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docs/ops/normalization/NormalizeL2_1.md
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**Category**: *Normalization* **Category**: *Normalization*
**Short description**: *NormalizeL2* operation performs L2 normalization of the 1st input tensor in slices specified by the 2nd input. **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** **Attributes**
* *eps* * *eps*
* **Description**: *eps* is the number to be added/maximized to/with the variance to avoid division by zero when normalizing the value. For example, *eps* equal to 0.001 means that 0.001 is used if all the values in normalization are equal to zero. * **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 * **Range of values**: a positive floating-point number
* **Type**: `float` * **Type**: `float`
* **Default value**: None
* **Required**: *yes* * **Required**: *yes*
* *eps_mode* * *eps_mode*
* **Description**: Specifies how *eps* is combined with L2 value calculated before division. * **Description**: Specifies how *eps* is combined with the sum of squares to avoid division by zero.
* **Range of values**: `add`, `max` * **Range of values**: `add` or `max`
* **Type**: `string` * **Type**: `string`
* **Default value**: None
* **Required**: *yes* * **Required**: *yes*
**Inputs** **Inputs**
* **1**: `data` - input tensor to be normalized. Type of elements is any floating point type. Required. * **1**: `data` - A tensor of type *T* and arbitrary shape. **Required.**
* **2**: `axes` - scalar or 1D tensor with axis indices for the `data` input along which L2 reduction is calculated. 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** **Outputs**
* **1**: Tensor of the same shape and type as the `data` input and normalized slices defined by `axes` input. * **1**: The result of *NormalizeL2* function applied to `data` input tensor. Normalized tensor of the same type and shape as the data input.
**Detailed Description** **Types**
Each element in the output is the result of division of corresponding element from the `data` input tensor by the result of L2 reduction along dimensions specified by the `axes` input: * *T*: arbitrary supported floating-point type.
* *T_IND*: any supported integer type.
output[i0, i1, ..., iN] = x[i0, i1, ..., iN] / sqrt(eps_mode(sum[j0,..., jN](x[j0, ..., jN]**2), eps)) **Examples**
Where indices `i0, ..., iN` run through all valid indices for the 1st input and summation `sum[j0, ..., jN]` have `jk = ik` for those dimensions `k` that are not in the set of indices specified by the `axes` input of the operation. One of the corner cases is when `axes` is an empty list, then we divide each input element by itself resulting value 1 for all non-zero elements. Another corner case is where `axes` input contains all dimensions from `data` tensor, which means that a single L2 reduction value is calculated for entire input tensor and each input element is divided by that value. *Example: Normalization over channel dimension for `NCHW` layout*
`eps_mode` selects how the reduction value and `eps` are combined. It can be `max` or `add` depending on `eps_mode` attribute value.
**Example**
```xml ```xml
<layer id="1" type="NormalizeL2" ...> <layer id="1" type="NormalizeL2" ...>
@ -57,7 +67,34 @@ Where indices `i0, ..., iN` run through all valid indices for the 1st input and
<dim>24</dim> <dim>24</dim>
</port> </port>
<port id="1"> <port id="1">
<dim>2</dim> <!-- value is [2, 3] that means independent normalization in each channel --> <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*
```xml
<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> </port>
</input> </input>
<output> <output>