[Deep-Special] [Lec1] Week4. Deep Neural Network - Programming Assignment1. Building your Deep Neural Network

📔 [Lec1] Neural Networks & Deep Learning

Building your Deep Neural Network: Step by Step

이번 시간에는 deep neural network를 구현하는데 있어서 필요한 함수들을 구현할 것입니다. 그리고 해당 과제에서 구현한 함수를 사용해 다음 과제에서는 'Cat vs Non-Cat ' Image Classification Task를 해결해 볼 것입니다. 

 

Coursera Rule로 인해 정답 코드를 공개할 수는 없습니다. 과제를 하시면서 궁금한 점이 있으시다면 언제든지 연락주시길 바랍니다!

📩 leeyj0511@naver.com

댓글도 환영입니다!😃

 

After this assignment you will be able to:

• Use non-linear units like ReLU to improve your model
• Build a deeper neural network (with more than 1 hidden layer)
• Implement an easy-to-use neural network class

Superscript[l], Superscript(i), Lowerscript(i)

Let's get started!

 

그럼 시작해보자! - Again, -20.11.10.Tue. pm4:00-

 

2. Outline of the Assignment

To buid your neural network, you'll be implementing several 'helper functions'. These helper functions will be used in the next assignment to build a two-layer neural network and L-layer neural network.

Specifics

• 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 L-layer ). 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.

이번 시간에 구현할 과제입니다

 

• 예를 들어 3개의 layer로 구성된 Neural Network라면 n-1인 2개의 layer는 Linear ReLU Forward로 구현한다. 그리고 마지막 layer는 Linear Sigmoid Forward로 구현한다.

 

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.

⇒ Forward Function에 대응하는 Backward Function이 있다. 따라서 Forward마다 cache에 값을 잘 저장해 줘야 한다. (강의에서 계속해서 강조했던 부분과 같다)

3. Initialization

두개의 helper function을 작성할 것이다. 첫 번째 함수는 2-layer 파라미터를 초기화 시키는데 사용됩니다. 두 번째 함수는 L-layer의 초기화 과정을 일반화 합니다.

(과제를 구현하는 과정에서 함수의 역할을 보다 잘 이해하실 수 있을 것으로 기대합니다!)

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).

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)(12288,209) (with m=209m=209 examples) then:

Instructions:

• L-1번의 [LINEAR → RELU] 블럭과 1번의 [LINEAR→SIGMOID]블럭이 있다

• Use random initialization for the weight matrices. Use np.random.randn(shape) * 0.01.

• Use zeros initialization for the biases. Use np.zeros(shape).

• We will store n[l], the number of units in different layers, in a variable layer_dims. For example, the layer_dims for the "Planar Data classification model" from last week would have been [2,4,1]: There were two inputs, one hidden layer with 4 hidden units, and an output layer with 1 output unit. This means W1's shape was (4,2), b1 was (4,1), W2 was (1,4) and b2 was (1,1). Now you will generalize this to  layers!

• Here is the implementation for L=1 (one layer neural network). It should inspire you to implement the general case (L-layer neural network).

  if L == 1: parameters["W" + str(L)] = np.random.randn(layer_dims[1], layer_dims[0]) * 0.01 parameters["b" + str(L)] = np.zeros((layer_dims[1], 1))

  ⇒ 요구사항이 많으면 으엑...😬인데... 게다가 영어다... 🤪 -> 과제를 마치고 다시 한번 과제를 리뷰하니깐 이해가 가더군요...ㅎㅎ

4 - Forward propagation module

➡️ Process

• Weight Initialization → Linear Forward

4.1 - Linear Forward

Now that you have initialized your parameters, you will do the forward propagation module. You will start by implementing some basic functions that you will use later when implementing the model. You will complete three functions in this order:

• LINEAR
• LINEAR -> ACTIVATION where ACTIVATION will be either ReLU or Sigmoid.
• [LINEAR -> RELU]  (L-1) -> LINEAR -> SIGMOID (whole model)

The linear forward module (vectorized over all the examples) computes the following equations:

⇒ ⭐ 땡큐 문제다.!

4.2 - Linear-Activation Forward

In this notebook, you will use two activation functions:

• Sigmoid: σ(Z)=σ(WA+b)=11+e−(WA+b)σ(Z)=σ(WA+b)=11+e−(WA+b). We have provided you with the sigmoid function. This function returns two items: the activation value "a" and a "cache" that contains "Z" (it's what we will feed in to the corresponding backward function). To use it you could just call:

  A, activation_cache = sigmoid(Z)

• ReLU: The mathematical formula for ReLu is A=RELU(Z)=max(0,Z)A=RELU(Z)=max(0,Z). We have provided you with the relu function. This function returns two items: the activation value "A" and a "cache" that contains "Z" (it's what we will feed in to the corresponding backward function). To use it you could just call:

  A, activation_cache = relu(Z)

Note: In deep learning, the "[LINEAR->ACTIVATION]" computation is counted as a single layer in the neural network, not two layers.

d) L-Layer Model

For even more convenience when implementing the LLlayer Neural Net, you will need a function that replicates the previous one (linear_activation_forward with RELU) L−1L−1 times, then follows that with one linear_activation_forward with SIGMOID.

⇒ L-1번쨰 layer와 L번쨰 layer를 한 번에 처리해주는 Function을 구현해보자!

Tips:

• Use the functions you had previously written
• Use a for loop to replicate [LINEAR->RELU] (L-1) times
• Don't forget to keep track of the caches in the "caches" list. To add a new value c to a list, you can use list.append(c).

5 - Cost function

Now you will implement forward and backward propagation. You need to compute the cost, because you want to check if your model is actually learning.

Exercise: Compute the cross-entropy cost JJ, using the following formula:

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여기서부터 Backprop입니다. 숨을 크게 내쉬고 집중합시다! - 20.11.10.Tue. pm4:30-

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6 - Backward propagation module

Just like with forward propagation, you will implement helper functions for backpropagation. Remember that back propagation is used to calculate the gradient of the loss function with respect to the parameters.

 

Now, similar to forward propagation, you are going to build the backward propagation in three steps:

• LINEAR backward
• LINEAR -> ACTIVATION backward where ACTIVATION computes the derivative of either the ReLU or sigmoid activation
• [LINEAR -> RELU]X (L-1) -> LINEAR -> SIGMOID backward (whole model)

6.1 - Linear backward

For layer l, the linear part is: Z[l]=W[l]A[l−1]+b[l]Z[l]=W[l]A[l−1]+b[l] (followed by an activation).

Suppose you have already calculated the derivative dZ[l]=∂∂Z[l]dZ[l]=∂L∂Z[l]. You want to get (dW[l],db[l],dA[l−1])(dW[l],db[l],dA[l−1]).

6-2. Linear-Ac

tivation backward

Next, you will create a function that merges the two helper functions: linear_backward and the backward step for the activation linear_activation_backward.

To help you implement linear_activation_backward, we provided two backward functions:

• sigmoid_backward: Implements the backward propagation for SIGMOID unit. You can call it as follows:

dZ = sigmoid_backward(dA, activation_cache)

• relu_backward: Implements the backward propagation for RELU unit. You can call it as follows:

dZ = relu_backward(dA, activation_cache)

If g(.)g(.) is the activation function, sigmoid_backward and relu_backward compute

6.3 - L-Model Backward

Now you will implement the backward function for the whole network. Recall that when you implemented the L_model_forward function, at each iteration, you stored a cache which contains (X,W,b, and z). In the back propagation module, you will use those variables to compute the gradients. Therefore, in the L_model_backward function, you will iterate through all the hidden layers backward, starting from layer LL . On each step, you will use the cached values for layer ll to backpropagate through layer ll . Figure 5 below shows the backward pass.

이거 어렵다... 6.3!! - 20.11.10.Tue

🙋‍♂️🙋‍♂️🙋‍♂️ 🙇‍♂️🙇‍♂️🙇‍♂️

 

Summary

• Neural Networks and Deep Learning의 마지막 주 과제 중 하나를 수행했습니다
• 해당 과제를 구현하는 과정에서 그동안 배웠던 지식들을 하나의 결과로 만들어 내는 것을 경험할 수 있었습니다
• 특히 Shallow Network(2-layer) 뿐만아니라 L-layer(L-개의 layer)를 학습시킬 수 있는 함수를 구현했는데요. 향후 Advanced한 모델을 학습하고 구현할 때 이러한 경험이 도움이 될 것으로 생각합니다
• 직접 고민하고 코드로 구현하는 과정을 통해 한 단계 성장할 수 있기를 바랍니다