(\ref{eqn4-12}) ) \end{aligned}$$ holds true. Eq. (\[eqn4-13\]) completes the proof. Theorem \[thm2\] and Theorem \[thm3\] state that assumption A5u-m-1 holds in the initial loss landscape of the Kawaguchi model initialized by the even initialization method.

Thus, it follows from Theorem \[thm1\] that assumptions A1p-m and A5u-m (A5u-m-1) hold in the initial loss landscape of the Kawaguchi model initialized by the even initialization method, both of which were introduced by Kawaguchi (2016). Therefore, no poor local minimum exists in the initial loss landscape of the Kawaguchi model initialized by the even initialization method according to Corollary 3.2 presented by Kawaguchi (2016). Specifically, the following four statements hold true: 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.

Discussion and Related Work {#discuss}
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In this section, we compare the even initialization proposed in the subsection \[even\_weight\] with the existing methods. First, let us briefly review several existing methods on the initialization for weights in neural networks.

The following uniform distribution has been often used for setting the initial value for a weight of a 