However, such a method easily leads to severe overfitting.

We respond to each comment one by one. We mention this in Line 148; however, we will make it clear in the final draft. Conversely, SSL algorithms use the unlabeled data but they do not consider the class imbalance. We will make this point clear in the final draft. However, to avoid the confusion, we will substitute X,Y to α,β in the final draft.

In this supplement, we provide additional empirical visualizations of our approach in Section A.1. Next, we provide details on experimental setup in Section A.2. Mean and standard deviation (s.d.) metric scores across 3 random seeds In COMET we utilize a residual network to parameterize an underlying energy function. We illustrate the underlying architecture of the energy function in Figure 2. The energy function takes as input an image at We remove normalization layers from our residual network. To infer global factors from an input image, we utilize a convolutional encoder in Figure 3. We illustrate the overall architecture in Figure 4. Training Details.

For obtaining such decompositions, two separate lines of work exist.

Devoid of some assumption, aPU learning is impossible [6].

Wireless communication systems can significantly benefit from the availability of spatially consistent representations of the wireless channel to efficiently perform a wide range of communication tasks. Towards this purpose, channel charting has been introduced as an effective unsupervised learning technique to achieve both locally and globally consistent radio maps. In this letter, we propose Chartwin, a case study on the integration of localization-oriented channel charting with dynamic Digital Network Twins (DNTs). Numerical results showcase the significant performance of semi-supervised channel charting in constructing a spatially consistent chart of the considered extended urban environment. The considered method results in $\approx$ 4.5 m localization error for the static DNT and $\approx$ 6 m in the dynamic DNT, fostering DNT-aided channel charting and localization.

In semi-supervised learning (SSL) for enhancing the performance of graph neural networks (GNNs) with unlabeled data, introducing mutually independent decision factors for cross-validation is regarded as an effective strategy to alleviate pseudo-label confirmation bias and training collapse. However, obtaining such factors is challenging in practice: additional and valid information sources are inherently scarce, and even when such sources are available, their independence from the original source cannot be guaranteed. To address this challenge, In this paper we propose a Differentiated Factor Consistency Semi-supervised Framework (DiFac), which derives differentiated factors from a single information source and enforces their consistency. During pre-training, the model learns to extract these factors; in training, it iteratively removes samples with conflicting factors and ranks pseudo-labels based on the shortest stave principle, selecting the top candidate samples to reduce overconfidence commonly observed in confidence-based or ensemble-based methods. Our framework can also incorporate additional information sources. In this work, we leverage the large multimodal language model to introduce latent textual knowledge as auxiliary decision factors, and we design a accountability scoring mechanism to mitigate additional erroneous judgments introduced by these auxiliary factors. Experiments on multiple benchmark datasets demonstrate that DiFac consistently improves robustness and generalization in low-label regimes, outperforming other baseline methods.

Neuro-symbolic (Nesy) learning improves the target task performance of models by enabling them to satisfy knowledge, while semi/self-supervised learning (SSL) improves the target task performance by designing unsupervised pretext tasks for unlabeled data to make models satisfy corresponding assumptions. We extend the Nesy theory based on reliable knowledge to the scenario of unreliable knowledge (i.e., assumptions), thereby unifying the theoretical frameworks of SSL and Nesy. Through rigorous theoretical analysis, we demonstrate that, in theory, the impact of pretext tasks on target performance hinges on three factors: knowledge learn-ability with respect to the model, knowledge reliability with respect to the data, and knowledge completeness with respect to the target. We further propose schemes to operationalize these theoretical metrics, and thereby develop a method that can predict the effectiveness of pretext tasks in advance. This will change the current status quo in practical applications, where the selections of unsupervised tasks are heuristic-based rather than theory-based, and it is difficult to evaluate the rationality of unsupervised pretext task selection before testing the model on the target task. In experiments, we verify a high correlation between the predicted performance--estimated using minimal data--and the actual performance achieved after large-scale semi-supervised or self-supervised learning, thus confirming the validity of the theory and the effectiveness of the evaluation method.

Lung diseases, including lung cancer and COPD, are significant health concerns globally. Traditional diagnostic methods can be costly, time-consuming, and invasive. This study investigates the use of semi supervised learning methods for lung sound signal detection using a model combination of MFCC+CNN. By introducing semi supervised learning modules such as Mix Match, Co-Refinement, and Co Refurbishing, we aim to enhance the detection performance while reducing dependence on manual annotations. With the add-on semi-supervised modules, the accuracy rate of the MFCC+CNN model is 92.9%, an increase of 3.8% to the baseline model. The research contributes to the field of lung disease sound detection by addressing challenges such as individual differences, feature insufficient labeled data.