openvino/docs/ops/normalization/NormalizeL2_1.md

# NormalizeL2 {#openvino_docs_ops_normalization_NormalizeL2_1}

**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*

```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>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>
    </input>
    <output>
        <port id="2">
            <dim>6</dim>
            <dim>12</dim>
            <dim>10</dim>
            <dim>24</dim>
        </port>
    </output>
</layer>
```