# LRN¶

Versioned name : LRN-1

Category : Normalization

Short description : Local response normalization.

Detailed description : Local Response Normalization performs a normalization over local input regions. Each input value is divided by

$(bias + \frac{alpha}{{size}^{len(axes)}} \cdot \sum_{i} data_{i})^{beta}$

The sum is taken over a region of a side length size and number of dimensions equal to number of axes. The region is centered at the input value that’s being normalized (with zero padding added if needed).

Here is an example for 4D data input tensor and axes =  :

sqr_sum[a, b, c, d] =
sum(data[a, max(0, b - size / 2) : min(data.shape, b + size / 2 + 1), c, d] ** 2)
output = data / (bias + (alpha / size ** len(axes)) * sqr_sum) ** beta

Example for 4D data input tensor and axes = [2, 3] :

sqr_sum[a, b, c, d] =
sum(data[a, b, max(0, c - size / 2) : min(data.shape, c + size / 2 + 1),  max(0, d - size / 2) : min(data.shape, d + size / 2 + 1)] ** 2)
output = data / (bias + (alpha / size ** len(axes)) * sqr_sum) ** beta

Attributes :

• alpha

• Description : alpha represents the scaling attribute for the normalizing sum. For example, alpha equal 0.0001 means that the normalizing sum is multiplied by 0.0001.

• Range of values : no restrictions

• Type : float

• Default value : None

• Required : yes

• beta

• Description : beta represents the exponent for the normalizing sum. For example, beta equal 0.75 means that the normalizing sum is raised to the power of 0.75.

• Range of values : positive number

• Type : float

• Default value : None

• Required : yes

• bias

• Description : bias represents the offset. Usually positive number to avoid dividing by zero.

• Range of values : no restrictions

• Type : float

• Default value : None

• Required : yes

• size

• Description : size represents the side length of the region to be used for the normalization sum. The region can have one or more dimensions depending on the second input axes indices.

• Range of values : positive integer

• Type : int

• Default value : None

• Required : yes

Inputs

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

• 2 : axes - 1D tensor of type T_IND which specifies indices of dimensions in data which define normalization slices. Required.

Outputs

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

Types

• T : any supported floating point type.

• T_IND : any supported integer type.

Example

<layer id="1" type="LRN" ...>
<data alpha="1.0e-04" beta="0.75" size="5" bias="1"/>
<input>
<port id="0">
<dim>6</dim>
<dim>12</dim>
<dim>10</dim>
<dim>24</dim>
</port>
<port id="1">
<dim>1</dim>         <!-- value is  that means independent normalization for each pixel along channels -->
</port>
</input>
<output>
<port id="2">
<dim>6</dim>
<dim>12</dim>
<dim>10</dim>
<dim>24</dim>
</port>
</output>
</layer>