Convergence Analysis of the Dynamics of a Special Kind of Two-Layered Neural Networks with _1 and _2 Regularization

Code

• github.com/FengNiMa/ReLU_Convergence
  pytorch★ 0

Abstract

In this paper, we made an extension to the convergence analysis of the dynamics of two-layered bias-free networks with one ReLU output. We took into consideration two popular regularization terms: the _1 and _2 norm of the parameter vector w, and added it to the square loss function with coefficient /2. We proved that when is small, the weight vector w converges to the optimal solution w (with respect to the new loss function) with probability (1-)(1-A_d)/2 under random initiations in a sphere centered at the origin, where is a small value and A_d is a constant. Numerical experiments including phase diagrams and repeated simulations verified our theory.

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