# MVN¶

Versioned name : MVN-6

Category : Normalization

Short description : Calculates mean-variance normalization of the input tensor.

Detailed description

MVN subtracts mean value from the input blob:

$o_{i} = i_{i} - ReduceMean(i_{k}, axes)$

If normalize_variance is set to true, the output blob is divided by variance. When normalizing the value, the number eps is added to the variance to avoid division by zero. According to the eps_mode flag’s value, eps is added inside or outside the sqrt:

• If eps_mode is inside_sqrt :

$o_{i}=\frac{o_{i}}{\sqrt {\sum {o_{k}^2}+\epsilon}}$
• If eps_mode is outside_sqrt :

$o_{i}=\frac{o_{i}}{\sqrt {\sum {o_{k}^2}}+\epsilon}$

Attributes

• normalize_variance

• Description : normalize_variance is a flag that specifies whether to perform variance normalization.

• Range of values :

• false - do not normalize variance

• true - normalize variance

• Type : boolean

• Required : yes

• eps

• Description : eps is the number to be added to the variance to avoid division by zero when normalizing the value.

• Range of values : a positive floating-point number

• Type : float

• Required : yes

• eps_mode

• Description : Choose where to add epsilon.

• Range of values :

• inside_sqrt - add epsilon inside sqrt

• outside_sqrt - add epsilon outside of sqrt

• Type : string

• Required : yes

Inputs

• 1 : data - Input tensor to be normalized of type T and arbitrary shape. Required.

• 2 : axes - 1D tensor which specifies indices of dimensions in data that define normalization slices. Allowed range of axes is [-r; r-1] where r = rank(data), the order can be not sorted. Negative value means counting dimensions from the back. Type T_IND. Required.

Outputs

• 1 : Output tensor of the same shape and type as the data input tensor.

Types

• T : any floating point type.

• T_IND : int64 or int32.

Example

<layer ... type="MVN">
<data eps="1e-9" eps_mode="inside_sqrt" normalize_variance="true"/>
<input>
<port id="0">
<dim>6</dim>
<dim>12</dim>
<dim>10</dim>
<dim>24</dim>
</port>
<port id="1">
<dim>3</dim>         <!-- value of [0,2,3] means independent normalization per channels -->
</port>
</input>
<output>
<port id="2">
<dim>6</dim>
<dim>12</dim>
<dim>10</dim>
<dim>24</dim>
</port>
</output>
</layer>