Strength of Minibatch Noise in SGD
arXiv:2102.05375
Abstract
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.
ICLR 2022 spotlight
References in corpus (7)
- Theory of Deep Learning IIb: Optimization Properties of SGD
- Understanding the Role of Momentum in Stochastic Gradient Methods
- Multiplicative noise and heavy tails in stochastic optimization
- A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networks
- Recent advances in deep learning theory
- Shape Matters: Understanding the Implicit Bias of the Noise Covariance
- On the Distributional Properties of Adaptive Gradients