ConvolutionBackpropData

Versioned name: ConvolutionBackpropData-1

Category: Convolution

Short description: Computes the gradients of a Convolution operation with respect to the input. Also known as a Deconvolution or 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.

ConvolutionBackpropData accepts the same set of attributes as a regular Convolution operation, 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 attribute.

Output shape when specified as an input output_shape, specifies only spatial dimensions. No batch or channel dimension should be passed along with H, W or other spatial dimensions. If output_shape is omitted, then pads_begin, pads_end or auto_pad are used to determine output spatial shape [Y_1, Y_2, ..., Y_D] by input spatial shape [X_1, X_2, ..., X_D] 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 (similar to ONNX definition at https://github.com/onnx/onnx/blob/master/docs/Operators.md#convtranspose):

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[]

    • Default value: None

    • 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[]

    • Default value: None

    • 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[]

    • Default value: None

    • 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[]

    • Default value: None

    • 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.

      • None (not specified): use explicit padding values from pads_begin and pads_end.

      • same_upper (same_lower) the input is padded to match the output size. In case of odd padding value an extra padding is added at the end (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 padding 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

  • groups

    • Description: groups denotes the number of groups input channels and output channels are divided into.

    • Range of values: integer value greater than 0

    • Type: int

    • Default value: 1

    • Required: no

  • data_format

    • Description: data_format denotes the data format of the input and output data.

    • Range of values: NXC or NCX (S means HW for 2D convolution, DHW for 3D convolution)

    • Type: string

    • Default value: NXC

    • Required: no

  • filter_format

    • Description: filter_format denotes the data format of the filter.

    • Range of values: XIO or OIX (X means HW for 2D convolution, DHW for 3D convolution)

    • Type: string

    • Default value: XIO

    • Required: no

Inputs:

  • 1: data – input tensor of rank 3 or greater. Required.

  • 2: filter – convolution kernel tensor. The format is specified by filter_format. 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 integer tensor that specifies spatial shape of the output. Optional. 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.

Outputs:

  • 1: output – output tensor of the same rank as input data tensor.

Convolution ConvolutionBackpropFilters