discarded most of these assumptions and proved that the following four statements for a deep nonlinear neural network with only two out of the seven assumptions: 1) the loss function is non-convex and non-concave, 2) every local minimum is a global minimum, 3) every critical point that is not a global minimum is a saddle point, and 4) bad saddle points exist.

In this paper, we propose a new weight initialization method (called [*even initialization*]{}) for wide and deep nonlinear neural networks with the ReLU activation function: weights are initialized independently and identically according to a probability distribution whose probability density function is even on $[ -1/n, 1/n]$ where $n$ is the number of neurons in the layer. Using the research results presented by Kawaguchi (2016), we prove that no poor local minimum exists in the initial loss landscape in the wide and deep nonlinear neural network initialized by the even initialization method that we propose. We also show that the weight values initialized by the even initialization method are contained in those initialized by both of the (often used) standard initialization and He initialization methods.

Weight Initialization without Local Minima {#initialize_weight}
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In this section, we propose a weight 