Convolution

Versioned name: Convolution-1

Category: Convolution

Short description: Reference

Detailed description: Reference

In this description, \(r\) denotes the spatial rank. We describe the convolution for each sample in a batch of \(N\) inputs; the results are combined into an output batch of size \(N\).

The convolution is implemented as if each sample input first has \(p_b\) zeros inserted before and p_e zeros inserted for the channels on the spatial axes, giving a padded input size of \(p_b+p_e+X_I\).

The kernel is stretched by a factor of d on each of its spatial dimensions. The last index of the stretched kernel is then \(d(X_K-1)\) so the shape is \(d(X_K-1)+1\).

The padded input and the dilated kernel are then ungrouped into g equal-sized input and kernel segments; padded input segment \(i\) and dilated kernel segment \(i\) are convolved. The convolution is only performed where there is complete spatial overlap between the shifted kernel and the padded input, so there will be \(p_b+p_e+X_I-d(X_K-1)\) outputs. The output segments are then regrouped along the output channel axis. Finally, all but the results on a multiple of \(d\) spatial axis are removed, so the output will have size:

\[\left\lfloor \frac{p_b+p_e+X_I-d(X_K-1)-1}{s} \right\rfloor +1\]

Attributes

  • strides

    • Description: strides is how much the convolution output is down-sampled to produce the output.

    • Range of values: Non-negative integer values.

    • Type: int[r]

    • Variable: \(s\)

    • Default value: None

    • Required: yes

  • pads_begin

    • Description: pads_begin is a number of zeros to add to the beginning of each spatial axis.

    • Range of values: Non-negative integers.

    • Type: int[r]

    • Variable: \(p_b\)

    • 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 zeros to add to the end of each spatial axis.

    • Range of values: Non-negative integers.

    • Type: int[r]

    • Variable: \(p_e\)

    • Default value: None

    • Required: yes

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

  • dilations

    • Description: dilations denotes the amount to stretch the kernel before convolving.

    • Range of values: positive integers.

    • Type: int[r]

    • Variable: \(d\)

    • 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 - No padding (\(p_b=p_e=0\)).

    • Type: string

    • Default value: None

    • Required: no

    • Note: pads_begin and pads_end attributes are ignored when auto_pad is specified.

With same_upper and same_lower the padding is chosen to make the pre-stride output spatial shape the same as the input shape. When possible, \(p_b=p_e\). If the total padding needed is odd, same_upper makes \(p_e=p_b+1\), same_lower makes p_b=p_e+1. In either case,

\[p_b+p_e=d(X_I-1).\]
  • groups

    • Description: groups denotes the number of groups input and output channels are divided into.

    • Range of values: integer value greater than 0

    • Type: int

    • Variable: g

    • Default value: 1

    • Required: no

  • data_format

    • Description: data_format denotes the data format of the input and output data.

    • Range of values: NXC or NCX (X means HW for 2D convolution, DHW for 3D convolution)

    • Type: string

    • Default value: NXC

    • Required: no

  • filter_format

    • Description: filter_format denotes the data format of the filter.

    • Range of values: XIO or OIX (X means HW for 2D convolution, DHW for 3D convolution)

    • Type: string

    • Default value: XIO

    • Required: no

Inputs:

  • 1: input - the input tensor. The format is specified by data_format. Required.

  • 2: filter - convolution kernel tensor. The format is specified by filter_format. The size of the kernel is derived from the shape of this input and not specified by any attribute. Required.

  • 3: bias - a 1-D tensor adds to channel dimension of input. Broadcasting is supported. Optional.

Outputs:

  • 1: output – output tensor. The format is specified by data_format.