initialization method for a wide and deep neural network model. There is no local minimum in the initial weight space of the wide and deep neural network initialized by the weight initialization method. The weight values initialized by the weight initialization method are contained in those initialized by both of the standard initialization and He initialization methods. In other words, there exists an interval of initial weights where there is no local minimum in both cases of the standard initialization and He initialization methods.

Kawaguchi Model {#kawa-model}
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This subsection presents a description of the deep nonlinear neural network model analyzed by Kawaguchi (2016) (we call it [*Kawaguchi model*]{} here). We will propose a new weight initialization method for the Kawaguchi model in the subsection \[even\_weight\].

First, we consider the following neuron. The net input $U_n$ to a neuron $n$ is defined as: $U_n = \sum_mW_{nm}I_m$, where $W_{nm}$ represents the weight connecting the neurons $n$ and $m$, $I_m$ represents the input signal from the neuron $m$. It is noteworthy that biases are omitted for the sake of simplicity. The output signal is defined as $\varphi(U_n)$ where $\varphi(u) {\stackrel{\rm def}{=}}\max(0, u)$ for any $u \in {\mbox{\boldmath $R$}}$ and is called [*Rectified 