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Update 17.3-卷积的反向传播原理.md
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公式修复
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sxjeru authored Feb 25, 2023
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Expand Up @@ -136,13 +136,19 @@ $$
正向公式:

$$z_{111} = w_{111} \cdot a_{11} + w_{112} \cdot a_{12} + w_{121} \cdot a_{21} + w_{122} \cdot a_{22}$$

$$z_{112} = w_{111} \cdot a_{12} + w_{112} \cdot a_{13} + w_{121} \cdot a_{22} + w_{122} \cdot a_{23}$$

$$z_{121} = w_{111} \cdot a_{21} + w_{112} \cdot a_{22} + w_{121} \cdot a_{31} + w_{122} \cdot a_{32}$$

$$z_{122} = w_{111} \cdot a_{22} + w_{112} \cdot a_{23} + w_{121} \cdot a_{32} + w_{122} \cdot a_{33}$$

$$z_{211} = w_{211} \cdot a_{11} + w_{212} \cdot a_{12} + w_{221} \cdot a_{21} + w_{222} \cdot a_{22}$$

$$z_{212} = w_{211} \cdot a_{12} + w_{212} \cdot a_{13} + w_{221} \cdot a_{22} + w_{222} \cdot a_{23}$$

$$z_{221} = w_{211} \cdot a_{21} + w_{212} \cdot a_{22} + w_{221} \cdot a_{31} + w_{222} \cdot a_{32}$$

$$z_{222} = w_{211} \cdot a_{22} + w_{212} \cdot a_{23} + w_{221} \cdot a_{32} + w_{222} \cdot a_{33}$$

求$J$对$a_{22}$的梯度:
Expand Down Expand Up @@ -180,18 +186,21 @@ z_{11} &= w_{111} \cdot a_{111} + w_{112} \cdot a_{112} + w_{121} \cdot a_{121}
\end{aligned}
\tag{10}
$$

$$
\begin{aligned}
z_{12} &= w_{111} \cdot a_{112} + w_{112} \cdot a_{113} + w_{121} \cdot a_{122} + w_{122} \cdot a_{123} \\\\
&+ w_{211} \cdot a_{212} + w_{212} \cdot a_{213} + w_{221} \cdot a_{222} + w_{222} \cdot a_{223}
\end{aligned}\tag{11}
$$

$$
\begin{aligned}
z_{21} &= w_{111} \cdot a_{121} + w_{112} \cdot a_{122} + w_{121} \cdot a_{131} + w_{122} \cdot a_{132} \\\\
&+ w_{211} \cdot a_{221} + w_{212} \cdot a_{222} + w_{221} \cdot a_{231} + w_{222} \cdot a_{232}
\end{aligned}\tag{12}
$$

$$
\begin{aligned}
z_{22} &= w_{111} \cdot a_{122} + w_{112} \cdot a_{123} + w_{121} \cdot a_{132} + w_{122} \cdot a_{133} \\\\
Expand Down Expand Up @@ -325,6 +334,7 @@ $$
$$
z = x * w
$$

$$
loss = \frac{1}{2}(z-y)^2
$$
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