PhD Candidate
The University of Texas at Austin
Areas of Interest
- Artificial Intelligence
- Theory
Poster
Implicit Regularization and Convergence for Weight Normalization
Abstract
Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the weight normalization (WN) method [Salimans and Kingma, 2016] and a variant called reparametrized projected gradient descent (rPGD) for overparametrized least-squares regression. WN and rPGD reparametrize the weights with a scale g and a unit vector w and thus the objective function becomes non-convex. We show that this non-convex formulation has beneficial regularization effects compared to gradient descent on the original objective. These methods adaptively regularize the weights and converge close to the minimum l2 norm solution, even for initializations far from zero. For certain stepsizes of g and w , we show that they can converge close to the minimum norm solution. This is different from the behavior of gradient descent, which converges to the minimum norm solution only when started at a point in the range space of the feature matrix, and is thus more sensitive to initialization.
Bio
Xiaoxia (Shirley) Wu is a Ph.D. student at The University of Texas at Austin, advised by Rachel Ward. Previously, she was a research intern, mentored by Léon Bottou, at Facebook AI Research (FAIR) where she worked on batch/weight normalization. She was also a visiting student at Simons Institute for the Theory of Computing (UC Berkeley) in Fall 2018 and Summer 2019, and Institute for Advanced Study (Princeton) in Fall 2019. Her primary research interests lie in the area of optimization, including stochastic and robust optimization. Her current research is on understanding and improving the optimization methods for non-convex landscapes (neural networks), such as adaptive gradient methods and normalization methods. She was a recipient of the UT Austin Graduate School Fellowship.
