Pad¶

Versioned name: Pad-12

Category: Data movement

Short description: Pad operation extends an input tensor on edges. The amount and value of padded elements are defined by inputs and attributes.

Detailed Description: The pad_mode attribute specifies a rule by which new element values are generated. For example, whether they are filled with a given constant or generated based on the input tensor content. The number of new elements to be added (positive value) or removed (negative value) is set by the pads_begin and pads_end inputs.

The following examples illustrate how output tensor is generated for the Pad layer for a given inputs:

Positive pads example:¶

pads_begin = [0, 1]
pads_end = [2, 3]

DATA =
[[1,  2,  3,  4]
[5,  6,  7,  8]
[9, 10, 11, 12]]

depending on the pad_mode attribute:

pad_mode = "constant":

OUTPUT =
[[ 0,  1,  2,  3,  4,  0,  0,  0 ]
[ 0,  5,  6,  7,  8,  0,  0,  0 ]
[ 0,  9, 10, 11, 12,  0,  0,  0 ]
[ 0,  0,  0,  0,  0,  0,  0,  0 ]
[ 0,  0,  0,  0,  0,  0,  0,  0 ]]

pad_mode = "edge":

OUTPUT =
    [[ 1,  1,  2,  3,  4,  4,  4,  4 ]
    [ 5,  5,  6,  7,  8,  8,  8,  8 ]
    [ 9,  9, 10, 11, 12, 12, 12, 12 ]
    [ 9,  9, 10, 11, 12, 12, 12, 12 ]
    [ 9,  9, 10, 11, 12, 12, 12, 12 ]]

pad_mode = "reflect":

OUTPUT =
[[  2,  1,  2,  3,  4,  3,  2,  1 ]
[  6,  5,  6,  7,  8,  7,  6,  5 ]
[ 10,  9, 10, 11, 12, 11, 10,  9 ]
[  6,  5,  6,  7,  8,  7,  6,  5 ]
[  2,  1,  2,  3,  4,  3,  2,  1 ]]

pad_mode = "symmetric":

OUTPUT =
[[ 1,  1,  2,  3,  4,  4,  3,  2 ]
[ 5,  5,  6,  7,  8,  8,  7,  6 ]
[ 9,  9, 10, 11, 12, 12, 11, 10 ]
[ 9,  9, 10, 11, 12, 12, 11, 10 ]
[ 5,  5,  6,  7,  8,  8,  7,  6 ]]

Negative pads example:¶

pads_begin = [-1, -1]
pads_end = [-1, -1]

DATA =
[[1,  2,  3,  4]
[5,  6,  7,  8]
[9, 10, 11, 12]]
Shape(3, 4)

for all of the pad_mode attribute options:

pad_mode = "constant"
pad_mode = "edge"
pad_mode = "reflect"
pad_mode = "symmetric"

OUTPUT =
[[ 6, 7 ]]
Shape(1, 2)

Mixed pads example:¶

pads_begin = [2, -1]
pads_end = [-1, 3]

DATA =
[[1,  2,  3,  4]
[5,  6,  7,  8]
[9, 10, 11, 12]]
Shape(3, 4)

pad_mode = "constant":

OUTPUT =
[[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[2, 3, 4, 0, 0, 0],
[6, 7, 8, 0, 0, 0]]
Shape(4, 6)

pad_mode = "edge":

OUTPUT Shape(4, 6) =
[[2, 3, 4, 4, 4, 4],
[2, 3, 4, 4, 4, 4],
[2, 3, 4, 4, 4, 4],
[6, 7, 8, 8, 8, 8]]
Shape(4, 6)

pad_mode = "reflect":

OUTPUT =
[[10, 11, 12, 11, 10, 9],
[6,   7,  8,  7,  6, 5],
[2,   3,  4,  3,  2, 1],
[6,   7,  8,  7,  6, 5]]
Shape(4, 6)

pad_mode = "symmetric":

OUTPUT =
[[6, 7, 8, 8, 7, 6],
[2, 3, 4, 4, 3, 2],
[2, 3, 4, 4, 3, 2],
[6, 7, 8, 8, 7, 6]]
Shape(4, 6)

Attributes

pad_mode
- Description: pad_mode specifies the method used to generate the padding values.
- Range of values: Name of the method in string format:
  - constant - padded values are taken from the pad_value input. If the input is not provided, the padding elements are equal to zero.
  - edge - padded values are copied from the respective edge of the input data tensor.
  - reflect - padded values are a reflection of the input data tensor. Values on the edges are not duplicated, pads_begin[D] and pads_end[D] must be not greater than data.shape[D] – 1 for any valid D.
  - symmetric - padded values are symmetrically added from the input data tensor. This method is similar to the reflect, but values on edges are duplicated. Refer to the examples above for more details. pads_begin[D] and pads_end[D] must be not greater than data.shape[D] for any valid D.
- Type: string
- Required: yes

Inputs

1: data tensor of arbitrary shape and type T. Required.
2: pads_begin 1D tensor of type T_INT. Number of elements matches the shape rank of data input. Specifies the number of padding elements to add at the beginning of each axis. Negative value means cropping the corresponding dimension’s value. Required.
3: pads_end 1D tensor of type T_INT. Number of elements matches the shape rank of data input. Specifies the number of padding elements to add at the end of each axis. Negative value means cropping the corresponding dimension’s value. Required.
4: pad_value scalar tensor of type T. Takes effect only if pad_mode == "constant" only. All padding elements are populated with this value or with 0 if the input is not provided. This input should not be set with other values of pad_mode. Optional.

Outputs

1: Padded output tensor of type T with dimensions max(pads_begin[D] + data.shape[D] + pads_end[D], 0) for each D from 0 to len(data.shape) - 1.

Types

T: any numeric type.
T_INT: any integer type.

Example: constant mode (positive pads)

 <layer ... type="Pad" ...>
     <data pad_mode="constant"/>
     <input>
         <port id="0">
             <dim>1</dim>
             <dim>3</dim>
             <dim>32</dim>
             <dim>40</dim>
         </port>
         <port id="1">
             <dim>4</dim>     <!-- pads_begin = [0, 5, 2, 1]  -->
         </port>
         <port id="2">
             <dim>4</dim>     <!-- pads_end = [1, 0, 3, 7] -->
         </port>
         <port id="3">
                             <!-- pad_value = 15.0 -->
         </port>
     </input>
     <output>
         <port id="0">
             <dim>2</dim>     <!-- 2 = 0 + 1 + 1 = pads_begin[0] + input.shape[0] + pads_end[0] -->
             <dim>8</dim>     <!-- 8 = 5 + 3 + 0 = pads_begin[1] + input.shape[1] + pads_end[1] -->
             <dim>37</dim>    <!-- 37 = 2 + 32 + 3 = pads_begin[2] + input.shape[2] + pads_end[2] -->
             <dim>48</dim>    <!-- 48 = 1 + 40 + 7 = pads_begin[3] + input.shape[3] + pads_end[3] -->
                             <!-- all new elements are filled with 15.0 value -->
         </port>
     </output>
 </layer>

Example: constant mode (positive and negative pads)

 <layer ... type="Pad" ...>
     <data pad_mode="constant"/>
     <input>
         <port id="0">
             <dim>2</dim>
             <dim>3</dim>
             <dim>32</dim>
             <dim>40</dim>
         </port>
         <port id="1">
             <dim>4</dim>     <!-- pads_begin = [0, -2, -8, 1]  -->
         </port>
         <port id="2">
             <dim>4</dim>     <!-- pads_end = [-1, 4, -6, 7] -->
         </port>
         <port id="3">
                             <!-- pad_value = 15.0 -->
         </port>
     </input>
     <output>
         <port id="0">
             <dim>1</dim>     <!-- 2 = 0 + 2 + (-1) = pads_begin[0] + input.shape[0] + pads_end[0] -->
             <dim>5</dim>     <!-- 5 = (-2) + 3 + 4 = pads_begin[1] + input.shape[1] + pads_end[1] -->
             <dim>18</dim>    <!-- 18 = (-8) + 32 (-6) = pads_begin[2] + input.shape[2] + pads_end[2] -->
             <dim>48</dim>    <!-- 48 = 1 + 40 + 7 = pads_begin[3] + input.shape[3] + pads_end[3] -->
                             <!-- all new elements are filled with 15.0 value -->
         </port>
     </output>
 </layer>

Example: edge mode

 <layer ... type="Pad" ...>
     <data pad_mode="edge"/>
     <input>
         <port id="0">
             <dim>1</dim>
             <dim>3</dim>
             <dim>32</dim>
             <dim>40</dim>
         </port>
         <port id="1">
             <dim>4</dim>     <!-- pads_begin = [0, 5, 2, 1]  -->
         </port>
         <port id="2">
             <dim>4</dim>     <!-- pads_end = [1, 0, 3, 7] -->
         </port>
     </input>
     <output>
         <port id="0">
             <dim>2</dim>     <!-- 2 = 0 + 1 + 1 = pads_begin[0] + input.shape[0] + pads_end[0] -->
             <dim>8</dim>     <!-- 8 = 5 + 3 + 0 = pads_begin[1] + input.shape[1] + pads_end[1] -->
             <dim>37</dim>    <!-- 37 = 2 + 32 + 3 = pads_begin[2] + input.shape[2] + pads_end[2] -->
             <dim>48</dim>    <!-- 48 = 1 + 40 + 7 = pads_begin[3] + input.shape[3] + pads_end[3] -->
         </port>
     </output>
 </layer>