反向传播不扩展到多个层

Question

我有一个简单的神经网络，它接受3个输入，产生1个输出。我有一个反向传播算法，我一直在用它来训练网络。它似乎适用于1层和2层网络，但对于3层网络，无论输入如何，我总是得到0.5的输出

我自己从Michael Nielsen的书和james Loy的博客中推导出了算法。它适用于1层和2层，但我在网上找不到关于为什么它不适用于更多层的信息

def backprop(self):
    # application of the chain rule to find derivative of the loss function with respect to weights
    output_error = 2 * (self.y - self.output) * sigmoid_derivative(self.output)
    d_weights3 = np.dot(self.layer2.T, output_error)
    previous_error = output_error
    error_new = np.dot(previous_error, self.weights3.T)*sigmoid_derivative(self.layer2)
    d_weights2 = np.dot(self.layer1.T, error_new)
    previous_error = error_new
    d_weights1 = np.dot(self.input.T, (np.dot(previous_error, self.weights2.T) * sigmoid_derivative(self.layer1)))

    # update the weights with the derivative (slope) of the loss function
    self.weights1 += d_weights1
    self.weights2 += d_weights2
    self.weights3 += d_weights3