Frequency principle/spectral bias
phenomenon observed in the study of Artificial Neural Networks
The frequency principle/spectral bias is a phenomenon observed in the study of artificial neural networks (ANNs), specifically deep neural networks (DNNs). It describes the tendency of deep neural networks to fit target functions from low to high frequencies during the training process.
This phenomenon is referred to as the frequency principle (F-Principle) by Zhi-Qin John Xu et al. or spectral bias by Nasim Rahaman et al. The F-Principle can be robustly observed in DNNs, regardless of overparametrization. A key mechanism of the F-Principle is that the regularity of the activation function translates into the decay rate of the loss function in the frequency domain.
The discovery of the frequency principle has inspired the design of DNNs that can quickly learn high-frequency functions. This has applications in scientific computing, image classification, and point cloud fitting problems. Furthermore, it provides a means to comprehend phenomena in practical applications and has inspired numerous studies on deep learning from the frequency perspective.
Main results (informal)
Experimental results
In one-dimensional problems, the Discrete Fourier Transform (DFT) of the target function and the output of DNNs can be obtained, and we can observe from Fig.1 that the blue line fits the low-frequency faster than the high-frequency.
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