SquaredDifference

Versioned name: SquaredDifference-1

Category: Arithmetic binary

Short description: SquaredDifference performs element-wise subtract and square the result operation with two given tensors applying broadcasting rule specified in the auto_broadcast attribute.

Detailed description As a first step input tensors a and b are broadcasted if their shapes differ. Broadcasting is performed according to auto_broadcast attribute specification. As a second step Substract and Square the result operation is computed element-wise on the input tensors a and b according to the formula below:

\[o_{i} = (a_{i} - b_{i})^2\]

Attributes:

• auto_broadcast

  • Description: specifies rules used for auto-broadcasting of input tensors.

  • Range of values:

    • none - no auto-broadcasting is allowed, all input shapes must match

    • numpy - numpy broadcasting rules, description is available in Broadcast Rules For Elementwise Operations

  • Type: string

  • Default value: “numpy”

  • Required: no

Inputs

• 1: A tensor of type T and arbitrary shape. Required.

• 2: A tensor of type T and arbitrary shape. Required.

Outputs

• 1: The result of element-wise subtract and square the result operation. A tensor of type T with shape equal to broadcasted shape of two inputs.

Types

• T: any numeric type.

Examples

Example 1 - no broadcasting

 <layer ... type="SquaredDifference">
     <data auto_broadcast="none"/>
     <input>
         <port id="0">
             <dim>256</dim>
             <dim>56</dim>
         </port>
         <port id="1">
             <dim>256</dim>
             <dim>56</dim>
         </port>
     </input>
     <output>
         <port id="2">
             <dim>256</dim>
             <dim>56</dim>
         </port>
     </output>
 </layer>

Example 2: numpy broadcasting

 <layer ... type="SquaredDifference">
     <data auto_broadcast="numpy"/>
     <input>
         <port id="0">
             <dim>8</dim>
             <dim>1</dim>
             <dim>6</dim>
             <dim>1</dim>
         </port>
         <port id="1">
             <dim>7</dim>
             <dim>1</dim>
             <dim>5</dim>
         </port>
     </input>
     <output>
         <port id="2">
             <dim>8</dim>
             <dim>7</dim>
             <dim>6</dim>
             <dim>5</dim>
         </port>
     </output>
 </layer>