Convolution model – Step by Step – v2
这部分代码我一开始做是错的，想了好久细节才写出来，我觉得搞深度学习的很有必要把这个作业过一遍，为了让大家都能顺利完成，我把我的代码贴出来。
zero_pad
这部分看似就一行代码，但是需要仔细想想。
# 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)
"""
### START CODE HERE ### (≈ 1 line)
X_pad = np.pad(X, ((0,0), (pad,pad), (pad,pad), (0,0)), 'constant', constant_values = (0,0))
### END CODE HERE ###
return X_pad
conv_single_step
# 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, 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 = np.multiply(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
conv_forward
这个算是最复杂的一部分了，有很多细节，比如移动框的地方。
# 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 = h*stride + f
horiz_start = w*stride
horiz_end = w*stride + f
# Use the corners to define the (3D) slice of a_prev_pad (See Hint above the cell). (≈1 line)
a_slice_prev = conv_single_step(a_prev_pad[vert_start:vert_end,horiz_start:horiz_end],W[:,:,:,c],b[:,:,:,c])
# 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] = a_slice_prev
### 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
pool_forward
这里需要注意我们channel没有变化。
# 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))
### START CODE HERE ###
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
for w in range(n_W): # loop on the 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" (≈4 lines)
vert_start = h*stride
vert_end = h*stride + f
horiz_start = w*stride
horiz_end = w*stride + 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.average(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 correct
assert(A.shape == (m, n_H, n_W, n_C))
return A, cache
后面是optional的部分，反向传播的，也挺麻烦的
conv_backward
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)
"""
### 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 shapes
dA_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
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 = h*stride + f
horiz_start = w*stride
horiz_end = w*stride + 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 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 correct
assert(dA_prev.shape == (m, n_H_prev, n_W_prev, n_C_prev))
return dA_prev, dW, db
create_mask_from_window
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
distribute_value
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
"""
### 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 = float(dz)/(n_H*n_W)
# Create a matrix where every entry is the "average" value (≈1 line)
a = np.ones((n_H,n_W),dtype=np.float32)*average
### END CODE HERE ###
return a
pool_backward
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
"""
### 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.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 = h*stride + f
horiz_start = w*stride
horiz_end = w*stride + 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,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)
### END CODE ###
# Making sure your output shape is correct
assert(dA_prev.shape == A_prev.shape)
return dA_prev
总体来说这份作业还是很提高人水平的，就算我之前已经独立写过好几个比较大的tensorflow的项目，但是我对这种细节了解的还不是那么清楚，更不要说有cache来进行反向传播这种巧妙的机制。
