# Cras: Curriculum Regularization and Adaptive Semi-Supervised Learning with Noisy Labels
## 3 Proposed Method
It should be noted that the designed weights are suitable for the loss function used in DivideMix; to apply \(s\) to other loss functions, it may be necessary to redesign the weights accordingly. The weights can easily be designed by allowing the weights to take on larger values as the number of labeled samples decreases. As the number of classes increases, the classification becomes more difficult, and the model tends to output lower prediction probabilities. As a result, the MSE values of the unsupervised loss in DivideMix become smaller. To solve this problem, the weight \(\lambda_{a}\) is expressed as follows. \[\lambda_{a}=C\cdot\mathcal{W}(r^{(k)}). \tag{14}\]

Finally, using \(\lambda_{a}\) and replacing it with \(\lambda_{u}\) in (8), our final loss function is defined as follows. \[\mathcal{L}=\mathcal{L}_{CE}+\lambda_{a}\mathcal{L}_{u}+\mathcal{L}_{reg}. \tag{15}\]

## 4 Experiments

### Datasets and Implementation Details

We used two simulated datasets and two real-world datasets in our experiments, in line with recent studies [24; 25; 38]. Table 1 summarizes the statistics of the datasets used, which are described in detail below. It should be noted that our use of training, validation, and test data also followed previous studies. Noise patterns in the real world can be classified into three types: symmetric (Sym.) noise [52], asymmetric (Asym.) noise [53], and instance-dependent noise [54]. Symmetric noise occurs when labels for a certain fraction of samples are randomly altered to labels representing different classes. In contrast, asymmetric noise involves the alteration of labels to labels of closely related classes, mirroring the type of label noise typically seen in real-world scenarios. Instance-dependent noise is a more complex form of label noise, where the noise is influenced by both the class and the unique features of each instance [55]. Our experiments encompassed datasets influenced by all of these types of noise. #### 4.1.1 Simulated Noisy Datasets

In the experiments, the CRAS method was evaluated on two standard benchmarks, CIFAR-10 and CIFAR-100 [26], with noisy labels generated using simulated noisy datasets. The experiments were conducted with two types of simulated noisy labels: those generated from symmetric noise and asymmetric noise, as described in refs. [25; 33; 56]. The network used for both the CIFAR-10 and CIFAR-100 experiments was an 18-layer PreAct ResNet [57], trained for 300 epochs with a batch size of 128. The initial learning rate was set to 0.02 and this was reduced by a factor of 10 at 150 epochs for CIFAR-10 and 200 epochs for CIFAR-100. The warm-up period for the proposed CR was set to 25 epochs for CIFAR-10 and 60 epochs for CIFAR-100. Most of the parameters of CRAS were kept similar to those of DivideMix and ELR+ and were found to be robust to changes in the noise rate. For instance, the parameter \(m\) was set to 0.4 for CIFAR-10 and 0.6 for CIFAR-100, for all noise rates, and the threshold \(\tau\) was set to 0.95 for both of these datasets. The threshold for the GMM was set to 0.5 for all of the experiments, in contrast with DivideMix, which has a threshold of 0.6 only for the case of 90% symmetric noise. #### 4.1.2 Real-World Datasets

The CRAS method was evaluated on two real-world datasets, Clothing1M and WebVision 1.0 (specifically, the mini-WebVision dataset described in refs. [20; 21]). Clothing1M is a dataset containing one million training images collected from online shopping websites, with an estimated noise rate of 38.5% [58]. By theoretical hypothesis testing, [PERSON] et al. [59] showed that the noisy labels contained in Clothing1M were affected by complex noise, called instance-dependent label noise, which depends on individual features. WebVision contains 2.4 million images crawled from the web using the 1000 concepts in ImageNet ILSVRC12. The mini-WebVision dataset includes the first 50 classes of the subset of WebVision that comprises Google images, and has an estimated noise rate of 20% [11]. In our