## 2 The Related Work
Feed-forward neural networks demonstrate the superiority of mathematical models in a variety of applications, but as the size of the dataset keeps growing, the feed-forward neural network's original performance cannot keep up with the demands of engineering. As a result, many researchers have focused on developing improved feed-forward neural networks to deal with large-scale datasets. The feed-forward neural network is optimized primarily from two aspects: on the one hand, random weighting by weight set in selected is used to enhance the performance of the algorithm, as mentioned in [34; 35; 36; 37]; on the other hand, large datasets are processed by using the method of sample selection, as described in [38; 39], in order to enhance the algorithm's performance. The method of random weight optimization is commonly used by scholars. Because it offers effective learning capabilities, feed-forward neural networks are frequently employed in mathematical modeling [34]. Recently, some advanced stochastic learning algorithms have been developed slowly, a feed-forward neural network with a random hidden nodes approach was proposed in [34]. Weights and bias are generated randomly depending on the input data and kinds of activation functions, allowing the model's level of generalization to be controlled. In [35], a training iterative solution for large-scale datasets is developed, and the regularization model is used to initially generate a learning model with improved generalization ability. When dealing with large-scale datasets, good applicability and effectiveness are achieved. In [36], a distributed learning algorithm of a feed-forward neural network with random weights is proposed by using an event-triggered communication scheme. To reduce needless transmission overhead, the method adopts a discrete-time zero-gradient and strategy solution and introduces an event-triggered communication approach. In [37], a new feed-forward neural network method for initializing weights is proposed, which linearizes the whole network at the equilibrium point, especially the initial weights and deviations. Ref. [40] offered a linear algebraic approach based on the Cauchy inequality that guaranteed the output of neurons in the active area, sped up convergence, and drastically decreased the number of algorithm iterations for sample extraction. Many scholars discuss hot topics [38] such as combining Monte Carlo simulations (MCSs) and implementing efficient sampling of feed-forward neural networks (FNNs). The authors of [39] put forward a kind of incremental learning method based on a hybrid fuzzy neural network framework from the angle of the dataset to improve the performance of the algorithm. Feed-forward neural network optimization has drawn a lot of interest in the era of big data. To lower the sample size, feed-forward neural network optimization now primarily uses the processing of random weights, although researchers have only been able to increase the performance of these networks in isolation. In order to handle enormous datasets, this research suggests a random weighting feed-forward neural network scheme based on a decomposition approach. This scheme not only ensures the network's integrity but also the random performance of feed-forward neural networks. However, the sample feature extraction's actual applicability is not exhaustive; large-scale datasets only use random weights, which have poor feed-forward neural network performance.