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July 13, 2020 02:58
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# Defining the sigmoid function for activations | |
def sigmoid(x): | |
return 1/(1+np.exp(-x)) | |
# Derivative of the sigmoid function | |
def sigmoid_prime(x): | |
return sigmoid(x) * (1 - sigmoid(x)) | |
# Input data | |
x = np.array([0.1, 0.3]) | |
# Target | |
y = 0.2 | |
# Input to output weights | |
weights = np.array([-0.8, 0.5]) | |
# The learning rate, eta in the weight step equation | |
learnrate = 0.5 | |
# the linear combination performed by the node (h in f(h) and f'(h)) | |
h = x[0]*weights[0] + x[1]*weights[1] | |
# or h = np.dot(x, weights) | |
# The neural network output (y-hat) | |
nn_output = sigmoid(h) | |
# output error (y - y-hat) | |
error = y - nn_output | |
# output gradient (f'(h)) | |
output_grad = sigmoid_prime(h) | |
# error term (lowercase delta) | |
error_term = error * output_grad | |
# Gradient descent step | |
del_w = [ learnrate * error_term * x[0], | |
learnrate * error_term * x[1]] | |
# or del_w = learnrate * error_term * x |
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