# GroupConvolution¶

Versioned name : GroupConvolution-1

Category : Convolution

Short description : Computes 1D, 2D or 3D GroupConvolution of input and kernel tensors.

Detailed description : Splits input into multiple groups, convolves them with group filters as in regular convolution and concatenates the results. More thorough explanation can be found in ImageNet Classification with Deep Convolutional Neural Networks

Attributes : The operation has the same attributes as a regular Convolution. Number of groups is derived from the kernel shape.

• 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[]

• Required : yes

• 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[]

• Required : yes

• Note : the attribute is ignored when auto_pad attribute is specified.

• 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[]

• 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[]

• Required : yes

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

• same_lower - the input is padded to match the output size. In case of odd padding value an extra padding is added at the beginning.

• valid - do not use padding.

• Type : string

• Default value : explicit

• Required : no

Inputs :

• 1 : Input tensor of type T and rank 3, 4 or 5. Layout is [N, GROUPS \* C_IN, Z, Y, X] (number of batches, number of channels, spatial axes Z, Y, X). Required.

• 2 : Convolution kernel tensor of type T and rank 4, 5 or 6. Layout is [GROUPS, C_OUT, C_IN, Z, Y, X] (number of groups, number of output channels, number of input channels, spatial axes Z, Y, X),

• Note Number of groups is derived from the shape of the kernel and not specified by any attribute.

• Note : Type of the convolution (1D, 2D or 3D) is derived from the rank of the input tensors and not specified by any attribute:

• 1D convolution (input tensors rank 3) means that there is only one spatial axis X

• 2D convolution (input tensors rank 4) means that there are two spatial axes Y, X

• 3D convolution (input tensors rank 5) means that there are three spatial axes Z, Y, X

Outputs :

• 1 : Output tensor of type T and rank 3, 4 or 5. Layout is [N, GROUPS \* C_OUT, Z, Y, X] (number of batches, number of output channels, spatial axes Z, Y, X).

Types :

• T : any numeric type.

Example : 1D GroupConvolution

<layer type="GroupConvolution" ...>
<input>
<port id="0">
<dim>1</dim>
<dim>12</dim>
<dim>224</dim>
</port>
<port id="1">
<dim>4</dim>
<dim>1</dim>
<dim>3</dim>
<dim>5</dim>
</port>
</input>
<output>
<port id="2" precision="FP32">
<dim>1</dim>
<dim>4</dim>
<dim>224</dim>
</port>
</output>

2D GroupConvolution

<layer type="GroupConvolution" ...>
<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>

3D GroupConvolution

<layer type="GroupConvolution" ...>
<input>
<port id="0">
<dim>1</dim>
<dim>12</dim>
<dim>224</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>
<dim>5</dim>
</port>
</input>
<output>
<port id="2" precision="FP32">
<dim>1</dim>
<dim>4</dim>
<dim>224</dim>
<dim>224</dim>
<dim>224</dim>
</port>
</output>