## 5 Conclusions  
In this section, we will discuss the problem of sample classification.  
As shown in Figure 16, the pure samples always maintain a very high purity rate, while the performance of complex samples is complex, with a rapid decline from the average purity rate of the data. Dirty samples always have low purity. This result justifies our idea of distinguishing the two samples.  
The complex sample can guide model training at the beginning and solves the problem of \"when to update\". In the middle and late stages of the experiment, a part of the complex sample with the ability to guide the training of the model became the pure sample. The remaining complex samples have an increasing proportion of noisy labels. The complex samples gradually lose the ability to guide model updates.  
This paper studies the problem of noisy label learning in deep learning, which is an important issue in the cheap and fast implementation of deep learning. This paper proposes  
Figure 16: Results on the CIFAR-10 dataset. Noise settings, Symmetry-20%. **Left**: Label precision (%) vs. epochs; **Right**: Number vs. epochs.  
Figure 15: **Left**: Results on the CIFAR-10 dataset. Noise settings, Symmetry-20%. precision accuracy (%) vs. epochs; **Right**: Results on Mnist dataset Noise settings, Symmetry-50%. precision accuracy (%) vs. epochs.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Index** & **Methods** & **Label Precision** \\ \hline
1 & JoSDW-S & 95.03 \\
2 & JoSDW-SD & 96.66 \\
3 & JoSDW & 97.23 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Average precision accuracy (%) on Mnist Symmetry-50% over the last 10 epochs.  
a robust JoSDW to improve the performance of deep neural networks with noisy labels. The key idea of JoSDW is to train two neural networks with the same structure at the same time and select high clean sample labels through a small-loss sample selection strategy. Then, the samples obtained in the first screening continue to be classified by the prediction results of the two neural networks. Those with the same prediction result are pure samples, and those with different prediction results are called complex samples. Simultaneously update according to the respective cross-entropy loss and a joint loss. We conduct experiments on three datasets (MNIST, CIFAR-10, CIFAR-100) to prove that JoSDW can train the depth model robustly under the noisy label.  
In the future, our work can be divided into three points: first, we will explore label correction methods to recover discarded low-confidence sample labels to improve the utilization of samples. Second, we will try an ensemble of noisy label learning methods, which will be combined with methods such as boosting ensembles [8] and Nested Dropout [18]; Third, the current methods of noisy learning are mainly applied to artificially set noisy datasets, and with the rise of unsupervised learning, we will focus on the combination of pseudo-labels generated by clustering and noisy learning.  
Conceptualization, Y.Z.; methodology, Y.Z.; software, Y.Z.; validation, M.B.; formal analysis, J.X.; investigation, M.B.; resources, J.X.; data curation, M.B.; writing--original draft preparation, Y.Z.; writing--review and editing, J.X.; visualization, Y.Z.; supervision, H.X.; project administration, H.X.; funding acquisition, H.X. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Publicly available datasets were analyzed in this study. This data can be found here: [[http://yann.lecun.com/exdb/mnist/](http://yann.lecun.com/exdb/mnist/)]([http://yann.lecun.com/exdb/mnist/](http://yann.lecun.com/exdb/mnist/)), [[https://www.cs.toronto.edu/~kriz/cifar.html](https://www.cs.toronto.edu/~kriz/cifar.html)]([https://www.cs.toronto.edu/~kriz/cifar.html](https://www.cs.toronto.edu/~kriz/cifar.html)) (accessed on 30 December 2021).  
The authors declare no conflict of interest.