On the Noisy Gradient Descent that Generalizes as SGD
This work addresses the theoretical understanding of generalization in deep learning for researchers, but it is incremental as it builds on existing noise regularization concepts.
The study tackled the problem of whether the specific class of gradient noise is essential for generalization in deep learning, showing that noise distributions different from SGD's can also effectively regularize gradient descent, with a variant improving large batch training without harming generalization.
The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and the covariance structure of gradient noise are critical for regularization, it remains unclear whether or not the class of noise distributions is important. In this work we provide negative results by showing that noises in classes different from the SGD noise can also effectively regularize gradient descent. Our finding is based on a novel observation on the structure of the SGD noise: it is the multiplication of the gradient matrix and a sampling noise that arises from the mini-batch sampling procedure. Moreover, the sampling noises unify two kinds of gradient regularizing noises that belong to the Gaussian class: the one using (scaled) Fisher as covariance and the one using the gradient covariance of SGD as covariance. Finally, thanks to the flexibility of choosing noise class, an algorithm is proposed to perform noisy gradient descent that generalizes well, the variant of which even benefits large batch SGD training without hurting generalization.