# MVN¶

Versioned name : MVN-1

Category : Normalization

Short description : Calculates mean-variance normalization of the input tensor. Supports two normalization techniques: Instance/Contrast Normalization and Layer Normalization.

Detailed description

Based on across_channels attribute mean value is calculated using one of formulas below:

1. if true mean value is calculated using Layer Normalization:

$\mu_{n} = \frac{\sum_{c}^{C}\sum_{h}^{H}\sum_{w}^{W} i_{nchw}}{C \* H \* W}$
2. if false mean value is calculated using Instance/Contrast Normalization:

$\mu_{nc} = \frac{\sum_{h}^{H}\sum_{w}^{W} i_{nchw}}{H \* W}$

where $$i_{nchw}$$ is an input tensor parametrized by $$n$$ batches, $$c$$ channels and $$h,w$$ spatial dimesnions.

If reduction_axes attribute is provided mean value is calculated based on formula:

$\mu_{n} = ReduceMean(i_{k}, reduction_axes)$

Afterwards MVN subtracts mean value from the input blob.

If normalize_variance is set to true, the output blob is divided by variance:

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

where $$\sigma_{k}^2$$ is the variance calculated based on mean value, $$\epsilon$$ is a value added to the variance for numerical stability and corresponds to epsilon attribute.

Attributes

• across_channels

• Description : across_channels is a flag that specifies whether mean values are shared across channels. If true mean values and variance are calculated for each sample across all channels and spatial dimensions (Layer Normalization), otherwise calculation is done for each sample and for each channel across spatial dimensions (Instance/Contrast Normalization).

• Range of values :

• false - do not share mean values across channels

• true - share mean values across channels

• Type : boolean

• Required : yes

• reduction_axes

• Description : 1D tensor of unique elements and type T_IND which specifies indices of dimensions in data that define normalization slices. Negative value means counting dimensions from the back.

• Range of values : allowed range of axes is [-r; r-1] where r = rank(data), the order cannot be sorted

• Type : int

• Required : yes

• 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. For example, epsilon equal to 0.001 means that 0.001 is added to the variance.

• Range of values : a positive floating-point number

• Type : double

• Required : yes

• Note Important: it is necessary to use only one of across_channels or reduction_axes attributes, they cannot be defined together.

Inputs

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

Outputs

• 1 : normalized tensor of type T and shape as input tensor.

Types

• T : any floating point type.

• T_IND : int64 or int32.

Examples

Example: with across_channels attribute

<layer ... type="MVN">
<data across_channels="true" eps="1e-9" normalize_variance="true"/>
<input>
<port id="0">
<dim>6</dim>
<dim>12</dim>
<dim>10</dim>
<dim>24</dim>
</port>
</input>
<output>
<port id="2">
<dim>6</dim>
<dim>12</dim>
<dim>10</dim>
<dim>24</dim>
</port>
</output>
</layer>

Example: with reduction_axes attribute

<layer ... type="MVN">
<data reduction_axes="2,3" eps="1e-9" normalize_variance="true"/>
<input>
<port id="0">
<dim>6</dim>
<dim>12</dim>
<dim>10</dim>
<dim>24</dim>
</port>
</input>
<output>
<port id="2">
<dim>6</dim>
<dim>12</dim>
<dim>10</dim>
<dim>24</dim>
</port>
</output>
</layer>