《深度学习——Andrew Ng》第二课第一周编程作业

Initialization

作业通过三种不同的初始化参数的方式（zero、random、he），对神经网络进行参数初始化，通过对比，得出每种初始化方式的特征。最后结论为he初始化是最好的方式。

程序

原始数据集：

import numpy as npimport matplotlib.pyplot as pltimport sklearnimport sklearn.datasetsfrom init_utils import sigmoid, relu, compute_loss, forward_propagation, backward_propagationfrom init_utils import update_parameters, predict, load_dataset, plot_decision_boundary, predict_dec#%matplotlib inlineplt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plotsplt.rcParams['image.interpolation'] = 'nearest'plt.rcParams['image.cmap'] = 'gray'# load image dataset: blue/red dots in circlestrain_X, train_Y, test_X, test_Y = load_dataset()def model(X, Y, learning_rate=0.01, num_iterations=15000, print_cost=True, initialization="he"):    """    Implements a three-layer neural network: LINEAR->RELU->LINEAR->RELU->LINEAR->SIGMOID.    Arguments:    X -- input data, of shape (2, number of examples)    Y -- true "label" vector (containing 0 for red dots; 1 for blue dots), of shape (1, number of examples)    learning_rate -- learning rate for gradient descent    num_iterations -- number of iterations to run gradient descent    print_cost -- if True, print the cost every 1000 iterations    initialization -- flag to choose which initialization to use ("zeros","random" or "he")    Returns:    parameters -- parameters learnt by the model    """    grads = {}    costs = []  # to keep track of the loss    m = X.shape[1]  # number of examples    layers_dims = [X.shape[0], 10, 5, 1]    # Initialize parameters dictionary.    if initialization == "zeros":        parameters = initialize_parameters_zeros(layers_dims)    elif initialization == "random":        parameters = initialize_parameters_random(layers_dims)    elif initialization == "he":        parameters = initialize_parameters_he(layers_dims)    # Loop (gradient descent)    for i in range(0, num_iterations):        # Forward propagation: LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID.        a3, cache = forward_propagation(X, parameters)        # Loss        cost = compute_loss(a3, Y)        # Backward propagation.        grads = backward_propagation(X, Y, cache)        # Update parameters.        parameters = update_parameters(parameters, grads, learning_rate)        # Print the loss every 1000 iterations        if print_cost and i % 1000 == 0:            print("Cost after iteration {}: {}".format(i, cost))            costs.append(cost)    # plot the loss    plt.plot(costs)    plt.ylabel('cost')    plt.xlabel('iterations (per hundreds)')    plt.title("Learning rate =" + str(learning_rate))    plt.show()    return parameters# GRADED FUNCTION: initialize_parameters_zerosdef initialize_parameters_zeros(layers_dims):    """    Arguments:    layer_dims -- python array (list) containing the size of each layer.    Returns:    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])                    b1 -- bias vector of shape (layers_dims[1], 1)                    ...                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])                    bL -- bias vector of shape (layers_dims[L], 1)    """    parameters = {}    L = len(layers_dims)  # number of layers in the network    for l in range(1, L):        ### START CODE HERE ### (≈ 2 lines of code)        parameters['W' + str(l)] = np.zeros((layers_dims[l], layers_dims[l - 1]))        parameters['b' + str(l)] = np.zeros((layers_dims[l], 1))        ### END CODE HERE ###    return parametersprint("******************** zero initialization ****************")parameters = model(train_X, train_Y, initialization = "zeros")print ("On the train set:")predictions_train = predict(train_X, train_Y, parameters)print ("On the test set:")predictions_test = predict(test_X, test_Y, parameters)# GRADED FUNCTION: initialize_parameters_randomdef initialize_parameters_random(layers_dims):    """    Arguments:    layer_dims -- python array (list) containing the size of each layer.    Returns:    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])                    b1 -- bias vector of shape (layers_dims[1], 1)                    ...                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])                    bL -- bias vector of shape (layers_dims[L], 1)    """    np.random.seed(3)  # This seed makes sure your "random" numbers will be the as ours    parameters = {}    L = len(layers_dims)  # integer representing the number of layers    for l in range(1, L):        ### START CODE HERE ### (≈ 2 lines of code)        parameters['W' + str(l)] = np.random.randn(layers_dims[l], layers_dims[l - 1]) * 10        parameters['b' + str(l)] = np.zeros((layers_dims[l], 1))        ### END CODE HERE ###    return parametersprint("******************** random initialization ****************")parameters = model(train_X, train_Y, initialization = "random")print ("On the train set:")predictions_train = predict(train_X, train_Y, parameters)print ("On the test set:")predictions_test = predict(test_X, test_Y, parameters)# GRADED FUNCTION: initialize_parameters_hedef initialize_parameters_he(layers_dims):    """    Arguments:    layer_dims -- python array (list) containing the size of each layer.    Returns:    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])                    b1 -- bias vector of shape (layers_dims[1], 1)                    ...                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])                    bL -- bias vector of shape (layers_dims[L], 1)    """    np.random.seed(3)    parameters = {}    L = len(layers_dims) - 1  # integer representing the number of layers    for l in range(1, L + 1):        ### START CODE HERE ### (≈ 2 lines of code)        parameters['W' + str(l)] = np.random.randn(layers_dims[l], layers_dims[l - 1]) * np.sqrt(            2. / layers_dims[l - 1])        parameters['b' + str(l)] = np.zeros((layers_dims[l], 1))        ### END CODE HERE ###    return parametersprint("******************** He initialization ****************")parameters = model(train_X, train_Y, initialization = "he")print ("On the train set:")predictions_train = predict(train_X, train_Y, parameters)print ("On the test set:")predictions_test = predict(test_X, test_Y, parameters)

运行结果

********** zero initialization ******
Cost after iteration 0: 0.6931471805599453
Cost after iteration 1000: 0.6931471805599453
Cost after iteration 2000: 0.6931471805599453
Cost after iteration 3000: 0.6931471805599453
Cost after iteration 4000: 0.6931471805599453
Cost after iteration 5000: 0.6931471805599453
Cost after iteration 6000: 0.6931471805599453
Cost after iteration 7000: 0.6931471805599453
Cost after iteration 8000: 0.6931471805599453
Cost after iteration 9000: 0.6931471805599453
Cost after iteration 10000: 0.6931471805599455
Cost after iteration 11000: 0.6931471805599453
Cost after iteration 12000: 0.6931471805599453
Cost after iteration 13000: 0.6931471805599453
Cost after iteration 14000: 0.6931471805599453
On the train set:
Accuracy: 0.5
On the test set:
Accuracy: 0.5

********** random initialization ******
Cost after iteration 0: inf
Cost after iteration 1000: 0.6239560077799974
Cost after iteration 2000: 0.5981988756495555
Cost after iteration 3000: 0.5639165098349239
Cost after iteration 4000: 0.5501730606234159
Cost after iteration 5000: 0.5444478976702423
Cost after iteration 6000: 0.5374387172653514
Cost after iteration 7000: 0.47472803691077003
Cost after iteration 8000: 0.397783817035777
Cost after iteration 9000: 0.39347128330744535
Cost after iteration 10000: 0.39202801461972386
Cost after iteration 11000: 0.389225947340669
Cost after iteration 12000: 0.38615256867920933
Cost after iteration 13000: 0.3849845104125972
Cost after iteration 14000: 0.3827782795015039
On the train set:
Accuracy: 0.83
On the test set:
Accuracy: 0.86

********** He initialization ******
Cost after iteration 0: 0.8830537463419761
Cost after iteration 1000: 0.6879825919728063
Cost after iteration 2000: 0.6751286264523371
Cost after iteration 3000: 0.6526117768893807
Cost after iteration 4000: 0.6082958970572938
Cost after iteration 5000: 0.5304944491717495
Cost after iteration 6000: 0.4138645817071794
Cost after iteration 7000: 0.31178034648444414
Cost after iteration 8000: 0.23696215330322562
Cost after iteration 9000: 0.1859728720920683
Cost after iteration 10000: 0.1501555628037181
Cost after iteration 11000: 0.12325079292273544
Cost after iteration 12000: 0.09917746546525931
Cost after iteration 13000: 0.08457055954024274
Cost after iteration 14000: 0.07357895962677363
On the train set:
Accuracy: 0.993333333333
On the test set:
Accuracy: 0.96

Process finished with exit code 0

结论

You have seen three different types of initializations. For the same number of iterations and same hyperparameters the comparison is:

**Model** **Train accuracy** **Problem/Comment** 3-layer NN with zeros initialization 50% fails to break symmetry 3-layer NN with large random initialization 83% too large weights 3-layer NN with He initialization 99% recommended method

What you should remember from this notebook:
- Different initializations lead to different results
- Random initialization is used to break symmetry and make sure different hidden units can learn different things
- Don’t intialize to values that are too large
- He initialization works well for networks with ReLU activations.