Properties and Potential Applications of Random Functional-Linked Types of Neural Networks

Random functional-linked types of neural networks (RFLNNs), e.g., the extreme learning machine (ELM) and broad learning system (BLS), which avoid suffering from a time-consuming training process, offer an alternative way of learning in deep structure. The RFLNNs have achieved excellent performance in various classification and regression tasks, however, the properties and explanations of these networks are ignored in previous research. This paper gives some insights into the properties of RFLNNs from the viewpoints of frequency domain, and discovers the presence of frequency principle in these networks, that is, they preferentially capture low-frequencies quickly and then fit the high frequency components during the training process. These findings are valuable for understanding the RFLNNs and expanding their applications. Guided by the frequency principle, we propose a method to generate a BLS network with better performance, and design an efficient algorithm for solving Poison's equation in view of the different frequency principle presenting in the Jacobi iterative method and BLS network.