Fixed a calculation error in the backpropagation process (#607)

A-基础教程/A2-神经网络基本原理/en-us/Step7 - DNN/16.2-L2正则.md

@@ -157,7 +157,7 @@ $$
 \begin{aligned}
 \frac{dJ}{dW2}&=\frac{dJ}{dZ2}\frac{dZ2}{dW2}+\frac{dJ}{dW2}
 \\
-&=(Z2-Y)\cdot A1^T+\lambda \odot W2 
+&=A1^T\cdot (Z2-Y)+\lambda \odot W2 
 \end{aligned}
 \tag{9}
 $$
@@ -170,9 +170,9 @@ $$dB2=dZ2 \tag{10}$$
 
 再继续反向传播到第一层网络：
 
-$$dZ1 = W2^T \times dZ2 \odot A1 \odot (1-A1) \tag{11}$$
+$$dZ1 = dZ2 \cdot W2^T   \odot A1 \odot (1-A1) \tag{11}$$
 
-$$dW1= dZ1 \cdot X^T + \lambda \odot W1 \tag{12}$$
+$$dW1=  X^T \cdot dZ1+ \lambda \odot W1 \tag{12}$$
 
 $$dB1= dZ1 \tag{13}$$
 
@@ -183,13 +183,13 @@ $$dB1= dZ1 \tag{13}$$
         dZ = delta_in
         m = self.x.shape[1]
         if self.regular == RegularMethod.L2:
-            self.weights.dW = (np.dot(dZ, self.x.T) + self.lambd * self.weights.W) / m
+            self.weights.dW = (np.dot(self.x.T, dZ) + self.lambd * self.weights.W) / m
         else:
-            self.weights.dW = np.dot(dZ, self.x.T) / m
+            self.weights.dW = np.dot(self.x.T, dZ) / m
         # end if
         self.weights.dB = np.sum(dZ, axis=1, keepdims=True) / m
 
-        delta_out = np.dot(self.weights.W.T, dZ)
+        delta_out = np.dot(dZ, self.weights.W.T)
 
         if len(self.input_shape) > 2:
             return delta_out.reshape(self.input_shape)

A-基础教程/A2-神经网络基本原理/en-us/Step7 - DNN/16.3-L1正则.md

@@ -147,10 +147,10 @@ $$J(w,b) = J_0 + \lambda (\lvert W1 \rvert+\lvert W2 \rvert)$$
 $$
 \begin{aligned}
 dW2&=\frac{dJ}{dW2}=\frac{dJ}{dZ2}\frac{dZ2}{dW2}+\frac{dJ}{dW2} \\\\
-&=dZ2 \cdot A1^T+\lambda \odot sign(W2)
+&=A1^T \cdot dZ2+\lambda \odot sign(W2)
 \end{aligned}
 $$
-$$dW1= dZ1 \cdot X^T + \lambda \odot sign(W1) $$
+$$dW1= X^T \cdot dZ1 + \lambda \odot sign(W1) $$
 
 从上面的公式中可以看到，正则项在方向传播过程中，唯一影响的就是求W的梯度时，要增加一个$\lambda \odot sign(W)$，sign是符号函数，返回该值的符号，即1或-1。所以，我们可以修改`FullConnectionLayer.py`中的反向传播函数如下：
 
@@ -159,11 +159,11 @@ def backward(self, delta_in, idx):
     dZ = delta_in
     m = self.x.shape[1]
     if self.regular == RegularMethod.L2:
-        self.weights.dW = (np.dot(dZ, self.x.T) + self.lambd * self.weights.W) / m
+        self.weights.dW = (np.dot(self.x.T, dZ) + self.lambd * self.weights.W) / m
     elif self.regular == RegularMethod.L1:
-        self.weights.dW = (np.dot(dZ, self.x.T) + self.lambd * np.sign(self.weights.W)) / m
+        self.weights.dW = (np.dot(self.x.T, dZ) + self.lambd * np.sign(self.weights.W)) / m
     else:
-        self.weights.dW = np.dot(dZ, self.x.T) / m
+        self.weights.dW = np.dot(self.x.T, dZ) / m
     # end if
     self.weights.dB = np.sum(dZ, axis=1, keepdims=True) / m
     ......