6、神经网络与深度学习：从基础到实践

神经网络与深度学习：从基础到实践

1. 反向传播算法

反向传播是神经网络中用于计算梯度的重要算法，它能帮助我们更新网络的权重和偏置，以最小化损失函数。以下是反向传播的关键公式：
- (dA_1 = \frac{\partial J}{\partial A^{[1]}} = \frac{\partial J}{\partial Z^{[2]}}\frac{\partial Z^{[2]}}{\partial A^{[1]}} = [(A^{[3]} - Y)W^{[3]}A^{[2]}(1 - A^{[2]})][W^{[2]}] = dZ_2 W^{[2]})
- (dZ_1 = \frac{\partial J}{\partial Z^{[1]}} = \frac{\partial J}{\partial A^{[2]}}\frac{\partial A^{[2]}}{\partial Z^{[2]}}\frac{\partial Z^{[2]}}{\partial A^{[1]}}\frac{\partial A^{[1]}}{\partial Z^{[1]}} = [(A^{[3]} - Y)W^{[3]}][A^{[2]}(1 - A^{[2]})][W^{[2]}]\frac{\partial \sigma(Z^{[1]})}{\partial Z^{[1]}} = dA_1[A^{[1]}(1 - A^{[1]})])
- (dW_1 = \frac{\partial J}{\partial W^{[1]}} = \frac{\partial J}{\partial Z^{[1]}}\frac{\partial Z^{[1]}}{\partial W^{[1]}} = [(A^