# 反向傳播演算法

## 鏈式法則

f(x,y,z)=(x y)z” role=”presentation”>f(x,y,z)=(x y)zf(x,y,z)=(x y)z

f(x, y, z) = (x y)z

q=x y” role=”presentation”>q=x yq=x y

q=x y

f=qz” role=”presentation”>f=qzf=qz

f = qz

∂f∂q=z,∂f∂z=q” role=”presentation”>∂f∂q=z,∂f∂z=q∂f∂q=z,∂f∂z=q

\frac{\partial f}{\partial q} = z, \frac{\partial f}{\partial z}=q

∂qx=1,∂qy=1″ role=”presentation”>∂qx=1,∂qy=1∂qx=1,∂qy=1

\frac{\partial q}{x} = 1, \frac{\partial q}{y} = 1

∂f∂x,∂f∂y,∂f∂z” role=”presentation”>∂f∂x,∂f∂y,∂f∂z∂f∂x,∂f∂y,∂f∂z

\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}

∂f∂x=∂f∂q∂q∂x” role=”presentation”>∂f∂x=∂f∂q∂q∂x∂f∂x=∂f∂q∂q∂x

\frac{\partial f}{\partial x} = \frac{\partial f}{\partial q}\frac{\partial q}{\partial x}

∂f∂y=∂f∂q∂q∂y” role=”presentation”>∂f∂y=∂f∂q∂q∂y∂f∂y=∂f∂q∂q∂y

\frac{\partial f}{\partial y} = \frac{\partial f}{\partial q}\frac{\partial q}{\partial y}

∂f∂z=q” role=”presentation”>∂f∂z=q∂f∂z=q

\frac{\partial f}{\partial z} = q

## 反向傳播演算法

∂f∂q=z=−4, ∂f∂z=q=3″ role=”presentation”>∂f∂q=z=−4, ∂f∂z=q=3∂f∂q=z=−4, ∂f∂z=q=3

\frac{\partial f}{\partial q} = z = -4,\ \frac{\partial f}{\partial z} = q = 3

∂f∂x=∂f∂q∂q∂x=−4×1=−4, ∂f∂y=∂f∂q∂q∂y=−4×1=−4″ role=”presentation”>∂f∂x=∂f∂q∂q∂x=−4×1=−4, ∂f∂y=∂f∂q∂q∂y=−4×1=−4∂f∂x=∂f∂q∂q∂x=−4×1=−4, ∂f∂y=∂f∂q∂q∂y=−4×1=−4

\frac{\partial f}{\partial x} = \frac{\partial f}{\partial q} \frac{\partial q}{\partial x} = -4 \times 1 = -4,\ \frac{\partial f}{\partial y} = \frac{\partial f}{\partial q} \frac{\partial q}{\partial y} = -4 \times 1 = -4

### Sigmoid函式舉例

f(w,x)=11 e−(w0x0 w1x1 w2)” role=”presentation”>f(w,x)=11 e−(w0x0 w1x1 w2)f(w,x)=11 e−(w0x0 w1x1 w2)

f(w, x) = \frac{1}{1 e^{-(w_0 x_0 w_1 x_1 w_2)}}

∂f∂w0,∂f∂w1,∂f∂w2″ role=”presentation”>∂f∂w0,∂f∂w1,∂f∂w2∂f∂w0,∂f∂w1,∂f∂w2

\frac{\partial f}{\partial w_0}, \frac{\partial f}{\partial w_1}, \frac{\partial f}{\partial w_2}

f(x)=1xfc(x)=1 xfe(x)=exfw(x)=−(w0x0 w1x1 w2)” role=”presentation” style=”position: relative;”>f(x)=1xfc(x)=1 xfe(x)=exfw(x)=−(w0x0 w1x1 w2)f(x)=1xfc(x)=1 xfe(x)=exfw(x)=−(w0x0 w1x1 w2)

f(x) = \frac{1}{x} \\
f_c(x) = 1 x \\
f_e(x) = e^x \\
f_w(x) = -(w_0 x_0 w_1 x_1 w_2)

• 2018.08.06

• 2018.08.06

• 2018.08.06

• 2018.08.06

• 2018.08.06

• 2018.08.06