vault backup: 2023-10-17 15:44:10

Study/DL/吴恩达深度学习课程/Lesson 1.md

@@ -3,8 +3,16 @@
 $$\begin{align}
 正向传递\\
 z &= w^Tx + b \\
-a &= \sigma(z) \\
+a &= \sigma(z) = \frac{1}{1+e^{-x}} \\
 \hat{y} &= L(a) = -ylog(\hat{y}) - (1-y)log(1-\hat{y}) \ \ 其中(\hat{y} = a) \\
 反向传递 \\
-\frac{dL}{da}
+\frac{dL}{da} &= \frac{(a-y)}{a(1-a)} \\
+\frac{da}{dz} &= a(1-a) \\
+dz = \frac{dL}{dz} &= \frac{dL}{da} \cdot \frac{da}{dz} = a-y \\
+dw = \frac{dL}{dw} &= \frac{dL}{dz} \cdot \frac{dz}{dw} = xdz \\
+db = \frac{dL}{db} &= \frac{dL}{dz} \cdot \frac{dz}{db} = dz \\
+w &= w - \eta \cdot dw \\
+b &= b - \eta \cdot db
 \end{align}$$
+正向传递：计算网络输出。
+反向传递：更新模型参数。