Benign Oscillation of Stochastic Gradient Descent with Large Learning
  Rates
Miao Lu Beining Wu Xiaodong Yang Difan Zou
In this work, we theoretically investigate the generalization properties of
neural networks (NN) trained by stochastic gradient descent (SGD) algorithm
with large learning rates. Under such a training regime, our finding is that,
the oscillation of the NN weights caused by the large learning rate SGD
training turns out to be beneficial to the generalization of the NN, which
potentially improves over the same NN trained by SGD with small learning rates
that converges more smoothly. In view of this finding, we call such a
phenomenon "benign oscillation". Our theory towards demystifying such a
phenomenon builds upon the feature learning perspective of deep learning.
Specifically, we consider a feature-noise data generation model that consists
of (i) weak features which have a small $\ell_2$-norm and appear in each data
point; (ii) strong features which have a larger $\ell_2$-norm but only appear
in a certain fraction of all data points; and (iii) noise. We prove that NNs
trained by oscillating SGD with a large learning rate can effectively learn the
weak features in the presence of those strong features. In contrast, NNs
trained by SGD with a small learning rate can only learn the strong features
but makes little progress in learning the weak features. Consequently, when it
comes to the new testing data which consist of only weak features, the NN
trained by oscillating SGD with a large learning rate could still make correct
predictions consistently, while the NN trained by small learning rate SGD
fails. Our theory sheds light on how large learning rate training benefits the
generalization of NNs. Experimental results demonstrate our finding on "benign
oscillation".