**Versioned name**: *GroupConvolution-1*

**Category**: Convolution

**Short description**: Reference

**Detailed description**: Reference

**Attributes**

*strides***Description**:*strides*is a distance (in pixels) to slide the filter on the feature map over the (z, y, x) axes for 3D convolutions and (y, x) axes for 2D convolutions. For example,*strides*equal*4,2,1*means sliding the filter 4 pixel at a time over depth dimension, 2 over height dimension and 1 over width dimension.**Range of values**: positive integer numbers**Type**: int[]**Default value**: None**Required**:*yes*

*pads_begin***Description**:*pads_begin*is a number of pixels to add to the beginning along each axis. For example,*pads_begin*equal*1,2*means adding 1 pixel to the top of the input and 2 to the left of the input.**Range of values**: positive integer numbers**Type**: int[]**Default value**: None**Required**:*yes***Note**: the attribute is ignored when*auto_pad*attribute is specified.

*pads_end***Description**:*pads_end*is a number of pixels to add to the ending along each axis. For example,*pads_end*equal*1,2*means adding 1 pixel to the bottom of the input and 2 to the right of the input.**Range of values**: positive integer numbers**Type**: int[]**Default value**: None**Required**:*yes***Note**: the attribute is ignored when*auto_pad*attribute is specified.

*dilations***Description**:*dilations*denotes the distance in width and height between elements (weights) in the filter. For example,*dilation*equal*1,1*means that all the elements in the filter are neighbors, so it is the same as for the usual convolution.*dilation*equal*2,2*means that all the elements in the filter are matched not to adjacent elements in the input matrix, but to those that are adjacent with distance 1.**Range of values**: positive integer numbers**Type**: int[]**Default value**: None**Required**:*yes*

*auto_pad***Description**:*auto_pad*how the padding is calculated. Possible values:- None (not specified): use explicit padding values.
*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.

**Inputs**:

**1**: 4D or 5D input tensor. Required.**2**: Convolution kernel tensor. Weights layout is GOIYX (GOIZYX for 3D convolution), which means that*X*is changing the fastest, then*Y*, then*Input*,*Output*and*Group*. The size of kernel and number of groups are derived from the shape of this input and aren't specified by any attribute. Required.

**Mathematical Formulation**

- For the convolutional layer, the number of output features in each dimension is calculated using the formula:
\[ n_{out} = \left ( \frac{n_{in} + 2p - k}{s} \right ) + 1 \]

- The receptive field in each layer is calculated using the formulas:
- Jump in the output feature map:
\[ j_{out} = j_{in} * s \]

- Size of the receptive field of output feature:
\[ r_{out} = r_{in} + ( k - 1 ) * j_{in} \]

- Center position of the receptive field of the first output feature:
\[ start_{out} = start_{in} + ( \frac{k - 1}{2} - p ) * j_{in} \]

- Output is calculated using the following formula:
\[ out = \sum_{i = 0}^{n}w_{i}x_{i} + b \]

- Jump in the output feature map:

**Example**

<layer type="GroupConvolution" ...>

<data dilations="1,1" pads_begin="2,2" pads_end="2,2" strides="1,1"/>

<input>

<port id="0">

<dim>1</dim>

<dim>12</dim>

<dim>224</dim>

<dim>224</dim>

</port>

<port id="1">

<dim>4</dim>

<dim>1</dim>

<dim>3</dim>

<dim>5</dim>

<dim>5</dim>

</port>

</input>

<output>

<port id="2" precision="FP32">

<dim>1</dim>

<dim>4</dim>

<dim>224</dim>

<dim>224</dim>

</port>

</output>