ReLUs

Dynamics and Convergence of Weight Normalization for Training Neural Networks

Guido Montufar, Assistant Professor, Departments of Mathematics and Statistics, University of California, Los Angeles (UCLA)

Jan 29, 13:00 - 14:30

B1 L3 R3119

machine learning neural network optimization ReLUs

We present a result on the convergence of weight normalized training of artificial neural networks. In the analysis, we consider over-parameterized 2-layer networks with rectified linear units (ReLUs) initialized at random and trained with batch gradient descent and a fixed step size. The proof builds on recent theoretical works that bound the trajectory of parameters from their initialization and monitor the network predictions via the evolution of a ''neural tangent kernel'' (Jacot et al. 2018). We discover that training with weight normalization decomposes such a kernel via the so called ''length-direction decoupling''. This in turn leads to two convergence regimes. From the modified convergence we make a few curious observations including a natural form of ''lazy training'' where the direction of each weight vector remains stationary.