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Over-parameterized deep neural networks (DNNs) with sufficient capacity tomemorize random noise can achieve excellent generalization performance,challenging the bias-variance trade-off in classical learning theory. Recentstudies claimed that DNNs first learn simple patterns and then memorize noise;some other works showed a phenomenon that DNNs have a spectral bias to learntarget functions from low to high frequencies during training. However, we showthat the monotonicity of the learning bias does not always hold: under theexperimental setup of deep double descent, the high-frequency components ofDNNs diminish in the late stage of training, leading to the second descent ofthe test error. Besides, we find that the spectrum of DNNs can be applied toindicating the second descent of the test error, even though it is calculatedfrom the training set only.

Rethink the Connections among Generalization, Memorization and the Spectral Bias of DNNs