ConvolutionBackpropData#
Versioned name: ConvolutionBackpropData-1
Category: Convolution
Short description: Computes 1D, 2D or 3D ConvolutionBackpropData operation with respect to the input and kernel tensors. Also known as a Transposed Convolution.
Detailed description:
ConvolutionBackpropData takes the input tensor, weights tensor and output shape and computes the output tensor of a given shape. The shape of the output can be specified as an input 1D integer tensor explicitly or determined by other attributes implicitly. If output shape is specified as an explicit input, shape of the output exactly matches the specified size and required amount of padding is computed. More thorough explanation can be found in Transposed Convolutions.
ConvolutionBackpropData accepts the same set of attributes as a regular Convolution operation and additionally output_padding
attribute, but they are interpreted in a “backward way”, so they are applied to the output of ConvolutionBackpropData, but not to the input. Refer to a regular Convolution operation for detailed description of each Convolution attribute.
When output shape is specified as an input tensor output_shape
then it specifies only spatial dimensions. No batch or channel dimension should be passed along with spatial dimensions. If output_shape
is omitted, then pads_begin
, pads_end
or auto_pad
are used to determine output spatial shape [O_z, O_y, O_x]
by input spatial shape [I_z, I_y, I_x]
in the following way:
if auto_pads != None:
pads_begin[i] = 0
pads_end[i] = 0
Y_i = stride[i] * (X_i - 1) + ((K_i - 1) * dilations[i] + 1) - pads_begin[i] - pads_end[i] + output_padding[i]
where K_i
filter kernel dimension along spatial axis i
.
If output_shape
is specified, pads_begin
and pads_end
are ignored, and auto_pad
defines how to distribute padding amount around the tensor. In this case pads are determined based on the next formulas to correctly align input and output tensors:
total_padding[i] = stride[i] * (X_i - 1) + ((K_i - 1) * dilations[i] + 1) - output_shape[i] + output_padding[i]
if auto_pads != SAME_UPPER:
pads_begin[i] = total_padding[i] // 2
pads_end[i] = total_padding[i] - pads_begin[i]
else:
pads_end[i] = total_padding[i] // 2
pads_begin[i] = total_padding[i] - pads_end[i]
Attributes
strides
Description: strides has the same definition as strides for a regular Convolution but applied in the backward way, for the output tensor.
Range of values: positive integers
Type:
int[]
Required: yes
pads_begin
Description: pads_begin has the same definition as pads_begin for a regular Convolution but applied in the backward way, for the output tensor. May be omitted specified, in which case pads are calculated automatically.
Range of values: non-negative integers
Type:
int[]
Required: yes
Note: the attribute is ignored when auto_pad attribute is specified.
pads_end
Description: pads_end has the same definition as pads_end for a regular Convolution but applied in the backward way, for the output tensor. May be omitted, in which case pads are calculated automatically.
Range of values: non-negative integers
Type:
int[]
Required: yes
Note: the attribute is ignored when auto_pad attribute is specified.
dilations
Description: dilations has the same definition as dilations for a regular Convolution but applied in the backward way, for the output tensor.
Range of values: positive integers
Type:
int[]
Required: yes
auto_pad
Description: auto_pad has the same definition as auto_pad for a regular Convolution but applied in the backward way, for the output tensor.
explicit: use explicit padding values from
pads_begin
andpads_end
.same_upper the input is padded to match the output size. In case of odd padding value an extra padding is added at the end.
same_lower the input is padded to match the output size. In case of odd padding value an extra padding is added at the beginning.
valid - do not use padding.
Type:
string
Default value: None
Required: no
Note: pads_begin and pads_end attributes are ignored when auto_pad is specified.
output_padding
Description: output_padding adds additional amount of paddings per each spatial axis in the
output
tensor. It unlocks more elements in the output allowing them to be computed. Elements are added at the higher coordinate indices for the spatial dimensions. Number of elements in output_padding list matches the number of spatial dimensions indata
andoutput
tensors.Range of values: non-negative integer values
Type:
int[]
Default value: all zeros
Required: no
Inputs:
1: Input tensor of type T1 and rank 3, 4 or 5. Layout is
[N, C_INPUT, Z, Y, X]
(number of batches, number of input channels, spatial axes Z, Y, X). Required.2: Convolution kernel tensor of type T1 and rank 3, 4 or 5. Layout is
[C_INPUT, C_OUTPUT, Z, Y, X]
(number of input channels, number of output channels, spatial axes Z, Y, X). Spatial size of the kernel is derived from the shape of this input and aren’t specified by any attribute. Required.3:
output_shape
is 1D tensor of type T2 that specifies spatial shape of the output. If specified, padding amount is deduced from relation of input and output spatial shapes according to formulas in the description. If not specified, output shape is calculated based on thepads_begin
andpads_end
or completely according toauto_pad
. Optional.Note: Type of the convolution (1D, 2D or 3D) is derived from the rank of the input tensors and not specified by any attribute:
1D convolution (input tensors rank 3) means that there is only one spatial axis X,
2D convolution (input tensors rank 4) means that there are two spatial axes Y, X,
3D convolution (input tensors rank 5) means that there are three spatial axes Z, Y, X.
Outputs:
1: Output tensor of type T1 and rank 3, 4 or 5. Layout is
[N, C_OUTPUT, Z, Y, X]
(number of batches, number of kernel output channels, spatial axes Z, Y, X).
Types:
T1: any numeric type.
T2: any integer type.
Examples
Example 1: 2D ConvolutionBackpropData
<layer id="5" name="upsampling_node" type="ConvolutionBackpropData">
<data dilations="1,1" pads_begin="1,1" pads_end="1,1" strides="2,2" output_padding="0,0" auto_pad="explicit"/>
<input>
<port id="0">
<dim>1</dim>
<dim>20</dim>
<dim>224</dim>
<dim>224</dim>
</port>
<port id="1">
<dim>20</dim>
<dim>10</dim>
<dim>3</dim>
<dim>3</dim>
</port>
</input>
<output>
<port id="0" precision="FP32">
<dim>1</dim>
<dim>10</dim>
<dim>447</dim>
<dim>447</dim>
</port>
</output>
</layer>
Example 2: 2D ConvolutionBackpropData with output_padding
<layer id="5" name="upsampling_node" type="ConvolutionBackpropData">
<data dilations="1,1" pads_begin="0,0" pads_end="0,0" strides="3,3" output_padding="2,2" auto_pad="explicit"/>
<input>
<port id="0">
<dim>1</dim>
<dim>20</dim>
<dim>2</dim>
<dim>2</dim>
</port>
<port id="1">
<dim>20</dim>
<dim>10</dim>
<dim>3</dim>
<dim>3</dim>
</port>
</input>
<output>
<port id="0" precision="FP32">
<dim>1</dim>
<dim>10</dim>
<dim>8</dim>
<dim>8</dim>
</port>
</output>
</layer>
Example 3: 2D ConvolutionBackpropData with output_shape input
<layer id="5" name="upsampling_node" type="ConvolutionBackpropData">
<data dilations="1,1" pads_begin="1,1" pads_end="1,1" strides="1,1" output_padding="0,0" auto_pad="valid"/>
<input>
<port id="0">
<dim>1</dim>
<dim>20</dim>
<dim>224</dim>
<dim>224</dim>
</port>
<port id="1">
<dim>20</dim>
<dim>10</dim>
<dim>3</dim>
<dim>3</dim>
</port>
<port id="2">
<dim>2</dim> <!-- output_shape value is: [450, 450]-->
</port>
</input>
<output>
<port id="0" precision="FP32">
<dim>1</dim>
<dim>10</dim>
<dim>450</dim>
<dim>450</dim>
</port>
</output>
</layer>