文章目錄

• • 作業1：實現卷積神經網絡
  • • 1. 導入一些包
    • 2. 模型框架
    • 3. 卷積神經網絡
    • • 3.1 Zero-Padding
      • 3.2 單步卷積
      • 3.3 卷積神經網絡 - 前向傳播
    • 4. 池化層
    • 5. 卷積神經網絡 - 反向傳播
    • • 5.1 卷積層反向傳播
      • • 5.1.1 計算 dA
        • 5.1.2 計算 dW
        • 5.1.3 計算 db
      • 5.2 池化層 - 反向傳播
      • • 5.2.1 最大池化 - 反向傳播
        • 5.2.2 平均池化 - 反向傳播
        • 5.2.3 組合在一起 - 反向池化
  • 作業2：用TensorFlow實現卷積神經網絡
  • • 1. TensorFlow 模型
    • • 1.1 創建 placeholder
      • 1.2 初始化參數
      • 1.3 前向傳播
      • 1.4 計算損失
      • 1.5 模型

測試題：參考博文

筆記：04.卷積神經網絡 W1.卷積神經網絡

作業1：實現卷積神經網絡

1. 導入一些包

import numpy as np import h5py import matplotlib.pyplot as plt%matplotlib inline plt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of plots plt.rcParams['image.interpolation'] = 'nearest' plt.rcParams['image.cmap'] = 'gray'%load_ext autoreload %autoreload 2np.random.seed(1)

2. 模型框架

3. 卷積神經網絡

卷積神經網絡會將輸入轉化為一個維度大小不一樣的輸出

3.1 Zero-Padding

0 padding 會在圖片周圍填充 0 元素（下圖 $p=2$ ）

padding 的好處：

• 減少深層網絡里，圖片尺寸衰減問題
• 保留更多的圖片邊緣的信息

# 給第2、4個維度 padding 1層，3層像素 a = np.pad(a, ((0,0), (1,1), (0,0), (3,3), (0,0)), 'constant', constant_values = (..,..)) # GRADED FUNCTION: zero_paddef zero_pad(X, pad):"""Pad with zeros all images of the dataset X. The padding is applied to the height and width of an image, as illustrated in Figure 1.Argument:X -- python numpy array of shape (m, n_H, n_W, n_C) representing a batch of m imagespad -- integer, amount of padding around each image on vertical and horizontal dimensionsReturns:X_pad -- padded image of shape (m, n_H + 2*pad, n_W + 2*pad, n_C)"""### START CODE HERE ### (≈ 1 line)X_pad = np.pad(X, ((0,0), # 樣本(pad,pad), # 高(pad,pad), # 寬(0,0)),# 通道'constant', constant_values=(0))### END CODE HERE ###return X_pad

3.2 單步卷積

# GRADED FUNCTION: conv_single_stepdef conv_single_step(a_slice_prev, W, b):"""Apply one filter defined by parameters W on a single slice (a_slice_prev) of the output activation of the previous layer.Arguments:a_slice_prev -- slice of input data of shape (f, f, n_C_prev)W -- Weight parameters contained in a window - matrix of shape (f, f, n_C_prev)b -- Bias parameters contained in a window - matrix of shape (1, 1, 1)Returns:Z -- a scalar value, result of convolving the sliding window (W, b) on a slice x of the input data"""### START CODE HERE ### (≈ 2 lines of code)# Element-wise product between a_slice and W. Do not add the bias yet.s = a_slice_prev*W# Sum over all entries of the volume s.Z = np.sum(s)# Add bias b to Z. Cast b to a float() so that Z results in a scalar value.Z = Z + float(b)### END CODE HERE ###return Z

3.3 卷積神經網絡 - 前向傳播

$$n_H=?\frac{n_{H_{prev}}?f+2\times pad}{stride}?+1$$
$$n_W=?\frac{n_{W_{prev}}?f+2\times pad}{stride}?+1$$
$$n_C=\text{卷積過濾器數量}$$

# GRADED FUNCTION: conv_forwarddef conv_forward(A_prev, W, b, hparameters):"""Implements the forward propagation for a convolution functionArguments:A_prev -- output activations of the previous layer, numpy array of shape (m, n_H_prev, n_W_prev, n_C_prev)W -- Weights, numpy array of shape (f, f, n_C_prev, n_C)b -- Biases, numpy array of shape (1, 1, 1, n_C)hparameters -- python dictionary containing "stride" and "pad"Returns:Z -- conv output, numpy array of shape (m, n_H, n_W, n_C)cache -- cache of values needed for the conv_backward() function"""### START CODE HERE #### Retrieve dimensions from A_prev's shape (≈1 line) (m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape# Retrieve dimensions from W's shape (≈1 line)(f, f, n_C_prev, n_C) = W.shape# Retrieve information from "hparameters" (≈2 lines)stride = hparameters['stride']pad = hparameters['pad']# Compute the dimensions of the CONV output volume using the formula given above. # Hint: use int() to floor. (≈2 lines)n_H = (n_H_prev-f+2*pad)//stride + 1n_W = (n_W_prev-f+2*pad)//stride + 1# Initialize the output volume Z with zeros. (≈1 line)Z = np.zeros((m, n_H, n_W, n_C))# Create A_prev_pad by padding A_prevA_prev_pad = zero_pad(A_prev, pad)for i in range(m): # loop over the batch of training examplesa_prev_pad = A_prev_pad[i, :] # Select ith training example's padded activationfor h in range(n_H): # loop over vertical axis of the output volumefor w in range(n_W): # loop over horizontal axis of the output volumefor c in range(n_C): # loop over channels (= #filters) of the output volume# Find the corners of the current "slice" (≈4 lines)vert_start = h*stridevert_end = vert_start + fhoriz_start = w*stridehoriz_end = horiz_start + f# Use the corners to define the (3D) slice of a_prev_pad (See Hint above the cell). (≈1 line)a_slice_prev = a_prev_pad[vert_start:vert_end, horiz_start:horiz_end, :]# Convolve the (3D) slice with the correct filter W and bias b, to get back one output neuron. (≈1 line)Z[i, h, w, c] = np.sum(conv_single_step(a_slice_prev, W[:,:,:,c], b[:,:,:,c]))### END CODE HERE #### Making sure your output shape is correctassert(Z.shape == (m, n_H, n_W, n_C))# Save information in "cache" for the backpropcache = (A_prev, W, b, hparameters)return Z, cache

4. 池化層

池化層不改變通道數量，下面公式沒有padding， p = 0
$$n_H=?\frac{n_{H_{prev}}?f}{stride}?+1$$
$$n_W=?\frac{n_{W_{prev}}?f}{stride}?+1$$
$$n_C=n_{C_{prev}}$$

# GRADED FUNCTION: pool_forwarddef pool_forward(A_prev, hparameters, mode = "max"):"""Implements the forward pass of the pooling layerArguments:A_prev -- Input data, numpy array of shape (m, n_H_prev, n_W_prev, n_C_prev)hparameters -- python dictionary containing "f" and "stride"mode -- the pooling mode you would like to use, defined as a string ("max" or "average")Returns:A -- output of the pool layer, a numpy array of shape (m, n_H, n_W, n_C)cache -- cache used in the backward pass of the pooling layer, contains the input and hparameters """# Retrieve dimensions from the input shape(m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape# Retrieve hyperparameters from "hparameters"f = hparameters["f"]stride = hparameters["stride"]# Define the dimensions of the outputn_H = 1 + (n_H_prev - f) // striden_W = 1 + (n_W_prev - f) // striden_C = n_C_prev# Initialize output matrix AA = np.zeros((m, n_H, n_W, n_C)) ### START CODE HERE ###for i in range(m): # loop over the training examplesfor h in range(n_H): # loop on the vertical axis of the output volumefor w in range(n_W): # loop on the horizontal axis of the output volumefor c in range (n_C): # loop over the channels of the output volume# Find the corners of the current "slice" (≈4 lines)vert_start = h*stridevert_end = vert_start + fhoriz_start = w*stridehoriz_end = horiz_start + f# Use the corners to define the current slice on the ith training example of A_prev, channel c. (≈1 line)a_prev_slice = A_prev[i, vert_start:vert_end, horiz_start:horiz_end, c]# Compute the pooling operation on the slice. Use an if statment to differentiate the modes. Use np.max/np.mean.if mode == "max":A[i, h, w, c] = np.max(a_prev_slice)elif mode == "average":A[i, h, w, c] = np.mean(a_prev_slice)### END CODE HERE #### Store the input and hparameters in "cache" for pool_backward()cache = (A_prev, hparameters)# Making sure your output shape is correctassert(A.shape == (m, n_H, n_W, n_C))return A, cache

5. 卷積神經網絡 - 反向傳播

現代機器學習框架一般都會自動幫你實現反向傳播，下面再過一遍

5.1 卷積層反向傳播

5.1.1 計算 dA

$$dA+=\sum _{h=0}^{n_H}\sum _{w=0}^{n_W}{W}_c\times d{Z}_{hw}$$

• $W_c$ 是一個過濾器，$d{Z}_{hw}$ 是輸出的卷積層 $Z$ 的（h，w）位置的梯度

代碼：

da_prev_pad[vert_start:vert_end, horiz_start:horiz_end, :] += W[:,:,:,c] * dZ[i, h, w, c]

5.1.2 計算 dW

$$d{W}_c+=\sum _{h=0}^{n_H}\sum _{w=0}^{n_W}{a}_{slice}\times d{Z}_{hw}$$

代碼：

dW[:,:,:,c] += a_slice * dZ[i, h, w, c]

5.1.3 計算 db

$$db=\sum _h\sum _{w}d{Z}_{hw}$$
代碼：

db[:,:,:,c] += dZ[i, h, w, c] def conv_backward(dZ, cache):"""Implement the backward propagation for a convolution functionArguments:dZ -- gradient of the cost with respect to the output of the conv layer (Z), numpy array of shape (m, n_H, n_W, n_C)cache -- cache of values needed for the conv_backward(), output of conv_forward()Returns:dA_prev -- gradient of the cost with respect to the input of the conv layer (A_prev),numpy array of shape (m, n_H_prev, n_W_prev, n_C_prev)dW -- gradient of the cost with respect to the weights of the conv layer (W)numpy array of shape (f, f, n_C_prev, n_C)db -- gradient of the cost with respect to the biases of the conv layer (b)numpy array of shape (1, 1, 1, n_C)"""### START CODE HERE #### Retrieve information from "cache"(A_prev, W, b, hparameters) = cache# Retrieve dimensions from A_prev's shape(m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape# Retrieve dimensions from W's shape(f, f, n_C_prev, n_C) = W.shape# Retrieve information from "hparameters"stride = hparameters['stride']pad = hparameters['pad']# Retrieve dimensions from dZ's shape(m, n_H, n_W, n_C) = dZ.shape# Initialize dA_prev, dW, db with the correct shapesdA_prev = np.zeros(A_prev.shape) dW = np.zeros(W.shape)db = np.zeros((1, 1, 1, n_C))# Pad A_prev and dA_prev, 添加周圍pad像素A_prev_pad = zero_pad(A_prev, pad)dA_prev_pad = zero_pad(dA_prev, pad)for i in range(m): # loop over the training examples# select ith training example from A_prev_pad and dA_prev_pada_prev_pad = A_prev_pad[i]da_prev_pad = dA_prev_pad[i]for h in range(n_H): # loop over vertical axis of the output volumefor w in range(n_W): # loop over horizontal axis of the output volumefor c in range(n_C): # loop over the channels of the output volume# Find the corners of the current "slice"vert_start = h*stridevert_end = vert_start + fhoriz_start = w*stridehoriz_end = horiz_start + f# Use the corners to define the slice from a_prev_pada_slice = a_prev_pad[vert_start:vert_end, horiz_start:horiz_end, :]# Update gradients for the window and the filter's parameters using the code formulas given aboveda_prev_pad[vert_start:vert_end, horiz_start:horiz_end, :] += W[:,:,:,c]*dZ[i,h,w,c]dW[:,:,:,c] += a_slice*dZ[i,h,w,c]db[:,:,:,c] += dZ[i,h,w,c]# Set the ith training example's dA_prev to the unpaded da_prev_pad (Hint: use X[pad:-pad, pad:-pad, :])dA_prev[i, :, :, :] = da_prev_pad[pad:-pad, pad:-pad, :]### END CODE HERE #### Making sure your output shape is correctassert(dA_prev.shape == (m, n_H_prev, n_W_prev, n_C_prev))return dA_prev, dW, db

5.2 池化層 - 反向傳播

池化層沒有參數需要更新

5.2.1 最大池化 - 反向傳播

先建立一個輔助函數create_mask_from_window()：
$$X=\left[\begin{array}{ccc}1& & 3\\ 4& & 2\end{array}\right]\to M=\left[\begin{array}{ccc}0& & 0\\ 1& & 0\end{array}\right]$$
可以使用 x = np.max(X), A = (X == x)

def create_mask_from_window(x):"""Creates a mask from an input matrix x, to identify the max entry of x.Arguments:x -- Array of shape (f, f)Returns:mask -- Array of the same shape as window, contains a True at the position corresponding to the max entry of x."""### START CODE HERE ### (≈1 line)mask = (x == np.max(x))### END CODE HERE ###return mask

5.2.2 平均池化 - 反向傳播

平均池化，輸入的每個元素是一樣的重要對于輸出，反向傳播時：
$$dZ=1\to dZ=\left[\begin{array}{ccc}1/4& & 1/4\\ 1/4& & 1/4\end{array}\right]$$

def distribute_value(dz, shape):"""Distributes the input value in the matrix of dimension shapeArguments:dz -- input scalarshape -- the shape (n_H, n_W) of the output matrix for which we want to distribute the value of dzReturns:a -- Array of size (n_H, n_W) for which we distributed the value of dz"""### START CODE HERE #### Retrieve dimensions from shape (≈1 line)(n_H, n_W) = shape# Compute the value to distribute on the matrix (≈1 line)average = dz/(n_H*n_W)# Create a matrix where every entry is the "average" value (≈1 line)a =np.ones((n_H, n_W))*average### END CODE HERE ###return a

5.2.3 組合在一起 - 反向池化

def pool_backward(dA, cache, mode = "max"):"""Implements the backward pass of the pooling layerArguments:dA -- gradient of cost with respect to the output of the pooling layer, same shape as Acache -- cache output from the forward pass of the pooling layer, contains the layer's input and hparameters mode -- the pooling mode you would like to use, defined as a string ("max" or "average")Returns:dA_prev -- gradient of cost with respect to the input of the pooling layer, same shape as A_prev"""### START CODE HERE #### Retrieve information from cache (≈1 line)(A_prev, hparameters) = cache# Retrieve hyperparameters from "hparameters" (≈2 lines)stride = hparameters['stride']f = hparameters['f']# Retrieve dimensions from A_prev's shape and dA's shape (≈2 lines)m, n_H_prev, n_W_prev, n_C_prev = A_prev.shapem, n_H, n_W, n_C = dA.shape# Initialize dA_prev with zeros (≈1 line)dA_prev = np.zeros(A_prev.shape)for i in range(m): # loop over the training examples# select training example from A_prev (≈1 line)a_prev = A_prev[i]for h in range(n_H): # loop on the vertical axisfor w in range(n_W): # loop on the horizontal axisfor c in range(n_C): # loop over the channels (depth)# Find the corners of the current "slice" (≈4 lines)vert_start = h*stridevert_end = vert_start + fhoriz_start = w*stridehoriz_end = horiz_start + f# Compute the backward propagation in both modes.if mode == "max":# Use the corners and "c" to define the current slice from a_prev (≈1 line)a_prev_slice = a_prev[vert_start:vert_end, horiz_start:horiz_end, c]# Create the mask from a_prev_slice (≈1 line)mask = create_mask_from_window(a_prev_slice)# Set dA_prev to be dA_prev + (the mask multiplied by the correct entry of dA) (≈1 line)dA_prev[i, vert_start: vert_end, horiz_start: horiz_end, c] += mask*dA[i, h, w, c]elif mode == "average":# Get the value a from dA (≈1 line)da = dA[i, vert_start, horiz_start, c]# Define the shape of the filter as fxf (≈1 line)shape = (f, f)# Distribute it to get the correct slice of dA_prev. i.e. Add the distributed value of da. (≈1 line)dA_prev[i, vert_start: vert_end, horiz_start: horiz_end, c] += distribute_value(da, shape)### END CODE #### Making sure your output shape is correctassert(dA_prev.shape == A_prev.shape)return dA_prev

作業2：用TensorFlow實現卷積神經網絡

上次作業：02.改善深層神經網絡：超參數調試、正則化以及優化 W3. 超參數調試、Batch Norm和程序框架（作業：TensorFlow教程+數字手勢預測）

1. TensorFlow 模型

導入一些包

import math import numpy as np import h5py import matplotlib.pyplot as plt import scipy from PIL import Image from scipy import ndimage import tensorflow as tf from tensorflow.python.framework import ops from cnn_utils import *%matplotlib inline np.random.seed(1) import sys sys.path.append('/path/file') # Loading the data (signs) X_train_orig, Y_train_orig, X_test_orig, Y_test_orig, classes = load_dataset()

手勢數字數據集：

• 查看圖片

# Example of a picture index = 7 plt.imshow(X_train_orig[index]) print ("y = " + str(np.squeeze(Y_train_orig[:, index]))) y = 1

• 了解數據維度

X_train = X_train_orig/255. # 歸一化 X_test = X_test_orig/255. Y_train = convert_to_one_hot(Y_train_orig, 6).T Y_test = convert_to_one_hot(Y_test_orig, 6).T print ("number of training examples = " + str(X_train.shape[0])) print ("number of test examples = " + str(X_test.shape[0])) print ("X_train shape: " + str(X_train.shape)) print ("Y_train shape: " + str(Y_train.shape)) print ("X_test shape: " + str(X_test.shape)) print ("Y_test shape: " + str(Y_test.shape)) conv_layers = {}

輸出：

number of training examples = 1080 number of test examples = 120 X_train shape: (1080, 64, 64, 3) Y_train shape: (1080, 6) X_test shape: (120, 64, 64, 3) Y_test shape: (120, 6)

1.1 創建 placeholder

• placeholder 給輸入數據創建一個位子，后面給他 feed 數據，樣本數量維度可以置為 None

# GRADED FUNCTION: create_placeholdersdef create_placeholders(n_H0, n_W0, n_C0, n_y):"""Creates the placeholders for the tensorflow session.Arguments:n_H0 -- scalar, height of an input imagen_W0 -- scalar, width of an input imagen_C0 -- scalar, number of channels of the inputn_y -- scalar, number of classesReturns:X -- placeholder for the data input, of shape [None, n_H0, n_W0, n_C0] and dtype "float"Y -- placeholder for the input labels, of shape [None, n_y] and dtype "float""""### START CODE HERE ### (≈2 lines)X = tf.placeholder(tf.float32, shape=(None, n_H0, n_W0, n_C0), name='X')Y = tf.placeholder(tf.float32, shape=(None, n_y), name='Y')### END CODE HERE ###return X, Y

1.2 初始化參數

初始化權重/過濾器 $W_1,W_2$ tf.contrib.layers.xavier_initializer(seed = 0)
TensorFlow 會處理偏置，你無需擔心，還會自動初始化全連接層

W = tf.get_variable("W", [1,2,3,4], initializer = ...) # GRADED FUNCTION: initialize_parametersdef initialize_parameters():"""Initializes weight parameters to build a neural network with tensorflow. The shapes are:W1 : [4, 4, 3, 8]W2 : [2, 2, 8, 16]Returns:parameters -- a dictionary of tensors containing W1, W2"""tf.set_random_seed(1) # so that your "random" numbers match ours### START CODE HERE ### (approx. 2 lines of code)W1 = tf.get_variable(name='W1', shape=[4,4,3,8], dtype=tf.float32, initializer=tf.contrib.layers.xavier_initializer(seed=0))W2 = tf.get_variable(name='W2', shape=[2,2,8,16], dtype=tf.float32, initializer=tf.contrib.layers.xavier_initializer(seed=0))### END CODE HERE ###parameters = {"W1": W1,"W2": W2}return parameters tf.reset_default_graph() with tf.Session() as sess_test:parameters = initialize_parameters()init = tf.global_variables_initializer()sess_test.run(init)print("W1 = " + str(parameters["W1"].eval()[1,1,1]))print("W2 = " + str(parameters["W2"].eval()[1,1,1]))

輸出：

W1 = [ 0.00131723 0.1417614 -0.04434952 0.09197326 0.14984085 -0.03514394-0.06847463 0.05245192] W2 = [-0.08566415 0.17750949 0.11974221 0.16773748 -0.0830943 -0.08058-0.00577033 -0.14643836 0.24162132 -0.05857408 -0.19055021 0.1345228-0.22779644 -0.1601823 -0.16117483 -0.10286498]

1.3 前向傳播

• tf.nn.conv2d(X,W1, strides = [1,s,s,1], padding = 'SAME')，strides是各維度的步長，參考TF文檔
• tf.nn.max_pool(A, ksize = [1,f,f,1], strides = [1,s,s,1], padding = 'SAME')，ksize是窗口大小 fxf，參考TF文檔
• tf.nn.relu(Z1)，激活函數
• tf.contrib.layers.flatten(P)，將輸入 P，展平成一維向量 shape = [batch_size, k]，參考TF文檔
• tf.contrib.layers.fully_connected(F, num_outputs)，給一個展平的 F 輸入，返回用全連接層計算后的輸出，參考TF文檔（注：當訓練模型時，該模塊會自動初始化權重，并訓練，你無需初始化它）

模型架構：CONV2D -> RELU -> MAXPOOL -> CONV2D -> RELU -> MAXPOOL -> FLATTEN -> FULLYCONNECTED

參數如下：

• Conv2D: stride 1, padding is “SAME”
• ReLU
• Max pool: Use an 8 by 8 filter size and an 8 by 8 stride, padding is “SAME”
• Conv2D: stride 1, padding is “SAME”
• ReLU
• Max pool: Use a 4 by 4 filter size and a 4 by 4 stride, padding is “SAME”
• Flatten the previous output.
• FULLYCONNECTED (FC) layer: Apply a fully connected layer without an non-linear activation function. （不要計算激活輸出，TF有模塊會一起計算 激活和cost）

# GRADED FUNCTION: forward_propagationdef forward_propagation(X, parameters):"""Implements the forward propagation for the model:CONV2D -> RELU -> MAXPOOL -> CONV2D -> RELU -> MAXPOOL -> FLATTEN -> FULLYCONNECTEDArguments:X -- input dataset placeholder, of shape (input size, number of examples)parameters -- python dictionary containing your parameters "W1", "W2"the shapes are given in initialize_parametersReturns:Z3 -- the output of the last LINEAR unit"""# Retrieve the parameters from the dictionary "parameters" W1 = parameters['W1']W2 = parameters['W2']### START CODE HERE #### CONV2D: stride of 1, padding 'SAME'Z1 = tf.nn.conv2d(X, W1, strides=[1,1,1,1], padding='SAME')# RELUA1 = tf.nn.relu(Z1)# MAXPOOL: window 8x8, sride 8, padding 'SAME'P1 = tf.nn.max_pool(A1, ksize=[1,8,8,1],strides=[1,8,8,1],padding='SAME')# CONV2D: filters W2, stride 1, padding 'SAME'Z2 = tf.nn.conv2d(P1, W2, strides=[1,1,1,1],padding='SAME')# RELUA2 = tf.nn.relu(Z2)# MAXPOOL: window 4x4, stride 4, padding 'SAME'P2 = tf.nn.max_pool(A2, ksize=[1,4,4,1],strides=[1,4,4,1],padding='SAME')# FLATTENP2 = tf.contrib.layers.flatten(P2)# FULLY-CONNECTED without non-linear activation function (not not call softmax).# 6 neurons in output layer. Hint: one of the arguments should be "activation_fn=None" Z3 = tf.contrib.layers.fully_connected(P2, num_outputs=6, activation_fn=None)### END CODE HERE ###return Z3 tf.reset_default_graph()with tf.Session() as sess:np.random.seed(1)X, Y = create_placeholders(64, 64, 3, 6)parameters = initialize_parameters()Z3 = forward_propagation(X, parameters)init = tf.global_variables_initializer()sess.run(init)a = sess.run(Z3, {X: np.random.randn(2,64,64,3), Y: np.random.randn(2,6)})print("Z3 = " + str(a))

輸出：（可能是版本原因，跟標準答案不一樣）

Z3 = [[ 1.4416984 -0.24909666 5.450499 -0.2618962 -0.20669907 1.3654671 ][ 1.4070846 -0.02573211 5.08928 -0.48669922 -0.40940708 1.2624859 ]]

1.4 計算損失

• tf.nn.softmax_cross_entropy_with_logits(logits = Z3, labels = Y)，計算softmax激活 及 熵損失
• tf.reduce_mean，計算均值

# GRADED FUNCTION: compute_cost def compute_cost(Z3, Y):"""Computes the costArguments:Z3 -- output of forward propagation (output of the last LINEAR unit), of shape (6, number of examples)Y -- "true" labels vector placeholder, same shape as Z3Returns:cost - Tensor of the cost function"""### START CODE HERE ### (1 line of code)cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=Z3, labels=Y))### END CODE HERE ###return cost tf.reset_default_graph()with tf.Session() as sess:np.random.seed(1)X, Y = create_placeholders(64, 64, 3, 6)parameters = initialize_parameters()Z3 = forward_propagation(X, parameters)cost = compute_cost(Z3, Y)init = tf.global_variables_initializer()sess.run(init)a = sess.run(cost, {X: np.random.randn(4,64,64,3), Y: np.random.randn(4,6)})print("cost = " + str(a))

輸出：

cost = 4.6648693 # 跟標準答案不一樣

1.5 模型

• 創建 placeholders
• 初始化參數
• 前向傳播
• 計算損失
• 創建優化器

# GRADED FUNCTION: modeldef model(X_train, Y_train, X_test, Y_test, learning_rate = 0.009,num_epochs = 100, minibatch_size = 64, print_cost = True):"""Implements a three-layer ConvNet in Tensorflow:CONV2D -> RELU -> MAXPOOL -> CONV2D -> RELU -> MAXPOOL -> FLATTEN -> FULLYCONNECTEDArguments:X_train -- training set, of shape (None, 64, 64, 3)Y_train -- test set, of shape (None, n_y = 6)X_test -- training set, of shape (None, 64, 64, 3)Y_test -- test set, of shape (None, n_y = 6)learning_rate -- learning rate of the optimizationnum_epochs -- number of epochs of the optimization loopminibatch_size -- size of a minibatchprint_cost -- True to print the cost every 100 epochsReturns:train_accuracy -- real number, accuracy on the train set (X_train)test_accuracy -- real number, testing accuracy on the test set (X_test)parameters -- parameters learnt by the model. They can then be used to predict."""ops.reset_default_graph() # to be able to rerun the model without overwriting tf variablestf.set_random_seed(1) # to keep results consistent (tensorflow seed)seed = 3 # to keep results consistent (numpy seed)(m, n_H0, n_W0, n_C0) = X_train.shape n_y = Y_train.shape[1] costs = [] # To keep track of the cost# Create Placeholders of the correct shape### START CODE HERE ### (1 line)X, Y = create_placeholders(n_H0, n_W0, n_C0, n_y)### END CODE HERE #### Initialize parameters### START CODE HERE ### (1 line)parameters = initialize_parameters()### END CODE HERE #### Forward propagation: Build the forward propagation in the tensorflow graph### START CODE HERE ### (1 line)Z3 = forward_propagation(X, parameters)### END CODE HERE #### Cost function: Add cost function to tensorflow graph### START CODE HERE ### (1 line)cost = compute_cost(Z3, Y)### END CODE HERE #### Backpropagation: Define the tensorflow optimizer. Use an AdamOptimizer that minimizes the cost.### START CODE HERE ### (1 line)optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(cost)### END CODE HERE #### Initialize all the variables globallyinit = tf.global_variables_initializer()# Start the session to compute the tensorflow graphwith tf.Session() as sess:# Run the initializationsess.run(init)# Do the training loopfor epoch in range(num_epochs):minibatch_cost = 0.num_minibatches = m // minibatch_size# number of minibatches of size minibatch_size in the train setseed = seed + 1minibatches = random_mini_batches(X_train, Y_train, minibatch_size, seed)for minibatch in minibatches:# Select a minibatch(minibatch_X, minibatch_Y) = minibatch# IMPORTANT: The line that runs the graph on a minibatch.# Run the session to execute the optimizer and the cost, the feedict should contain a minibatch for (X,Y).### START CODE HERE ### (1 line)_ , temp_cost = sess.run([optimizer, cost], feed_dict={X:minibatch_X, Y:minibatch_Y})### END CODE HERE ###minibatch_cost += temp_cost / num_minibatches# Print the cost every epochif print_cost == True and epoch % 5 == 0:print ("Cost after epoch %i: %f" % (epoch, minibatch_cost))if print_cost == True and epoch % 1 == 0:costs.append(minibatch_cost)# plot the costplt.plot(np.squeeze(costs))plt.ylabel('cost')plt.xlabel('iterations (per tens)')plt.title("Learning rate =" + str(learning_rate))plt.show()# Calculate the correct predictionspredict_op = tf.argmax(Z3, 1)correct_prediction = tf.equal(predict_op, tf.argmax(Y, 1))# Calculate accuracy on the test setaccuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))print(accuracy)train_accuracy = accuracy.eval({X: X_train, Y: Y_train})test_accuracy = accuracy.eval({X: X_test, Y: Y_test})print("Train Accuracy:", train_accuracy)print("Test Accuracy:", test_accuracy)return train_accuracy, test_accuracy, parameters

• 訓練模型 100 epochs

_, _, parameters = model(X_train, Y_train, X_test, Y_test)

使用作業默認的學習率（0.009）和迭代次數（100），效果很差，只有60%，50%多的訓練準確率和測試準確率

更改為：learning_rate = 0.002, num_epochs = 600

Cost after epoch 0: 1.943088 Cost after epoch 5: 1.885871 Cost after epoch 10: 1.824765 Cost after epoch 15: 1.595936 Cost after epoch 20: 1.243416 Cost after epoch 25: 1.004351 Cost after epoch 30: 0.875302 Cost after epoch 35: 0.767196 Cost after epoch 40: 0.711865 Cost after epoch 45: 0.640964 Cost after epoch 50: 0.574520 。。。。 Cost after epoch 150: 0.207593 。。。。 Cost after epoch 300: 0.071819 。。。。 Cost after epoch 500: 0.013352 。。。。 Cost after epoch 595: 0.016594

Tensor("Mean_1:0", shape=(), dtype=float32) Train Accuracy: 0.9916667 Test Accuracy: 0.9

訓練集上準確率為 99%，測試集上準確率為 90%，存在一定的過擬合。

fname = "images/thumbs_up.jpg" image = np.array(ndimage.imread(fname, flatten=False)) my_image = scipy.misc.imresize(image, size=(64,64)) plt.imshow(my_image)

一起加油學習！沖啊！

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