ConvolutionBackwardData¶

General¶

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
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	De
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 ( visualization link ).	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 below index order when constructing an operation.

Inputs¶

Index	Argu
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	Argu
0	`diff_src`	Required

Supported data types¶

ConvolutionBackwardData operation supports the following data type combinations.

Diff_dst	We
f32	f32	f32	s32
bf16	bf16	bf16	s32
f16	f16	f16	s32

Convolution ConvolutionBackwardWeights