01神经网络和深度学习-Building your Deep Neural Network: Step by Step-第四周编程作业1

Myth丶恋晨 2022-05-12 10:54 178阅读 0赞

整个模型中使用的（激活）函数的结构如下：

**\[LINEAR -> RELU\] × (L-1) -> LINEAR -> SIGMOID**

即：

执行L-1次使用Relu激活函数的前向传播，执行一次使用sigmoid激活函数的前向传播；

执行一次使用sigmoid激活函数的后向传播，执行L-1次使用Relu激活函数的后向传播；

使用梯度更新参数。

#coding=utf-8
    import numpy as np
    import h5py
    import matplotlib.pyplot as plt
    from testCases_v2 import *
    from dnn_utils_v2 import sigmoid, sigmoid_backward, relu, relu_backward
    
    plt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of plots
    plt.rcParams['image.interpolation'] = 'nearest'
    plt.rcParams['image.cmap'] = 'gray'
    
    np.random.seed(1)
    
    # GRADED FUNCTION: initialize_parameters
    
    def initialize_parameters(n_x, n_h, n_y):
        """
        Argument:
        n_x -- size of the input layer
        n_h -- size of the hidden layer
        n_y -- size of the output layer
        
        Returns:
        parameters -- python dictionary containing your parameters:
                        W1 -- weight matrix of shape (n_h, n_x)
                        b1 -- bias vector of shape (n_h, 1)
                        W2 -- weight matrix of shape (n_y, n_h)
                        b2 -- bias vector of shape (n_y, 1)
        """
        
        np.random.seed(1)
        
        ### START CODE HERE ### (≈ 4 lines of code)
        W1 = np.random.randn(n_h, n_x) * 0.01
        b1 = np.zeros((n_h, 1))
        W2 = np.random.randn(n_y, n_h) * 0.01
        b2 = np.zeros((n_y, 1))
        ### END CODE HERE ###
        
        assert(W1.shape == (n_h, n_x))
        assert(b1.shape == (n_h, 1))
        assert(W2.shape == (n_y, n_h))
        assert(b2.shape == (n_y, 1))
        
        parameters = {"W1": W1,
                      "b1": b1,
                      "W2": W2,
                      "b2": b2}
        
        return parameters 
    
    # GRADED FUNCTION: initialize_parameters_deep
    
    def initialize_parameters_deep(layer_dims):
        """
        Arguments:
        layer_dims -- python array (list) containing the dimensions of each layer in our network
        
        Returns:
        parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                        Wl -- weight matrix of shape (layer_dims[l], layer_dims[l-1])
                        bl -- bias vector of shape (layer_dims[l], 1)
        """
        
        np.random.seed(3)
        parameters = {}
        L = len(layer_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.random.randn(layer_dims[l], layer_dims[l-1]) * 0.01
            parameters['b' + str(l)] = np.zeros((layer_dims[l], 1))
            ### END CODE HERE ###
            
            assert(parameters['W' + str(l)].shape == (layer_dims[l], layer_dims[l-1]))
            assert(parameters['b' + str(l)].shape == (layer_dims[l], 1))
    
            
        return parameters    
    
    # GRADED FUNCTION: linear_forward
    
    def linear_forward(A, W, b):
        """
        Implement the linear part of a layer's forward propagation.
    
        Arguments:
        A -- activations from previous layer (or input data): (size of previous layer, number of examples)
        W -- weights matrix: numpy array of shape (size of current layer, size of previous layer)
        b -- bias vector, numpy array of shape (size of the current layer, 1)
    
        Returns:
        Z -- the input of the activation function, also called pre-activation parameter 
        cache -- a python dictionary containing "A", "W" and "b" ; stored for computing the backward pass efficiently
        """
        
        ### START CODE HERE ### (≈ 1 line of code)
        Z = W.dot(A) + b
        ### END CODE HERE ###
        
        assert(Z.shape == (W.shape[0], A.shape[1]))
        cache = (A, W, b)
        
        return Z, cache
        
    # GRADED FUNCTION: linear_activation_forward
    
    def linear_activation_forward(A_prev, W, b, activation):
        """
        Implement the forward propagation for the LINEAR->ACTIVATION layer
    
        Arguments:
        A_prev -- activations from previous layer (or input data): (size of previous layer, number of examples)
        W -- weights matrix: numpy array of shape (size of current layer, size of previous layer)
        b -- bias vector, numpy array of shape (size of the current layer, 1)
        activation -- the activation to be used in this layer, stored as a text string: "sigmoid" or "relu"
    
        Returns:
        A -- the output of the activation function, also called the post-activation value 
        cache -- a python dictionary containing "linear_cache" and "activation_cache";
                 stored for computing the backward pass efficiently
        """
        
        if activation == "sigmoid":
            # Inputs: "A_prev, W, b". Outputs: "A, activation_cache".
            ### START CODE HERE ### (≈ 2 lines of code)
            Z, linear_cache = linear_forward(A_prev, W, b)
            A, activation_cache = sigmoid(Z)
            ### END CODE HERE ###
        
        elif activation == "relu":
            # Inputs: "A_prev, W, b". Outputs: "A, activation_cache".
            ### START CODE HERE ### (≈ 2 lines of code)
            Z, linear_cache = linear_forward(A_prev, W, b)
            A, activation_cache = relu(Z)
            ### END CODE HERE ###
        
        assert (A.shape == (W.shape[0], A_prev.shape[1]))
        cache = (linear_cache, activation_cache)
    
        return A, cache    
      
    # GRADED FUNCTION: L_model_forward
    
    def L_model_forward(X, parameters):
        """
        Implement forward propagation for the [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID computation
        
        Arguments:
        X -- data, numpy array of shape (input size, number of examples)
        parameters -- output of initialize_parameters_deep()
        
        Returns:
        AL -- last post-activation value
        caches -- list of caches containing:
                    every cache of linear_relu_forward() (there are L-1 of them, indexed from 0 to L-2)
                    the cache of linear_sigmoid_forward() (there is one, indexed L-1)
        """
    
        caches = []
        A = X
        L = len(parameters) // 2                  # number of layers in the neural network
        
        # Implement [LINEAR -> RELU]*(L-1). Add "cache" to the "caches" list.
        for l in range(1, L):
            A_prev = A 
            ### START CODE HERE ### (≈ 2 lines of code)
            A, cache = linear_activation_forward(A_prev, parameters['W' + str(l)], parameters['b' + str(l)], 'relu')
            caches.append(cache)
            ### END CODE HERE ###
        
        # Implement LINEAR -> SIGMOID. Add "cache" to the "caches" list.
        ### START CODE HERE ### (≈ 2 lines of code)
        AL, cache = linear_activation_forward(A, parameters['W' + str(L)], parameters['b' + str(L)], 'sigmoid')
        caches.append(cache)
        ### END CODE HERE ###
        
        assert(AL.shape == (1,X.shape[1]))
                
        return AL, caches
    
    # GRADED FUNCTION: compute_cost
    
    def compute_cost(AL, Y):
        """
        Implement the cost function defined by equation (7).
    
        Arguments:
        AL -- probability vector corresponding to your label predictions, shape (1, number of examples)
        Y -- true "label" vector (for example: containing 0 if non-cat, 1 if cat), shape (1, number of examples)
    
        Returns:
        cost -- cross-entropy cost
        """
        
        m = Y.shape[1]
    
        # Compute loss from aL and y.
        ### START CODE HERE ### (≈ 1 lines of code)
        cost = - 1.0 / m * np.sum(Y * np.log(AL) + (1 - Y) * np.log(1 - AL) )
        ### END CODE HERE ###
        
        cost = np.squeeze(cost)      # To make sure your cost's shape is what we expect (e.g. this turns [[17]] into 17).
        assert(cost.shape == ())
        
        return cost
    
    # GRADED FUNCTION: linear_backward
    
    def linear_backward(dZ, cache):
        """
        Implement the linear portion of backward propagation for a single layer (layer l)
    
        Arguments:
        dZ -- Gradient of the cost with respect to the linear output (of current layer l)
        cache -- tuple of values (A_prev, W, b) coming from the forward propagation in the current layer
    
        Returns:
        dA_prev -- Gradient of the cost with respect to the activation (of the previous layer l-1), same shape as A_prev
        dW -- Gradient of the cost with respect to W (current layer l), same shape as W
        db -- Gradient of the cost with respect to b (current layer l), same shape as b
        """
        A_prev, W, b = cache
        m = A_prev.shape[1]
        
        ### START CODE HERE ### (≈ 3 lines of code)
        dW = 1.0 / m * dZ.dot(A_prev.T)
        db = 1.0 / m * np.sum(dZ, axis = 1, keepdims = True)
        dA_prev = (W.T).dot(dZ) 
        ### END CODE HERE ###
        
        assert (dA_prev.shape == A_prev.shape)
        assert (dW.shape == W.shape)
        assert (db.shape == b.shape)
        
        return dA_prev, dW, db
    
    # GRADED FUNCTION: linear_activation_backward
    
    def linear_activation_backward(dA, cache, activation):
        """
        Implement the backward propagation for the LINEAR->ACTIVATION layer.
        
        Arguments:
        dA -- post-activation gradient for current layer l 
        cache -- tuple of values (linear_cache, activation_cache) we store for computing backward propagation efficiently
        activation -- the activation to be used in this layer, stored as a text string: "sigmoid" or "relu"
        
        Returns:
        dA_prev -- Gradient of the cost with respect to the activation (of the previous layer l-1), same shape as A_prev
        dW -- Gradient of the cost with respect to W (current layer l), same shape as W
        db -- Gradient of the cost with respect to b (current layer l), same shape as b
        """
        linear_cache, activation_cache = cache
        
        if activation == "relu":
            ### START CODE HERE ### (≈ 2 lines of code)
            dZ = relu_backward(dA, activation_cache)
            dA_prev, dW, db = linear_backward(dZ, linear_cache)
            ### END CODE HERE ###
            
        elif activation == "sigmoid":
            ### START CODE HERE ### (≈ 2 lines of code)
            dZ = sigmoid_backward(dA, activation_cache)
            dA_prev, dW, db = linear_backward(dZ, linear_cache)
            ### END CODE HERE ###
        
        return dA_prev, dW, db
        
    # GRADED FUNCTION: L_model_backward
    
    def L_model_backward(AL, Y, caches):
        """
        Implement the backward propagation for the [LINEAR->RELU] * (L-1) -> LINEAR -> SIGMOID group
        
        Arguments:
        AL -- probability vector, output of the forward propagation (L_model_forward())
        Y -- true "label" vector (containing 0 if non-cat, 1 if cat)
        caches -- list of caches containing:
                    every cache of linear_activation_forward() with "relu" (it's caches[l], for l in range(L-1) i.e l = 0...L-2)
                    the cache of linear_activation_forward() with "sigmoid" (it's caches[L-1])
        
        Returns:
        grads -- A dictionary with the gradients
                 grads["dA" + str(l)] = ...
                 grads["dW" + str(l)] = ...
                 grads["db" + str(l)] = ...
        """
        grads = {}
        L = len(caches) # the number of layers
        m = AL.shape[1]
        Y = Y.reshape(AL.shape) # after this line, Y is the same shape as AL
    
        # Initializing the backpropagation
        ### START CODE HERE ### (1 line of code)
        dAL = - (np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))
        ### END CODE HERE ###
        
        # Lth layer (SIGMOID -> LINEAR) gradients. Inputs: "AL, Y, caches". Outputs: "grads["dAL"], grads["dWL"], grads["dbL"]
        ### START CODE HERE ### (approx. 2 lines)
        current_cache = caches[L - 1]
        grads["dA" + str(L)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL, current_cache, activation = "sigmoid")
        ### END CODE HERE ###
        
        for l in reversed(range(L - 1)):
            # lth layer: (RELU -> LINEAR) gradients.
            # Inputs: "grads["dA" + str(l + 2)], caches". Outputs: "grads["dA" + str(l + 1)] , grads["dW" + str(l + 1)] , grads["db" + str(l + 1)] 
            ### START CODE HERE ### (approx. 5 lines)
            current_cache = caches[l]
            dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(l + 2)], current_cache, activation = "relu")
            grads["dA" + str(l + 1)] = dA_prev_temp
            grads["dW" + str(l + 1)] = dW_temp
            grads["db" + str(l + 1)] = db_temp
            ### END CODE HERE ###
    
        return grads
     
    # GRADED FUNCTION: update_parameters
    
    def update_parameters(parameters, grads, learning_rate):
        """
        Update parameters using gradient descent
        
        Arguments:
        parameters -- python dictionary containing your parameters 
        grads -- python dictionary containing your gradients, output of L_model_backward
        
        Returns:
        parameters -- python dictionary containing your updated parameters 
                      parameters["W" + str(l)] = ... 
                      parameters["b" + str(l)] = ...
        """
        
        L = len(parameters) // 2 # number of layers in the neural network
    
        # Update rule for each parameter. Use a for loop.
        ### START CODE HERE ### (≈ 3 lines of code)
        for l in range(L):
            parameters["W" + str(l + 1)] = parameters["W" + str(l + 1)] - learning_rate * grads["dW" + str(l + 1)]
            parameters["b" + str(l + 1)] = parameters["b" + str(l + 1)] - learning_rate * grads["db" + str(l + 1)]
        ### END CODE HERE ###
            
        return parameters
     
    if __name__=='__main__':  
        parameters = initialize_parameters(2,2,1)
        print("W1 = " + str(parameters["W1"]))
        print("b1 = " + str(parameters["b1"]))
        print("W2 = " + str(parameters["W2"]))
        print("b2 = " + str(parameters["b2"]))
        
        parameters = initialize_parameters_deep([5,4,3] )
        print("W1 = " + str(parameters["W1"]))
        print("b1 = " + str(parameters["b1"]))
        print("W2 = " + str(parameters["W2"]))
        print("b2 = " + str(parameters["b2"]))
        
        A, W, b = linear_forward_test_case()
        Z, linear_cache = linear_forward(A, W, b)
        print("Z = " + str(Z))
        
        A_prev, W, b = linear_activation_forward_test_case()
        A, linear_activation_cache = linear_activation_forward(A_prev, W, b, activation = "sigmoid")
        print("With sigmoid: A = " + str(A))
        A, linear_activation_cache = linear_activation_forward(A_prev, W, b, activation = "relu")
        print("With ReLU: A = " + str(A))
        
        X, parameters = L_model_forward_test_case()
        AL, caches = L_model_forward(X, parameters)
        print("AL = " + str(AL))
        print("Length of caches list = " + str(len(caches)))
    
        Y, AL = compute_cost_test_case()
        print("cost = " + str(compute_cost(AL, Y)))
    
        # Set up some test inputs
        dZ, linear_cache = linear_backward_test_case()
        dA_prev, dW, db = linear_backward(dZ, linear_cache)
        print ("dA_prev = "+ str(dA_prev))
        print ("dW = " + str(dW))
        print ("db = " + str(db))
    
        AL, linear_activation_cache = linear_activation_backward_test_case()
    
        dA_prev, dW, db = linear_activation_backward(AL, linear_activation_cache, activation = "sigmoid")
        print ("sigmoid:")
        print ("dA_prev = "+ str(dA_prev))
        print ("dW = " + str(dW))
        print ("db = " + str(db) + "\n")
        
        dA_prev, dW, db = linear_activation_backward(AL, linear_activation_cache, activation = "relu")
        print ("relu:")
        print ("dA_prev = "+ str(dA_prev))
        print ("dW = " + str(dW))
        print ("db = " + str(db))
    
        AL, Y_assess, caches = L_model_backward_test_case()
        grads = L_model_backward(AL, Y_assess, caches)
        print ("dW1 = "+ str(grads["dW1"]))
        print ("db1 = "+ str(grads["db1"]))
        print ("dA1 = "+ str(grads["dA1"]))
        
        parameters, grads = update_parameters_test_case()
        parameters = update_parameters(parameters, grads, 0.1)
    
        print ("W1 = "+ str(parameters["W1"]))
        print ("b1 = "+ str(parameters["b1"]))
        print ("W2 = "+ str(parameters["W2"]))
        print ("b2 = "+ str(parameters["b2"]))

运行结果：

![70][]

[70]: /images/20220512/ffb0636d103e4f1299b633bfa00f2725.png