Rethink the Connections among Generalization, Memorization and the Spectral Bias of DNNs
This work addresses a theoretical gap in understanding generalization and memorization in over-parameterized DNNs, which is incremental but clarifies connections to spectral bias.
The paper challenges the assumption that deep neural networks (DNNs) monotonically learn from low to high frequencies, showing that in deep double descent, high-frequency components diminish late in training, causing a second test error descent. It also finds that the DNN spectrum can predict this second descent using only training data.
Over-parameterized deep neural networks (DNNs) with sufficient capacity to memorize random noise can achieve excellent generalization performance, challenging the bias-variance trade-off in classical learning theory. Recent studies claimed that DNNs first learn simple patterns and then memorize noise; some other works showed a phenomenon that DNNs have a spectral bias to learn target functions from low to high frequencies during training. However, we show that the monotonicity of the learning bias does not always hold: under the experimental setup of deep double descent, the high-frequency components of DNNs diminish in the late stage of training, leading to the second descent of the test error. Besides, we find that the spectrum of DNNs can be applied to indicating the second descent of the test error, even though it is calculated from the training set only.