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ConvolutionBackwardData {#dev_guide_op_convolutionbackwarddata}
===============================================================
## General
ConvolutionBackwardData operation accepts \f$\diffdst\f$, \weights and optional
dst shape as inputs, and compute the \f$\diffsrc\f$.
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 | \f$PD_L\f$ | \f$PH_L\f$ | \f$PW_L\f$ | In the attributes we use `pads_begin` to indicate the corresponding vector of paddings |
| Padding: Back, bottom, and right | \f$PD_R\f$ | \f$PH_R\f$ | \f$PW_R\f$ | In the attributes we use `pads_end` to indicate the corresponding vector of paddings |
| Stride | \f$SD\f$ | \f$SH\f$ | \f$SW\f$ | In the attributes we use `strides` to indicate the corresponding vector of strides |
| Dilation | \f$DD\f$ | \f$DH\f$ | \f$DW\f$ | In the attributes we use `dilations` to indicate the corresponding vector of dilations |
Firstly, \f$total\_padding\f$ is calculated according to \f$src\_shape\f$ and \f$dst\_shape\f$.
Let \f$src\_h\f$ be height dimension of \f$src\_shape\f$ and \f$dst\_h\f$ be
height dimension of \f$dst\_shape\f$.
\f[
total\_padding_h = SH \times (src\_h - 1) + ((KH -1 ) \times DH + 1) - dst\_h + output\_padding_h
\f]
If `auto_pad` attribute is specified as `valid`:
\f[
PD_L = 0 \\
PD_R = 0
\f]
If `auto_pad` attribute is specified as `same_lower`:
\f[
PD_L = floor(total\_padding / 2) \\
PD_R = total\_padding - PD_L
\f]
If `auto_pad` attribute is specified as `same_upper`:
\f[
PD_L = total\_padding - PD_R \\
PD_R = floor(total\_padding / 2)
\f]
where:
- \f$dst\_shape\f$ is either an attribute or an input tensor,
- \f$output\_padding\f$ is an optional attribute.
## Operation attributes
| Attribute Name | Description | Value Type | Supported Values | Required or Optional |
|:-------------------------------------------------------------|:------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:-----------|:---------------------------------------------------------------------|:---------------------|
| [strides](@ref dnnl::graph::op::attr::strides) | Controls the strides the weights tensor is moved when computing convolution | s64 | A s64 list containing positive values | Required |
| [pads_begin](@ref dnnl::graph::op::attr::pads_begin) | Controls number of zeros to be add to the front/top/left of spatial dimensions | s64 | A s64 list containing non-negative values | Required |
| [pads_end](@ref dnnl::graph::op::attr::pads_end) | Controls number of zeros to be add to the back/bottom/right of spatial dimensions | s64 | A s64 list containing non-negative values | Required |
| [dilations](@ref dnnl::graph::op::attr::dilations) | Controls the amount of stretching the kernel before convolution ([visualization link](https://github.com/vdumoulin/conv_arithmetic/blob/master/README.md#dilated-convolution-animations)) | s64 | A s64 list containing positive values (>1 means dilated convolution) | Required |
| [auto_pad](@ref dnnl::graph::op::attr::auto_pad) | Controls how the padding is calculated | string | `none` (default), `same_upper`, `same_lower`, `valid` | Optional |
| [output_padding](@ref dnnl::graph::op::attr::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](@ref dnnl::graph::op::attr::groups) | Controls how input channels and output channels are divided into | s64 | A positive s64 value, `1` by default | Optional |
| [data_format](@ref dnnl::graph::op::attr::data_format) | Controls how to interpret the shape of `src` and `dst`. | string | `NCX`, `NXC` (default) | Optional |
| [weights_format](@ref dnnl::graph::op::attr::weights_format) | Controls how to interpret the shape of `weights`. | string | `OIX`, `XIO` (default) | Optional |
| [dst_shape](@ref dnnl::graph::op::attr::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 | Argument Name | Required or Optional |
|:------|:--------------|:---------------------|
| 0 | `diff_dst` | Required |
| 1 | `weights` | Required |
| 2 | `dst_shape` | Optional |
@note
The shape of \weights is
\f$(out\_channels, in\_channels / groups, spatial\_shape)\f$ for `OIX` format or
\f$(spatial\_shape, in\_channels / groups, out\_channels)\f$ for `XIO` format.
Both \f$in\_channels\f$ and \f$out\_channels\f$ 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 |
|
