insufficient for evaluating SSL robustness in open-world environments, and that internal diagnostic signals are necessary for more reliable robustness assessment under unlabeled contamination.