【deeplearning.ai】第二門課：提升深層神經網路——權重初始化
阿新 • • 發佈：2019-01-03
一、初始化
合理的權重初始化可以防止梯度爆炸和消失。對於ReLu啟用函式，權重可初始化為：
也叫作“He初始化”。對於tanh啟用函式，權重初始化為：
也稱為“Xavier初始化”。也可以使用下面這個公式進行初始化：
上述公式中的l指當前處在神經網路的第幾層，l-1為上一層。
二、程式設計作業
有如下二維資料：
訓練網路正確分類紅點和藍點。匯入需要的擴充套件包，其中init_utils.py在這裡下載
import numpy as np import matplotlib.pyplot as plt import sklearn import sklearn.datasets from init_utils import sigmoid, relu, compute_loss, forward_propagation, backward_propagation from init_utils import update_parameters, predict, load_dataset, plot_decision_boundary, predict_dec %matplotlib inline plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots plt.rcParams['image.interpolation'] = 'nearest' plt.rcParams['image.cmap'] = 'gray' # load image dataset: blue/red dots in circles train_X, train_Y, test_X, test_Y = load_dataset()
1、建立神經網路模型
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
2、將權重初始化為0
def 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): parameters['W' + str(l)] = np.zeros((layers_dims[l], layers_dims[l-1])) parameters['b' + str(l)] = np.zeros((layers_dims[l], 1)) return parameters
訓練網路：
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)訓練完成後繪製的cost曲線：
訓練準確率為0.5，測試準確率為0.5,。將測試集的預測結果輸出：
畫出分類界線：
這個模型將所有測試集都預測成了0，將權重初始化為0使網路沒有打破平衡，每個神經元都學到了相同的東西。
3、將權重隨機初始化為較大的數
def 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):
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))
return parameters訓練這個模型，得到cost曲線：
訓練集準確率為0.83，測試集準確率為0.86。分類界線如下：
可以看出cost一開始很大，是因為權重初始化得較大，使某些樣本的輸出（sigmoid啟用函式）非常接近0或1。糟糕的初始化可能導致梯度爆炸或消失，同時降低訓練速度。
4、使用He初始化
def 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):
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))
return parameterscost曲線：
訓練集的準確率為0.9933333，測試集的準確率為0.96。分類界線：
可以看出合理的權重初始化使網路效能得到了很好的改善。