Building your Deep Neural Network: Step by Step

符號說明
Notation:
- Superscript [l]denotes a quantity associated with the lthlayer.
- Example:a[L] is the Lth layer activation. W[L] andb[L]are the Lth layer parameters.
- Superscript(i)denotes a quantity associated with the ith example.
- Example:x

1 - Packages

匯入被作業需要的包和模組
Let’s first import all the packages that you will need during this assignment.
- numpy is the main package for scientific computing with Python.
- matplotlib is a library to plot graphs in Python.
- dnn_utils provides some necessary functions for this notebook.
- testCases provides some test cases to assess the correctness of your functions
- np.random.seed(1) is used to keep all the random function calls consistent. It will help us grade your work. Please don’t change the seed.
匯入包和模組

import numpy as np
import h5py
import matplotlib.pyplot as plt
from testCases_v2 import *
from testCases_v3 import *
from dnn_utils_v2 import sigmoid, sigmoid_backward, relu, relu_backward

設定繪圖配置檔案引數

%matplotlib inline 設定繪圖的配置檔案
plt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of
 
 plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'

設定隨機數種子，保證隨數的連續

np.random.seed(1) #設定隨機數種子

2 - Outline of the Assignment

To build your neural network, you will be implementing several “helper functions”. These helper functions will be used in the next assignment to build a two-layer neural network and an L-layer neural network. Each small helper function you will implement will have detailed instructions that will walk you through the necessary steps. Here is an outline of this assignment, you will:

• Initialize the parameters for a two-layer network and for an L-layer neural network.

• Implement the forward propagation module (shown in purple in the figure below).

  • Complete the LINEAR part of a layer’s forward propagation step (resulting in Z[l]).
  • We give you the ACTIVATION function (relu/sigmoid).
  • Combine the previous two steps into a new [LINEAR->ACTIVATION] forward function.
  • Stack the [LINEAR->RELU] forward function L-1 time (for layers 1 through L-1) and add a [LINEAR->SIGMOID] at the end (for the final layer L). This gives you a new L_model_forward function.

• Compute the loss.

• Implement the backward propagation module (denoted in red in the figure below).

  • Complete the LINEAR part of a layer’s backward propagation step.
  • We give you the gradient of the ACTIVATE function (relu_backward/sigmoid_backward)
  • Combine the previous two steps into a new [LINEAR->ACTIVATION] backward function.
  • Stack [LINEAR->RELU] backward L-1 times and add [LINEAR->SIGMOID] backward in a new L_model_backward function

• Finally update the parameters.
  
  Note that for every forward function, there is a corresponding backward function. That is why at every step of your forward module you will be storing some values in a cache. The cached values are useful for computing gradients. In the backpropagation module you will then use the cache to calculate the gradients. This assignment will show you exactly how to carry out each of these steps.

3 - Initialization

You will write two helper functions that will initialize the parameters for your model. The first function will be used to initialize parameters for a two layer model. The second one will generalize this initialization process to L layers.

3.1 - 2-layer Neural Network

Exercise: Create and initialize the parameters of the 2-layer neural network.

Instructions:

• The model’s structure is: LINEAR -> RELU -> LINEAR -> SIGMOID.
• Use random initialization for the weight matrices. Use np.random.randn(shape)∗0.01 with the correct shape.
• Use zero initialization for the biases. Use np.zeros(shape).
  定義初始化函式

def initialize_parameters(n_x,n_h,n_y):
    np.random.seed(1) #沒有這句得不到預期結果
    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))

    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

測試：

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"]))

結果：

W1 = [[ 0.01624345 -0.00611756]
 [-0.00528172 -0.01072969]]
b1 = [[ 0.]
 [ 0.]]
W2 = [[ 0.00865408 -0.02301539]]
b2 = [[ 0.]]

3.2 - L-layer Neural Network

The initialization for a deeper L-layer neural network is more complicated because there are many more weight matrices and bias vectors. When completing the initialize_parameters_deep, you should make sure that your dimensions match between each layer. Recall that n[l] is the number of units in layer l. Thus for example if the size of our input X is (12288,209) (with m=209 examples) then:

Remember that when we compute WX+b in python, it carries out broadcasting. For example, if:

Then WX+b will be: