18 lines
641 B
Markdown
18 lines
641 B
Markdown
# Neural Network and Deep Learning
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## Logistic Regression
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$$\begin{align}
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正向传递\\
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z &= w^Tx + b \\
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a &= \sigma(z) = \frac{1}{1+e^{-x}} \\
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\hat{y} &= L(a) = -ylog(\hat{y}) - (1-y)log(1-\hat{y}) \ \ 其中(\hat{y} = a) \\
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反向传递 \\
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\frac{dL}{da} &= \frac{(a-y)}{a(1-a)} \\
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\frac{da}{dz} &= a(1-a) \\
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dz = \frac{dL}{dz} &= \frac{dL}{da} \cdot \frac{da}{dz} = a-y \\
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dw = \frac{dL}{dw} &= \frac{dL}{dz} \cdot \frac{dz}{dw} = xdz \\
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db = \frac{dL}{db} &= \frac{dL}{dz} \cdot \frac{dz}{db} = dz \\
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w &= w - \eta \cdot dw \\
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b &= b - \eta \cdot db
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\end{align}$$
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正向传递：计算网络输出。
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反向传递：更新模型参数。 |