# The Effect of Blue Noise on the Optimization Ability of Hopfield Neural Network
## 2 Related Works  
Noise exists widely in every part of nature, and in practical data processing, Gaussian white noise is generally used to approximate the stochastic rise and fall of a system, while white noise is only an ideal situation, as judged by the definition and statistical properties of white noise. Since the assumptions are based solely on Gaussian white noise, the effect of actual colored noise is not considered. As a consequence, there is a risk that data processing theories and methods may not be sufficient to guarantee the reliability of the estimation results [13]; therefore, many researchers are committed to eliminating the influence of noise [14; 15]. However, it is difficult to eliminate the influence of colored noise due to the complex and changeable condition of noise. Therefore, in practical models, people use colored noise to accurately describe the behavioral system of objects [16; 17; 18]. For example, [PERSON] et al. [19] investigated adaptive grayscale compressive spectral imaging using optimal blue noise coding patterns. The importance of noise color in simulations of evolutionary systems was demonstrated by [PERSON] et al. [20]. [PERSON] [21] discussed wavelet analysis of red noise and its application in climate diagnosis. [PERSON] et al. [22] analyzed the effect of pink noise on EEG and memory performance in memory tasks. [PERSON] et al. [23] studied the phase-locking of ultra-low power consumption stochastic magnetic bits induced by colored noise. Although much work has been carried out by researchers on colored noise, there is a slight lack of research regarding adding colored noise to neural networks in order to achieve a close fit to real-world usage cases.  
[PERSON] et al. [24] introduced a novel approach that involves adding noise to the activation function of neural networks. It has been found that replacing this saturated activation function with noisy variants helps optimization in many cases, producing the most advanced or competitive results in different datasets and tasks, especially when training seems to be the most difficult. [PERSON] et al. [25] investigated an intelligent fault diagnosis method based on a multi-scale deep convolutional neural network (MSD-CNN) model and strong noise data enhancement. Through the data enhancement method for strong noise, the number and diversity of training samples of the MSD-CNN model are improved, so that the model is able to learn deeper features in the training stage. [PERSON] et al. [26] proposed an automated vision-based method for the surface condition recognition of concrete structures. An improved Dempster-Shafer (DS) algorithm was designed for decision-level image fusion. The robustness of the proposed method was verified by using images contaminated by various types and intensities of noise.  
After years of development, the solution rate of the neural network has reached a satisfactory effect on the optimization of the problem [27; 28; 29]. However, for the complex and changeable noise situation in the real environment, if the noise interference situation in the specific environment is not considered, the solution rate may be biased when the model is applied to the actual situation, so adding noise to neural network training is indeed necessary.