Label Noise SGD Provably Prefers Flat Global Minimizers
This work provides theoretical insights into implicit regularization in deep learning, addressing generalization issues for researchers and practitioners, though it builds incrementally on prior work by extending results to global convergence and broader settings.
The paper tackles the problem of understanding why label noise in stochastic gradient descent (SGD) improves generalization in overparametrized models, showing that SGD with label noise converges to flat global minimizers by implicitly regularizing the loss to penalize sharp minimizers, with an effective regularization parameter depending on step size, noise strength, and batch size.
In overparametrized models, the noise in stochastic gradient descent (SGD) implicitly regularizes the optimization trajectory and determines which local minimum SGD converges to. Motivated by empirical studies that demonstrate that training with noisy labels improves generalization, we study the implicit regularization effect of SGD with label noise. We show that SGD with label noise converges to a stationary point of a regularized loss $L(θ) +λR(θ)$, where $L(θ)$ is the training loss, $λ$ is an effective regularization parameter depending on the step size, strength of the label noise, and the batch size, and $R(θ)$ is an explicit regularizer that penalizes sharp minimizers. Our analysis uncovers an additional regularization effect of large learning rates beyond the linear scaling rule that penalizes large eigenvalues of the Hessian more than small ones. We also prove extensions to classification with general loss functions, SGD with momentum, and SGD with general noise covariance, significantly strengthening the prior work of Blanc et al. to global convergence and large learning rates and of HaoChen et al. to general models.