# 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:

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]
else:
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

• 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.

• 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

• 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 and pads_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

• 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 in data and output 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 the pads_begin and pads_end or completely according to auto_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">
<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">
<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">
<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>