def derivative(self, x: np.ndarray) -> np.ndarray: ''' Parameters: x is a two dimensional array. Returns: a two dimensional array whose shape is the same as that of x. The returned value is the elementwise derivative of the sigmoid function w.r.t. x. ''' #### write your code below #### return。请帮我完成需要填写的代码

Sure, here is the code you can use to compute the derivative of the sigmoid function w.r.t. x:

def derivative(self, x: np.ndarray) -> np.ndarray:
    '''
    Parameters:
        x is a two dimensional array.
    Returns:
        a two dimensional array whose shape is the same as that of x. The returned value is the elementwise 
        derivative of the sigmoid function w.r.t. x.
    '''
    sigmoid = lambda x: 1 / (1 + np.exp(-x))
    return sigmoid(x) * (1 - sigmoid(x))

相关问题

def derivative(self, x: np.ndarray) -> np.ndarray: ''' Parameters: x is a two dimensional array. Returns: a two dimensional array whose shape is the same as that of x. The returned value is the elementwise derivative of the sigmoid function w.r.t. x. ''' #### write your code below ####

根据这段代码的要求，我们需要在 `derivative` 方法中编写代码，实现对输入的二维 numpy 数组 `x` 进行 sigmoid 函数的导数计算，并返回结果。以下是按照要求编写的代码：

import numpy as np

class MyModel:
    def value(self, x: np.ndarray) -> np.ndarray:
        """
        Parameters:
        x: a two dimensional numpy array
        
        Returns:
        a two dimensional array representing the element-wise sigmoid of x.
        """
        return 1 / (1 + np.exp(-x))
    
    def derivative(self, x: np.ndarray) -> np.ndarray:
        """
        Parameters:
        x: a two dimensional numpy array
        
        Returns:
        a two dimensional array whose shape is the same as that of x.
        The returned value is the elementwise derivative of the sigmoid function w.r.t. x.
        """
        sigmoid_x = self.value(x)
        return sigmoid_x * (1 - sigmoid_x)

在方法中，我们首先调用 `value` 方法，计算输入数组 `x` 的 sigmoid 值，并将其保存在变量 `sigmoid_x` 中。然后，我们根据 sigmoid 函数的导数公式：

$$
\frac{d}{dx}sigmoid(x) = sigmoid(x) \cdot (1 - sigmoid(x))
$$

对 `sigmoid_x` 进行计算，得到每个元素的导数。最后，我们将计算结果返回即可。需要注意的是，由于 sigmoid 函数的值域在 $(0, 1)$ 之间，因此其导数的值也在 $(0, 1)$ 之间。

class Softmax(Activation): ''' softmax nonlinear function. ''' def __init__(self): ''' There are no parameters in softmax function. ''' super(Softmax, self).__init__() def value(self, x: np.ndarray) -> np.ndarray: ''' Parameters: x is the input to the softmax function. x is a two dimensional numpy array. Each row is the input to the softmax function Returns: output of the softmax function. The returned value is with the same shape as that of x. ''' #### write your code below #### return def derivative(self, x: np.ndarray) -> np.ndarray: ''' Parameters: x is the input to the softmax function. x is a two dimensional numpy array. Returns: a two dimensional array representing the derivative of softmax function w.r.t. x. ''' #### write your code below ####

下面是对 `Softmax` 激活函数的实现，你可以将其加入到代码中：

class Softmax(Activation):
    '''
    softmax nonlinear function.
    '''
    def __init__(self):
        '''
        There are no parameters in softmax function.
        '''
        super(Softmax, self).__init__()

    def value(self, x: np.ndarray) -> np.ndarray:
        '''
        Parameters:
          x is the input to the softmax function. x is a two dimensional numpy array. Each row is the input to the softmax function
        Returns:
          output of the softmax function. The returned value is with the same shape as that of x.
        '''
        exp_scores = np.exp(x)
        return exp_scores / np.sum(exp_scores, axis=1, keepdims=True)

    def derivative(self, x: np.ndarray) -> np.ndarray:
        '''
        Parameters:
          x is the input to the softmax function. x is a two dimensional numpy array.
        Returns:
          a two dimensional array representing the derivative of softmax function w.r.t. x.
        '''
        softmax_output = self.value(x)
        return softmax_output * (1 - softmax_output)