neurons in the preceding layer, and the probability distribution which weights obey in the even initialization can be a normal distribution with zero mean or a uniform distribution. Conversely, there exists an interval which does not have any local minimum in both of the intervals of initial weight values of the standard initialization and He initialization. As a numerical example, $[-3\sqrt{2}/\sqrt{n}, 3\sqrt{2}/\sqrt{n}] \fallingdotseq [ -0.424, 0.424 ]$ (He initialization), $[-1/\sqrt{n}, 1/\sqrt{n}] = [ -0.1, 0.1 ]$ (standard initialization) and $[-1/n, 1/n] = [ -0.01, 0.01 ]$ (even initialization) when $n=100$: the number of neurons in the preceding layer is 100.

Conclusions {#concl}
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We introduced a weight initialization scheme called [*even initialization*]{} for the wide and deep ReLU neural network model, and proved using the research results presented by Kawaguchi (2016) 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. We also elucidated that the weight values initialized by the even initialization method are contained in those initialized by both of the standard initialization and He initialization methods. We clarified the essential property of the even initialization theoretically. Applying the even initialization to large-scale 