Noisy labels pose a common challenge for training accurate deep neural networks. To mitigate label noise, prior studies have proposed various robust loss functions to achieve noise tolerance in the presence of label noise, particularly symmetric losses. However, they usually suffer from the underfitting issue due to the overly strict symmetric condition. In this work, we propose a simple yet effective approach for relaxing the symmetric condition, namely **$\epsilon$-softmax**, which simply modifies the outputs of the softmax layer to approximate one-hot vectors with a controllable error $\epsilon$. Essentially, ***$\epsilon$-softmax** not only acts as an alternative for the softmax layer, but also implicitly plays the crucial role in modifying the loss function.* We prove theoretically that **$\epsilon$-softmax** can achieve noise-tolerant learning with controllable excess risk bound for almost any loss function. Recognizing that **$\epsilon$-softmax**-enhanced losses may slightly reduce fitting ability on clean datasets, we further incorporate them with one symmetric loss, thereby achieving a better trade-off between robustness and effective learning. Extensive experiments demonstrate the superiority of our method in mitigating synthetic and real-world label noise.

Noisy labels pose a common challenge for training accurate deep neural networks. To mitigate label noise, prior studies have proposed various robust loss functions to achieve noise tolerance in the presence of label noise, particularly symmetric losses. However, they usually suffer from the underfitting issue due to the overly strict symmetric condition. In this work, we propose a simple yet effective approach for relaxing the symmetric condition, namely ** \epsilon -softmax**, which simply modifies the outputs of the softmax layer to approximate one-hot vectors with a controllable error \epsilon . Essentially, *** \epsilon -softmax** not only acts as an alternative for the softmax layer, but also implicitly plays the crucial role in modifying the loss function.*

Deep learning models rely heavily on large volumes of labeled data to achieve high performance. However, real-world datasets often contain noisy labels due to human error, ambiguity, or resource constraints during the annotation process. Instance-dependent label noise (IDN), where the probability of a label being corrupted depends on the input features, poses a significant challenge because it is more prevalent and harder to address than instance-independent noise. In this paper, we propose a novel hybrid framework that combines self-supervised learning using SimCLR with iterative pseudo-label refinement to mitigate the effects of IDN. The self-supervised pre-training phase enables the model to learn robust feature representations without relying on potentially noisy labels, establishing a noise-agnostic foundation. Subsequently, we employ an iterative training process with pseudo-label refinement, where confidently predicted samples are identified through a multistage approach and their labels are updated to improve label quality progressively. We evaluate our method on the CIFAR-10 and CIFAR-100 datasets augmented with synthetic instance-dependent noise at varying noise levels. Experimental results demonstrate that our approach significantly outperforms several state-of-the-art methods, particularly under high noise conditions, achieving notable improvements in classification accuracy and robustness. Our findings suggest that integrating self-supervised learning with iterative pseudo-label refinement offers an effective strategy for training deep neural networks on noisy datasets afflicted by instance-dependent label noise.

Despite the success of the carefully-annotated benchmarks, the effectiveness of existing graph neural networks (GNNs) can be considerably impaired in practice when the real-world graph data is noisily labeled. Previous explorations in sample selection have been demonstrated as an effective way for robust learning with noisy labels, however, the conventional studies focus on i.i.d data, and when moving to non-iid graph data and GNNs, two notable challenges remain: (1) nodes located near topological class boundaries are very informative for classification but cannot be successfully distinguished by the heuristic sample selection. (2) there is no available measure that considers the graph topological information to promote sample selection in a graph. To address this dilemma, we propose a $\textit{Topological Sample Selection}$ (TSS) method that boosts the informative sample selection process in a graph by utilising topological information. We theoretically prove that our procedure minimizes an upper bound of the expected risk under target clean distribution, and experimentally show the superiority of our method compared with state-of-the-art baselines.

Purpose: Deep neural networks (DNNs) have been widely applied in medical image classification, benefiting from its powerful mapping capability among medical images. However, these existing deep learning-based methods depend on an enormous amount of carefully labeled images. Meanwhile, noise is inevitably introduced in the labeling process, degrading the performance of models. Hence, it's significant to devise robust training strategies to mitigate label noise in the medical image classification tasks. Methods: In this work, we propose a novel Bayesian statistics guided label refurbishment mechanism (BLRM) for DNNs to prevent overfitting noisy images. BLRM utilizes maximum a posteriori probability (MAP) in the Bayesian statistics and the exponentially time-weighted technique to selectively correct the labels of noisy images. The training images are purified gradually with the training epochs when BLRM is activated, further improving classification performance. Results: Comprehensive experiments on both synthetic noisy images (public OCT & Messidor datasets) and real-world noisy images (ANIMAL-10N) demonstrate that BLRM refurbishes the noisy labels selectively, curbing the adverse effects of noisy data. Also, the anti-noise BLRM integrated with DNNs are effective at different noise ratio and are independent of backbone DNN architectures. In addition, BLRM is superior to state-of-the-art comparative methods of anti-noise. Conclusions: These investigations indicate that the proposed BLRM is well capable of mitigating label noise in medical image classification tasks.