# PReLU¶

Versioned name : PReLU-1

Category : Activation function

Short description : Parametric rectified linear unit element-wise activation function.

Detailed description

PReLU operation is introduced in this article.

PReLU performs element-wise parametric ReLU operation on a given input tensor, based on the following mathematical formula:

$\begin{split}PReLU(x) = \left\{\begin{array}{r} x \quad \mbox{if } x \geq 0 \\ \alpha x \quad \mbox{if } x < 0 \end{array}\right.\end{split}$

where α is a learnable parameter and corresponds to the negative slope, defined by the second input slope.

Another mathematical representation that may be found in other references:

$PReLU(x) = \max(0, x) + \alpha\cdot\min(0, x)$

Attributes : PReLU operation has no attributes.

Inputs

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

• 2 : slope. A tensor of type T and rank greater or equal to 1. Tensor with negative slope values. Required.

• Note : Channels dimension corresponds to the second dimension of data input tensor. If slope input rank is 1 and its dimension is equal to the second dimension of data input, then per channel broadcast is applied. Otherwise slope input is broadcasted with numpy rules, description is available in Broadcast Rules For Elementwise Operations.

Outputs

• 1 : The result of element-wise PReLU operation applied to data input tensor with negative slope values from slope input tensor. A tensor of type T and the same shape as data input tensor.

Types

• T : arbitrary supported floating-point type.

Examples

Example: 1D input tensor data

<layer ... type="Prelu">
<input>
<port id="0">
<dim>128</dim>
</port>
<port id="1">
<dim>1</dim>
</port>
</input>
<output>
<port id="2">
<dim>128</dim>
</port>
</output>
</layer>

Example: 2D input tensor data

<layer ... type="Prelu">
<input>
<port id="0">
<dim>20</dim>
<dim>128</dim>
</port>
<port id="1">
<dim>128</dim>
</port>
</input>
<output>
<port id="2">
<dim>20</dim>
<dim>128</dim>
</port>
</output>
</layer>

Example: 4D input tensor data

<layer ... type="Prelu">
<input>
<port id="0">
<dim>1</dim>
<dim>20</dim>
<dim>128</dim>
<dim>128</dim>
</port>
<port id="1">
<dim>20</dim>
</port>
</input>
<output>
<port id="2">
<dim>1</dim>
<dim>20</dim>
<dim>128</dim>
<dim>128</dim>
</port>
</output>
</layer>