Strength of Minibatch Noise in SGD
This work addresses a poorly understood but practically important issue in deep learning for researchers and practitioners, offering incremental theoretical advancements.
The authors tackled the problem of understanding the noise in stochastic gradient descent (SGD) caused by minibatch sampling, deriving a general formula to approximate SGD noise near minima and applying it to provide insights into training stability, generalization, and scaling laws in deep learning.
The noise in stochastic gradient descent (SGD), caused by minibatch sampling, is poorly understood despite its practical importance in deep learning. This work presents the first systematic study of the SGD noise and fluctuations close to a local minimum. We first analyze the SGD noise in linear regression in detail and then derive a general formula for approximating SGD noise in different types of minima. For application, our results (1) provide insight into the stability of training a neural network, (2) suggest that a large learning rate can help generalization by introducing an implicit regularization, (3) explain why the linear learning rate-batchsize scaling law fails at a large learning rate or at a small batchsize and (4) can provide an understanding of how discrete-time nature of SGD affects the recently discovered power-law phenomenon of SGD.