Создание из зацикленного класса в Python (с примером глубокого изучения)

Question

Попытка воспроизвести функцию потерь из примера , найденного здесь .Предоставленный код не показывает, как строить из зацикленного класса.Вот оригинальный код:

import numpy as np

def sigmoid(x):
    return 1.0/(1+ np.exp(-x))

def sigmoid_derivative(x):
    return x * (1.0 - x)

class NeuralNetwork:
    def __init__(self, x, y):
        self.input      = x
        self.weights1   = np.random.rand(self.input.shape[1],4) 
        self.weights2   = np.random.rand(4,1)                 
        self.y          = y
        self.output     = np.zeros(self.y.shape)

    def feedforward(self):
        self.layer1 = sigmoid(np.dot(self.input, self.weights1))
        self.output = sigmoid(np.dot(self.layer1, self.weights2))

        print(sum((self.y - self.output)**2))

    def backprop(self):
        # application of the chain rule to find derivative of the loss function with respect to weights2 and weights1
        d_weights2 = np.dot(self.layer1.T, (2*(self.y - self.output) * sigmoid_derivative(self.output)))
        d_weights1 = np.dot(self.input.T,  (np.dot(2*(self.y - self.output) * sigmoid_derivative(self.output), 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


if __name__ == "__main__":
    X = np.array([[0,0,1],
                  [0,1,1],
                  [1,0,1],
                  [1,1,1]])
    y = np.array([[0],[1],[1],[0]])
    nn = NeuralNetwork(X,y)

    for i in range(1500):
        nn.feedforward()
        nn.backprop()

    print(nn.output)


# Output:   
# [1.38353847]
# [1.11068749]
# [1.00565082]
# [1.00286219]
# [1.0027016]
# [1.00254482]
# [1.00239119]
# [1.00224046]
# [1.00209239]
# [1.00194675]
# [1.0018033]
# [1.00166184]
# [1.00152213]
# [1.00138396]
# [1.00124712]
# ....1500 times to converge

Вот сюжет, который я пытаюсь воспроизвести:

Что мне нужно сделать с кодом нижедобавлен в feedforward() для построения с помощью глобальной переменной loss?

import numpy as np

def sigmoid(x):
    return 1.0/(1+ np.exp(-x))

def sigmoid_derivative(x):
    return x * (1.0 - x)

class NeuralNetwork:
    def __init__(self, x, y):
        self.input      = x
        self.weights1   = np.random.rand(self.input.shape[1],4) 
        self.weights2   = np.random.rand(4,1)                 
        self.y          = y
        self.output     = np.zeros(self.y.shape)

    loss = []
    def feedforward(self):
        global loss
        self.layer1 = sigmoid(np.dot(self.input, self.weights1))
        self.output = sigmoid(np.dot(self.layer1, self.weights2))

        loss.append(sum((self.y - self.output)**2))
        print("loss is {}".format(loss))

#         print(sum((self.y - self.output)**2))
#         print(self.output)

    def backprop(self):
        # application of the chain rule to find derivative of the loss function with respect to weights2 and weights1
        d_weights2 = np.dot(self.layer1.T, (2*(self.y - self.output) * sigmoid_derivative(self.output)))
        d_weights1 = np.dot(self.input.T,  (np.dot(2*(self.y - self.output) * sigmoid_derivative(self.output), 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


if __name__ == "__main__":
    X = np.array([[0,0,1],
                  [0,1,1],
                  [1,0,1],
                  [1,1,1]])
    y = np.array([[0],[1],[1],[0]])
    nn = NeuralNetwork(X,y)

    for i in range(1500):
        nn.feedforward()
        nn.backprop()

    print(nn.output)


# TypeError                                 Traceback (most recent call last)
# <ipython-input-22-78313d1742df> in <module>()
#      46 
#      47     for i in range(1500):
# ---> 48         nn.feedforward()
#      49         nn.backprop()
#      50 

# TypeError: feedforward() missing 1 required positional argument: 'loss'

Answer 1

Вопрос : Что ... делать ... для построения графика с глобальной переменной loss?

Вместо использования global, make loss a class instance attribute.

class NeuralNetwork:
    def __init__(self, x, y):
        ...
        self.loss = []

    def feedforward(self):
        ...    
        selfloss.append(sum((self.y - self.output)**2))

Отредактировано с графиком:

    import numpy as np

    def sigmoid(x):
        return 1.0/(1+ np.exp(-x))

    def sigmoid_derivative(x):
        return x * (1.0 - x)

    class NeuralNetwork:
        def __init__(self, x, y):
            self.input      = x
            self.weights1   = np.random.rand(self.input.shape[1],4) 
            self.weights2   = np.random.rand(4,1)                 
            self.y          = y
            self.output     = np.zeros(self.y.shape)
            self.loss = []

        def feedforward(self):
            self.layer1 = sigmoid(np.dot(self.input, self.weights1))
            self.output = sigmoid(np.dot(self.layer1, self.weights2))
            self.loss.extend(sum((self.y - self.output)**2))

        def backprop(self):
            # application of the chain rule to find derivative of the loss function with respect to weights2 and weights1
            d_weights2 = np.dot(self.layer1.T, (2*(self.y - self.output) * sigmoid_derivative(self.output)))
            d_weights1 = np.dot(self.input.T,  (np.dot(2*(self.y - self.output) * sigmoid_derivative(self.output), 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


    if __name__ == "__main__":
        X = np.array([[0,0,1],
                      [0,1,1],
                      [1,0,1],
                      [1,1,1]])
        y = np.array([[0],[1],[1],[0]])
        nn = NeuralNetwork(X,y)

        iters = 1500 
        for i in range(iters):
            nn.feedforward()
            nn.backprop()

        import matplotlib.pyplot as plt
        y = nn.loss
        x = range(0, iters)
        plt.plot(x, y)
        plt.show()

        print(nn.output)

Answer 2

Вместо того, чтобы использовать глобальную переменную в своем классе, вы можете вернуть убыток вместо

    def feedforward(self):
        self.layer1 = sigmoid(np.dot(self.input, self.weights1))
        self.output = sigmoid(np.dot(self.layer1, self.weights2))

        return sum((self.y - self.output)**2)

, тогда должно быть достаточно следующего:

    lost = []
    for i in range(1500):
        lost.append(nn.feedforward())
        nn.backprop()

Отредактировано с графиком:

    import numpy as np

    def sigmoid(x):
        return 1.0/(1+ np.exp(-x))

    def sigmoid_derivative(x):
        return x * (1.0 - x)

    class NeuralNetwork:
        def __init__(self, x, y):
            self.input      = x
            self.weights1   = np.random.rand(self.input.shape[1],4) 
            self.weights2   = np.random.rand(4,1)                 
            self.y          = y
            self.output     = np.zeros(self.y.shape)

        def feedforward(self):
            self.layer1 = sigmoid(np.dot(self.input, self.weights1))
            self.output = sigmoid(np.dot(self.layer1, self.weights2))

            return sum((self.y - self.output)**2)[0]

        def backprop(self):
            # application of the chain rule to find derivative of the loss function with respect to weights2 and weights1
            d_weights2 = np.dot(self.layer1.T, (2*(self.y - self.output) * sigmoid_derivative(self.output)))
            d_weights1 = np.dot(self.input.T,  (np.dot(2*(self.y - self.output) * sigmoid_derivative(self.output), 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


    if __name__ == "__main__":
        X = np.array([[0,0,1],
                      [0,1,1],
                      [1,0,1],
                      [1,1,1]])
        y = np.array([[0],[1],[1],[0]])
        nn = NeuralNetwork(X,y)

        iters = 1500
        lost = []
        for i in range(iters):
            lost.append(nn.feedforward())
            nn.backprop()

        import matplotlib.pyplot as plt
        y = lost
        x = range(0, iters)
        plt.plot(x, y)
        plt.show()

        print(nn.output)