A Quantitative Analysis of the Effect of Batch Normalization on Gradient Descent

Despite its empirical success and recent theoretical progress, there generally lacks a quantitative analysis of the effect of batch normalization (BN) on the convergence and stability of gradient descent. In this paper, we provide such an analysis on the simple problem of ordinary least squares (OLS). Since precise dynamical properties of gradient descent (GD) is completely known for the OLS problem, it allows us to isolate and compare the additional effects of BN. More precisely, we show that u...