Differing from traditional semi-supervised learning, class-imbalanced semi-supervised learning presents two distinct challenges: (1) The imbalanced distribution of training samples leads to model bias towards certain classes, and (2) the distribution of unlabeled samples is unknown and potentially distinct from that of labeled samples, which further contributes to class bias in the pseudo-labels during the training. To address these dual challenges, we introduce a novel approach called Twice Class Bias Correction (TCBC). We begin by utilizing an estimate of the class distribution from the participating training samples to correct the model, enabling it to learn the posterior probabilities of samples under a class-balanced prior. This correction serves to alleviate the inherent class bias of the model. Building upon this foundation, we further estimate the class bias of the current model parameters during the training process. We apply a secondary correction to the model's pseudo-labels for unlabeled samples, aiming to make the assignment of pseudo-labels across different classes of unlabeled samples as equitable as possible. Through extensive experimentation on CIFAR10/100-LT, STL10-LT, and the sizable long-tailed dataset SUN397, we provide conclusive evidence that our proposed TCBC method reliably enhances the performance of class-imbalanced semi-supervised learning.

Due to the advantages of leveraging unlabeled data and learning meaningful representations, semi-supervised learning and contrastive learning have been progressively combined to achieve better performances in popular applications with few labeled data and abundant unlabeled data. One common manner is assigning pseudo-labels to unlabeled samples and selecting positive and negative samples from pseudo-labeled samples to apply contrastive learning. However, the real-world data may be imbalanced, causing pseudo-labels to be biased toward the majority classes and further undermining the effectiveness of contrastive learning. To address the challenge, we propose Contrastive Learning with Augmented Features (CLAF). We design a class-dependent feature augmentation module to alleviate the scarcity of minority class samples in contrastive learning. For each pseudo-labeled sample, we select positive and negative samples from labeled data instead of unlabeled data to compute contrastive loss. Comprehensive experiments on imbalanced image classification datasets demonstrate the effectiveness of CLAF in the context of imbalanced semi-supervised learning.

Monotonic Linear Interpolation (MLI) refers to the peculiar phenomenon that the error between the initial and converged model monotonically decreases along the linear interpolation, i.e., $(1-\alpha)\boldsymbol{\theta}_0 + \alpha \boldsymbol{\theta}_F$. Previous works focus on paired initial and converged points, relating MLI to the smoothness of the optimization trajectory. In this paper, we find a shocking fact that the error curves still exhibit a monotonic decrease when $\boldsymbol{\theta}_0$ is replaced with noise or even zero values, implying that the decreasing curve may be primarily related to the property of the converged model rather than the optimization trajectory. We further explore the relationship between $\alpha\boldsymbol{\theta}_F$ and $\boldsymbol{\theta}_F$ and propose scale invariance properties in various cases, including Generalized Scale Invariance (GSI), Rectified Scale Invariance (RSI), and Normalized Scale Invariance (NSI). From an inverse perspective, the MLI formula is essentially an equation that adds varying levels of noise (i.e., $(1-\alpha)\boldsymbol{\epsilon}$) to a nearly scale-invariant network (i.e., $\alpha \boldsymbol{\theta}_F$), resulting in a monotonically increasing error as the noise level rises. MLI is a special case where $\boldsymbol{\epsilon}$ is equal to $\boldsymbol{\theta}_0$.