ConvolutionBackwardData

ConvolutionBackwardData operation accepts \(\diffdst\), weights and optional dst shape as inputs, and compute the \(\diffsrc\).

If auto_pad attribute is specified to one of valid, same_upper and same_lower, pads_begin and pads_end attributes will be ignored. The paddings will be calculated by following the below formula:

Let the parameters be:

Parameter	Depth	Height	Width	Comment
Paddings: Front, top, and left	\(PD_L\)	\(PH_L\)	\(PW_L\)	In the attributes we use pads_begin to indicate the corresponding vector of paddings
Padding: Back, bottom, and right	\(PD_R\)	\(PH_R\)	\(PW_R\)	In the attributes we use pads_end to indicate the corresponding vector of paddings
Stride	\(SD\)	\(SH\)	\(SW\)	In the attributes we use strides to indicate the corresponding vector of strides
Dilation	\(DD\)	\(DH\)	\(DW\)	In the attributes we use dilations to indicate the corresponding vector of dilations

Firstly, \(total\_padding\) is calculated according to \(src\_shape\) and \(dst\_shape\). Let \(src\_h\) be height dimension of \(src\_shape\) and \(dst\_h\) be height dimension of \(dst\_shape\).

\[total\_padding_h = SH \times (src_h - 1) + ((KH -1 ) \times DH + 1) - \dst_h + output\_padding_h\]

If auto_pad attribute is specified as valid:

\[\begin{split}PD_L = 0 \\ PD_R = 0\end{split}\]

If auto_pad attribute is specified as same_lower:

\[\begin{split}PD_L = floor(total\_padding / 2) \\ PD_R = total\_padding - PD_L\end{split}\]

If auto_pad attribute is specified as same_upper:

\[\begin{split}PD_L = total\_padding - PD_R \\ PD_R = floor(total\_padding / 2)\end{split}\]

where:

• \(dst\_shape\) is either an attribute or an input tensor,

• \(output\_padding\) is an optional attribute.

Operation Attributes

Attribute Name	Description	Value Type	Supported Values	Required or Optional
strides	Controls the strides the weights tensor is moved when computing convolution	s64	A s64 list containing positive values	Required
pads_begin	Controls number of zeros to be add to the front/top/left of spatial dimensions, the attribute will be ignored when auto_pad attribute is specified to same_upper, same_lower or valid	s64	A s64 list containing non-negative values	Required
pads_end	Controls number of zeros to be add to the back/bottom/right of spatial dimensions, the attribute will be ignored when auto_pad attribute is specified to same_upper, same_lower or valid	s64	A s64 list containing non-negative values	Required
dilations	Controls the amount of stretching the kernel before convolution	s64	A s64 list containing positive values (>1 means dilated convolution)	Required
auto_pad	Controls how the padding is calculated	string	none (default), same_upper, same_lower, valid	Optional
output_padding	Adds additional amount of padding per each spatial axis in dst	s64	A s64 list containing non-negative values, all zeros by default	Optional
groups	Controls how input channels and output channels are divided into	s64	A positive s64 value, 1 by default	Optional
data_format	Controls how to interpret the shape of src and dst.	string	NCX, NXC (default)	Optional
weights_format	Controls how to interpret the shape of weights	string	OIX, XIO (default)	Optional
dst_shape	Denotes the shape of the dst tensor	s64	A s64 list containing positive values	Optional

Execution Arguments

The inputs and outputs must be provided according to the below index order when constructing an operation.

Inputs

Index	Argument Name	Required or Optional
0	diff_dst	Required
1	weights	Required
2	dst_shape	Optional

@note The shape of weights is \((out\_channels, in\_channels / groups, spatial\_shape)\) for OIX format or \((spatial\_shape, in\_channels / groups, out\_channels)\) for XIO format. Both \(in\_channels\) and \(out\_channels\) must be divisible by groups attribute.

@note Either dst_shape input or dst_shape attribute should be provided. If both provided, dst_shape input will precede over dst_shape attribute.

Outputs

Index	Argument Name	Required or Optional
0	diff_src	Required

Supported Data Types

ConvolutionBackwardData operation supports the following data type combinations.

Diff_dst	Weights	Diff_src	Dst_shape
f32	f32	f32	s32
bf16	bf16	bf16	s32
f16	f16	f16	s32