Ann Neural Network--sigmoid activation function programming exercise (Python implementation)

# ----------# # There is functions to finish:# First, in Activate (), write the sigmoid activation function.# Second, in Update (), write the gradient descent update rule. Updates should be# performed online, revising the weights after each data point.# # ----------ImportNumPy asNpclassSigmoid:"""This class models a artificial neuron with sigmoid activation function.    """    def __init__( Self, weights=Np.array ([1])):"""Initialize weights based on input arguments. Note that no type-checkingis being performed here for simplicity of code.        """         Self. Weights=Weights# note:you don't need to worry about these, attribues for this        # Programming Quiz, but these'll be a useful for if you want to create        # A network out of these sigmoid units!         Self. last_input= 0 # strength of last input         Self. Delta= 0 # Error Signal    defActivate Self, values):"""Takes in @param values, a list of numbers equal to length of weights.@return The output of a sigmoid unit with given inputs based on unitweights.        """                # YOUR CODE here                        # First calculate the strength of the input signal.Strength=Np.dot (values, Self. Weights) Self. last_input=Strength# Todo:modify Strength using the sigmoid activation function and        # return as output signal.        # hint:you Want to create a helper function to compute the        # Logistic function since you'll need it for the update function.Result=  Self. Logistic (Strength)returnResultdefLogistic Self, strength):return 1/(1+Np.exp (-Strength))defUpdate Self, values, train, ETA=.1):"""Takes in a 2D array @param values consisting of a LIST of inputs and a1D Array @param train, consisting of a corresponding list of expectedoutputs. Updates internal weights According to gradient descent usingthese values and an optional learning rate, @param eta.        """        # Todo:for Each data point ...         forX, Y_trueinch Zip(Values, train):# Obtain the output signal for theY_pred=  Self. Activate (X)# YOUR CODE here            # Todo:compute derivative of logistic function at input strength            # RECALL:D/DX Logistic (x) = Logistic (x) * (1-logistic (x))Dx=  Self. Logistic ( Self. Last_input)*(1 -  Self. Logistic ( Self. Last_input))Print("dx{}:".format(DX))Print('\ n')# Todo:update Self.weights based on learning, signal accuracy,            # function slope (derivative) and input valueDelta_w=Eta*(Y_true-y_pred)*Dx*XPrint("delta_w:{} weight before {}".format(Delta_w, Self. Weights)) Self. Weights+=Delta_wPrint("delta_w:{} weight after {}".format(Delta_w, Self. Weights))Print('\ n')defTest ():"""A Few tests to make sure, the Perceptron class performs as expected.Nothing should show on the output if all the assertions pass.    """    defSum_almost_equal (Array1, Array2, tol= 1e-5):return sum(ABS(array1-Array2))<Tol U1=Sigmoid (weights=[3,-2,1])assert ABS(U1.activate (Np.array ([1,2,3]))- 0.880797)< 1e-5U1.update (Np.array ([[1,2,3]]), Np.array ([0]))assertSum_almost_equal (U1.weights, Np.array ([2.990752,-2.018496,0.972257])) U2=Sigmoid (weights=[0,3,-1]) U2.update (Np.array ([[-3,-1,2],[2,1,2]]), Np.array ([1,0]))assertSum_almost_equal (U2.weights, Np.array ([-0.030739,2.984961,-1.027437]))if __name__ == "__main__": Test ()

OUTPUT

Running Test () ... dx0. 104993585404:d elta_w:[-0.0092478  -0.01849561 -0.02774341] Weight before [3,-2,1]delta_w:[-0.0092478  -0.01849561 -0.02774341] weight after [2.9907522  -2.01849561  0.97225659]dx0. 00664805667079:d elta_w:[-0.00198107 -0.00066036  0.00132071] Weight before [0,3,-1]delta_w:[-0.00198107 -0.00066036  0.00132071] weight after [-1.98106867e-03   2.99933964e+00  -9.98679288e-01]dx0. 196791859198:d elta_w:[-0.02875794 -0.01437897 -0.02875794] Weight before [-1.98106867e-03   2.99933964e+00  -9.98679288e-01]delta_w:[-0.02875794 -0.01437897 -0.02875794] weight after [-0.03073901  2.98496067 -1.02743723]all Done!

Ann Neural Network--sigmoid activation function programming exercise (Python implementation)