def conv_backward_naive(dout, cache): """ A naive implementation of the backward pass for a convolutional layer. Inputs: - dout: Upstream derivatives. - cache: A tuple of (x, w, b, conv_param) as in conv_forward_naive Returns a tuple of: - dx: Gradient with respect to x - dw: Gradient with respect to w - db: Gradient with respect to b """ dx, dw, db = None, None, None ############################################################################# # TODO: Implement the convolutional backward pass. # ############################################################################# x = cache[0] w = cache[1] b = cache[2] conv_param = cache[3] pad = conv_param['pad'] stride = conv_param['stride'] (N, C, H, W) = x.shape (F, C, HH, WW) = w.shape # Calculate x_col using the im2col helper function x_col = im2col.im2col_indices(x, field_height=HH, field_width=WW, padding=pad, stride=stride) # Calculate w_row using the im2col helper function w_row = im2col.im2col_indices(w, field_height=HH, field_width=WW, padding=0, stride=1) # Reshape the output gradient into col form dout_col = im2col.im2col_indices(dout, field_height=1, field_width=1, padding=0, stride=1) # Calculate and reshape the dx gradient dx_col = w_row.dot(dout_col) dx = im2col.col2im_indices(dx_col, x.shape, field_height=HH, field_width=WW, padding=pad, stride=stride) # Calculate and reshape the dw gradient dw_row = x_col.dot(dout_col.T) dw = im2col.col2im_indices(dw_row, w.shape, field_height=HH, field_width=WW, padding=0, stride=1) # Calculate and reshape the db gradient db = np.sum(dout_col, axis=1) pass ############################################################################# # END OF YOUR CODE # ############################################################################# return dx, dw, db
def max_pool_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a max-pooling layer.
Inputs:
- dout: Upstream derivatives
- cache: A tuple of (x, pool_param) as in the forward pass.
Returns:
- dx: Gradient with respect to x
"""
dx = None
###########################################################################
# TODO: Implement the max-pooling backward pass #
###########################################################################
x, pool_param, mask = cache
N, C, H, W = x.shape
dx = np.zeros(x.shape)
for i in range(N):
for j in range(C):
m_temp = im2col_indices(np.reshape(mask[i][j], (1, 1, H, W)),
pool_param['pool_height'],
pool_param['pool_width'], 0,
pool_param['stride'])
dout_temp = np.reshape(dout[i][j], (-1))
dx[i, j, :, :] = col2im_indices(m_temp * dout_temp, (1, 1, H, W),
pool_param['pool_height'],
pool_param['pool_width'], 0,
pool_param['stride'])
pass
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx
def max_pool_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a max pooling layer.
Inputs:
- dout: Upstream derivatives
- cache: A tuple of (x, pool_param) as in the forward pass.
Returns:
- dx: Gradient with respect to x
"""
#############################################################################
# TODO: Implement the max pooling backward pass #
#############################################################################
x, pool_param, x_col, switches = cache
HH, WW = pool_param['pool_height'], pool_param['pool_width']
stride = pool_param['stride']
N, C, H, W = x.shape
dx_col = np.zeros_like(x_col)
dout_flat = dout.transpose(2, 3, 0, 1).ravel()
dx_col[switches, np.arange(switches.size)] = dout_flat
dx = col2im_indices(dx_col, (N * C, 1, H, W),
HH,
WW,
padding=0,
stride=stride).reshape(x.shape)
#############################################################################
# END OF YOUR CODE #
#############################################################################
return dx
def max_pool_forward_naive(x, pool_param):
"""
A naive implementation of the forward pass for a max pooling layer.
Inputs:
- x: Input data, of shape (N, C, H, W)
- pool_param: dictionary with the following keys:
- 'pool_height': The height of each pooling region
- 'pool_width': The width of each pooling region
- 'stride': The distance between adjacent pooling regions
Returns a tuple of:
- out: Output data
- cache: (x, pool_param)
"""
out = None
#############################################################################
# TODO: Implement the max pooling forward pass #
#############################################################################
# Unpack params
(N, C, H, W) = x.shape
HH = pool_param['pool_height']
WW = pool_param['pool_width']
stride = pool_param['stride']
# Calculate H' and W'
H_ = 1 + (H - HH) / stride
W_ = 1 + (W - WW) / stride
# Calculate x_col using the im2col helper function
x_col = im2col.im2col_indices(x, HH, WW, padding=0, stride=stride)
# Reshape into pools over all channels
x_col_pools = x_col.T.reshape(-1, HH*WW).T
# Perform the max-pooling
switches = np.argmax(x_col_pools, axis=0)
out_maxpool = x_col_pools[switches, np.arange(x_col_pools.shape[-1])]
# Reshape into columns
out_maxpool_col = out_maxpool.reshape(-1, C).T
# Reshape the output using the col2im helper function
out = im2col.col2im_indices(out_maxpool_col, (N,C,H_,W_), field_height=1, field_width=1, padding=0, stride=1)
pass
#############################################################################
# END OF YOUR CODE #
#############################################################################
cache = (x, switches, pool_param)
return out, cache
def max_pool_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a max pooling layer.
Inputs:
- dout: Upstream derivatives
- cache: A tuple of (x, pool_param) as in the forward pass.
Returns:
- dx: Gradient with respect to x
"""
dx = None
#############################################################################
# TODO: Implement the max pooling backward pass #
#############################################################################
x, pool_param = cache
pool_height = pool_param['pool_height']
pool_width = pool_param['pool_width']
stride = pool_param['stride']
N, C, H, W = x.shape
HH = (H - pool_height) // stride + 1
WW = (W - pool_width) // stride + 1
#k, i, j = get_im2col_indices(x.shape, pool_height, pool_width, 0, stride)
#pool_col = x[:, k, i, j]
pool_col = im2col_indices(x, pool_height, pool_width, 0, stride)
pool_col = pool_col.reshape(C, pool_height * pool_width, -1).transpose(
1, 0, 2).reshape(pool_height * pool_width, -1)
pool_max_index = np.argmax(pool_col, axis=0)
#print('pool_max_index', len(pool_max_index))
dx_col = np.zeros(pool_col.shape)
#print('dx_col.shape', dx_col.shape)
#print('dout.shape--before', dout.shape)
dout = dout.transpose(1, 2, 3, 0).reshape(dout.size)
#print('dout.shape', dout.shape)
dx_col[pool_max_index, range(len(pool_max_index))] = dout
dx_col = dx_col.reshape(pool_height * pool_width, C, -1).transpose(
1, 0, 2).reshape(C * pool_height * pool_width, -1)
dx = col2im_indices(dx_col, x.shape, pool_height, pool_width, 0, stride)
#print(dx)
#############################################################################
# END OF YOUR CODE #
#############################################################################
return dx
def max_pool_backward_naive(dout, cache): """ A naive implementation of the backward pass for a max pooling layer. Inputs: - dout: Upstream derivatives - cache: A tuple of (x, pool_param) as in the forward pass. Returns: - dx: Gradient with respect to x """ dx = None ############################################################################# # TODO: Implement the max pooling backward pass # ############################################################################# x = cache[0] switches = cache[1] pool_param = cache[2] (N, C, H, W) = x.shape HH = pool_param['pool_height'] WW = pool_param['pool_width'] stride = pool_param['stride'] # Calculate x_col using the im2col helper function x_col = im2col.im2col_indices(x, field_height=HH, field_width=WW, padding=0, stride=stride) # Reshape into pools over all channels # x_col_pools = x_col.T.reshape(-1, HH*WW).T x_col_pools = x_col.reshape(-1,HH*WW).T # Reshape the output gradient into col form dout_col = im2col.im2col_indices(dout, field_height=1, field_width=1, padding=0, stride=1) # Since we're taking the gradient of a max function, # we route the output gradient to the inputs that had # the max values on the forward pass using the cached switches. dx_col_pools = np.zeros(x_col_pools.shape) dx_col_pools[switches, np.arange(dx_col_pools.shape[-1])] = dout_col.T.flatten() # Reshape into col form dx_col = dx_col_pools.T.reshape(x_col.T.shape).T # Finally, reshape dx_col dx = im2col.col2im_indices(dx_col, x.shape, field_height=HH, field_width=WW, padding=0, stride=stride) pass ############################################################################# # END OF YOUR CODE # ############################################################################# return dx
def max_pool_forward_naive(x, pool_param):
"""
A naive implementation of the forward pass for a max-pooling layer.
Inputs:
- x: Input data, of shape (N, C, H, W)
- pool_param: dictionary with the following keys:
- 'pool_height': The height of each pooling region
- 'pool_width': The width of each pooling region
- 'stride': The distance between adjacent pooling regions
No padding is necessary here. Output size is given by
Returns a tuple of:
- out: Output data, of shape (N, C, H', W') where H' and W' are given by
H' = 1 + (H - pool_height) / stride
W' = 1 + (W - pool_width) / stride
- cache: (x, pool_param)
"""
out = None
###########################################################################
# TODO: Implement the max-pooling forward pass #
###########################################################################
N, C, H, W = x.shape
H_d = int(1 + (H - pool_param['pool_height']) / pool_param['stride'])
W_d = int(1 + (W - pool_param['pool_width']) / pool_param['stride'])
out = np.zeros((N, C, H_d, W_d))
mask = np.zeros(x.shape)
for i in range(N):
for j in range(C):
x_temp = np.reshape(x[i][j], (1, 1, H, W))
x_temp = im2col_indices(x_temp, pool_param['pool_height'],
pool_param['pool_width'], 0,
pool_param['stride'])
out[i, j, :, :] = np.reshape(np.amax(x_temp, axis=0),
(1, 1, H_d, W_d))
inds = np.argmax(x_temp, axis=0)
temp = np.zeros(x_temp.shape)
temp[inds, range(H_d * W_d)] = 1
mask[i, j, :, :] = col2im_indices(temp, (1, 1, H, W),
pool_param['pool_height'],
pool_param['pool_width'], 0,
pool_param['stride'])
pass
###########################################################################
# END OF YOUR CODE #
###########################################################################
cache = (x, pool_param, mask)
return out, cache
def conv_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a convolutional layer.
Inputs:
- dout: Upstream derivatives of shape (N, C, H, W)
- cache: A tuple of (x, w, b, conv_param) as in conv_forward_naive
- x: Input data of shape (N, C, H, W)
- w: Filter weights of shape (F, C, HH, WW)
- b: Biases, of shape (F,)
Returns a tuple of:
- dx: Gradient with respect to x
- dw: Gradient with respect to w
- db: Gradient with respect to b
"""
dx, dw, db = None, None, None
###########################################################################
# TODO: Implement the convolutional backward pass. #
###########################################################################
x, w, b, conv_param = cache
N, C, H, W = x.shape
F, _, HH, WW = w.shape
_, _, h_out, w_out = dout.shape
stride = conv_param['stride']
pad = conv_param['pad']
# dx = np.zeros_like(x)
# dw = np.zeros_like(w)
# db = np.zeros_like(b)
db = np.sum(dout, axis=(0, 2, 3))
dout = dout.transpose(1, 2, 3, 0)
dout = dout.reshape(dout.shape[0], -1)
import cs231n.im2col as im2col
X_col = im2col.im2col_indices(x, HH, WW, padding=pad, stride=stride)
W_col = w.reshape(F, -1)
dw = np.dot(dout, X_col.T)
dx = np.dot(W_col.T, dout)
dw = dw.reshape(F, C, HH, WW)
dx = im2col.col2im_indices(dx, x.shape, field_height=HH, field_width=WW, padding=pad, stride=stride)
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dw, db
def max_pool_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a max pooling layer.
Inputs:
- dout: Upstream derivatives
- cache: A tuple of (x, pool_param) as in the forward pass.
Returns:
- dx: Gradient with respect to x
"""
dx = None
###########################################################################
# TODO: Implement the max pooling backward pass #
###########################################################################
x, pool_param = cache
num_data, num_channels, im_height, im_width = x.shape
pool_height, pool_width, stride = (pool_param['pool_height'],
pool_param['pool_width'],
pool_param['stride'])
out_height = (im_height - pool_height) // stride + 1
out_width = (im_width - pool_width) // stride + 1
x_reshaped = x.reshape(num_data * num_channels, 1, im_height, im_width)
x_col = im2col_indices(x_reshaped,
pool_height,
pool_width,
padding=0,
stride=stride)
dx_col = np.zeros(x_col.shape)
max_idx = np.argmax(x_col, axis=0)
dx_col[max_idx, np.arange(dout.size)] = dout.transpose(2, 3, 0, 1).ravel()
dx = col2im_indices(dx_col,
(num_data * num_channels, 1, im_height, im_width),
pool_height,
pool_width,
padding=0,
stride=stride)
dx = dx.reshape(x.shape)
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx
def conv_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a convolutional layer.
Inputs:
- dout: Upstream derivatives.
- cache: A tuple of (x, w, b, conv_param) as in conv_forward_naive
Returns a tuple of:
- dx: Gradient with respect to x
- dw: Gradient with respect to w
- db: Gradient with respect to b
"""
dx, dw, db = None, None, None
###########################################################################
# TODO: Implement the convolutional backward pass. #
###########################################################################
x, w, b, conv_param = cache
pad, stride = conv_param['pad'], conv_param['stride']
num_data = dout.shape[0]
num_filters, num_channels, filter_height, filter_width = w.shape
dout_matrix = dout.transpose(1, 2, 3, 0).reshape(num_filters, -1)
cols = im2col_indices(x,
filter_height,
filter_width,
padding=pad,
stride=stride)
filter_matrix = w.reshape(num_filters, -1)
db = np.sum(dout, axis=(0, 2, 3))
dw = np.reshape(dout_matrix.dot(cols.T), w.shape)
dx_col = filter_matrix.T.dot(dout_matrix)
dx = col2im_indices(dx_col,
x.shape,
filter_height,
filter_width,
padding=pad,
stride=stride)
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dw, db
def conv_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a convolutional layer.
Inputs:
- dout: Upstream derivatives.
- cache: A tuple of (x, w, b, conv_param) as in conv_forward_naive
Returns a tuple of:
- dx: Gradient with respect to x
- dw: Gradient with respect to w
- db: Gradient with respect to b
"""
dx, dw, db = None, None, None
x, w, b, conv_param = cache
N, C, H, W = x.shape
f_filter, c_fitler, h_filter, w_filter = w.shape
###########################################################################
# TODO: Implement the convolutional backward pass. #
###########################################################################
db = np.sum(dout, axis=(0, 2, 3))
x_col = im2col.im2col_indices(x,
h_filter,
w_filter,
padding=conv_param['pad'],
stride=conv_param['stride'])
dout_reshaped = dout.transpose(1, 2, 3, 0).reshape(f_filter, -1)
dw = np.dot(dout_reshaped, x_col.T)
dw = dw.reshape(w.shape)
w_shape = w.reshape(f_filter, -1)
dX_col = np.dot(w_shape.T, dout_reshaped)
dx = im2col.col2im_indices(dX_col,
x.shape,
h_filter,
w_filter,
padding=conv_param['pad'],
stride=conv_param['stride'])
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dw, db
def max_pool_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a max pooling layer.
Inputs:
- dout: Upstream derivatives
- cache: A tuple of (x, pool_param) as in the forward pass.
Returns:
- dx: Gradient with respect to x
"""
dx = None
###########################################################################
# TODO: Implement the max pooling backward pass #
###########################################################################
x, pool_param = cache
N, C, H, W = x.shape
x_reshaped = x.reshape(N * C, 1, H, W)
h_out = int(1 +
(H + 2 * 0 - pool_param['pool_height']) / pool_param['stride'])
w_out = int(1 +
(W + 2 * 0 - pool_param['pool_width']) / pool_param['stride'])
x_col = im2col.im2col_indices(x_reshaped,
pool_param['pool_height'],
pool_param['pool_width'],
padding=0,
stride=pool_param['stride'])
max_idx = np.argmax(x_col, axis=0)
dx_col = np.zeros_like(x_col)
dout_ = dout.transpose(2, 3, 0, 1).ravel()
dx_col[max_idx, range(max_idx.size)] = dout_
dx = im2col.col2im_indices(dx_col, (N * C, 1, H, W),
pool_param['pool_height'],
pool_param['pool_width'],
padding=0,
stride=pool_param['stride'])
dx = dx.reshape(x.shape)
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx
def conv_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a convolutional layer.
Inputs:
- dout: Upstream derivatives.
- cache: A tuple of (x, w, b, conv_param) as in conv_forward_naive
Returns a tuple of:
- dx: Gradient with respect to x
- dw: Gradient with respect to w
- db: Gradient with respect to b
"""
dx, dw, db = None, None, None
#############################################################################
# TODO: Implement the convolutional backward pass. #
#############################################################################
x, w, b, conv_param = cache
stride = conv_param['stride']
pad = conv_param['pad']
#print('pad', pad)
N, C, H, W = x.shape
F, C, HH, WW = w.shape
#Hdot = 1 + (H+2*pad - HH) // stride
#Wdot = 1 + (W + 2*pad -WW) // stride
x_col = im2col_indices(x, HH, WW, pad, stride)
#print('x_col shape', x_col.shape)
w_transfer = w.reshape(F, -1)
dout_t = dout.transpose(1, 2, 3, 0).reshape(F, -1)
dx_col = np.dot(w_transfer.T, dout_t)
dx = col2im_indices(dx_col, x.shape, HH, WW, pad, stride)
dw_transfer = np.dot(dout_t, x_col.T)
dw = dw_transfer.reshape(w.shape)
db = np.sum(dout_t, axis=1)
#############################################################################
# END OF YOUR CODE #
#############################################################################
return dx, dw, db
def conv_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a convolutional layer.
Inputs:
- dout: Upstream derivatives.
- cache: A tuple of (x, w, b, conv_param) as in conv_forward_naive
Returns a tuple of:
- dx: Gradient with respect to x
- dw: Gradient with respect to w
- db: Gradient with respect to b
"""
from cs231n.im2col import im2col_indices, col2im_indices
x, w, b, conv_param = cache
stride, pad = conv_param['stride'], conv_param['pad']
F, C, HH, WW = w.shape
N, C, H, W = x.shape
dx, dw, db = None, None, None
###########################################################################
# TODO: Implement the convolutional backward pass. #
###########################################################################
db = np.sum(dout, axis=(0, 2, 3))
# dout has shape (N, F, H_new, W_new)
# dout_reshape has shape (F, H_new*W_new*N)
dout_reshape = dout.transpose(1, 2, 3, 0).reshape((F, -1))
# x_col has shape (C*HH*WW, N*H_new*W_new)
x_col = im2col_indices(x, HH, WW, padding=pad, stride=stride)
dw_ = np.dot(dout_reshape, x_col.transpose())
dw = dw_.reshape(F, C, HH, WW)
w_reshape = w.reshape(F, -1)
dx_ = np.dot(w_reshape.transpose(), dout_reshape)
dx = col2im_indices(dx_, x.shape, HH, WW, padding=pad, stride=stride)
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dw, db
def max_pool_backward_naive(dout, cache):
"""
A naive implementation of the backward pass for a max pooling layer.
Inputs:
- dout: Upstream derivatives
- cache: A tuple of (x, pool_param) as in the forward pass.
Returns:
- dx: Gradient with respect to x
"""
from cs231n.im2col import im2col_indices, col2im_indices
dx = None
###########################################################################
# TODO: Implement the max pooling backward pass #
###########################################################################
x, pool_param = cache
N, C, H, W = x.shape
pool_height, pool_width, stride = pool_param['pool_height'], \
pool_param['pool_width'], pool_param['stride']
out_mask = pool_param['out_mask']
N, C, H_new, W_new = dout.shape
dout_ = dout.transpose(2, 3, 0, 1).reshape([N * C * H_new * W_new])
dx_ = dout_ * out_mask
dx_ = col2im_indices(dx_, [N * C, 1, H, W],
pool_height,
pool_width,
padding=0,
stride=stride)
#print(out_mask)
dx = dx_.reshape(N, C, W, H)
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx
def conv_forward_naive(x, w, b, conv_param):
"""
A naive implementation of the forward pass for a convolutional layer.
The input consists of N data points, each with C channels, height H and width
W. We convolve each input with F different filters, where each filter spans
all C channels and has height HH and width HH.
Input:
- x: Input data of shape (N, C, H, W)
- w: Filter weights of shape (F, C, HH, WW)
- b: Biases, of shape (F,)
- conv_param: A dictionary with the following keys:
- 'stride': The number of pixels between adjacent receptive fields in the
horizontal and vertical directions.
- 'pad': The number of pixels that will be used to zero-pad the input.
Returns a tuple of:
- out: Output data, of shape (N, F, H', W') where H' and W' are given by
H' = 1 + (H + 2 * pad - HH) / stride
W' = 1 + (W + 2 * pad - WW) / stride
- cache: (x, w, b, conv_param)
"""
out = None
#############################################################################
# TODO: Implement the convolutional forward pass. #
# Hint: you can use the function np.pad for padding. #
#############################################################################
# Unpack params
pad = conv_param['pad']
stride = conv_param['stride']
(N, C, H, W) = x.shape
(F, C, HH, WW) = w.shape
# Calculate H' and W'
H_ = 1 + (H + 2 * pad - HH) / stride
W_ = 1 + (W + 2 * pad - WW) / stride
# TODO: Add some exception throwing here if H_ and W_ are not ints
# Calculate x_col using the im2col helper function
x_col = im2col.im2col_indices(x, HH, WW, padding=pad, stride=stride)
# Calculate w_row using the im2col helper function
w_row = im2col.im2col_indices(w, HH, WW, padding=0, stride=1)
# Pad out x_col with ones so we can use the bias trick
x_col_1 = np.vstack((x_col, np.ones(x_col.shape[-1])))
# Pad out w_row with the bias term b
w_row_1 = np.vstack((w_row, b))
# Perform the convolution
out_ = np.dot(w_row_1.T, x_col_1)
# Reshape the output using the col2im helper function
out = im2col.col2im_indices(out_, (N,F,H_,W_), field_height=1, field_width=1, padding=0, stride=1)
pass
#############################################################################
# END OF YOUR CODE #
#############################################################################
cache = (x, w, b, conv_param)
return out, cache