NormalizeL2

Versioned name: NormalizeL2-1

Category: Normalization

Short description: NormalizeL2 operation performs L2 normalization on a given input data along dimensions specified by axes input.

Detailed Description

Each element in the output is the result of dividing the corresponding element of data input by the result of L2 reduction along dimensions specified by the axes input:

output[i0, i1, ..., iN] = x[i0, i1, ..., iN] / sqrt(eps_mode(sum[j0,..., jN](x[j0, ..., jN]**2), eps))

Where indices i0, ..., iN run through all valid indices for the data input and summation sum[j0, ..., jN] has jk = ik for those dimensions k that are not in the set of indices specified by the axes input of the operation. eps_mode selects how the reduction value and eps are combined. It can be max or add depending on eps_mode attribute value.

Particular cases:

  1. If axes is an empty list, then each input element is divided by itself resulting value 1 for all non-zero elements.

  2. If axes contains all dimensions of input data, a single L2 reduction value is calculated for the entire input tensor and each input element is divided by that value.

Attributes

  • eps

    • Description: eps is the number applied by eps_mode function to the sum of squares to avoid division by zero when normalizing the value.

    • Range of values: a positive floating-point number

    • Type: float

    • Required: yes

  • eps_mode

    • Description: Specifies how eps is combined with the sum of squares to avoid division by zero.

    • Range of values: add or max

    • Type: string

    • Required: yes

Inputs

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

  • 2: axes - Axis indices of data input tensor, along which L2 reduction is calculated. A scalar or 1D tensor of unique elements and type T_IND. The range of elements is [-r, r-1], where r is the rank of data input tensor. Required.

Outputs

  • 1: The result of NormalizeL2 function applied to data input tensor. Normalized tensor of the same type and shape as the data input.

Types

  • T: arbitrary supported floating-point type.

  • T_IND: any supported integer type.

Examples

Example: Normalization over channel dimension for NCHW layout

 <layer id="1" type="NormalizeL2" ...>
     <data eps="1e-8" eps_mode="add"/>
     <input>
         <port id="0">
             <dim>6</dim>
             <dim>12</dim>
             <dim>10</dim>
             <dim>24</dim>
         </port>
         <port id="1">
             <dim>1</dim>         <!-- axes list [1] means normalization over channel dimension -->
         </port>
     </input>
     <output>
         <port id="2">
             <dim>6</dim>
             <dim>12</dim>
             <dim>10</dim>
             <dim>24</dim>
         </port>
     </output>
 </layer>

Example: Normalization over channel and spatial dimensions for NCHW layout

 <layer id="1" type="NormalizeL2" ...>
     <data eps="1e-8" eps_mode="add"/>
     <input>
         <port id="0">
             <dim>6</dim>
             <dim>12</dim>
             <dim>10</dim>
             <dim>24</dim>
         </port>
         <port id="1">
             <dim>3</dim>         <!-- axes list [1, 2, 3] means normalization over channel and spatial dimensions -->
         </port>
     </input>
     <output>
         <port id="2">
             <dim>6</dim>
             <dim>12</dim>
             <dim>10</dim>
             <dim>24</dim>
         </port>
     </output>
 </layer>