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 x, pool_param = cache pool_height, pool_width, stride = pool_param['pool_height'], pool_param['pool_width'], pool_param['stride'] N, C, H, W = x.shape ############################################################################# # TODO: Implement the max pooling backward pass # ############################################################################# assert (H - pool_height) % stride == 0, 'Invalid height' assert (W - pool_width) % stride == 0, 'Invalid width' x_shape = x.reshape(N*C,1,H,W) x_col = im2col.im2col_indices(x_shape, field_height=pool_height, field_width=pool_width, padding=0, stride=stride) x_arg = np.argmax(x_col, axis=0) dx = np.zeros((pool_height*pool_width, len(x_arg))) dx[np.argmax(x_col, axis=0), xrange(len(x_arg))] = dout.transpose(2,3,0,1).reshape(-1) dx = im2col.col2im_indices(dx, (N * C, 1, H, W), pool_height, pool_width, padding=0, stride=stride) dx = dx.reshape(x.shape) ############################################################################# # END OF YOUR CODE # ############################################################################# return dx
def backward(self, X, grad):
N, W_out, H_out, D_out = grad.shape
N, W_in, H_in, D_in = X.shape
#Preprocess 'a' for im2col utility
grad = np.rollaxis(grad, 3, 1)
grad = np.rollaxis(grad, 0, 4) # D_out X H_out X W_out X N
X = np.rollaxis(X, 3, 1)
a_columnar = im2col_indices(X, self.field, self.field, self.padding,
self.stride) #[FFD X W_out*H_out*N]
grad = grad.reshape(D_out, N * W_out * H_out)
dWeight = np.dot(grad, a_columnar.T) #[ D_out X FFD ]
dBias = np.sum(grad, axis=1) #D_out
dActivation = np.dot(grad.T, self.weights).T #[FFD_out X N*W_out**2]
dActivation = col2im_indices(dActivation, (N, D_in, W_in, H_in),
self.field, self.field, self.padding,
self.stride) # N X D_in X W_in X H_in
#Move D axis to end
dX = np.rollaxis(dActivation, 1, 4) #N X W_in X H_in X D_in
self.dw = dWeight
self.db = dBias
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, x_cols = cache
stride, pad = conv_param["stride"], conv_param["pad"]
db = np.sum(dout, axis=(0, 2, 3))
num_filters, _, filter_height, filter_width = w.shape
dout_reshaped = dout.transpose(1, 2, 3, 0).reshape(num_filters, -1)
dw = dout_reshaped.dot(x_cols.T).reshape(w.shape)
dx_cols = w.reshape(num_filters, -1).T.dot(dout_reshaped)
dx = im2col.col2im_indices(dx_cols, x.shape, filter_height, filter_width, pad, stride)
#############################################################################
# END OF YOUR CODE #
#############################################################################
return dx, dw, db
def backward(self, x, dy):
N, c, h, w = x.shape
xshaped = x.reshape(N * c, 1, h, w)
xcol = im2col.im2col_indices(xshaped, self.kernel_h, self.kernel_w,
self.pad, self.stride)
dxcol = np.zeros_like(xcol)
dy = dy.transpose(2, 3, 0, 1).ravel()
dxcol[self.params['max_x'], range(self.params['max_x'].size)] = dy
dx = im2col.col2im_indices(dxcol, (N * c, 1, h, w), self.kernel_h,
self.kernel_w, self.pad, self.stride)
dx = dx.reshape(x.shape)
return dx
def conv_backward_naive(dout, cache, debug=False):
"""
卷积层的反向传播实现
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, x_cols = cache
stride, pad = conv_param['stride'], conv_param['pad']
db = np.sum(dout, axis=(0, 2, 3))
F, _, HH, WW = w.shape
dout_reshape = np.reshape(dout.transpose(1, 2, 3, 0), (F, -1))
dw = dout_reshape.dot(x_cols.T).reshape(w.shape)
dx_cols = w.reshape(F, -1).T.dot(dout_reshape)
from im2col import col2im_indices
dx = col2im_indices(dx_cols,
x.shape,
field_height=HH,
field_width=WW,
padding=pad,
stride=stride,
verbose=True)
if debug:
print "dout's shape: {}".format(str(dout.shape))
print "dout's reshape: {}".format(str(dout_reshape.shape))
print "x's shape: {}".format(str(x.shape))
print "x's cols: {}".format(str(x_cols.shape))
print "w's shape: {}".format(str(w.shape))
print "b's shape: {}".format(str(b.shape))
print "stride: {}".format(str(conv_param["stride"]))
print "padding: {}".format(str(conv_param["pad"]))
return dx, dw, db
def backward(self, x, dy):
xcol = im2col.im2col_indices(x, self.kernel_h, self.kernel_w, self.pad,
self.stride)
dy = dy.transpose(1, 2, 3, 0).reshape(self.kernel_number, -1)
db = np.sum(dy, axis=1)
dw = np.dot(dy,
xcol.T).reshape(self.kernel_number, self.kernel_h,
self.kernel_w, -1).transpose(0, 3, 1, 2)
self.params['dw'] = dw
self.params['db'] = db
W_shaped = self.params['w'].reshape(self.kernel_number, -1)
dx = np.dot(dy.T, W_shaped).T
dx_im = im2col.col2im_indices(dx, x.shape, self.kernel_h,
self.kernel_w, self.pad, self.stride)
return dx_im
def backward(self, out_grad):
n_filters, c_kernel, h_kernel, w_kernel = self._weight.shape
self._grad_bias = np.sum(out_grad, axis=(0, 2, 3))
self._grad_bias = self._grad_bias.reshape(n_filters, -1)
x_col = im2col_indices(self.x, h_kernel, w_kernel, padding=self._padding, stride=self._stride)
out_grad_reshaped = out_grad.transpose(1, 2, 3, 0).reshape(n_filters, -1)
self._grad_weight = out_grad_reshaped @ x_col.T
self._grad_weight = self._grad_weight.reshape(self._weight.shape)
weight_reshaped = self._weight.reshape(n_filters, -1)
grad_x_col = weight_reshaped @ out_grad_reshaped
grad_x = col2im_indices(grad_x_col, self.x.shape, h_kernel, w_kernel, padding=padding, stride=stride)
return grad_x
def conv_backward_naive(dout, cache, debug=False):
"""
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, x_cols = cache
stride, pad = conv_param['stride'], conv_param['pad']
db = np.sum( dout, axis=(0, 2, 3) )
F, _, HH, WW = w.shape
dout_reshape = np.reshape(dout.transpose(1,2,3,0), (F, -1))
dw = dout_reshape.dot(x_cols.T).reshape(w.shape)
dx_cols = w.reshape(F, -1).T.dot(dout_reshape)
from im2col import col2im_indices
dx = col2im_indices(dx_cols, x.shape, field_height=HH, field_width=WW, padding=pad, stride=stride, verbose=True)
if debug:
print "dout's shape: {}".format( str(dout.shape) )
print "dout's reshape: {}".format( str(dout_reshape.shape))
print "x's shape: {}".format( str(x.shape) )
print "x's cols: {}".format( str(x_cols.shape))
print "w's shape: {}".format( str(w.shape) )
print "b's shape: {}".format( str(b.shape) )
print "stride: {}".format( str(conv_param["stride"]) )
print "padding: {}".format( str(conv_param["pad"]) )
return dx, dw, db
def cnn_backward_pass(dout, cache, debug=False):
"""
A naive implementation of the backward pass for a convolutional layer.
Inputs:
- dout: Upstream derivatives.
- cache: A tuple of (x, w, b, stride, padding) as in cnn_backward_pass
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, stride, padding, x_cols = cache
db = np.sum(dout, axis=(0, 2, 3))
F, _, HH, WW = w.shape
dout_reshape = np.reshape(dout.transpose(1, 2, 3, 0), (F, -1))
dw = dout_reshape.dot(x_cols.T).reshape(w.shape)
dx_cols = w.reshape(F, -1).T.dot(dout_reshape)
dx = col2im_indices(dx_cols,
x.shape,
field_height=HH,
field_width=WW,
padding=padding,
stride=stride,
verbose=False)
if debug:
print "dout's shape: {}".format(str(dout.shape))
print "dout's reshape: {}".format(str(dout_reshape.shape))
print "x's shape: {}".format(str(x.shape))
print "x's cols: {}".format(str(x_cols.shape))
print "w's shape: {}".format(str(w.shape))
print "b's shape: {}".format(str(b.shape))
print "stride: {}".format(str(stride))
print "padding: {}".format(str(padding))
return dx, dw, db
def backward(self, delta, alpha):
stimulusCols = im2col_indices(self.stimulus, self.filterHeight,
self.filterWidth, self.padding,
self.stride)
filterCols = self.filters.reshape((self.numFilters, -1))
activationCols = self.activation.transpose(1, 2, 3, 0).reshape(
self.numFilters, -1)
deltaCols = delta.transpose(1, 2, 3, 0).reshape(
self.numFilters, -1) * conv.aprime(activationCols)
inputPartial = col2im_indices(
np.dot(deltaCols.transpose(1, 0),
filterCols), self.stimulus.shape, self.filterHeight,
self.filterWidth, self.padding, self.stride)
self.filters -= alpha * np.dot(
deltaCols, stimulusCols.transpose(1, 0)).reshape(
self.filters.shape)
self.bias -= alpha * np.sum(deltaCols, axis=1).reshape(
self.bias.shape)
return inputPartial
def backward(self, x: np.ndarray, dy: np.ndarray) -> np.ndarray:
n_filter, d_filter, h_filter, w_filter = self.weight.shape
db = np.sum(dy, axis=(0, 2, 3))
self.dbias = db.reshape(n_filter, -1)
X_col = im2col_indices(x,
h_filter,
w_filter,
padding=self.padding,
stride=self.stride)
dout_reshaped = dy.transpose(1, 2, 3, 0).reshape(n_filter, -1)
dW = dout_reshaped @ X_col.T
self.dweight = dW.reshape(self.weight.shape)
W_reshape = self.weight.reshape(n_filter, -1)
dX_col = W_reshape.T @ dout_reshaped
dX = col2im_indices(dX_col,
x.shape,
h_filter,
w_filter,
padding=self.padding,
stride=self.stride)
return dX
def backward(self, x: np.ndarray, dy: np.ndarray) -> np.ndarray:
def dmaxpool(dX_col, dout_col, pool_cache):
dX_col[pool_cache, range(dout_col.size)] = dout_col
return dX_col
x = x.reshape((x.shape[0], 1, 2 * x.shape[2], -1))
X_col = im2col_indices(x,
self.size,
self.size,
padding=0,
stride=self.stride)
n, d, w, h = x.shape
dX_col = np.zeros_like(X_col)
dout_col = dy.transpose(2, 3, 0, 1).ravel()
# dX = dmaxpool(dX_col, dout_col, pool_cache)
dX = col2im_indices(dX_col, (n * d, 1, h, w),
self.size,
self.size,
padding=0,
stride=self.stride)
dX = dX.reshape(x.shape)
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 x, w, b, conv_param = cache pad, stride = conv_param['pad'], conv_param['stride'] F, C, HH, WW = w.shape x_cols = im2col.im2col_indices(x, HH, WW, pad, stride) N, F, H_, W_ = dout.shape ############################################################################# # TODO: Implement the convolutional backward pass. # ############################################################################# dout_reshape = dout.reshape(N, -1) db = np.sum(dout, axis=(0, 2, 3)) dout_reshaped = dout.transpose(1, 2, 3, 0).reshape(F, -1) dw = dout_reshaped.dot(x_cols.T).reshape(w.shape) dx_cols = w.reshape(F, -1).T.dot(dout_reshaped) dx = im2col.col2im_indices(dx_cols, x.shape, HH, WW, pad, stride) ############################################################################# # END OF YOUR CODE # ############################################################################# return dx, dw, db
def _backward(self, dout):
# dout (N,Cout,H_,W_)
# W (Cout, Cin, F, F)
W = self.W['val']
n_filter, d_filter, h_filter, w_filter = W.shape
db = np.sum(dout, axis=(0, 2, 3))
db = db.reshape(n_filter, -1)
dout_reshaped = dout.transpose(1, 2, 3, 0).reshape(n_filter, -1)
dW = dout_reshaped @ self.X_col.T
dW = dW.reshape(W.shape)
W_reshape = W.reshape(n_filter, -1)
dX_col = W_reshape.T @ dout_reshaped
dX = im2col.col2im_indices(dX_col,
self.X.shape,
h_filter,
w_filter,
padding=1,
stride=1)
return dX #, dW, db
# Same convolution
conv = nn.Conv2d(cd.inp.shape[1], out_channels, kernel_size,
padding=padding, bias=True)
conv.weight.data = cd.convweights
#conv.bias.data = torch.zeros(out_channels)
conv.bias.data = cd.bias
output = conv(cd.inp)
output.backward(cd.convloss if padding == 0 else cd.convlossPad1)
print(f"output {to_cpp(output)}")
print(f"dinput {to_cpp(cd.inp.grad)}")
print (f"weights {to_cpp(conv.weight)}")
print(f"dweights {to_cpp(conv.weight.grad)}")
# now with im2col
n_filter = cd.convweights.shape[0]
x_col = im2col_indices(inp.detach().numpy(), kernel_size, kernel_size, padding=padding)
W_reshape = cd.convweights.detach().numpy().reshape(n_filter, -1)
dout_reshaped = cd.convloss.detach().numpy().transpose(1, 2, 3, 0).reshape(n_filter, -1)
if(padding == 1):
dout_reshaped = cd.convlossPad1.detach().numpy().transpose(1, 2, 3, 0).reshape(n_filter, -1)
dX_col = W_reshape.T @ dout_reshaped
dX = col2im_indices(dX_col, cd.inp.shape, kernel_size, kernel_size, padding=padding)
for h in range(kernel_size):
for w in range(kernel_size):
dilated[:, :, dilation * h, dilation * w] = kernel[:, :, h, w]
# forward pass with transposed kernel
n_filters = cd.convweights.shape[0]
inp_reshaped = inp.detach().numpy().transpose(1, 2, 3,
0).reshape(n_filters, -1)
W_reshape = dilated.reshape(n_filters, -1)
out_col = W_reshape.T @ inp_reshaped
# image is recovered through col2im
out_image = col2im_indices(out_col,
cd.inp.shape,
dilated_size,
dilated_size,
padding=padding)
is_eq(output, out_image)
################################################################################################
### Backward Pass
dout_col = im2col_indices(cd.convlossTrans.detach().numpy(),
dilated_size,
dilated_size,
padding=padding)
#dout_reshaped = cd.convlossTrans.detach().numpy().transpose(1, 2, 3, 0).reshape(n_filter, -1)
dX_col = W_reshape @ dout_col
c, _, h, w = inp.shape
dX = dX_col.reshape(n_filters, h, w, c).transpose(3, 0, 1, 2)
is_eq(dX, inp.grad)
