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

TL;DR

This paper investigates the properties of random functional-linked neural networks like ELM and BLS, revealing a frequency principle that explains their learning behavior and guiding improved network design and algorithms.

Contribution

It uncovers the frequency principle in RFLNNs and proposes a method to enhance BLS performance based on this insight.

Findings

RFLNNs preferentially learn low frequencies first

The frequency principle is confirmed in RFLNNs

A new algorithm for solving Poisson's equation is developed

Abstract

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.