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Previous studies have shown that deep neural networks (DNNs) with commonsettings often capture target functions from low to high frequency, which iscalled Frequency Principle (F-Principle). It has also been shown thatF-Principle can provide an understanding to the often observed goodgeneralization ability of DNNs. However, previous studies focused on the lossfunction of mean square error, while various loss functions are used inpractice. In this work, we show that the F-Principle holds for a general lossfunction (e.g., mean square error, cross entropy, etc.). In addition, DNN'sF-Principle may be applied to develop numerical schemes for solving variousproblems which would benefit from a fast converging of low frequency. As anexample of the potential usage of F-Principle, we apply DNN in solvingdifferential equations, in which conventional methods (e.g., Jacobi method) isusually slow in solving problems due to the convergence from high to lowfrequency.

Frequency Principle in Deep Learning with General Loss Functions and Its Potential Application