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# cross-entropy代价函数是怎么推出来的

以$$\frac{\partial C}{\partial b }$$为例。\
已知：

$$
\begin{eqnarray}
\frac{\partial C}{\partial b}
\= \frac{\partial C}{\partial a}\frac{\partial a}{\partial z}\frac{\partial z}{\partial b}
\= \frac{\partial C}{\partial a} \sigma'(z).
\tag{73}\end{eqnarray}
$$

且发现公式73中的$$\sigma'(z)$$是导致学得慢的原因，希望把它去掉。\
我们希望$$\frac{\partial C}{\partial b }$$的样子为：

$$
\frac{\partial C}{\partial b } = (a-y)
$$

以此反推出：

$$
\begin{eqnarray}
\frac{\partial C}{\partial a} = \frac{a-y}{a(1-a)}
\tag{75}\end{eqnarray}
$$

因此得出：

$$
\begin{eqnarray}
C = -\[y \ln a + (1-y) \ln (1-a)]+ {\rm constant},
\tag{76}\end{eqnarray}
$$

\[?]公式中的常数项是怎么去掉的？