10. Cost 解决方案

我的 MSE 实现过程如下：

class MSE(Node):
    def __init__(self, y, a):
        """
        The mean squared error cost function.
        Should be used as the last node for a network.
        """
        # Call the base class' constructor.
        Node.__init__(self, [y, a])

    def forward(self):
        """
        Calculates the mean squared error.
        """
        # NOTE: We reshape these to avoid possible matrix/vector broadcast
        # errors.
        #
        # For example, if we subtract an array of shape (3,) from an array of shape
        # (3,1) we get an array of shape(3,3) as the result when we want
        # an array of shape (3,1) instead.
        #
        # Making both arrays (3,1) insures the result is (3,1) and does
        # an elementwise subtraction as expected.
        y = self.inbound_nodes[0].value.reshape(-1, 1)
        a = self.inbound_nodes[1].value.reshape(-1, 1)
        m = self.inbound_nodes[0].value.shape[0]

        diff = y - a
        self.value = np.mean(diff**2)

MSE 反映的是等式 (5)，其中 y 是目标输出，a 是神经网络计算的输出。然后将误差进行平方 (diff**2)，也可以写成 np.square(diff)。最后，我们需要对平方误差求和并除以示例总数 m。可以通过 np.mean 或 (1 /m) * np.sum(diff**2) 进行计算。

注意 y 和 a 的顺序并不重要，(a - y) 可以调换顺序，值还是相同的。