안녕하세요, HELLO
오늘은 DeepLearning.AI에서 진행하는 앤드류 응(Andrew Ng) 교수님의 딥러닝 전문화의 네 번째 과정인 "Convolutional Neural Networks"을 정리하려고 합니다.
"Convolutional Neural Networks"의 강의를 통해 '자율 주행, 얼굴 인식, 방사선 이미지 인식' 등을 이해하고, CNN 모델에 대해서 배우게 됩니다. 강의는 아래와 같이 구성되어 있습니다.
~ Foundations of Convolutional Neural Networks
~ Deep Convolutional Models: Case Studies
~ Object Detection
~ Special Applications: Face recognition & Neural Style Transfer
"Convolutional Neural Networks" (Andrew Ng)의 1주차 "Convolutional Neural Networks: Step by Step" 실습 내용입니다. 실습 과정을 마무리하면 아래와 같이 CNN에 대해서 익숙해질 겁니다.
- Explain the convolution operation
- Apply two different types of pooling operation
- Identify the components used in a convolutional neural network (padding, stride, filter,...) and their purpose
- Build a convolutional neural network
CHAPTER 1. 'Packages'
CHAPTER 2. 'Outline of the Assignment'
CHAPTER 3. 'Convolutional Neural Networks'
CHAPTER 4. 'Pooling Layer'
CHAPTER 5. 'Backpropagation in Convolutional Neural Networks (OPTIONAL / UNGRADED)'
CHAPTER 1. 'Packages'
import numpy as np
import h5py
import matplotlib.pyplot as plt
from public_tests import *
%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 2
np.random.seed(1)
CHAPTER 2. 'Outline of the Assignment'
You will be implementing the building blocks of a convolutional neural network! Each function you will implement will have detailed instructions to walk you through the steps:
- Convolution functions, including:
- Zero Padding
- Convolve window
- Convolution forward
- Convolution backward (optional)
- Pooling functions, including:
- Pooling forward
- Create mask
- Distribute value
- Pooling backward (optional)
CHAPTER 3. 'Convolutional Neural Networks'
Although programming frameworks make convolutions easy to use, they remain one of the hardest concepts to understand in Deep Learning. A convolution layer transforms an input volume into an output volume of different size, as shown below.
In this part, you will build every step of the convolution layer. You will first implement two helper functions: one for zero padding and the other for computing the convolution function itself.
□ Zero-padding
Zero-padding adds zeros around the border of an image, The main benefits of padding are:
- It allows you to use a CONV layer without necessarily shrinking the height and width of the volumes. This is important for building deeper networks, since otherwise the height/width would shrink as you go to deeper layers. An important special case is the "same" convolution, in which the height/width is exactly preserved after one layer.
- It helps us keep more of the information at the border of an image. Without padding, very few values at the next layer would be affected by pixels at the edges of an image.
# GRADED FUNCTION: zero_pad
def 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 images
pad -- integer, amount of padding around each image on vertical and horizontal dimensions
Returns:
X_pad -- padded image of shape (m, n_H + 2 * pad, n_W + 2 * pad, n_C)
"""
#(≈ 1 line)
# X_pad = None
# YOUR CODE STARTS HERE
X_pad = np.pad(X, ((0,0), (pad, pad), (pad, pad), (0,0)), mode='constant', constant_values = (0, 0))
# YOUR CODE ENDS HERE
return X_pad
np.random.seed(1)
x = np.random.randn(4, 3, 3, 2)
x_pad = zero_pad(x, 3)
print ("x.shape =\n", x.shape)
print ("x_pad.shape =\n", x_pad.shape)
print ("x[1,1] =\n", x[1, 1])
print ("x_pad[1,1] =\n", x_pad[1, 1])
fig, axarr = plt.subplots(1, 2)
axarr[0].set_title('x')
axarr[0].imshow(x[0, :, :, 0])
axarr[1].set_title('x_pad')
axarr[1].imshow(x_pad[0, :, :, 0])
zero_pad_test(zero_pad)
After submitting codes, we can see the padded images as like that.
□ Single Step of Convolution
In this part, implement a single step of convolution, in which you apply the filter to a single position of the input. This will be used to build a convolutional unit, which:
- Takes an input volume
- Applies a filter at every position of the input
- Outputs another volume (usually of different size)
In a computer vision application, each value in the matrix on the left corresponds to a single pixel value. You convolve a 3x3 filter with the image by multiplying its values element-wise with the original matrix, then summing them up and adding a bias. In this first step of the exercise, you will implement a single step of convolution, corresponding to applying a filter to just one of the positions to get a single real-valued output.
# GRADED FUNCTION: conv_single_step
def 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, the result of convolving the sliding window (W, b) on a slice x of the input data
"""
#(≈ 3 lines of code)
# Element-wise product between a_slice_prev and W. Do not add the bias yet.
# s = None
# Sum over all entries of the volume s.
# Z = None
# Add bias b to Z. Cast b to a float() so that Z results in a scalar value.
# Z = None
# YOUR CODE STARTS HERE
s = np.multiply(W, a_slice_prev)
Z = np.sum(s)
Z = np.sum((Z, float(b)), dtype=np.float)
# YOUR CODE ENDS HERE
return Z
np.random.seed(1)
a_slice_prev = np.random.randn(4, 4, 3)
W = np.random.randn(4, 4, 3)
b = np.random.randn(1, 1, 1)
Z = conv_single_step(a_slice_prev, W, b)
print("Z =", Z)
conv_single_step_test(conv_single_step)
assert (type(Z) == np.float64 or type(Z) == np.float32), "You must cast the output to float"
assert np.isclose(Z, -6.999089450680221), "Wrong value"
# Z = -6.999089450680221
# All tests passed!□ Convolutional Neural Networks - Forward Pass
# GRADED FUNCTION: conv_forward
def conv_forward(A_prev, W, b, hparameters):
"""
Implements the forward propagation for a convolution function
Arguments:
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 = int((n_H_prev - f + 2 * pad) / stride + 1)
n_W = int((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_prev
A_prev_pad = zero_pad(A_prev, pad)
for i in range(m): # loop over the batch of training examples
a_prev_pad = A_prev_pad[i, :, :, :] # Select ith training example's padded activation
for h in range(n_H): # loop over vertical axis of the output volume
for w in range(n_W): # loop over horizontal axis of the output volume
for 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 * stride
vert_end = vert_start + f
horiz_start = w * stride
horiz_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] = conv_single_step(a_slice_prev, W[:, :, :, c], b[:, :, :, c])
### END CODE HERE ###
# Making sure your output shape is correct
assert(Z.shape == (m, n_H, n_W, n_C))
# Save information in "cache" for the backprop
cache = (A_prev, W, b, hparameters)
return Z, cache
np.random.seed(1)
A_prev = np.random.randn(2, 5, 7, 4)
W = np.random.randn(3, 3, 4, 8)
b = np.random.randn(1, 1, 1, 8)
hparameters = {"pad" : 1,
"stride": 2}
Z, cache_conv = conv_forward(A_prev, W, b, hparameters)
print("Z's mean =\n", np.mean(Z))
print("Z[0,2,1] =\n", Z[0, 2, 1])
print("cache_conv[0][1][2][3] =\n", cache_conv[0][1][2][3])
conv_forward_test(conv_forward)
CHAPTER 4. 'Pooling Layer'
The pooling (POOL) layer reduces the height and width of the input. It helps reduce computation, as well as helps make feature detectors more invariant to its position in the input. The two types of pooling layers are:
□ Forward Pooling
We are going to implement MAX-POOL and AVG-POOL, in the same function.
# GRADED FUNCTION: pool_forward
def pool_forward(A_prev, hparameters, mode = "max"):
"""
Implements the forward pass of the pooling layer
Arguments:
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 output
n_H = int(1 + (n_H_prev - f) / stride)
n_W = int(1 + (n_W_prev - f) / stride)
n_C = n_C_prev
# Initialize output matrix A
A = np.zeros((m, n_H, n_W, n_C))
for i in range(m): # loop over the training examples
for h in range(n_H): # loop on the vertical axis of the output volume
# Find the vertical start and end of the current "slice" (≈2 lines)
vert_start = h * stride
vert_end = vert_start + f
for w in range(n_W): # loop on the horizontal axis of the output volume
# Find the vertical start and end of the current "slice" (≈2 lines)
horiz_start = w * stride
horiz_end = horiz_start + f
for c in range (n_C): # loop over the channels of the output volume
# 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, : , : , c]
# Compute the pooling operation on the slice.
# Use an if statement to differentiate the modes.
# Use np.max and np.mean.
if mode == "max":
A[i, h, w, c] = np.max(a_prev_slice[vert_start:vert_end, horiz_start:horiz_end])
elif mode == "average":
A[i, h, w, c] = np.mean(a_prev_slice[vert_start:vert_end, horiz_start:horiz_end])
# Store the input and hparameters in "cache" for pool_backward()
cache = (A_prev, hparameters)
# Making sure your output shape is correct
#assert(A.shape == (m, n_H, n_W, n_C))
return A, cache
# Case 1: stride of 1
np.random.seed(1)
A_prev = np.random.randn(2, 5, 5, 3)
hparameters = {"stride" : 1, "f": 3}
A, cache = pool_forward(A_prev, hparameters, mode = "max")
print("mode = max")
print("A.shape = " + str(A.shape))
print("A[1, 1] =\n", A[1, 1])
A, cache = pool_forward(A_prev, hparameters, mode = "average")
print("mode = average")
print("A.shape = " + str(A.shape))
print("A[1, 1] =\n", A[1, 1])
pool_forward_test(pool_forward)
What you should remember:
- A convolution extracts features from an input image by taking the dot product between the input data and a 3D array of weights (the filter).
- The 2D output of the convolution is called the feature map
- A convolution layer is where the filter slides over the image and computes the dot product
- This transforms the input volume into an output volume of different size
- Zero padding helps keep more information at the image borders, and is helpful for building deeper networks, because you can build a CONV layer without shrinking the height and width of the volumes
- Pooling layers gradually reduce the height and width of the input by sliding a 2D window over each specified region, then summarizing the features in that region
CHAPTER 5. 'Backpropagation in Convolutional Neural Networks (OPTIONAL / UNGRADED)'
□ Convolutional Layer Backward Pass
In modern deep learning frameworks, you only have to implement the forward pass, and the framework takes care of the backward pass, so most deep learning engineers don't need to bother with the details of the backward pass. The backward pass for convolutional networks is complicated. If you wish, you can work through this optional portion of the notebook to get a sense of what backprop in a convolutional network looks like.
When in an earlier course you implemented a simple (fully connected) neural network, you used backpropagation to compute the derivatives with respect to the cost to update the parameters. Similarly, in convolutional neural networks you can calculate the derivatives with respect to the cost in order to update the parameters. The backprop equations are not trivial and were not derived in lecture, but are briefly presented below.
def conv_backward(dZ, cache):
"""
Implement the backward propagation for a convolution function
Arguments:
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)
"""
# Retrieve information from "cache"
# (A_prev, W, b, hparameters) = None
(A_prev, W, b, hparameters) = cache
# Retrieve dimensions from A_prev's shape
# (m, n_H_prev, n_W_prev, n_C_prev) = None
(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) = None
(f, f, n_C_prev, n_C) = W.shape
# Retrieve information from "hparameters"
# stride = None
# pad = None
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 shapes
dA_prev = np.zeros((m, n_H_prev, n_W_prev, n_C_prev))
dW = np.zeros((f, f, n_C_prev, n_C))
db = np.zeros((1, 1, 1, n_C))
# Pad A_prev and dA_prev
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_pad
a_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 volume
for w in range(n_W): # loop over horizontal axis of the output volume
for c in range(n_C): # loop over the channels of the output volume
# Find the corners of the current "slice"
vert_start = h * stride
vert_end = vert_start + f
horiz_start = w * stride
horiz_end = horiz_start + f
# Use the corners to define the slice from a_prev_pad
a_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 above
da_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 unpadded da_prev_pad (Hint: use X[pad:-pad, pad:-pad, :])
dA_prev[i, :, :, :] = da_prev_pad[pad:-pad, pad:-pad, :]
# Making sure your output shape is correct
assert(dA_prev.shape == (m, n_H_prev, n_W_prev, n_C_prev))
return dA_prev, dW, db
# We'll run conv_forward to initialize the 'Z' and 'cache_conv",
# which we'll use to test the conv_backward function
np.random.seed(1)
A_prev = np.random.randn(10, 4, 4, 3)
W = np.random.randn(2, 2, 3, 8)
b = np.random.randn(1, 1, 1, 8)
hparameters = {"pad" : 2,
"stride": 2}
Z, cache_conv = conv_forward(A_prev, W, b, hparameters)
# Test conv_backward
dA, dW, db = conv_backward(Z, cache_conv)
print("dA_mean =", np.mean(dA))
print("dW_mean =", np.mean(dW))
print("db_mean =", np.mean(db))
assert type(dA) == np.ndarray, "Output must be a np.ndarray"
assert type(dW) == np.ndarray, "Output must be a np.ndarray"
assert type(db) == np.ndarray, "Output must be a np.ndarray"
assert dA.shape == (10, 4, 4, 3), f"Wrong shape for dA {dA.shape} != (10, 4, 4, 3)"
assert dW.shape == (2, 2, 3, 8), f"Wrong shape for dW {dW.shape} != (2, 2, 3, 8)"
assert db.shape == (1, 1, 1, 8), f"Wrong shape for db {db.shape} != (1, 1, 1, 8)"
assert np.isclose(np.mean(dA), 1.4524377), "Wrong values for dA"
assert np.isclose(np.mean(dW), 1.7269914), "Wrong values for dW"
assert np.isclose(np.mean(db), 7.8392325), "Wrong values for db"
print("\033[92m All tests passed.")
□ Pooling Layer - Backward Pass
let's implement the backward pass for the pooling layer, starting with the MAX-POOL layer. Even though a pooling layer has no parameters for backprop to update, you still need to backpropagate the gradient through the pooling layer in order to compute gradients for layers that came before the pooling layer.
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.
"""
# (≈1 line)
# mask = None
# YOUR CODE STARTS HERE
mask = (x == np.max(x))
# YOUR CODE ENDS HERE
return mask
np.random.seed(1)
x = np.random.randn(2, 3)
mask = create_mask_from_window(x)
print('x = ', x)
print("mask = ", mask)
x = np.array([[-1, 2, 3],
[2, -3, 2],
[1, 5, -2]])
y = np.array([[False, False, False],
[False, False, False],
[False, True, False]])
mask = create_mask_from_window(x)
assert type(mask) == np.ndarray, "Output must be a np.ndarray"
assert mask.shape == x.shape, "Input and output shapes must match"
assert np.allclose(mask, y), "Wrong output. The True value must be at position (2, 1)"
print("\033[92m All tests passed.")
Why keep track of the position of the max? It's because this is the input value that ultimately influenced the output, and therefore the cost. Backprop is computing gradients with respect to the cost, so anything that influences the ultimate cost should have a non-zero gradient. So, backprop will "propagate" the gradient back to this particular input value that had influenced the cost.
□ Average Pooling - Backward Pass
In max pooling, for each input window, all the "influence" on the output came from a single input value--the max. In average pooling, every element of the input window has equal influence on the output. So to implement backprop, you will now implement a helper function that reflects this.
For example if we did average pooling in the forward pass using a 2x2 filter, then the mask you'll use for the backward pass will look like:
This implies that each position in the 𝑑𝑍 matrix contributes equally to output because in the forward pass, we took an average.
def distribute_value(dz, shape):
"""
Distributes the input value in the matrix of dimension shape
Arguments:
dz -- input scalar
shape -- the shape (n_H, n_W) of the output matrix for which we want to distribute the value of dz
Returns:
a -- Array of size (n_H, n_W) for which we distributed the value of dz
"""
# 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 = None
# YOUR CODE STARTS HERE
a = np.ones(shape) * average
# YOUR CODE ENDS HERE
return a
a = distribute_value(2, (2, 2))
print('distributed value =', a)
assert type(a) == np.ndarray, "Output must be a np.ndarray"
assert a.shape == (2, 2), f"Wrong shape {a.shape} != (2, 2)"
assert np.sum(a) == 2, "Values must sum to 2"
a = distribute_value(100, (10, 10))
assert type(a) == np.ndarray, "Output must be a np.ndarray"
assert a.shape == (10, 10), f"Wrong shape {a.shape} != (10, 10)"
assert np.sum(a) == 100, "Values must sum to 100"
print("\033[92m All tests passed.")
□ Putting it Together: Pooling Backward
You now have everything you need to compute backward propagation on a pooling layer.
def pool_backward(dA, cache, mode = "max"):
"""
Implements the backward pass of the pooling layer
Arguments:
dA -- gradient of cost with respect to the output of the pooling layer, same shape as A
cache -- 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
"""
# 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.shape
m, 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 axis
for w in range(n_W): # loop on the horizontal axis
for c in range(n_C): # loop over the channels (depth)
# Find the corners of the current "slice" (≈4 lines)
vert_start = h * stride
vert_end = vert_start + f
horiz_start = w * stride
horiz_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] += np.multiply(mask, dA[i, h, w, c])
elif mode == "average":
# Get the value da from dA (≈1 line)
da = dA[i, h, w, 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)
# Making sure your output shape is correct
assert(dA_prev.shape == A_prev.shape)
return dA_prev
np.random.seed(1)
A_prev = np.random.randn(5, 5, 3, 2)
hparameters = {"stride" : 1, "f": 2}
A, cache = pool_forward(A_prev, hparameters)
print(A.shape)
print(cache[0].shape)
dA = np.random.randn(5, 4, 2, 2)
dA_prev1 = pool_backward(dA, cache, mode = "max")
print("mode = max")
print('mean of dA = ', np.mean(dA))
print('dA_prev1[1,1] = ', dA_prev1[1, 1])
print()
dA_prev2 = pool_backward(dA, cache, mode = "average")
print("mode = average")
print('mean of dA = ', np.mean(dA))
print('dA_prev2[1,1] = ', dA_prev2[1, 1])
assert type(dA_prev1) == np.ndarray, "Wrong type"
assert dA_prev1.shape == (5, 5, 3, 2), f"Wrong shape {dA_prev1.shape} != (5, 5, 3, 2)"
assert np.allclose(dA_prev1[1, 1], [[0, 0],
[ 5.05844394, -1.68282702],
[ 0, 0]]), "Wrong values for mode max"
assert np.allclose(dA_prev2[1, 1], [[0.08485462, 0.2787552],
[1.26461098, -0.25749373],
[1.17975636, -0.53624893]]), "Wrong values for mode average"
print("\033[92m All tests passed.")
■ 마무리
"Convolutional Neural Networks" (Andrew Ng)의 1주차 "Convolutional Neural Networks: Step by Step" 실습에 대해서 정리해봤습니다.
그럼 오늘 하루도 즐거운 나날 되길 기도하겠습니다
좋아요와 댓글 부탁드립니다 :)
감사합니다.
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