Addressing Spectral Bias of Deep Neural Networks by Multi-Grade Deep Learning

Deep neural networks (DNNs) have showcased their remarkable precision in approximating smooth functions. However, they suffer from the {\it spectral bias}, wherein DNNs typically exhibit a tendency to prioritize the learning of lower-frequency components of a function, struggling to effectively capture its high-frequency features. This paper is to address this issue. Notice that a function having only low frequency components may be well-represented by a shallow neural network (SNN), a network having only a few layers. By observing that composition of low frequency functions can effectively approximate a high-frequency function, we propose to learn a function containing high-frequency components by composing several SNNs, each of which learns certain low-frequency information from the given data.