When Confidence Collapses: Robust Pseudo-Label Selection for Extremely Sparse Semi-Supervised Learning

Semi-supervised learning (SSL) reduces annotation costs by exploiting abundant unlabeled data, yet its behavior under extremely sparse supervision remains poorly understood. We systematically investigate this regime and identify a common failure mode in confidence-driven pseudo-label selection, where an overfit classification head produces saturated confidence scores that become poorly discriminative. As a result, existing selection strategies can retain large numbers of unreliable pseudo-labels, causing training performance to peak prematurely and subsequently regress. Motivated by this observation, we propose a confidence-robust pseudo-label selection framework that combines a Confidence Calibration Prior with Weak-Strong Consistency. The Confidence Calibration Prior uses a fixed confidence floor and a per-class top-$K$ constraint to control pseudo-label selection without relying solely on the confidence distribution, while Weak-Strong Consistency improves the reliability of the selected supervision. We further use MoCo pretraining as a complementary representation initialization and evaluate the resulting framework under a unified protocol across three image-classification benchmarks and multiple label densities. Experiments show that our method consistently improves over representative confidence-driven baselines in the extremely sparse regime, while its advantage becomes dataset-dependent as the labeling budget increases. These results reveal an operating boundary of confidence-driven pseudo-label selection and motivate sparse-label SSL methods that are less dependent on the confidence distribution of the classification head.